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?

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    $\begingroup$ It seems to me that you've just restated the measurement problem without anything specific to the Copenhagen interpretation. $\endgroup$
    – ACuriousMind
    Commented Oct 14, 2022 at 9:33
  • $\begingroup$ @ACuriousMind Copenhagen interpretation is axiom #2 $\endgroup$ Commented Oct 14, 2022 at 9:33
  • $\begingroup$ @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. $\endgroup$ Commented Oct 14, 2022 at 9:36
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    $\begingroup$ 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. $\endgroup$ Commented Oct 14, 2022 at 9:41
  • $\begingroup$ @StephenG-HelpUkraine I will remove that line. I just want the explanation of the contradiction. I did not ask in bad faith. $\endgroup$ Commented Oct 14, 2022 at 10:01

1 Answer 1


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.

  • $\begingroup$ Thank you. Would you say the leading contender in a deeper theory is hidden variables or non-linear Schrodinger equation? $\endgroup$ Commented Oct 14, 2022 at 10:02
  • $\begingroup$ I stick with the Copenhagen QM. $\endgroup$
    – John
    Commented Oct 14, 2022 at 10:07
  • $\begingroup$ 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. $\endgroup$ Commented Oct 14, 2022 at 10:45
  • $\begingroup$ 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. $\endgroup$
    – John
    Commented Oct 14, 2022 at 14:39
  • $\begingroup$ 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? $\endgroup$ Commented Oct 14, 2022 at 15:24

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