Youtube comments of Lepi Doptera (@lepidoptera9337).

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  388. The Tesla factory receives spodumene (LiAlSi2O6), i.e. a mineral with a very high lithium content from the port of Corpus Christi and chemically removes the lithium, leaving aluminum silicates as a by-product. Tesla claims to do this without needing a large amount of acid (which probably just means that the acid is recycled in a closed chemical process). What these guys are talking about is about enriching water soluble lithium brines at the mining site. I suspect that to Tesla what matters is the availability of lithium rather than the total cost of production. They can absorb prices above the market price because they are making vehicles with very high margins. What they can not tolerate is to not have enough lithium in the market to keep making as many vehicles as they can sell. Supply risk management is a totally different goal than cost optimization, so the economics is potentially very different for Tesla. There may also be other reasons like quality control... if their process produces either "better" lithium than what they can buy or "good enough" lithium at a lower cost, then that's a winning strategy as well. Tesla did describe their chemistry in a video, by the way. The main advantage seems to be that they don't have to buy expensive sulfuric acid and they don't end up with byproducts that are expensive to dispose. If I understand this correctly, this is like 19th century inorganic chemistry. You could do this at home with a chemistry kit and maybe a somewhat higher temperature burner. It's a different matter doing it at large scale, of course, but in principle this is, as far as chemical factories go, kindergarten level.
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  394. ​ @SteveKelly1  The particle language goes back to Einstein's 1905 paper on the photoelectric effect. In that paper he gives a congenial explanation for the macroscopic photoelectric data in terms of the quantization of the electromagnetic field. But at the same time he commits his actual biggest blunder. After having identified quanta of energy, he immediately concludes in a single sentence that these quanta have to have location properties like Newtonian corpuscles. That conclusion isn't backed up by any observational detail of the photoelectric effect. It doesn't match the well known definition of energy as a system property. It's also completely unnecessary for the remainder of the paper. It's a completely unforced slip of Einstein's mind. Unfortunately other authors after Einstein have picked up this mistake and they kept building on it (to this day). What physicists mean by "a particle" is actually a quantum of energy, momentum, angular momentum and charge. Neither of these properties refers to a "small, localized object". They are all system properties. The theory does not describe particles. It describes changes in the energy of systems. You can find this clearly expressed in Heisenberg's matrix mechanics paper where initial and final energy was used as index into the matrices. That's the correct interpretation except that it's not just energy but the quad of energy/momentum/angular momentum and charges. Why these? Because these are the only locally conserved quantities in nature. Everything else changes, but these quantities get transferred from system to system. We have language for property exchanges. Energy FLOWS. It does NOT take a path. The entire concept of path makes no sense because systems are random subdivisions of nature. They don't even have to be some continuous regions of spacetime. Even in classical mechanics the energy of a spring is not localized, for instance. It's in the entire spring. The kinetic energy of an extended object is not in the center of mass of that object, either. We never had this illusion that energy etc. has to be focused in some tiny region of spacetime. That is purely an invention (and not a good one) of non-relativistic quantum mechanics. In quantum field theory it's even worse. the only well defined states are the plane waves of the (interaction) free theory. Everything else is a jumbled mess without any known physical interpretation. Whatever happens in the interaction volume can only be described with classical quantities if we look at it from infinitely far away. In other words: the closer we look, the blurrier nature gets. It doesn't get more "point-like". So, no, not only do particles not travel along paths, there simply are no particles. There are initial and final system states and they are characterized by changes in energy, momentum, angular momentum and charge. That is a fundamentally different (and 100% correct) way of looking at the world.
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  460.  @filosofiadetalhista  Where am I attacking you? You are trivially wrong on a number of things and I am merely pointing that out. I would suggest that you leave your hurt ego at home. It has no use in science. There is no such thing as wave function collapse. A wave function is an abstract description of a quantum mechanical ensemble (i.e. a hypothetical infinite repetition of the same experiment). Just like a probability distribution a construction that depends on an average over an infinite number of hypothetical events isn't being changed by a single actual event. Copenhagen doesn't talk about collapse anywhere. It talks about the reversible dynamics of a completely isolated unitary ensemble of one system (as described by the Schroedinger equation) and the irreversible energy exchange between the first and an ADDITIONAL second system that performs "the measurement" (that's the function of the Born Rule). The entire "collapse" language is simply nonsense that you have picked up on the internet. It is, as far as I know, not even defined in textbooks. One system IS NOT EQUAL to two systems, hence there is a need for a second formula. Reversible dynamics IS NOT EQUAL to irreversible dynamics, hence there is, again, a need for a second formula. That's why the Born rule has to exist in one form or another. From a logical perspective all of this is crystal clear. What is not obvious is why our education system does such a poor job explaining these otherwise trivial facts almost 120 years after they were first properly identified. There is an incredible amount of confusion and very little clarity about the ontological connection between reality and the theory going on, both at the layman and the professional level. That confusion has to stop. With regards to your second point... the wave function approach does not lead to ultra-precise physics. It's a remnant of the initial non-relativistic phase of quantum mechanics. It explains some trivial systems (particle in a box, hydrogen atom) with reasonable precision and completely falls apart on pretty much everything else (it's almost useless on scattering problems like in high energy physics). One can not do quantum field theory with normalized wave functions and we don't. Reality IS NOT like the non-relativistic Schroedinger equation suggests. It just happens that the step up in mathematical difficulty between the non-relativistic case that has ontological problems and the relativistic field theory case that doesn't have them is enormous. It's far too much for most students to absorb. It also doesn't buy the practitioner anything to learn a theory that has very little predictive power at low energies where effective potential theories suffice and are much, much easier to use (like in solid state physics).
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  511.  @eljcd  The initial calculation by Feynman? It is not naive. It's actually quite congenial and it works, with some difficulties. What is certain is that we haven't found anything better for over 70 years, which tells us that it's not all bad. Is it the best possible model for how quantum fields work? Certainly not. I am highly skeptical that the real/virtual particle picture is the best way to describe quantum fields myself. That, however, has absolutely nothing to do with the multiverse question. QFT tells us how to calculate with quantum fields and which kinds of quantum fields can exist, at all, but it does not tell us which kinds of quantum fields should actually exist. I am not aware that there were a whole lot of complaints about that in the past. If we were to put the same "prediction" criteria for the universe on plain QFT that we are putting on string theory, then we would have to conclude that it predicts an infinite number of possible universes. Instead we accept that it can't predict any. It can only describe the one we see. What happened with the introduction of string theory is that people had overblown hopes that it would reduce the number of possible quantum field theories to one. It didn't do that. It seemingly reduced it to a very, very large number. Unfortunately, so far nobody seems to have found the actual solution to the universe inside string theory, either. It may be in there, it may not be. And with that a serious philosophical mistake crept into the discussion: since string theory (which effectively has done nothing for physics proper so far) predicts a very large number of possible low energy universes, then maybe there have to be a large number of low energy universes. That is total nonsense, of course. The situation on the ground has simply not changed: we can describe the low energy universe very well, but we still can't predict it. We are still roughly where we were in the 1970s, when the SM was more or less finalized structurally. That is not a very long stretch of stagnation in physics. It was much worse in the 19th century when we had a more or less spotless (if inaccurate) theory of motion of matter without having any theory of matter, at all. So take the "discussion" with a grain of salt. It is far more about egos of different groups of people, neither of whom has a solution, than it is about the actual state of physics. Physics is just fine, it simply didn't make as much progress as some elderly physicist would like to have seen. Will Susskind be able to die in peace, having seen the holy land at least from afar? No. He can talk to Moses and Newton and Einstein about that experience when he gets to heaven. :-)
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  512.  @eljcd  I think there are a number of attempts to use more or less plain QFT to work around the gravity problem. There is the double copy group which says that basically two copies of the color force can produce gravity. I have yet to understand how that is supposed to work even even at the kindergarten level, so I can't comment. Then there is an attempt at making gravity a massive field, which could possibly explain dark energy, but the model seems to suffer from cosmological stability problems... quantum gravity seems a bit like playing Whack-a-mole, whenever a model is successful in one area, it has serious, if not deadly problems in another. My perspective as an experimentalist is a bit more focused on observations, right now. I don't believe that we will get the funding/develop technology to get beyond the 1TeV accelerator barrier within my remaining lifetime. So that leaves astronomical and cosmological observations. If you have been watching the success of gravitational wave astronomy and radio astronomy to image black holes, then it becomes somewhat evident that building new (space based?) observatories for gravitational, optical and radio-astronomy is the way to go. Nature has given us such a beautiful laboratory of absolutely monstrous extreme systems in the universe. We can never hope to replicate the conditions near and inside those objects in the lab, but we can harvest much of this information from a distance. That is where the near term progress of physics lies, IMHO.
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  983.  @tTtt-ho3tq  Science historically you are correct. We discovered Maxwell first, then we noticed that it was Lorentz and not Galileo invariant. That caused a lot of confusion and eventually Einstein sorted it out by showing that one could build a Lorentz invariant version of classical mechanics. It was only discovered in hindsight that all of this had basically been sitting on a few pages of algebra right in front of out eyes all along. I did, of course, not claim that a high schooler can solve this puzzle with nothing more than the algebraic tools that we teach in K-12. It took hundreds of physicists between Galileo and Einstein to put the pieces together, both experimentally as well as logically. All I am saying is that today, in hindsight, a smart student can understand all of this with nothing more than K-12 algebra and a bit of calculus and the concepts we teach about space, time and with the usual definitions for physical quantities like distance, duration, velocity etc.. Will this ever be easy to "grok" for a human being who is used to a world that looks Galilean? Probably not, at least not to ordinary humans who have been trained in our current public school system that is still very much based on 19th century thought patterns. The world is a little more complicated at the core than it appears on the surface. That's just a fact. We need to start teaching children this lesson earlier than we do today and then they will have an easier time to adjust to the actual scientific realities.
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  1084. The problem does not occur in Earth's reference frame. It occurs in SOME reference frame moving relative to Earth. As long as all causality is restricted to speed <c, all observers will agree that event A happened before event B if A happens before B in the reference frame of A and B. If the causality is connecting these events at >c, however, there is a reference frame in which B will come before A, i.e. in case of the grandfather paradox some observer will see you being born before your grandfather. I didn't think this through entirely, but intuitively one might expect time to flow in the opposite direction on the FTL ship itself (apart from the fact that it acquires an imaginary component which makes the system unstable). I Might be wrong about the last part, but the general lore about tachyonic systems is that they are always unstable. Now, all of this only holds if nature is actually relative. If it is not, then one can construct systems which have different energy bands, just like phonons and charge carriers in semiconductors. We would be in one of these bands and tachyons in another. There would be a gap between the two. By supplying enough energy one can "jump" the gap and then the new state would be in the higher band. We have accelerated protons to roughly 7TeV so far without observing this energy gap and "jump". We have been able to observe much, much higher energy cosmic rays (I believe by a factor of a million) and they still didn't become tachyonic, so if such a band exists, then it's at energies above the highest energy cosmic ray that has been observed. It would be completely useless for either communication or travel.
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  1324.  @macschomo  No, but it's not caused by quantum fluctuations, either, we just don't have a good language to talk about these things. We can see the problem already in the ground state energy, which ought to be enormous, according to the usual calculation methodology. Instead the effective ground state energy is tiny. So that tells us that something at the interface of quantum mechanics of fields and the underlying geometry of spacetime is broken. It's probably the same technicality that makes it so hard to deal with gravity in a quantum mechanical way. So where does this problem come from? For one thing, it comes from our definition of "physical event", which is classical and point-like. That, already, would cause an infinite energy term in the most naive formulation, right? We can not even implement a single "point" in spacetime with a proper physical system without running into the infinity problem, but our theory then happily goes on to integrate over an infinite number of four dimensional spacetime integrals to get to a finite result (with some very heavy lifting in the symmetries department that offset some infinities against others). Moreover, the ground state energy was infinite in classical mechanics, already, if you remember... if we integrate the energy density of a point charge all the way to r=0, then we end up with a divergent integral, so the problem is not even quantum mechanical, it is a general conceptual difficulty with the infinitely "small". Nature does not have that problem. It simply does not "start" with spacetime, at all. It does not seem to care about the "infinitely small". It only cares about whatever scale is of relevance based on the total energy in the system. Instead, spacetime "is" what "stays behind" in an abstract way (that can, as I said, not implemented with physical systems) once we strip all matter and radiation out of the actual physical solutions. Now, if I could tell you how to implement this with a mathematical model, then I would be in line for the physics Nobel. As far as I know nobody can do this, yet, but we can still point to where the problem originates: from dragging the classical mechanics picture too far into quantum mechanics.
