Does quantum mechanics violate conservation of energy?

In all quantum mechanics experiments we must begin with a coherent preparation of a system which will display measurements that can be predicted with great certainty. If we slightly modify this preparation to a different preparation which displays different measurements, then we explain this difference as being due to a change in the state description, the new preparation has a new description, and the new description may be used to predict the outcomes of the new measurements with similar certainty.

But what about the change in the measurements, can we be so sure that the change in measurements is explained by the change to the preparation. Take for example an optical interference experiment (Mikelson or Mach-Zehnder), when we change the phase of one path so that we get destructive interference at the detector instead of constructive interference, this is a tremendoes change in the measurable statistics. But this great change in the measurements can be done with the insertion of a plate. How does the insertion of a plate cause the statistics to be measured with such a drastic difference. Because it changes the state description. Shouldn't the change in preparation be able to explain the change in measurements in a causal manner that is consistent with the classical laws?

 

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And this violates conservation of energy in what way?

 

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Hi al,
I've chnged the thread title to make it a question rather than a crazy assertion.
Like Alex says, your logic is not clear. Can you explain more clearly why you suspect than energy is not conserved? It would help if you could put numbers or equations on the energy quantities involved.

 

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Your questions,

and

My answer would be that there is an obvious violation of conservation of energy occurring, so let me quickly explain.

As classically thinking physicists we must always understand any displacement of a physical system as being due to a driving force which acts upon the system, and thus requires an input of energy and momentum.

So lets look at another example, optical interference with a double slit and horizontally polarized light. In the ordinary preparation (with interference) there is a statistical arrangement of the measurements which can be predicted with great certainty in bands of constructive and destructive interference.

The change in preparation is a simple insertion of a half wave plate in front of one slit (which rotates the polarization to vertical and destroys interference). In the second preparation (with no interference) there is a spatially displaced statistical arrangement of the measurements which can be predicted with great certainty, with no bands of interference.

As classical physicists, we must be capable of explaining how this difference in the measurable statistics has come about.

But do we explain the difference? No. There must be something like a driving force which is acting on the system in the second preparation which causes the displacement of photons from constructive and destructive interference to non-interference.

We have no such driving force. The apparent reason for the change; "distinguishing information" or "a change to the state description". Both explanations fail miserably by the standards of classical physics and the requirement of the laws of conservation of energy and momentum.

The insertion of a half wave plate does not displace photons from one measurement position to the other en masse.

No math required, just simple classical logic.

 

Since your 'simple classical logic' does not take into account the wave like nature of the photon, it is not applicable in this situation.

 

Mentioning "the wave nature of the photon" is an illegitimate response to my questions.

 

Why?

 

So you are saying that because the interference pattern has information it has energy and since it changes when you close a slit, that's an energy change without an energy input?

 

I think a better question would be, "what happens if the half wave plate was the only way to go for the particle?". There would be zero probability that it would go in that direction, but then the particle would not go into another direction because that pathway is not available. So then would the particle just in effect vanish?

The only way I could see energy being conserved here is if the particle jumped behind the half wave plate. It would have to force a particle jump for conservation of energy to hold.

 

Your 'must be' classical logic is nonsense.

 

Al confess I don't see this at the moment. Surely the interference pattern that has disappeared has been replaced by 2 spots, one from each stream of non-interfering photons passing through each slit. Although the energy distribution at the detector has changed, because the light and dark bands have gone, there is no net displacement, and so no net energy transfer. It seems to me the whole phenomenon is what you would expect from classical wave physics, isn't it? In which case I don't see - at present - why quantum theory needs to come into it, or why there is any violation of conservation of energy.

Am I missing something?

 

So If you know any better then explain your way , If you don't have an explanation don't fire up in saying is a nonsense

 

My way is to not use 'must be' classical logic when evaluating quantum systems. Or any other physics.

 

Quote of Russ_Watters

No, what I'm saying is that the interference changes to non-interference, which must have been caused by something physical. To say that "a change to the state description" is the cause is insufficient. The photons don't just get up and move to a different distribution without any causal force acting on them. The only change to the preparation that causes the new distribution of non-interference is the insertion of the HWP. This only changes the state description. Insufficient.

Now brucep

Actually it isn't. I'm just thinking like a classical physicist would.

Now exchemist,

Yes, you are missing my whole point. I'm not saying that there is a net displacement, the net displacement is always zero because the position distribution in both preparations has the same uncertainty with the same average position. No net displacement. But within the uncertainty, the distribution changes, from interference fringes to no interference fringes. And what do we as quantum physicists explain is the driving force behind this displacement of statistics? Distinguishing information and a change to the state description. Insufficient. When interference is destroyed or re-created in the quantum eraser experiment there is an action taking place on the statistics which is for free as far as energy and momentum conservation is concerned.

 

I don't think you're missing much. The theory of QM can be derived from the two slit experiment so he's mixing up domains of applicability with his 'must be' classical logic requiring no mathematical model. Energy is conserved regardless his expectations based on flawed 'must be' classical logic.

 

Actually, the explanation of how energy is conserved in quantum mechanics is a theory which does not take into account aall possibilities in quantum experiment. Quantum mechanics states that if the Hamiltonian is invariant under a specific space-time displacement, then the dynamical variable/operator which is associated with that specific generator of displacement is a constant of motion. Believe you me, this theory is seriously lacking if it wants to explain all possible preparations of quantum mechanics. Insufficient. There are preparation changes (as I've suggested above) which defy energy conservation.

 

To the question, "Does quantum mechanics violate conservation of energy?"

Yes, it does in some cases, but I don't think this would be one of those cases from post #1.

I think the problem here is that even though there is a probability of a particle being at different locations at once, when a measurement is made then that particle wave function will collapse and then there will only be one particle. Not part of a particle here or some left over part of the particles wave over there, there would still just be one particle that will be at one of these locations once it is measured.

 

And how does that violate conservation of energy?

If you calculate the energy eigenvalue before and after the particle has been collapsed, you will find them to be same.

 

It doesn't. I thought I was clear in saying that it wouldn't be one of those cases. Conservation of energy is violated in particle pair production.

The particle will just not go in the direction of the half wave plate. Then the same amount of energy will be found in the other slit as that was emitted. It will look as the particle just has only chosen the other path.

 

Grep'ed for Noether, got nothin'.

So: Happy reading.