Comments by "Lepi Doptera" (@lepidoptera9337) on "Understanding Quantum Mechanics #4: It's not so difficult!" video.

  1. It is not the math that bogs people down. They don't understand what it means.
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  2. You are very confused about these things. A measurement is simply an irreversible energy transfer and wave functions do not represent single quantum systems. They only represent ensembles of quantum systems.
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  3. Then you can surely tell me what a quantum is. ;-)
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  4. There is nothing complicated here. This is high school math in slightly different notation with zero physics in it.
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  5. So does she. She doesn't know the difference between repeating formalism and "understanding".
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  6. Yes, none of which matter for physics because they only ever involve a null-set. We simply do not care about things like point-wise convergence (or, better, lack thereof) in physics, no matter how interesting they might be for the mathematician.
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  7. No, it's not correct. The probability is given by the Born rule.
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  8. When I throw dice and the outcome of a throw is four, does that make the probability of the outcome four 100%? You are mistaking a property of an ensemble of systems (i.e. infinitely many copies of the same system) with the measurement of a state of a single system. After you have done your measurement in quantum mechanics, the system is destroyed. It's not simply repeating itself with a new initial value. A typical quantum system is a decaying nucleus. When you make a measurement, then you will find one of two states: 1) The original nucleus is still there or 2) The nucleus has decayed and instead there is a new nucleus in its place. The other decay product, e.g. a released gamma, has deposited the decay energy in your detector. You never get back from state 2) to the initial state. There is no "ensemble" to be had from the same experiment. You have to start over with a "brand new", not yet decayed nucleus. This is the gist of all quantum mechanical experiments: they are, by definition, unique and irreversible. We can make many copies of the same setup if we like and do the measurement over and over, again. That will, eventually, give us an estimator for the square of the absolute value of "the wave function". We will never get the wave function itself. The measurements can only give us the absolute value at any give time and place but never the phase.
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  9. Not really. You can rearrange the wave function with a diffraction function. Unitarity guarantees that the total is still one, even though the system has changed completely. An ideal spectrometer does exactly that.
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  10. Complex numbers have geometric meaning. They represent rotations through their phase and scaling by their magnitude. A complex number does not represent a quantum system. It can only represent properties of an ensemble of such systems.
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  11. Yes, but do you know WHY that is so? ;-)
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  12.  @briang.valentine4311  We are actually not using the complete vector space in quantum mechanics. We are always using subsets that are not even subspaces. ;-)
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  13.  @briang.valentine4311  That's because you don't know the first thing about quantum mechanics while I do. ;-)
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  14.  @BrianGValentine  I am. It's not my problem that you don't want to learn. ;-)
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  15. Or so you think. You will know better, eventually. ;-)
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  16. Die addition geht genauso wie in jedem normalen Vectorraum.
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