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  1491.  @ChuckCreagerJr  I agree. Some people do awful things to other people. Being dumped or even cheated on is, however, one of the less awful ones. Domestic violence and other forms of abuse, sometimes for economic gain, are far, far worse. One of my best human experiences was a dinner at the house of a female co-worker. Also present were her teenage daughter, her current boyfriend and her daughter's father and former husband. The four were having the most pleasant intellectual conversations and they genuinely seemed to get along with each other just fine. I was informed that this dinner was a weekly ritual. I asked her about her divorce later and she told me that she and her former husband had both come to the conclusion that they had made a mistake when they got married, that they both loved their daughter equally and that they did not want to let their failure to be a couple come between either of them and the child. The result of that thinking process was a terrific arrangement as far as I can tell. At the opposite end of a spectrum I once made the mistake of wanting to drop off a donation at a women's shelter. I walked up to the front door and rang the doorbell. The result was frantic shuffling behind the door and a threat to call the police immediately if I didn't leave. The situation was only rectified by one of the employees who knew me personally. Why was I being greeted with such a response? Because the shelter had been receiving violent threats from the husband of one of the sheltered women. They were genuinely afraid that the guy might show up to commit an act of violence. So, yes, human relations can be traumatic, but they don't have to be. It's all about what we make of them.
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  1571.  @TheMightyAbs  The unfortunate side effect of it is that the US and other well developed countries have been depleting economically less developed countries of educated people. This has been happening for a long time, of course. One can see the devastating effects even in some smaller European countries that are struggling and that have been moving to the political right of the spectrum. What else can be expected if we are removing young, left leaning middle class voters? Poland, Hungary and the former Eastern part of Germany are good examples of the political consequences of this migration. Of course this doesn't spell impending doom for China, but it means that the country is changing very quickly. China did try to mitigate the consequences of their one-child policies, but there is only so much it can do. I went to visit some time ago and I saw plenty of young people from rural areas in the big cities. The problem is that most of these young people were working low end jobs in hotels and restaurants. They weren't building a future for themselves by moving up the socioeconomic ladder. China's last young generations are now depleting the villages without actually adding all that much to the country's GDP. At the upper end the country has created millions of young employees with four year higher education or better, many of whom are now unemployed, so the growth in technological, service and administrative positions has not even kept up with the successful part of China's educational efforts.
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  1631.  @xiupsilon876  Yes, there has been a lot of theoretical research in that area and even Sabine Hossenfelder has recently published an article about a different type of "hidden variable" approach if I am not mistaken. There are a couple of problems with a phrase like "quantum mechanics is incomplete". What do we mean by that? Incomplete because we can not know position and momentum with arbitrary precision at the same time? That's not a quantum mechanical property to begin with. It's a general mathematical property of functions with L2-norm (that's what the mathematicians call "energy"). It's just as valid for water waves as it is for classical electromagnetic waves as it is for quark and gluon quantum fields. Wifi routers have a protocol that uses time-energy uncertainty to shape radio-wave packets in a certain way. Our engineers are using this principle in mechanical, electrical and information systems daily. This can never be "undone" because it runs into a fundamental mathematical property of continuous functions. If Einstein would have wanted that, then he didn't even realize that the classical world had exactly the same limitations as soon as continua were involved. Incomplete because photons, electrons etc. do not behave like classical particles? Absolutely nothing in the universe behaves like a classical particle. A classical particle in physics was always an abstraction to simplify problems like the Kepler problem to the level where it can be (almost) solved in closed mathematical form. All it ever meant was that we reduce the dynamics of an extended classical body to the dynamics of its center of mass, i.e. we neglect rotations and internal degrees of freedom. As it turns out, there are approx. one dozen single particle Hamiltonians that are integrable (that have general closed form solutions) and some of them (like the three dimensional Kepler problem and the four dimensional harmonic oscillator) are mathematically equivalent. Every other "particle problem" does not have a closed form solution and we can not predict its motion for arbitrary long times. If we connect three or four masses with rigid sticks and ask what the general rotation of these masses are, then it takes about a thousand pages of mathematics and physical discussion to sort out the possible modes of rotation of such systems under symmetry conditions and there is no solution for a completely asymmetric rotator, at all. That system is already completely chaotic. So what, exactly, are we losing in quantum mechanics compared to classical systems? If anything, the hydrogen atom is a much better behaved system than a general Newtonian rotator ever was. Finally, quantum mechanics the way Einstein saw it was not a physical theory. It was more like thermodynamics, a framework that connects different types of physical properties with each other but that does not say anything, at all, about a specific physical system. The physical theory that makes solid statements about nature is quantum field theory. It builds on what Einstein knew, but it goes far beyond it. Even Heisenberg mentions in that paper I just read that he does not believe (this is in 1925, I believe) that a quantum mechanical theory of the electromagnetic field is even possible. Feynman and others gave us such a theory in the 1948 to mid 1950's time frame, i.e. we went from knowing nothing about quantum fields to a complete (if unexplored) theory in another 30 years. That theory happens to be the one that has the best numerical match between theoretical prediction and experiment of all of our theories, to date. It's better than Newtonian mechanics/general relativity in the solar system by a factor of 100 or so, if I am not mistaken. So, then what does it take to make quantum theory complete? A predictive formula of when the next photon will appear in a photon detector? Do we have such a formula for the lottery numbers? The roulette wheels in Las Vegas? When two cars will collide the next time at any given intersection? Whether it will rain at 3:12pm next Thursday? If we do not have those predictors, then why does it bother us so much that they also do not exist for photons? Just my two cents.
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  1699.  @mikeanderson8158  The conserved properties of the vacuum are energy, momentum, angular momentum and charge. This is the combination of system properties that we call "quanta" and an event in quantum mechanics is the exchange of such a quantum between two systems. That such an exchange event has a duration is experimentally verifiable because it expresses itself in time-energy uncertainty. We can produce ultra-short pulses of light and the quanta in such pulses have a finite energy distribution that is inverse proportional to the duration of these pulses. The length of the time aperture of our energy measurement does influence the measured amount of energy. If we want perfect energy resolution, then we have to make that time window infinitely long. The same is true for momentum resolution. If we want to reduce the uncertainty in momentum to zero, then our detector system has to be infinitely large. None of this changes in string theory, as far as I can tell. String theory adds internal degrees of freedom to the physical vacuum that behave like compactified dimensions (at least that's the naive interpretation for some versions of it), but the structure of reality stay the same as in ordinary quantum mechanics, at least in the free field limit (which implies flat spacetime). It's not clear to me what field states in string theory mean for the strong field case, but that problem already exists in general relativity. Even classical energy density seems to lose its original meaning in strongly curved spacetime, so if the classical theory has that complication, then it will likely persist in any quantum model just as well.
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  2051.  @jth4242  I didn't say that it's impossible to derive actual physical "elementary processes". What I said is that Feynman diagrams are not equivalent to these processes. That does not mean that there are no other representations of the behavior of quantum fields that can yield a much better interpretation. Personally I strongly suspect that there are and I gave you an example of recent theoretical insight into one possible such avenue. The problem with Feynman diagrams is simply that they weren't derived from physical insight but they are a purely mathematical necessity to get through the calculations in a naive way, at all. Why are Feynman diagrams like that? Because the path integral formulation of quantum mechanics, which is a quantization procedure, basically assumes that one can describe the world in terms of quanta, which are irreversible energy exchanges at the boundary of a quantum field. By pushing this irreversibility (that does not exist there) into the volume, we are opening up a whole slew of mathematical problems, which we then have to solve with more or less ad-hoc methods. Even our best solutions have remnants of trouble (like an extremely high calculated vacuum self-energy term) that do not exist in nature. In nature quantum fields behave like extremely smooth objects all the way across the universe (if they didn't, then we couldn't see all the way back to the beginning of time with telescopes). There are no dizzying virtual particles popping in and out of existence all over the place as poor visualizations of spacetime want to make you believe. Atoms in the ground state remain in the grounds state until actively excited etc... all of this tells you that something in our math is wrong. It's good enough to calculate a lot of things, but it's still not good enough to be satisfied with it. And we aren't. That's why very smart people are still thinking about the problem. QFT with Feynman diagrams is, by far, not the last word, neither mathematically nor in terms of physical interpretation.
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  2059. @Imjust Observing Violation of any of the conservation laws. I don't know if you guys are aware of this (it does not seem you are), but an atom has to be brought into an excited state to release a photon. That means that a mixed state between exited and ground-state is simply some of the ensemble being in the excited state and some of it being in the ground state. The same atom, however, can never be in both states at the same time because that energy will, eventually, have to be released. Energy that is not in the system can not be released. Energy that is in the system can not stay in it forever because of the decay time constant. Goodness, gracious, kids. This ain't rocket science. One simply has to be able to distinguish between ensemble properties and individual system properties. What QM can't tell us for mixed states is which of the actual states one particular atom is in, that's all. This does have severe consequences for the phase space of systems that have many degrees of freedom, but even for those the total energy is the total energy, no matter how much it spreads out over the mix. You can make the same argument for any conserved quantity. Momentum, angular momentum, spin, charge, lepton number, whatever. These conservation laws are not just being obeyed in the average. They are being obeyed by any one of the samples in the ensemble. To think otherwise is unphysical. Maybe you really need to take a few lab classes in the atomic physics department to remind yourself how nature actually works. That is the problem with all this double slit nonsense and Schroedinger's cat etc. These toy examples do not force you to think about real physics. They all gloss over all the stuff that is of actual importance in real world experiments. Do you really think we would build a multi-billion dollar 17km circumference accelerator if protons would be equally likely in all possible momentum states????? Seriously? End rant.
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  2587.  @richardchapman1592  There are no particles. What would "observing an infinitely small speck" mean, anyway? That's just nonsense. So what are we observing? We are observing energy changing from one system to another. That's why it is called "quantum mechanics" and not "particle mechanics". Quanta are small amounts of energy. Energy is the ability of a system to perform work on another system. It's a system property. We teach this in high school. We never teach that energy has size. We never teach that energy has position. We never teach that energy moves. Energy can flow from one system to another and it can change from one form to another (e.g. kinetic to potential). Forget about "particles" as fast as you can. It's a completely useless concept that causes nothing but problems and the math of the theory says absolutely nothing about it. The math starts with energy, momentum, angular momentum and charges and ends with an estimation of event frequencies. At no point can you tickle "particles" out of it. And what about waves? Waves are a perfectly classical phenomenon. Water has waves. Air has waves. Do water and air have to be quantized to explain waves? No, of course not. Waves are also representations of the Poincare group. The only requirement to get waves are a) linearity (check) and b) translation symmetry (check). All of this is high school level physics, by the way. We are teaching all of it correctly... right until people hit QM 101 and then intellectual hell breaks lose because the confusion that the founders felt is still lingering around in language like "particles"... for absolutely no reason. In reality all of this was perfectly understood by 1932, latest.
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  2703.  @benjalucian1515  You are looking at all the wrong details. All of that is made up or based on Chinese whispers. The people who wrote the gospels weren't there when it happened. The important part of the story is that the Jewish people had been living under occupation for six centuries, similar to the Palestinians today. They were losing hope and some of them were, literally, losing it. There would have been the equivalent of an Intifada movement which was waiting for the one guy to shout "Now!". The temple, which was the one somewhat unifying political force among the Jewish people knew this. The Romans knew this. The Romans had told the temple priests what would happen once that guy made that noise and the temple priests understood that the Romans didn't just talk bloodbath. They meant bloodbath. And then Jesus shows up and keeps saying "I am not saying it's now... I am not saying it's now... I am not saying I am the guy.... but I am the guy.". What would you have done to save the lives of your family if you had been in the temple? Let the guy walk around with his "I am not saying it's now..." story or feed him to the Romans? Exactly. They fed him to the Romans. It bought them 35 years before they eventually ran out of time because some other guys were shouting "Now!". You just have to get past all the irrelevant details. Nobody cares what the colors of the lamp posts on Jerusalem's High Street were and if any of the Evangelists got it right. What matters is that there was a massacre in Jerusalem in 70AD and THAT is the true background of the Jesus story.
