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It seems like the Copenhagen interpretation is just self contradictory. These two axioms are contradictory:

  1. Quantum Mechanics describes all the particles in the universe

  2. Measurement devices evolve superpositions into eigenstates.

Suppose an electron is in a state $|\psi \rangle $ and all the particles of a measurement device are in a state $|m\rangle$.

If we apply axiom #1 on the state $|\psi \rangle \otimes |m\rangle$, we can evolve it using the Schrodinger equation. The decoherence theorem, which is an application of the Schrodinger equation, says that the electron will evolve into a mixed state. The decoherence theorem applies because the measurement device has 10^23 particles.

If we apply axiom #2 on the state $|\psi\rangle \otimes |m\rangle$, it says that the electron will evolve into an eigenstate.

A mixed state contains all eigenvectors, and not just one. Since a mixed state $\neq$ an eigenstate, we have a contradiction.

What is the way out of this contradiction?

Leopard Mamba
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    It seems to me that you've just restated the measurement problem without anything specific to the Copenhagen interpretation. – ACuriousMind Oct 14 '22 at 09:33
  • @ACuriousMind Copenhagen interpretation is axiom #2 – Leopard Mamba Oct 14 '22 at 09:33
  • @ACuriousMind Many worlds and Von Neumann consciousness collapse do not have that axiom. In those, measurement devices do not evolve a superposition into an eigenstate. But instead, we obtain a single eigenstate only after a conscious observer gets entangled. Depending on whether we believe in just one or all of those worlds to be real, we get Von Neumann and Many worlds respectively. – Leopard Mamba Oct 14 '22 at 09:36
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    This just seems opinion based to me. You are in essence asking why some people may not have abandoned the Copenhagen Interpretation. That's just an opinion people hold for a variety of their own reasons. No definitive answer is possible. – StephenG - Help Ukraine Oct 14 '22 at 09:41
  • @StephenG-HelpUkraine I will remove that line. I just want the explanation of the contradiction. I did not ask in bad faith. – Leopard Mamba Oct 14 '22 at 10:01

1 Answers1

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Equations of physics are all time-reversal symmetric. But we know the Universe is in fact not (second law of Thermodynamics). How can modern Physics be redeemed of this contradiction?

The truth is that all physical theories have limitations. What you wrote is true, but it only means that the Quantum Theory the way we know it now has a limited sphere of applicability. We have to live with the theories we have, be mindful of their shortcomings and be careful to not to use them beyond the intended range of validity (here belong the Schodinger cats and the like) until something more general (=wider range) comes about. In the meantime we try to come up with something more universal. This is what they call research.

John
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  • Thank you. Would you say the leading contender in a deeper theory is hidden variables or non-linear Schrodinger equation? – Leopard Mamba Oct 14 '22 at 10:02
  • I stick with the Copenhagen QM. – John Oct 14 '22 at 10:07
  • But your first paragraph isn't a contradiction. Newton's laws can derive the Second law. Copenhagen is contradictory. If the contradiction can't be resolved, there are non-contradictory models like Von Neumann consciousness collapse or Many worlds. – Leopard Mamba Oct 14 '22 at 10:45
  • Newton's mechanics, when strictly adhered to, does ${\it not}$ produce the Second Law. Check Poincare recurrence theorem and Loschmidt's paradox. That's why it is a Law of Nature and not a theorem. Boltzman has cheated a bit when proving the H-theorem: his ${Stosszahlansatz}$ was not benign at all. That's where the irreversibility crept in. One can only wonder if it was this impossibility to derive the Second Law from mechanics that drove Boltzman into depression. – John Oct 14 '22 at 14:39
  • Thanks, I'll have to read up about this. So, if the universe were classical, applying Newton's laws on each and every particle in a large system wouldn't give you the correct time evolution? If Newton's laws contradict with the second law, one of them have to be right and the other wrong. Which one is wrong? – Leopard Mamba Oct 14 '22 at 15:24
  • I read up on Loschmidt's paradox and it seems like Newton's laws are correct and Boltzmann's derivation is wrong. Which of the axioms in my post is wrong? I think axiom #2 must be wrong. Axiom #1 is more akin to Newton's laws, as it talks about particle to particle interactions. It must be obeyed, which should make axiom #2 wrong. – Leopard Mamba Oct 14 '22 at 15:46
  • Loschmidt is just saying that since dynamical laws are time-reversal symmetric, how come we never observe entropy increase? By the way, this has nothing to do with Copenhagen Interpretation. This was just to illustrate that one cannot expect his/her theory to describe everything out there to be useful. – John Oct 14 '22 at 15:49
  • https://physics.stackexchange.com/questions/19970/does-the-scientific-community-consider-the-loschmidt-paradox-resolved-if-so-wha I was reading Fortsaint's answer here. It convinced me that Boltzmann made a mistake in the derivation. The second law does not always hold. You are correct, we shouldn't expect theories to be valid everywhere. I think axiom #2 is more likely the invalid one in my post. Because axiom #1 is more akin to Newton's laws, as in, it describes microscopic interactions. – Leopard Mamba Oct 14 '22 at 15:55
  • I am afraid this is not exactly what Fortsaint said (unless you made a typo). The Second Law does always hold (that's an empirical fact). The mistake was that the H-theorem wasn't a theorem in a rigorous sense. It did not show how Newton's laws describe entropy growth, but it showed how entropy would grow if you made one small convincingly looking but yet probabilistic assumption, i.e. the Stosszahlansatz. – John Oct 14 '22 at 16:22
  • I'm sorry, I was referring to the third comment on that answer. It gave a mistake which led to the derivation of an asymmetric law from symmetric Newtonian ones.The second law must not hold in the reversed velocity system, as it contradicts with Newton's law, like Fortsaint said. But I think I get your point regarding Quantum Mechanics. You're saying that Copenhagen is good enough for experiments, even though it strictly contradicts with axiom #1. I get that. – Leopard Mamba Oct 14 '22 at 16:35
  • Copenhagen tells us what appears to happen. Even though it must be false, we don't yet know which is the true one between Many worlds, consciousness collapse, gravitational collapse, etc. So Copenhagen is the "best" we can do without bias. – Leopard Mamba Oct 14 '22 at 16:36