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  2725. Good question. I don't know, but when it comes to Feynman I would be careful. He does, as Maudlin say, give a lot of beautiful intuitive explanations, but it turns out that many of them are wrong and while they seem to lead to short term insight, they are doing an enormous amount of damage in the long term because they are "just not so". Maudlin's own explanation of the twin paradox is wrong, by the way. It's not the motion of the clocks that changes the clocks. Clocks never change. Clocks are simply ways to measure causality between different physical systems. If you want to understand the twin paradox, then you have to go back to the actual observations. What really happens if a clock is moving relative to us? It gets redshifted when it moves away and blueshifted when it moves towards us. It also gets delayed when it is at a distance from us. These are the actual physical effects that are related to relative motion and displacement. So when the traveling twin starts his journey, the clock of the stationary twin gets redshifted for him (and the traveler's clock gets redshifted by the exact same amount for the stationary observer). The "magic" happens when the traveler turns around: he experiences the change in the stationary observer's clock right away: it turns from red to blue. For the stationary observer, however, that event only happens a long time after the traveler has turned around because he keeps receiving the traveler's redshifted signals even while the traveler is already on his way back. That's caused by the inevitable signal delay between distant systems. We are always seeing the past of a system that isn't where we are. We can never see its "present", i.e. its actual physical state. This means we are seeing the redshifted past of the traveler longer than we are seeing his blueshifted past and that is the self-consistency reason why the traveler has aged less than we have. One could argue that the concept of "proper time" describes this phenomenon in another way, but there is a problem with that: it requires "god mode", i.e. in order for us to know the "current proper time" of a system in motion we would need to know where it is right now... but in reality we only know where it was a considerable time ago. In that sense Einstein's formulation of special relativity breaks with its very own principles that we should only care about what is and not what we imagine should be.
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  2744.  @marcozec5019  One has to understand measurement as a real, hands on, expensive lab hardware kind of process. It is not some "esoterical, mathematical, philosophical" abstract. A typical quantum mechanical measurement apparatus is like a spectrometer, which consists of an aperture/grating system that separates different wavelengths of light, followed by a detector, which could be a photodiode, a CCD camera, a photomultiplier tube or just the unaided human eye. It turns out that we can build many different kinds of spectrometers of this kind, that select different properties of the light. The most simple grating is a single slit, which detects if light is coming through one particular spatial region. The next kind is a lens followed by a single slit, which detects if light is coming from a certain direction. The first kind of measurement is a position measurement, the lens makes it a momentum measurement. With an input slit and a fine physical grating we arrive at a true spectrometer that measures the energy distribution in the incoming light. We can add a "temporal aperture" and then get time dependent distributions as well. What never changes is the actual detector, which always removes energy from the electromagnetic field. What the math of the theory describes (in an abstract way) is the particular physical effect of our physical apertures/lenses/gratings etc.. This is almost never mentioned in theory textbooks. For that you have to study experimental physics textbooks which explain "how" a particular measurement can be done with actual physical means. There is, unfortunately, no trivial correspondence between experimental hardware and the operator calculus that we can find in theory books. There simply can't be because there are no "ideal" experiments. A quantum mechanical "measurement operator" can, at most, be crudely approximated with actual lab hardware and there is a lot of art and hard work to that experimental process. Most of the "fundamental problems" in quantum mechanics stem from the different kinds of approximations that we have to make to get from real hardware to the operator calculus. They exist in the theory but they don't exist in reality because the limits of the theory that cause the perceived problems are being made obsolete by the actual physical processes that are happening in an actual measurement. One can learn some fundamental insight from that, as well, but they are usually lost in the theoretical literature which suffers a little bit from naval gazing. If all you do all day long is to look at the structure of the ideal theory, all you will ever find are the problems with the theory, whether they are actually present in reality or not. Most of them are not.
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  2853.  @gsmollin2  Except that Einstein didn't believe his own explanation. Read his paper and you will find a sentence in there in which he immediately identifies those quanta of energy with Newtonian corpuscles that have position and path. That sentence is 100% wrong. It is also 100% unmotivated by the actual experimental evidence. Most importantly it is unnecessary. Nowhere does the photoelectric effect require that photons have position and path properties. It's complete intellectual nonsense but Einstein never managed to get rid of this unnecessary assumption in his own mental models as far as I can tell. Every time he talks about quanta he refers to them as if they were Newtonian corpuscles. To this day most people can't let go of that nonsense. MWI doesn't follow from Copenhagen. It's a complete misunderstanding of Copenhagen. Copenhagen simply tells you the facts on the ground: quantum mechanics is a theory of independent ensembles (because individual experimental outcomes are not predictable) and it requires two of those: the ensemble of the free quantum system and the ensemble of the quantum system plus the measurement system because the actual physically measured outcomes depend on the spectral absorption function of the measurement system. Everett didn't understand either of those statements. Einstein may have come close to understanding the ensemble character, but I kind of doubt he ever understood where that came from (hint: it comes from special relativity!). End of story. ;-)
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  3041.  @jefferyzielke7665  You would be boring her if you tried asking her about the stuff she does for a living. That was my point. I don't study quantum gravity. I used to do experimental physics, which means I can differentiate between where the theorists would like us to be and where we really are. We are nowhere close to the parameter ranges that they are talking about, please trust me on that. It's like a snail talking about flying to Pluto squared... that's roughly the size of the parametric desert between current experiments and quantum gravity. Baring a technological miracle that gap will simply not close in anybody's lifetime, probably not even in the entire 21st century. I wouldn't suggest any career for Dr. Hossenfelder. She has made her choices. If you are a young physicists in your first couple semesters in university, right now, I would suggest that you stay far away from high energy physics, especially anything that uses an accelerator facility. It's not that there aren't interesting detail problems there, but the next big breakthroughs won't be happening for decades, well outside your likely career horizon. Astronomy, on the other hand, is going through a technological revolution, right now. There will be amazing new instruments for fifty years to come (especially space based, long baseline interferometers). The amount of data that's in the sky is absolutely astonishing and it's ripe for the taking. That's the much safer bet. Having said that, most physicists end up in other fields, anyway. Solid state physics and material sciences always offer solid employment opportunities in industry, if that is what somebody is interested in. Positions in astronomy are rare and hard to get and that won't change... so unless you are top of your field... tough luck.
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  3233.  @BlackEyedGhost0  There is literally nothing to split. Structurally the phenomenology of this universe is fully understood. It's worthwhile to point out that Galileo might already have had the Theory of Everything around 1630, when he basically gave an equivalent of Einstein's Elevator to express that relativity was an important property of nature. He could not have known just how important it was, but it took us 400 years to go from his relativity principle to a fully worked out theoretical framework that can elaborate the consequences of relativity systematically. It took this long because one can not just sit down with pen and paper and guess ones way through these equations, even though in hindsight the math is pretty obvious. We always need observations and experiments to guide us step by step. That is why it is so unfortunate that the public discussion is driven by pen and paper theorists rather than the people who are actually designing experiments (they are busy and don't care about public outreach). The public thinks that physics is very esoteric. In reality everything that happens at places like CERN is rather hands-on and professional. Critics like Sabine are, at best, driven by their frustration with the slow progress at the experimental front... but that's a matter of technology and investment. One can't go from Galileo's telescope (which was worse than the worst ten bucks binoculars are today) to JWST in a generation. One can't go from his fall experiments to LHC without centuries of effort by millions of people. That's just the price of knowledge.
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  3332.  @2tehnik  All the measurement bullshit comes from people who didn't study relativistic quantum field theory or, if they did, lack the intuition to connect it to the fundamental questions of "reality" in quantum mechanics. Historically the study of quantum mechanical systems basically split at the end of the 1920s, shortly after the more or less final version of non-relativistic quantum mechanics was agreed upon. A number of physicists who were interested in low energy systems like solid matter and atomic and molecular spectra kept working with the non-relativistic theory, which can achieve reasonable accuracy for a number of problems but suffers from (mostly imaginary) interpretation issues because it is not a good theory of the world in general. It just happens to work if we squint and don't care too much about certain details. That's exactly how classical mechanics works in comparison to relativity. It's conceptually false but still good enough for many simple problems. The more serious faction of physicists like Dirac, however, realized immediately that non-relativistic QM was both insufficient and a kluge. They began to construct relativistic versions of the theory, initially very much in the style of the Schroedinger equation. These early attempts produced enormous mathematical problems and were very hard to work with. More importantly, they did not reproduce the plethora of ever higher energy physics data that came from ever more energetic accelerators easily. It took these physicists twenty years (all the way towards the late 1940s) to develop mathematical methods that could tackle non-trivial problems (like Feynman's path integrals and Feynman diagrams). It took another twenty years (bringing us closer to the 1970s) to tackle divergence problems and to develop what is called gauge theory that is the backbone of the standard model of physics. As a by-product of these mathematically very challenging problems the comparatively trivial issues of quantum mechanical measurement etc. are falling by the wayside completely. It is trivial to explain the source of uncertainty in a relativistic worldview and it is just as trivial to explain why the world seems to reduce to classical physics on its own without somebody staring at it all the time. So why are there still people who just can't take the relativistic quantum field theory "yes" for an answer? Beats me. Some people just don't want to get out of their Schroedinger comfort zone, I guess, no matter how poorly it matches to actual reality.
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  3411.  @Tense  I am not an educator. I used to be an experimental physicist, so I have actually "seen" trillions of quanta myself. I have zero interest in teaching, the authoring of textbooks or the editing of YouTube videos. I am simply telling you what reality looks like because I have actual experience with it. As part of that I can tell you why your high school teacher would actually have been your best bet to understand quantum mechanics at the fundamental level and what went wrong historically with the teaching of quantum mechanics at the university level. Why is this important to me? Because I am one of the victims of that failed teaching strategy. You can't even imagine how confused I was after my own introductory QM 101 class. Not about the math, that's easy enough, but about what the math means. That confusion lifts after you become an experimentalist with an interest in the topic, but one should not have to spend years in high energy physics labs measuring energy, momentum, angular momentum and charge transfers between systems to arrive at the conclusion that the six word "Quanta are small amounts of energy." high school level description opens up all of quantum mechanics to a completely trivial understanding by absolutely everybody who remembers the 13 word high school definition of energy (Energy is the ability of a system to perform work on another system.). Yes. Physics is THAT simple but we are complicating it with endless numbers of useless layman books and videos about it. ;-)
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  4056.  @nicholaslogan5185  Even with atoms it's at most wave mechanics and you are learning the wrong lesson if you are listening to the usual wave-particle duality nonsense that permeates the internet. The reason why atoms, neutrons, electrons, photons and buckyballs show similar wave-like behavior is because we aren't measuring either of those "things" in a geometric scattering experiment. We are measuring the behavior of the quantum equivalent of kinetic energy. Energy always behaves the same, no matter what kind of system exchanges it with an aperture. That is the correct explanation on the level of quantum mechanics. There is no such thing as collapse. What people falsely call collapse is an irreversible energy absorption process. The energy that was originally in the quantum field is now in an "external" system called "detector". So where do "waves" come from? They come from boundary conditions of linear equations. Because linear systems do not interact with themselves in the bulk (free space) the solutions on any part of their boundaries can only depend on the conditions on the remainder of the boundary. And because of homogeneity and isotropy the only relevant geometric quantities are the differences in distance between the boundary points. Guess what that leads to? It leads to EXACTLY the same quantitative behavior in the far field that you were taught in high school about the optical double slit! We don't even need light for this. The double slit works with water waves just fine... and for the exact same reason: small ripples on a liquid's surface are sufficiently linear and they don't interact with themselves. So you were, indeed, told everything there is to know about this system, even for atoms. What you were not taught is WHY the optical solution is universal. That requires a bit more abstraction than we are teaching at the high school level, but not much more. This is all physics and math undergrad material. The real step up to quantum mechanics, if you want, would be the realization that quantum mechanics is an ensemble theory. Ensembles are infinite repetitions of the same experiment, using the assumption that all individual copies are completely independent of all other copies. In that case we can apply Kolmogorov's axioms to the problem. You may have been told in high school that the solution to Kolmogorov is probability theory. That is true, but it's not the entire solution. One can, with a bit of juggling, find a solution that is based on scalar products in an abstract vector space and that solution is, if tailored to the requirements of relativistic physics what we call quantum mechanics.
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  4431.  @fermansmith6042  I am a PhD, but it doesn't matter. Physics, science in general, is probably best compared to an apprenticeship. It's not just the theoretical knowledge that you are being taught in classes. It's the work on a variety of problems, usually collaboratively in small and large groups, that make you "a scientist". It's the (lifelong) learning from others in your field. That's no different from being a goldsmith or an NFL player or any other kind of specialized professional. Either you can make pretty jewelry or play the game or you can't. One can not really communicate that to others. Even the lingo is subtle and different enough from "normal language" that communication with people who are not familiar with it is limited. The physics community has its own sets of concepts about reality that can not even be found in other sciences. I know about a dozen active scientists from other fields who are utterly flustered by the way physicists "think" about the world. I tried explaining some in person... with little success. Well, neither do I understand how a chemist can figure out a 40 step reaction without ending up with useless chemical "mush". They can. I can't. I can do my stuff, which they can't. That's why we have different job descriptions. This is not to say that physics is something special. You can find this phenomenon also among musicians, authors and artists. Ask someone how they compose a serious piece of music and you will get a bunch of textbook answers which will do absolutely nothing for you to replicate that achievement. You won't even be able to write a simple melody that way. Human experiences are unique that way and physics is one of these experiences. If you want it, then you have to live it. Peace!
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  4560. @ They have been teaching the photoelectric effect in Germany for over 40, if not over 50 years. That is exactly how quantum mechanics works. It simply a specialized example of the general scheme. It tells you that photons are quanta of energy. Where in that experiment do you see particles? Nowhere. It's a macroscopic experiment which is usually carried out with photon numbers on the order of 10^12-10^15 or so. Where else have you seen something infinitely small? And how did you do that? I am an experimental high energy physicist and I have never seen a single particle in my life. What I have seen by the trillions were irreversible energy exchanges between the physical vacuum and the matter of my detectors. The difference between an atom and a quantum is fairly trivial: an atom is a persistent object that can be observed many times. A quantum only "exists" exactly once: as the amount of energy that flows between two systems during an emission or an absorption event. Easy, right? I would almost call the difference between "many times" and "exactly once" kindergarten level physics. No, not so easy at all, actually. It is this seemingly trivial difference that makes it so hard to get used to quantum mechanics because it has enormous consequences. It does, for instance, not allow us to assign "paths" to quanta. Yes, you will have to start over with everything you believe you know because NONE of it is as you think. That is not my problem. It's yours. You have to forget everything about atomism because quantum mechanics is NOT atomism. It's pretty much the opposite of atomism. Oh, and you will have to learn special relativity, because quantum mechanics is a direct consequence of it. If you have never heard that before, then you are in for quite a shock. There is no version of quantum mechanics that can be understood without it. ;-)
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  4614.  @kusha010  One has to get used to the idea that in modern physics system properties come before matter. It is a very different way of thinking about the world. Call it an acquired taste, if you like, or an effort in "unlearning". It certainly didn't come easy to me. You are correct that energy and momentum exchange can have the same effect on you as a stone that is being thrown at you. That's what makes it hard for us to let go of the "particle" fantasy. On the surface the exchange of these properties looks very much like the exchange of bits of matter. Back in the 18th and 19th centuries they were using the concept of the "phlogiston", a mythical material carrier of heat energy, for exactly that purpose. It turned out to be a scientific dead end and we eventually accepted that heat is microscopic kinetic energy. The problem with localizing energy and momentum in particles is that they don't behave the same way at the microscopic level as quanta do. A free quantum of energy can be anywhere, while a particle has to be somewhere. The observations of the behavior of energy transfer do not agree with the expectations of material particle behavior. The mathematical difference is somewhat subtle. A free quantum behaves like a member of an unmeasured quantum mechanical ensemble (a plane wave), while an actual particle behaves like a sequence of measurements that are connected by conditional probabilities. It shows a random walk behavior around a classical path. We are doing a very poor job in physics education to teach the difference between unconditional and conditional probabilities.
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  4679. @ All I am saying is that generating more code faster doesn't solve the problem. Truthfully, most code doesn't solve any problems that couldn't be solved without any code at all. A hundred odd years ago Sears-Roebuck was doing exactly the same that Amazon is doing today. And I mean EXACTLY the same. They gave customers a printed catalog in the mail, customers filled out a form and mailed it back to Sears. Sears packed all the items into boxes in one of their warehouses and then those boxes got delivered to the customer. What's the difference between back then and today? 24-72 hour delivery compared do 4-6 week delivery. That's it. Nothing more, nothing less. What does Netflix do? The same as Blockbuster and movie theatres used to do and terrestrial and then cable tv providers... they deliver multimedia content. In all of these cases customer satisfaction only depends on one metric: that the merchandise arrives in good condition in a reasonable amount of time (what is considered reasonable has changed over time) at the customer's destination (which in case of multimedia used to be the local movie theatre until tv took over). What happens "in the code" is entirely irrelevant, to the customer AND to your big boss. The code may even have huge flaws as long as the customer doesn't notice because the organization compensates. That's why this entire "formal proving of requirements" thing is ridiculously impractical. It does NOTHING to solve the actual requirement: customer satisfaction.
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  5030.  @navpreetsinghnoorie1942  There is no measurement problem in quantum mechanics. Every day physicists at CERN and other places are making trillions of single quantum measurements. Not once does nature present a problem to them. There is a lot of poor understanding about what measurement means around, though. A measurement is simply an irreversible energy transfer. It is that in both classical mechanics and in quantum theory. In classical mechanics we simply don't care because there is plenty of energy to be measured, so we aren't disrupting the system that we are making that measurement on. In quantum mechanics however the energy that we are measuring (the quantum) is the entire energy of the system. After the measurement that energy is gone and the system has been completely destroyed. That's the actual physics of measurement in quantum theory. In 1931 or so a guy named von Neumann wrote a book about the mathematics of quantum theory. In that book "measurement" becomes redefined as a histogram of such single quantum measurements on an infinite ensemble of identical copies of the actual physical quantum system. And with that the mathematician von Neumann confused half a dozen generations of theorists about the meaning of "measurement". Some of these theorists are so confused that they keep going around claiming that there has to be a problem. There isn't. They simply didn't dare to look at what an actual physical measurement is and the math they keep staring at won't tell them if they don't open a paper written before von Neumann's book. If you dare to look at Heisenberg's matrix mechanics papers, however, it should become very obvious what the connection between actual physics and von Neumann's math is. I will let you do that on your own time. Good luck! :-)
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  5174.  @Treblaine Design by bureaucracy tends to go overboard with regulations. R-20 in all building is better than R-120 in a few buildings. That we don't have enough energy is simply not true. We are merely using it poorly. Our ancestors were living and freezing in unheated buildings. Those overcoats that you see on old paintings... those were not just for fashion. People needed them because the average indoors temperature in winter was maybe 5 degrees C. If you had 10 degrees C in your bedroom or above, then you were either lucky rich or you were sleeping next to the cow and the horse. Lung disease was common, with or without coal, coal just caused a different form of it than sleeping in the cold. Like you said, Germany is a really bad example for everything. They are doing everything in absolutes. "Wollt Ihr den totalen Krieg?" is the standard setting of the German soul. All or nothing, with little room for compromise. I wouldn't take that seriously. As long as people and countries are continuing to transition to renewable energy at this pace we will be all A-OK - in terms of energy consumption. The climate is probably a lost cause at this point. We can't CO2-save ourselves out of Noah's real flood, manmade version. We may be able to use some serious geo-engineering. Elon Musk now has a rocket that can take a lot of foil into orbit... and he will be able to launch it a hundred times a day. That will do it. The astronomers will, of course, get very spotty vision, but that's OK. Elon Musk's rocket can also launch all of their space observatories. ;-)
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  5251. Because it is also isolated and therefor the trigger system is also not in a classical state from the viewpoint of an external observer. The "solution" to this was known long before Schroedinger. It's called the "Poincare recurrence theorem". It basically says that an isolated system has a finite phase space and within that phase space the system takes on all possible states if we are willing to wait long enough. This means that no matter how unlikely the initial state was, eventually, after a very, very, very long time the system will return to its initial state. The so called "Poincare recurrence time scale" is insanely long, though. Much, much longer than the lifetime of the universe. And the quantum mechanical recurrence time scale is much longer than that, still. But since Schroedinger didn't perform a time scale separation in his example his argument that we don't know if the cat lives or dies is valid. Eventually the cat will live, again (for a very short amount of time). This doesn't contradict the reality that a cat in a closed box is always dead (because it runs out of oxygen). Reality is simply the short term solution and Schroedinger's choice of superposition is the long term solution. One can calculate this explicitly for an atomic system with an initial state <excited atom| vacuum ground state| that decays into a new state <atom in ground state| single photon in vacuum|. In a completely isolated (mirrored) box the photon emitted by the atom will, eventually, be reabsorbed by the atom and it will get back to its initial excited state again. That is the real solution to Schroedinger's cat. It's trivial and says absolutely nothing about quantum mechanics.
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  6113.  @Tomdiana  We aren't limited in materials. Tell me one material that you want to buy that you can't? We are limited on some finished goods right now. Why? Because semiconductors that you don't order don't get made. If they don't get made, then they won't get made for at least half a year. That's simply how long it takes from start to finish to make these things. People didn't order during the pandemic. But now you also can't make twice as many to catch up because production lines are usually utilized to 90% or more and it takes years to build a new production line. This has absolutely nothing to do with monetary policy. We didn't print money to make stuff, anyway. We were printing money so that people who became unemployed could stay in their homes and rental apartments. What would you have done, instead? Let the banks eat it? The landlords who have to pay the banks? Or just evict tens of millions, like we did during the Great Depression? How did that work out? Got some nice photographs by Dorothea Lange out of it, didn't you? Desperate homeless people on the roadside from nowhere to nowhere and in shacks that wouldn't even be used to house chickens today. Oh, yes, and great 1930s pre-code screwball comedies showing actors playing people who were partying while the rest of the country was fighting for survival. Good times! That is what you get from not printing money. It's not rational economic policy. It doesn't work. We tried it. Now, nobody says that printing money is enough. We also have to pry it back from the hands that collect most of it at the end of the day... the 0.01%. That's where higher taxes come in. You giveth and then you taketh away, so you can giveth some more to those who need it.
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  6125.  @blahdiblah2169  It was never "shut up and calculate". For me it was always "I don't understand QM101 at all, so let's go to the library and see if we can't find something that makes sense". It took me several weeks of more or less random digging in old journals and textbooks, but then I found Feynman's 1948 paper on the path integral formulation of the Schroedinger equation and then the lights went on. From there I began dabbling in quantum field theory and it took me years (I suck at theory) to understand why the QFT guys don't give a frell about measurement operators. And then I did a PhD in experimental high energy physics and there you notice very quickly that what your detectors are measuring are always energy and momentum. You aren't measuring some random linear operator over a general Hilbert space. It's not math but the most concrete physics in the world. It's the relativistic miniature version of collisions between massive objects that you have seen in high school physics, except that there are no massive objects, but the formulas for kinetic energy and momentum exchanges are still valid. And then I read some more about it and I found Mott's paper from 1929 that explains why plane waves with high momenta automatically form particle tracks in detectors and another set of lights went on. And at that point you can completely abandon the QM 101 nonsense about particles. There are no particles. There are only quanta and quanta are energy and momentum and angular momentum exchanges between fields. And once you know all of that, then you can go back and re-read the old papers of Heisenberg and others from the 1920s and you will find that you were never asked to shut up and calculate. It's all in those old papers, already. The entire physics intuition that you needed to make it successfully in QM101 was already there. What had simply happened in my case is that the guy who read QM101 to us (literally... he didn't give a frell) was not a high energy physicist, he didn't care about foundations of quantum mechanics, he had never built a relativistic detector, he had never read a thing about path integrals, he had never read Heisenberg's papers, either. He knew the formalism from abstract modern textbooks that didn't mention any of that and that was enough for him to do his job in solid state physics. He was the last guy on Earth who should have been teaching QM 101. That is not a problem with quantum mechanics. That is a problem with how we teach quantum mechanics to undergrads. And that, my friends, is exactly the state of quantum mechanics "teaching" on the internet. You are getting a completely mutilated version of a non-relativistic approximation of quantum field theory (which is the only real physical theory that is self consistent) presented by people who don't know that what they are showing you is not the real deal. They simply don't know what they don't know. That is physics DK. And now you have to decide if you want to download Mott's 1929 paper and Heisenberg's 1927 papers (or thereabouts) and read a good textbook or two on QFT and go through Feynman's derivation of the path integral for the Schroedinger equation (one of the most beautiful theory papers in all of physics IMHO) or if you want to pretend that you know it all when you don't know anything, whatsoever. Take care.
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  6207.  @carparkmartian2193  von Neumann explains EXACTLY what happens during a quantum measurement. You clearly didn't read the chapter you are referencing. It is NOT collapse of the wave function but irreversible energy transfer. He even says where the energy goes, eventually: it gets radiated away by the measurement system as heat. That's the one and only correct explanation. Dirac made it clear that he understood that quanta are amounts of energy. The measurement process is therefor an energy transfer process. Dirac's work culminated in quantum field theory in which there is not even a measurement process. We are simply looking at scattering of plane waves from infinity to infinity. Griffith's tells you in his foreword that he doesn't understand quantum mechanics and that he only cares about the "shut up and calculate" aspects and then he proceeds in his entire textbook to prove that he indeed does not understand quantum mechanics. It's one of the worst books in the market. It's telling that you didn't give me a meaningful definition, either. You didn't find one, did you? :-) The measurement postulate is NOT a description of collapse. It's a recipe for strong measurement which tells you exactly what is going on in quantum mechanics: it's an irreversible energy transfer between two systems: quanta of energy get transferred from the quantum system to the measurement system. Nothing happens to the original wave function after that. It simply seizes to be a meaningful description of the original quantum mechanical ensemble because the coupling between the two (ensembles of) systems has changed the experiment.
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  6575.  @YngvinLion  Wave function collapse is not a thing. The correct way of looking at it is in the context of reversible and irreversible physical processes. Only the irreversible ones are "real". Why? Because a reversible process doesn't leave a long term trace in the world. It comes and it goes. It's forgotten, even by the universe. The intellectual challenge, of course, is to leave the confines of your mental nursery behind. In high school and in early undergrad education even at the university level we are building up this fantasy that the world is reversible. In reality, however, the reversible processes are irrelevant. Hamiltonian mechanics can't tell you how many times the Earth has been around the sun. Only rock erosion can. All we know and learn about this world comes from the very processes theorists dislike because they are hard to calculate. ;-) Similarly the randomness/determinism pair is childish thinking. The primary observation is not that the universe is random. It's that the future is not predictable. 19th century physics could not predict the future any better than we can and not for a lack of computing power. The future is simply not fixed, no matter how hard one looks. So how did they come up with that determinism fantasy? Because after an eternity (well, 300,000 years) of human evolution in an environment that seemed random and hostile, they finally managed to predict one thing: an elliptical orbit of a planet. That was it. They couldn't even do two planets. Today we know that two is already too many. One is it, plus a harmonic oscillator and a handful of other systems. It was that tiny success that lead to the hubris of "determinism". It's not a scientific term. It's philosophical nonsense. So that leaves the question where the universe seeds "indeterminism" (NOT the same as randomness!) from? Relativity. A simple look at a space time diagram can show you that it comes from space-like events. And that is the entire story here.
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  6689.  @andersjjensen  None of the technological stuff in hyperloop is either hard or new. We have been doing maglev for half a century now, if not more. We can do any size vacuum system you like basically on custom order. The train's passenger cabin is, essentially, a narrow body jet. All the technical criticism of the system is total bullshit. One can talk about economics and demand and that, if anything, is a serious problem for any and all transportation systems. The talk about implosions is just male teenage phantasies gone wild. People had billions of large, evacuated glass tubes at home for more than half a century and very few of them imploded. Yes, one can make thin walled vessels implode. Can one make thinned walled vessel implode that have proper wall thickness and welds and an occasional stabilization ring? No. One can not. At least not without doubling or tripling the pressure of Earth's atmosphere. Unless you are god that's not going to happen. What happens when there is a leak? Nothing. The system detects it and slows the trains down to a safe velocity. What happens when there is a really large leak? The system detects it and slows trains down while flooding the tube along the entire length in a minute or so. Even a shock wave that might spreads from one of your "imploded" sections could only do so at the speed of sound. That's approx. 20km per minute. After that it hits the air that's already in the tube and that's that. That's where things stop. Look, "chemist". I know that you have no intuition for physics and engineering. Why don't you leave this stuff to those of us who do this for a living?
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  6751. There are no particles. Quanta are small amounts of energy. When we detect one we get a "click" in a detector. The "clicks", i.e. when and where these detectors absorb a small amount of energy seem random. We therefor start to collect statistical information (histograms) about them. In the limit of large numbers these histograms become probability distributions. The theory predicts these probability distributions as the product between a wave function, its conjugate complex and a Hermitian projection operator that represents the absorption spectrum of a physical measurement system (the detector). What happens is that almost nobody who makes these videos actually knows WHY the formalism looks the way it looks. For that you would have to read Heisenberg's matrix mechanics papers, where this is somewhat laid out in a language that still relates to physics and that will give you a bit of physics intuition about what is happening. A few years later a mathematician called von Neuman generalized the relatively straight forward physics and math in Heisenberg's papers to an abstract mathematical formalism that comes from functional analysis (the mathematics of linear operators and function spaces). At that point the connection to measured quanta of energy disappears from the textbooks and is replaced with a general notion of "quantum mechanical state". You also lose a sense that this "state" means the state of a quantum mechanical ensemble, i.e. an infinite repetition of the same experiment. Instead it starts looking like as if the wave function relates to an individual system. That is complete nonsense. It was never constructed that way, neither by Heisenberg nor by von Neumann. It's just easy to loose sight of the translation between physical measurements ("clicks") and mathematical formulas.
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  6891.  @WayOfAges  I am calling the people who can't explain quantum mechanics this easily unintelligent. A better phrase would be "intellectually lazy". These facts about quantum mechanics have been known for a long time. OK, the derivation directly from Kolmogorov might be only thirty years old, or something. I don't remember the earliest paper in which I saw it being done. Maybe it was from the 1980s, which would put it into the 40 year category, but I wouldn't rule out that there are much earlier papers that I simply haven't seen, yet. I am not a science historian and I won't spend weeks or months in the library to dig up some obscure paper from the 1940s that only three people have ever read. So, yeah, my own QM 101 professor was in that category of "intellectually lazy teacher". He didn't care to explain what it was that we were doing there. He just threw the linear algebra at us without any physical connection to the real world. He could have known better, IF he had read the literature that existed at the time. This problem is endemic in the physics community. Professors who are being tasked with teaching a subject are usually very good at their specialties and crap at everything else (as you might expect). Quantum mechanics is not even a specialty. It's a general framework that is being used in many actual physical disciplines like atomic and molecular spectroscopy, nuclear physics and solid state physics. Everybody knows how to use it but almost nobody knows WHY it works and WHY it works the way it works. That almost nobody knows, however, has nothing to do with it being unknown. It's known extremely well because it is extremely trivial. It just happens that nobody teaches these trivialities and the language that we are teaching, even in university, is basically 100% false. The math is all correct, but the way we are talking about the math is about as misleading as one can make it. That's a phenomenon of science history.
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  7012.  @janellegrace5815  I am tired of people who treat reality like it's a religion. Just because Marx and other people wrote something over a hundred years ago does not make it true and it does not make it the last word. We have tried socialism (as in the control of the means of production by the government). Socialist states have built slave labor camps. Hence socialism is NOT foreign to slavery. There is undeniable historical proof of that. Hence Marx was wrong. Now, we do know how slavery works. We knew this way before Marx. We didn't need him to elaborate on this. It works by dehumanizing humans. It strips them of their sentient quality to justify their inhumane treatment. It did that, even in theory, at least since Aristotle who wrote: "Where then there is such a difference as that between soul and body, or between men and animals (as in the case of those whose business is to use their body, and who can do nothing better), the lower sort are by nature slaves, and it is better for them as for all inferiors that they should be under the rule of a master. For he who can be, and therefore is, another's and he who participates in rational principle enough to apprehend, but not to have, such a principle, is a slave by nature." Aristotle says nothing about capitalism here. He simply entombs the right of the strong to enslave the weak as a matter of natural law. The bible does the same. It took humanism to declare these points of view immoral and reprehensible. Did socialist rulers care? Of course not. They exerted brutal power under the disguise of serving Marxist ideas (incorrectly or not) and they established slave labor. Now, you wanted respectful discussion? There it was. And it's gone in a flash because I can tell that the next thing you will pull is a no true Scotsman fallacy. Take care.
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  7160.  @sundhaug92  If you are on microcontrollers knowing how to set up the MMU is, unfortunately, a requirement, or, at the very least it is very helpful. I would, of course, not reinvent the standard libraries or write a file system library from scratch. That is completely pointless. I did write a specialized bare metal scheduler in a day once. It worked like a charm and was 100% stable. Why did I do that? Because there simply wasn't enough memory on that microcontroller to fit an OS in for that purpose alone and even if there had been, reading the documentation would have taken longer than implementing that one piece of code that I needed myself. One has to know where to put an end to reinventing the wheel, though. In the microcontroller world many low level libraries and "drivers" are hopelessly overcomplicating things because the programmers of those libraries are trying to satisfy a lot of different needs with an unsuitable approach. Hardware libraries can not replace operating systems, no matter how "universal" they are trying to be, but it seems that is what many coders of those libraries are being asked to do. In my experience bit-banging the hardware registers very often solves problems much faster and more reliably. So, yeah... shaving that code is actually a viable approach. In moderation. If somebody needs a file system, real multitasking, dynamic memory allocation and inter-process communication in addition to an ethernet library, then the gloves are off. That is not worth reinventing.
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  7375.  @RFC3514  There is no random noise in quantum fields. That there can't be follows from the fluctuation-dissipation theorem (also second year undergrad physics). Random systems also violate basic physics like energy and momentum conservation. Quantum mechanics does none of that. What quantum mechanics does is to introduce an element of UNCERTAINTY. We simply can't tell when the next quantum event will happen and where. THAT is what follows directly from relativity. Why? Because in a relativistic universe the local future depends on physics which in the local present happens in a space-like separated volume of spacetime. Here is a simple example: a Mars probe detects a radiation event on Mars, RIGHT NOW. We have to wait for ten minutes (that's the time the radio signals of the probe take from Mars to Earth) before the radio signal arrives. At the time it arrives, though, it is a completely new and unknowable physical event. Nothing we can do here and now can predict what that signal from our Mars probe contains. That unpredictability drives quantum mechanics. You can formalize this with ensembles and Kolmogorov axioms and then (somewhat unexpectedly) you will find Pythagoras in your calculations. Pythagoras leads to scalar products which are invariant under unitary groups... and suddenly you got the entire matrix mechanics thing popping up in a calculation that was all about statistically independent individual events. THAT is how you get RATIONALLY to quantum mechanics. It's pretty boring, actually, except for the Pythagoras bit. ;-)
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  7389.  @NyscanRohid  There is no measurement problem. Every day physicists are doing trillions on trillions of quantum measurements. Every single measurement is the transfer of a small amount of energy from a quantum system (like an atom that sends out some light) to the measurement system (a photodetector). All of this is covered perfectly fine by the high school textbook definitions of energy and systems. As you can see, there are always two systems involved in a measurement. If you try to lump both systems into one (which one can, due to the definition of "system" as "a partition of nature by a physicist"), then the energy transfer process simply can't be defined and we can't talk logically about "a measurement" at all. What people call "the measurement problem" is the search for nature's equivalent of the second "measurement system". It's all around you. It's the physical vacuum. If an atom sends out light, then that light travels at the speed of light away from the location of the atom. Since nothing can be faster than the speed of light, the energy in that light is entirely lost to the local "atom system". The atom can never get it back. That irreversible loss of energy from the localized system to the infinity of space, that is the reason why nature constantly makes measurements on her own. When was this known? Very early. You can find this explanation in von Neumann's seminal book about the mathematical structure of quantum mechanics. It's in chapter six, I believe. The book was published in 1932, but you can find similar language in works of Heisenberg and Bohr a couple years earlier, around 1927 to 1929 or so, if I remember correctly. Its basically contemporary knowledge with the Copenhagen interpretation. Most modern textbooks aren't discussing it because it is such a triviality, but that doesn't mean that we don't understand it. It just means that the average student never gets to hear this explanation.
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  7625.  @neillibertine3044  What are the most general systems that we know about? Fields. If we want a fundamental theory, then we have to study fields. Unfortunately it turns out that fields are very hard to study, both experimentally and theoretically. That's why we don't start physics with fields but with systems with discrete "components" like "chunks of matter". For instance, the most important of all solvable classical particle systems, the Kepler problem, is handled by abstracting a gravitational field and the matter fields away. We decide that we don't care about the nature of matter and assign a classical kinetic energy to chunks of it and we decide that we don't care about the details of gravitation and we describe it in a simplified way as a potential energy term (that depends on the distance of the centers of mass of our chunks). We are then solving the equations that transform kinetic energy in potential energy and vice versa (while obeying global momentum and angular momentum conservation). The critical term that describes which particular system we are analyzing (Kepler problem, harmonic oscillator, pendulum etc.) is therefor the potential energy term. It is here that we can realize that potential energy does not belong to any particular constituent of the system but to the system as a whole. No matter how many parts (chunks of matter, springs etc.) the system has, there is always one potential energy term that describes all of it. You are correct that this is not how we are teaching classical mechanics in high school. We are, however, teaching exactly this in the first theory classes in university by introducing the Lagrange and Hamilton formalisms. Then, a semester later, or so, we are teaching students how to "quantize" these classical systems by using the Schroedinger formalism, which replaces the kinetic energy term with a Laplacian and the potential energy term with a multiplicative linear operator. If you happen to take classes on electrodynamics (the most simple of fundamental physical field theories), then you can later learn in your graduate level QED class how one goes from the Hamiltonian of the electromagnetic field to the quantized field equations by inserting it into a path integral. That, like the Schroedinger equation, is a quantization procedure. It is, however, a much, much more complicated one with sheer endless mathematical consequences that are still not fully understood, yet. In any case, the big picture is that we never work with "chunks of matter" in these theoretical descriptions. We are always working on the level of system energy.
    1
  7626.  @neillibertine3044  "first thing first, if an atom is in higher energy state how it come to so." Usually by absorbing a photon, i.e. from the electromagnetic field. That is already a simplifying description because "an atom" is actually an electromagnetically bound system. The atom/em field distinction is already a system boundary made by physicists, it's not one made by nature. So when you say "extra energy from outside", then you are already using the system language that I was talking about. That atoms are "particles" are semi-classical approximations that you were taught to believe in in school because it is extremely difficult (and in most cases also unnecessary) to describe atoms with quantum field theory. The only difference between us is that I know when I am dealing with an approximation of that kind and you are glossing over it. "Field theory, field whether scalar like temperature or vector like electric, dont exist without particles." Why does an electromagnetic field not exist without particles? The classical field description is through either a four vector with a scalar electric field potential and a three vector for the magnetic vector potential. You can expand that to a four-by-four tensor for the electric and magnetic field components, if you like. Once you quantize that you won't get particles, either. What you will get are field quanta, which are energy/momentum/angular momentum (spin) values. There will never be "an object" jumping out of a quantized em field. Experimentally that is fully supported by something as trivial as solar panels. They absorb electromagnetic field energy at 1e15Hz and convert it into a different form of electromagnetic field energy at near 0Hz. No particles needed. "About kepler description, there is no conservation of angular momentum for elliptical orbit, so keplers description is faulty." You really need to go back to your physics books for that one. It's completely false.
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  7769.  @professornebula6545  Where did I mention randomness with regards to microscopic processes? I didn't. One can actually prove pretty easily that the microscopic world can not be random. Random process inevitably create dissipation and we don't observe dissipation. There is even a fitting name for this proof: fluctuation-dissipation theorem. Energy, momentum and a few other quantities are perfectly conserved locally as far as we know. This is so both at the macro- and at the microscopic level. What is locally not "conserved", so to speak, is our knowledge about the world. How comes? It's caused by phenomena like non-integrability for classical Newtonian systems (which make the claim that everything can be calculated nonsensical, even at the most primitive level of physics) and even more so by relativity once we look at the world the way it really is. In a relativistic universe all systems are necessarily open. Energy, momentum and angular momentum are constantly "escaping" towards infinity. That leakage is what makes the local state unpredictable. We can't do the local accounting unless we "collect" all the missing energy etc. with some "hermetic" detector array that surrounds our local coordinates. To get the information about the measured results back we also have to wait for the finite time that a measured signal takes to propagate back to us from our distant collecting array. So that means that the current state can only be fully known in the future and even then only if we are extremely diligent (which is not even possible). In practice this means that the present is entangled with the future. It's not just any near term future. It's the entire future of the universe. THAT is what causes the world to be non-deterministic. It doesn't mean that it's random, but it means that it's not knowable, neither to us nor to nature. If you want a poetic description, try this: How do you know what you look like? You need to look into a mirror. Well, surprise! So does nature and because she doesn't have a mirror, she can't tell you what she looks like, either. Makes sense? You are correct about one thing. Whether I have a PhD or not makes no difference to my arguments. It does make a difference to me, because it means that I have been thinking about this very thoroughly for a very long time. Much, much more thoroughly than most people. That causes a level of mental clarity that is otherwise hard to achieve. You can get there, as well, you just have to spend the fifty years on this stuff that I put in, already, and unlike you I am exercising every day on the internet by trying to explain physics to people, whether they want to hear it, or not. Every time I am repeating my argument I am learning, whether any of you are listening, or not. I am much, much more knowledgeable about the basics of physics than I was 20+ years ago when I began talking about physics on the internet. I used to tell people a lot of bs about quantum mechanics back then, but then I noticed that I was talking bs and I began learning. Today I know better. I am self-correcting. Can you do that, yet?
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  7966.  @neillibertine3044  Matter is an emergent phenomenon of quantum fields. Protons and neutrons are bound states of quarks and gluons. Nuclei are bound states of protons and neutrons, atoms are bound states of nuclei and electrons, molecules are bound states of atoms and so on. Where quanta come in is during system changes. Nature doesn't know about systems. Nature is all one entity. Systems are definitions by physicists. We know that these artificial entities interact by exchanging globally preserved physical properties like energy, momentum, angular momentum, electric charge etc.. "A quantum" is an irreversible exchange of one or several of these properties. For thermodynamic reasons energy always has to change (that follows from the third law that does not allow zero temperature, which basically leads to a minimal thermal background energy density condition). So if any detectable change in a physical system should occur, there has to be an irreversible energy exchange. That is what we call "preparation" (aka "source") and "observation" (aka "detector"). As you can see, quantum mechanics is therefor a systems theory. It describes how physical systems interact with each other using measurable (classical) physical quantities. No particles required at any time. Classical mechanics is also a system theory, by the way, you were just never taught to understand it that way. If you had been taught properly, then the "emotional" transition to quantum mechanics would have been trivial.
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  7972.  @ModernSoftwareEngineeringYT  All I am saying is that methodology doesn't scale. The more complex it is, the less it scales down. Just because something works for Google and Microsoft (and we could argue that absolutely nothing works at Microsoft, in terms of quality), doesn't mean that it works in general. Yes, if you can afford independent teams for design and test and validation, then you should be able to produce better software. How many software development companies can afford that? And those who can, do they really produce better software because of the methodology or because they have more developers and not everybody is stressed out to the breaking point? I would suggest it's the latter. In comparison, how much software is being developed by single people? A lot. Worse, still, I used to do embedded systems, where I did everything except for the mechanical engineering. I did the circuit, the PCB, the debugging and I wrote all of the code that ran on the microcontroller. That product has 100% uptime. There was never a single line of documentation written by an architect. There was never a product definition and there is no test code. I simply wrote a functional software product around my own hardware. I don't think that I even documented the register maps other than in the source code. It still works without any methodology, whatsoever. Why? Not because I am a good software developer, either. I simply took the time to test every bit of the functionality manually. I knew my product in and out before it was ever shipped. That is my experience. It's my religion. I would not suggest that you try it that way at Boeing or a major game development team.
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  8421.  @greghansen38  Scattering matrices don't have ontological problems. They are describing the scattering of waves from infinity with the outgoing solutions also being probed at infinity. This eliminates questions like "what is a measurement" completely (not that that's hard to answer in non-relativistic QM but one has to drag thermodynamics into the mix, which is not necessary in relativistic theory). It eliminates the classical-quantum system boundary. Infinity always provides more than enough degrees of freedom for decoherence without having to construct "measurement objects". Phase doesn't matter at infinity, it all automatically boils down to amplitudes, just to name a few advantages. I do agree with you all the way that we are not teaching classical scattering theory nearly enough. It is extremely important in practice (optics, electromagnetic systems engineering, radar, medical imaging etc.) but the average physics student gets to see almost nothing about it. I certainly didn't, except for a trivial 2-d Coulomb toy problem. We also didn't learn relativistic dynamics enough to have a solid handle on collisions and high-boost systems. That leaves accelerator physics mostly in the dark, even from a classical perspective. I was taught some nuclear physics, but basically all in the non-relativistic approximation. High energy physics? Forget about it. That, however, is the real "footprint" of the universe. OK, it would have been different at a university that had an active high energy physics program, but even those lectures (I took them later as part of my PhD) were kind of very basic and insufficient to understand QFT on more than a surface level. One can, of course, learn important lessons about QM from atomic, molecular and solid state physics, but the fact that we are teaching the formalism independently of its applications makes connecting the dots harder, IMHO. I hope that younger professors are slowly getting a better handle on how to give students a working knowledge of QM, because for sure mine didn't.
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  8601. Yes, it would be if you are approaching it from the mathematical side, which tells you very little about physics. I would suggest you try to understand the physics, first, before you learn the math. That makes it a lot clearer what is going on. Quantum mechanics is about quanta of energy that get exchanged between systems. It is NOT about objects. It is NOT about particles and it is NOT about waves. When systems exchange quanta of energy, they also exchange momentum, angular momentum and charges like electric charge or leptonic charge. Energy and momentum are not quantized, but angular momentum and charges are. They only come in integer multiples of a minimal quantity (usually expressed in Planck units and electron charge, but these are arbitrary numbers due to the choice of our units - in rational units they should be set equal to 1). In an experiment the detection of one quantum is basically one "click" of a detector. In the ideal scenario such a detector can tell us where and when a quantum was detected and how much energy, momentum, angular momentum and charge it had. A single detection carries basically no relevant physical information about the systems that emitted these quanta, so we have to bunch an infinite number of them into a quantum mechanical ensemble and then we can form frequentist counts aka histograms aka probability distributions with them. Because we are now working in an ensemble theory, we can assume that each member of the ensemble is isolated and that means that sub-ensembles are statistically independent of each other. This leads to the usual Kolmogorov axioms for probability theory. It turns out that these axioms for statistically independent ensembles can also be satisfied with complex and quaternion based functions (and probably product algebras built from these basic elements, but that's less often used). The resulting functions are normalized elements in Hilbert spaces (normalized because the number of members in an ensemble does not change during the evolution of the ensemble), which basically leads to unitary dynamics, i.e. rotations in finite and infinite dimensional linear spaces. In the trivial finite dimensional case these rotations can be described by Heisenberg's unitary matrices, in the infinite dimensional case we need linear operators and partial differential equations. And that is basically what quantum mechanics is: the theory of unitary rotations, except that there is not much physics in that because that part is basically a simplifying assumption (that all the copies of the system we start out with are still there when we detect the results). In experiments that's far from true. We actually lose most quanta of energy in most of our experiments. The experimentalists are simply fudging that loss with an arbitrary (experimentally measured) number that we call "quantum efficiency" and the theorists never get to see that fudge, so many of them think that "unitarity" is some god-like property of quantum physics. It's nothing like that. It's just what's left over after the experimentalists have cleaned the data. If you keep that in mind you will start to understand why the mathematical structure of quantum mechanics is so meaningless. It's an artificial construct, not a property of observational reality. It has that in common with Hamiltonian mechanics, but that's another rant. ;-)
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  8613.  @Qichar  Photons are small amounts of energy. They are not objects that the field is made of. These amounts of energy also depend on the measurement system, so they do not already "exist" in the field before the actual measurement is made. The field has some energy, but it is not atomistically made out of these bits and pieces that we just pick up at the end. Instead the measurement process itself selects how much energy it absorbs and where and when that absorption happens. Intuitively that's probably the hardest part to get used to. If you want a game of luck analogy, imagine a game of roulette, but the player decides which kind of wheel he wants to play with. He can get a wheel with 37 positions like in the standard version or he can pick one with just four, or another one with 19 possible outcomes. In quantum mechanics the choice of measurement is equivalent to the wheel the player would pick in the roulette example. You also have to let go of the idea that photons interact. They don't. Quantum mechanics is a theory of statistically independent ensembles in which every single outcome is completely independent of all other outcomes. There are physical systems for which this assumption holds (like the free electromagnetic field) and then there are systems for which it does not hold (and that's experimentally testable!). In the latter case the formulas of standard quantum mechanics do not apply. One can construct formulas even for that case and the first example of such a system that I am aware of was given by Mott in the year 1929. The problem with the way we teach quantum mechanics is that we do not mention these very important assumptions about the theory, which leads people to speculate about completely irrelevant things like "single photon interference". There is simply no such thing. The theory rules it out explicitly in the way it is constructed and the reason why this works is because the electromagnetic field does not interact with itself measurably at optical wavelengths.
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  8883. What answers are you disappointed with? The determinism question? That has an absolutely trivial answer but you are asking the wrong guys. Neither philosophers nor biologists have a good handle on it. It's the physicists who do. The trivial answer is that the world is not deterministic. It was never deterministic. For the longest time humans couldn't make any sense of the world. Most processes seemed confusing, at best, and random at worst. Eventually we made a little bit of progress with Newtonian mechanics. Suddenly we could answer questions about the trajectories of single objects. We could, in particular, predict the motion of a planet from first principles. That was the major scientific breakthrough of the 18th century. It was so huge, indeed, that people were immediately over-extrapolating it. If one could predict the motion of one planet with absolute certainty, then shouldn't it be possible to use the same methods to predict the motion of absolutely everything else? That is the idea that lies behind naive determinism. It is as obvious as it is false. Newton himself already noticed that he didn't get anywhere with his methods when he was contemplating the notion of two planets that are interacting with each other. Today we know with absolute mathematical certainty that this motion is NOT predictable. The three body problem is, in general, not solvable. Hard determinism does not apply to it. It's far worse, actually. We know that among all possible systems in Newtonian mechanics (of which there is a very, very large infinity) only a handful are deterministically predictable in the sense of 18th and 19th century determinism. Every other system does not behave in a way that would allow us to predict its long term future. It gets much worse if we try to apply determinism in special relativity and quantum mechanics. I will spare you the details, but 20th century physics knows that the future is open. It is not only unknowable to us but it is, in general, unknowable to nature. Nature simply doesn't care to pre-select one possible future from all possible futures. It doesn't operate in the way 18th century thinkers imagined. In other words... everybody who is still hunting for determinism in science is hunting for a snark. It's simply the wrong way to think about nature, on all levels, small and large.
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  9193.  @richardchapman1592  The wave function is not a description of the state of one system. It's the description of the averages of the quantum mechanical ensemble, i.e. of an infinite repetition of the same experiment. Quantum mechanics also doesn't describe particles. That's one of the worst scientific misnomers. Quanta are small amounts of energy, momentum, angular momentum and charge. The trivial reason why quanta behave so "strangely" is because they are not objects. They are irreversible energy transfers. Energy never behaved like an object, not even in classical mechanics. We could never assign a fixed position to energy. It was always a system property. Once you make these adjustments to your intuition about quantum mechanics all the "strangeness" goes away. The most simple classical analog are dice. A quantum would be the equivalent of an individual outcome of a dice throw, i.e. a "3" or a "5". I would not be the equivalent of the dice. The wave function represents the probability distribution of the dice, i.e. for fair dice that's just the fraction p(n) = 1/6 for every possible outcome. In quantum mechanics that's a complex function, of course and the Born rule is description of the measurement. For dice we could construct measurement operators like "The outcome is even.", "The outcome is odd." or "The outcome is a prime number.", but these are trivial for classical probabilities. We even use these "measurements" in classical games of luck like Blackjack, Roulette etc..
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  9440.  @pb0xAF09  So, please, write down the exact kind of documentation that you require for a browser. I dare you. Not for my sake. I already know that it is impossible, but for yours. I am not saying that it's impossible to write exact requirements for some code. The embedded software that I am writing right now has a couple hundred completely orthogonal functions, all of which do some very specific things in a very specific order, which is ensured by hardware interrupts. The thing is... I don't even need specifications for this code. It's a single developer project, the functionality is fluid because I am the designer of the hardware and I determine which function the software will have. If something turns out to be too hard to implement, I will simply remove it from the list of wants and the customer who buys the product will never know that such a function could even have existed. The control flow will be correct by design (it's a state machine) and all memory is allocated statically, hence I don't have to worry about little buggy things like buffer overflows. This is exactly the kind of software that one could fully specify and test. But why in the world would one? Whether a single function works or not can be tested by hand at the time of writing. That's it. Now, your web browser OTOH... that's a totally different beast. Anybody can kill that thing with a piece of crappy javascript that calculates pi to the power of e to a trillion decimal places and there is absolutely nothing that your requirements document and test suite can do about that. Javascript is a requirement and it happens to be a Turing complete language, hence you are up against the halt problem. I would suggest you take a few lessons in computer science before you make claims like the ones you made. They don't reflect well on you. :-)
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  10018.  @Danny_6Handford  "Many famous and main stream scientist think..." Stop right there. What scientists THINK is NOT science. Science is the rational description of nature. All I ever remember seeing in the primary (papers) and secondary literature (textbooks) are formulas and plots for the density of the universe. That's what the theory predicts. It does not predict size. Can you show me a paper that contains a size prediction or, even better, a size measurement? "...that the size of the universe before it started to expand..." Nobody has ever seen a non-expanding universe. I don't know where you are taking that idea from? Diagrams that stop at some arbitrary time scale? That's a choice by whoever made the diagram, it's not an actual measurement of an initially static universe. There are suggestions out there that the universe is inflating eternally, but those are extrapolations. There is no data and there is not even math to arrive at that conclusion. What the universe does on unobservable scales is unknown and will potentially stay unknown forever. "The math appears to support this idea..." Science is not math. Math is just a description of what we observe. We can extrapolate beyond what we have seen and sometimes that extrapolation is correct. Often it is not. You might as well be throwing dice for all your cosmological needs if you go "by the math". Nobody in physics works that way. We know at all times what has been observed and what is pure extrapolation. In this case everything before the electroweak unification scale is complete extrapolation. That doesn't get you anywhere close to "the universe was the size of an atom". "We now know that our universe produces billions of black holes and I am probably not the only one that thinks black holes are the “seeds” for the creation of a new universe but only a tiny percentage of them will create a new universe." OK, that's just poetry in motion now. There is not even math to support the idea that what's inside a black hole is a new universe. The math that we have predicts an extremely hot and violent environment that cooks all information about the past out of what fell in. What we "believe" based on the extrapolation of "the math" is that what comes out of a black hole is mostly featureless black body radiation. Only a tiny percentage of the infalling baryonic matter can re-emerge as baryonic matter. Maybe not even that.
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  10623.  @pawelczubinski6413  That's not the physics behind all of this. That's the solution theory of the Schroedinger equation as presented to you by von Neumann, a mathematician who at the time was deeply involved with functional analysis. A quantum measurement, as in ONE detection of a quantum of energy, is the exchange of one quantum of energy between the quantum system and an external system that we usually call the "measurement system". What "collapse" means is simply that the quantum system before the measurement had either less energy or more energy than after the measurement. If it has the same amount of energy, then a measurement did simply not take place and the ensemble of the system can be described by the unitary evolution of the ensemble's wave function. If you read Heisenberg's papers on matrix mechanics (1925, I believe), then you will find that the energy differences between "before the measurement" and "after the measurement" (that's the amount of energy which we call "the quantum") are still part of the theoretical description. By 1932 when von Neuman writes his abstract mathematical treatise on the math of the Copenhagen interpretation, that immediate connection between the actual physics of quantized energy transfer and the "state" based theory of the quantum mechanical ensemble had been severed sufficiently so that future generations who are learning von Neumann's math were and are having a hard time to actually derive from it what happens at the level of the physical system. That's an artifact of the way we teach introductory quantum mechanics. We tell you the math but we don't tell you what it actually means. In this case, of course, you have to understand the actual physics of the process, the mathematical structure of the theory tells you absolutely nothing about what is going on.
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  11519.  @lolroflmaoization  The wave function is not a physical object. Nature knows nothing about it. It's a mathematical abstract. Mathematical abstracts can't collapse. It's like saying the probability distribution of dice collapses from 1/6 to 1 when we roll a "3". That's just total nonsense. A single system is NEVER in superposition. What we are measuring is a quantum of energy. Let's say our system is an excited atom. Before the measurement of a photon emission from that atom the atom was in the excited state. There was nothing uncertain about that. After the measurement the atom has lost a photon's worth of energy and it is now in a de-excited state. Again, there is absolutely nothing uncertain about it. A single atom can simply not be in a superposition. Either it has that much energy or it does not have that much energy. What can be in superposition is our knowledge of an ensemble of atoms BEFORE we have the measurement results. Nature does not know what we know or don't know about either a single atom or an ensemble. Nature does not care about the uncertainty of our knowledge. Hence it does not care about the wave function. Where this gets really unpleasant, and this what really upsets people who are not used to it, is that the detection of a quantum does NOT give full information about the ensemble state. The same preparation of spin state (all up in the x-direction) will give a 50% mix of ups and downs if we perform the same spin projection measurement in the y-direction. There seems to be some randomization going on here that classically does not exist. Where does it come from? It comes from the unknown state of the measurement system's ensemble. We can simply NEVER collect all the information about the world that we would need classically to describe all of nature with a classical state. THAT Is what upsets people.
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  11631.  @djjfive  Well, the ITER homepage is factual and truthful, something which one can't say about some of the commercial companies that peddle tiny fusion reactor designs. It will be interesting to see if any of them can as much as light a candle. Personally I doubt it. ITER will certainly produce strong bursts of neutrons and heat, which will amount to mostly a radioactivity cleanup problem in my opinion. I found the fusion community to be quite honest about their goals and aspirations in the past. I went on a tour at Garching a long time ago and asked the scientist who showed us the facility what the community thought fusion could accomplish in commercial terms. He responded that a best commercial estimate for the cost of fusion energy was four times the cost of electricity from coal at the time. That was based on JET sized baseline designs without any cost for fuel breeding and processing, of course. With ITER sized facilities plus (as of yet non-existing) blanket physics and the rock bottom cost of solar and wind energy we are probably looking at ten times the cost per kWh now. In other words: magnetic confinement fusion will simply not happen commercially. That doesn't mean it won't happen. I can see it being the power source for future interplanetary and certainly for interstellar spacecraft. We will master 25T, then 30T and eventually even 40-50T magnet technology. Even a child can ignite a fusion plasma in a 50T field with a match (in comparison to the difficulties for a 12T Tokamak). Those reactors will squeeze tens of GW out of a few cubic meters of plasma volume. That's roughly the power of a space shuttle solid rocket booster, but burning for many hours or even days, while the spacecraft will accelerate to hundreds, maybe thousands of kilometers per second. That is where fusion will live. It will not power your LED light bulbs, other than in form of solar panels. And that's fine. Solar panels are great.
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  11681.  @zoeherriot  I didn't say that the problem doesn't exist. I said that the problem already exists in your own education. Schooling of humans is just as faulty as the training of neural networks. It is NOT "an IT problem". It is a general problem with the way in which neural classifiers assess the world. They do quick but superficial similarity assessments rather than actual logical root cause analysis. In general, a neural network is just a giant lookup table. If what is in it doesn't match the input vector, then a more or less random output will be generated. Tesla's cars, for instance, have simply never "seen" a giant white surface that keeps getting bigger rapidly, so they can't tell that it's dangerous. That's all there is to it. If you would convert the representation of the input data into a velocity dependent "time to collision" estimate first, then the frontal collision problem would never occur because the neural network would always "know" that it is dealing with a dangerous situation. The forward looking video feed is simply not that representation and it's not in some magical way equivalent to that representation. We do have systems like that, by the way. It's the ground avoidance and collision warning system on planes. The machine knows exactly what is going to happen ten seconds from now and gives the pilot a stern "Pull up! Pull up! Pull up!" warning. If the pilot does not react or the reaction does not convert into a proper attitude change of the plane then the result is completely predictable. There are similar warnings for air speed to avoid a stall and collision avoidance systems that give banking warnings like "Bank left!". Why did we build such systems into planes? Because pilots were frequently flying their plains into the ground, a non-recoverable stall (it takes only ten seconds of faulty control input to do that unless you are flying a fighter jet) and into other planes.
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  11782.  @JohnSmith-ut5th  Don't get me wrong. Feynman's book is great. He gives a great insight into the phenomenon of how path integrals work and how they create semi-classical effects (by destructive interference of rapidly oscillating terms that are far away from the classical trajectory that minimizes the classical action). One has to understand that he comes from high energy physics background, though. In that particular case, high energy quanta do behave, in a sense, like classical particles when they are being subjected to weak measurements in detectors. A weak measurements is one that does not remove the entire energy of the original quantum but instead only makes many small momentum changes while the energy is being slowly absorbed by a detector medium in many steps. How this happens form the standpoint of a pure wave theory has first been pointed out by Mott in 1929. It's basically an application of the equivalent of conditional probabilities in quantum mechanics: if we localize a quantum weakly at some coordinate x, then we incur a small momentum uncertainty, which for a next weak measurement will give us the same coordinate plus the classical estimate for the location change due to the initial momentum plus a stochastic term that came from the momentum uncertainty of the localization. In essence, experimental high energy physicist can treat the quanta they are detecting in their experiments like classical particles that make a little random dance around the classical trajectory. In the detector the energy of an e.g. 1Gev "particle" changes in steps of hundreds of eV to MeV per interaction and hundreds and thousands of such interactions occur before all the energy is used up. That's what creates those nice particle tracks that show up in all the high energy experiments. However, in the interaction point of the beams in an accelerator experiment, that is the point where the actually interesting physics happens during collisions, this weak measurement approximation does not apply. There quanta are exchanging all of their energy/momenta at once and no classical paths exist . That's where we have to go through the entire infinite sum of Feynman graphs to elaborate all physically allowed interaction processes. That is what the path integrals and their perturbation series (Feynman diagrams) were really invented (or shall we say discovered) for. At that point we are back to the same principles that apply in low energy quantum interactions like the photoelectric effect: quanta only exist as physically useful entities during the interaction of quantum fields, when the entire energy of a state is being exchanged. When these fields are not interacting, however, then they behave like wave phenomena. End rant. :-)
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  11876. That's not what the EPR paper argues. You should read it in detail when you have the time. The main problem with the paper is not how it uses quantum mechanics but how it defines "completeness". Here is the original language: "Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory. We shall call this the condition of completeness." It requires that elements of physical reality are mapped to elements of the theory. Copenhagen does that just fine. The actual "problem" with Copenhagen is that it has a theoretical element that DOES NOT exist in physical reality: the wave function. A wave function is an ensemble average, i.e. it's a mathematical abstract. Nature only has exactly one copy of each physical quantum system, while in the theory we postulate an infinite ensemble of statistically independent but otherwise identical copies. That is exactly the same procedure that we use to define probabilities and one can, indeed, derive the structure of quantum mechanics from Kolmogorov's axioms without much difficulty. So it's not that the theory isn't "complete". It's actually more than complete by this definition. It requires something on paper that nature doesn't provide itself in experiments and observations. So while the paper is technically correct (it shuts up and calculates correctly), it completely missed to identify the source of the ontological problems with non-relativistic quantum mechanics.
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  12036. ​ @LateNightRadioe  We can agree about all of that. To address your question... do I believe that one can find an algorithm to stop people from hating and doing nasty things to each other? No. Historically mankind has always tried to implement such systems in form of laws and religions and, foolishly, even in the hope that the rule of the one just king (emperor, chancellor, party leader etc.) would set things right. Any and all attempts proved futile, even though some produced short term and sometimes lasting net positive results. Facebook is, on that scale, a rather tiny blip of a phenomenon. I can even tell you that I do not believe that American Democracy is on the brink because of Facebook or the internet in general. These are just lame excuses. A significant part of the American electorate is merely falling into the same trap as the good German people who cheered for Hitler before the war. They believe that a strong man (it never seems to be a strong woman) can magically make all their discomfort with reality disappear. That discomfort is real, it is not imagined, it won't go away magically and no strong man can make it go away, either. No algorithm can heal it, no amount of "discussion" on the internet can reduce it. We all have an itch that we can not scratch. It's called being human, it's called being mortal, it's called being lonely, it's called being poor and there are many, many more such limitations that we can't overcome because of the biology of our species. Having said all of that, communication has become a tool of mass destruction. If we don't want to destroy ourselves, then we will have to regulate it and that is a discussion that has to happen on a much larger scale than that about the algorithms of internet advertising companies.
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  12094.  @berryboi1574  You do have a point, of course, that in the US education has been left to the vultures and rent-seekers. The ideal combination for a person is to get a degree in a country with free higher education and to move to the US to make money. That brain drain is, among other things (like the lack of capital for investments and a risk oriented investment culture), a major force why economically smaller countries are at a technological disadvantage. This process has been going on for a long time. We need to reverse it to bring the entire world to the same level of development. In my opinion Northern Africa can be a very valuable extension of the European economic zone and historically it has been. It was the main grain producer for the Roman Empire, after all. Its fall had a lot do with the loss of its main food sources. Today all of Africa, including the Maghreb countries, are the main untapped source of worldwide human potential. It is young, it is hungry (for knowledge, thankfully a little less for food these days). It has natural resources, not just in form of minerals and beauty (for tourism), but also renewable energy, that could power Europe easily. Instead of the desperate exodus of Africa's poor who will trade the squalor of European immigration camps (at the ultimate risk of their lives) for the instability of their home countries, it's time to make Africa an attractive place to be. Let Northern Africa, in particular, return to its former glory, as the supplier of Europe's lifeblood.
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  12615. @jeffafa3096 The problem with physics on the internet is not restricted to Sabine. Most YouTubers either oversimplify the actual facts to the point where they present a completely false mental model (this is especially the case for everything related to quantum mechanics) or they are completely uneducated about the subject matter to begin with and they basically just regurgitate hearsay in a game of telephone. Either way you are not getting useful information. This, by the way, is not even restricted to the internet. I would make the same statement about most layman books (Hawking in particular wrote some horrible mental models into his layman books that the physics world is still trying to exorcise from the public's memory... with little success.) I only know a few domains well enough to talk about them. Physics is one, electrical engineering (at the circuit board level) another. I do not talk about chemistry, biology and ice fishing in any level of detail. I simply don't know enough about them. What I can tell you is that Sabine often enough misrepresents physics badly enough to disqualify her from being a good source. Of course some of what she says is correct, but the context in which she puts those snippets is designed to garner attention and to increase her view count. So where do you find "the truth"? In the physics library and the laboratory... in form of a full time 24/7/365 physics career. I hate to break it to you, but physics is no different from playing the piano. Either you can play the piano or you can't. No pianist in the world can tell you how one plays a Chopin piano concerto in Royal Albert Hall. Either you do or you don't. There is no trying and there definitely is no "peeking in".
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  12619.  @LennardA320  Yes, the cost+ scheme allows the contractor to charge a lot more than the actual project cost, but not because of the 10%, but because they can quote an almost arbitrary cost base. Now, a naive person may assume that the contractor pockets that money and all the government project managers are idiots. You can hold that religious belief until you actually meet a government program manager. I have. They are not idiots. They know exactly how much materials and services cost. Some of the people I worked with were among the sharpest minded people I have ever met. So why does the government "let" this happen? Because they have other projects with Bechtel that are not publicly disclosed and that they do not want to show up as a Congressional line item. Bechtel gets paid for those projects with excess money from the NASA contract. Did you never wonder why we are suddenly going back to the Moon? Because it's expensive and the US government needed an endless sink of money that they can hide secret programs behind. Unless, of course, you haven't noticed that there is a hot war going on in Europe and that the Chinese are also extremely active spying on us. Do you really think we are just standing by? Of course not. We simply aren't telegraphing either to the Russians or the Chinese what we are doing about it. What you should be really worried about, however, is the Saudi Arabian city called "Neom". The Saudis are pretending to dig sand for tens of billions of dollars, which looks even more crazy than the current moonshot programs of both the US and China. Of course they are not digging sand. They are hiding tens of billions of dollars of spending on their nuclear weapons program behind that project. I am sure you can find many similar, although smaller examples of "ridiculous" government spending around the world.
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  12687.  @MrDavibu  "Refactoring is more about data structures and how data is accessed and management of responsibility." That's my point. If refactoring moves the implementation or maintenance of a method from one team (member) to another, that's inefficient. People who were familiar with the code are now out of the loop and somebody has to learn it from scratch. Objects are, in many aspects, a false abstraction. In the real world "things" usually don't perform actions on themselves. A dog, for instance, doesn't walk itself. It is being walked. It may be walked by more than one person. It may be walked all by itself or together with multiple other dogs, which may not even belong to the same owner. So, where does walkingTheDog() belong? To personClass? To a dogOwnerClass that derives from personClass? But then we also need a dogWalkerClass that also derives from person but that does not have a fixed number of dogs as member variables, right? And no, one can not even exclude a more general walkingTheAnimal() method from catClass because there are plenty of people who are walking cats on a leash. :-) Linking actions to data is, in my opinion, a highly inflexible strategy that forces architects and teams to invent strange hierarchies that don't describe the real world well. Is it beneficial to press everything into such a narrow scheme? I doubt it. The only applications where I find classes and objects useful are GUIs. Everything else constantly tries to break out of this scheme in my experience. There is, of course, a need for libraries to isolate well defined groups of actions from each other. File IO is a different library than the low level SATA interface hardware library, is different from the file system library, which is different from a string library which is different from a word processor library. There is a natural hierarchy there. The word processor will never need to know about the block structure of a hard drive and the way the file system uses it. But then, again, these functions are so different that we would not be doing ourselves much of a favor by subclassing wordDocumentClass from stringClass from fileIOClass from blockDeviceClass from hardwareDriverClass.
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  12755.  @programmertheory  There are no classes in machine code. There are no objects, either. There are only relative addresses, data segments (heap and stack), program segments and jumps/branches/subroutine calls. That's it. None of the beauty/documentation/structure shit that programmers spend 90% of their time on stays alive after the compiler is finished. Not even the execution order of the code. I used to teach computer science as a TA a long time ago. We didn't teach OOP. We taught machine design, algorithms and compiler code transformations. We wanted the student to understand the difference between code, compile time and runtime. Once you understand that, you will focus on what survives all the way to runtime and the problems that creep in between the two that have absolutely nothing to do with the source code. OOP is usually procedural. It simply documents data structures and method libraries differently than code that is not based on class hierarchies. Real FP doesn't exist anyway, at least not outside of the madhouse where they put copies of GByte size arrays on the stack to "prevent side effects". That's why our CS class taught pointers/references early on and independent of any language. They have nothing to do with code or even language design. They are a law of nature. It's much easier to point to the mountain than to move the mountain. The main problem of OOP is that it introduces strong couplings early, often and without any need. Who does it appeal to? The micromanager. It allows the architect to control the team and the business people to measure the performance of employees in meaningless classes/objects/methods per month metrics. I have mostly given up on OOP. I go with introspection most of the time. In your example there would be a field called whatAmI in my data structure and it would have integer constants for MAN, WOLF, WEREWOLF and NONE in it. Any method that needs to differentiate between these would use a trivial case statement to execute the relevant code. Does it cost one integer and a couple of nanoseconds to execute the comparisons against the constants? Yes. Do I care? No. This saves weeks of refactoring.
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  12807.  @AlexandruVoda  That sounds really cool, except that in reality there is no such debate in the physics community about interpretations. Working physicists either use Copenhagen or they are doing quantum field theory. I have never met a single physicist in my life who uses MWI since it's pointless. That includes the folks who preach it like gospel like Sean Carrol. We know how quantum mechanics works. Quanta are small amounts of energy. We teach that in high school. Where and when a quantum of energy will be detected can not be predicted. We can only predict the average behavior of ensembles of quantum systems. There are two cases: 1) that quantum of energy stays in ONE isolated system. For that we need a unitary equation like the Schroedinger equation. 2) The quantum of energy gets transferred to a SECOND system which we call the measurement system. The physics of the measurement system is being described by the Born rule. Copenhagen is not some kind of random magic. It actually describes the physical reality of the physical measurement process. None of the other interpretations do. They try to avoid it. Hidden variables are ruled out by special relativity. The only mystery there is why Einstein didn't understand that when he co-wrote the EPR paper. Bell certainly did understand it. He even invalidated his own paper in the end by pointing that out. Most people simply don't read the Bell paper to the end (well, most people don't read the Bell paper, period), so they don't notice that Bell himself already knew that he was talking total nonsense. :-)
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  12948.  @tom47235  That's a common misconception. We are telling everybody in high school that "Photons are small amounts of energy.". This is, probably more by chance than by design, the correct way of looking at it. Both Planck and Einstein correctly interpreted macroscopic experiments (neither Planck spectra nor the original photoelectric effect measurements are resolving single photons) as signs of field quantization. Einstein did, however, add a completely superfluous and unfortunately misleading sentence in his photoelectric effect paper that won him the Nobel Prize. In this one sentence he claims that quanta of light have position properties. This doesn't follow from the experiment and it doesn't agree with anything 19th century physics knew about energy. It's just an ad-hoc fallback to Newton's corpuscular theory of light, which is 100% wrong. We can only speculate why Einstein did that. The sentence clearly passed the reviewers and to this day most people who read the paper probably read past it without ever thinking about its validity. The simple fact is that Einstein did not make this statement based on scientific observations. Quite to the contrary: it actually contradicts the experimental facts completely and is not compatible with our theoretical understanding of energy as a system property. More importantly, all quanta, including electrons, muons, neutrinos, quarks etc. are quanta of energy. They are the amounts of energy that is being exchanged between the free fields and the sources and absorbers in irreversible processes. Even the theory clearly says so if you care to look at it very carefully, i.e. beyond the "shut up and calculate" level, which is unfortunately the most common way that it is being taught. Curiously physicists have made this mistake twice before. Before heat was established as a form of internal energy, people talked about it as a "Stoff" called "the phlogiston". The phlogiston was supposed to be a material carrier of heat energy that was diffusing from one material into another whenever they made thermal contact. In very much the same way the "particle" nomenclature in quantum mechanics claims, for absolutely no rational reason, that particles are the carriers of the energy that gets exchanged in individual quantum processes. The second time we invoked a material carrier where there is none was when we claimed that electromagnetic waves were carried by the "aether". That, too, was just a materialist fallacy to explain energy flow as a mechanical phenomenon. Einstein overcame that fallacy in 1905 when he introduced special relativity. At the exact same time he invented a fallacy of his own that is based on the exact same misidentification of conservation laws with material carriers, by declaring quanta of energy to be material particles. Sometimes even physics is just a comedy of errors.
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