# Proof that the thermal interpretation of QM is wrong

A. Neumaier
If so, then how to know in general which superpositions are allowed and which are not?
The state of the universe determined everything. A quantum system is a subsystem of the universe. Hence it is at time ##t## in the state determined by the corresponding reduced density matrix at time ##t##. These are the allowed states of quantum systems.

If you are able to prepare a particular spin state (a superposition, say), it means that at the time of preparation, the state of the universe is such that the reduced density matrix of the spin is in this state. (See post #22 for full details.)

In a similar way, all preparable and all measurable information give little bits of information about the state of the universe, and from this information, one can draw theoretical conclusions.

julcab12
stevendaryl
Staff Emeritus
I'm not sure what assumption are you talking about?

Let me take a specific example. Suppose you have a collection of ##N## particles confined to a box of size ##L^3##, the points ##(x,y,z)## such that ##0 \leq x \leq L##, ##0 \leq y \leq L##, ##0 \leq z \leq L##. But initially, the wave function only has non-negligible support in a small corner ##0 \leq x \leq L/10##, ##0 \leq y \leq L/10##, ##0 \leq z \leq L/10##. So the actual particle distribution is uniform throughout the larger volume, while ##|\psi|^2## is uniform in the smaller volume, and neglible outside it. So there is initially a discrepancy between the actual and calculated particle distributions. Are you saying that eventually the discrepancy will disappear with time? (Or maybe we need to add some interactions?)

I assume that like Newtonian physics, if you wait long enough, the Poincare recurrence time, eventually the system will return arbitrarily closely to the initial state, with a big discrepancy between ##|\psi|^2## and the actual particle distribution? But that would seem to contradict the argument that if the two are ever in sync, they will remain in sync. I'm confused.

The state of the universe determined everything. A quantum system is a subsystem of the universe. Hence it is at time ##t## in the state determined by the corresponding reduced density matrix at time ##t##. These are the allowed states of quantum systems.

If you are able to prepare a particular spin state (a superposition, say), it means that at the time of preparation, the state of the universe is such that the reduced density matrix of the spin is in this state. (See post #22 for full details.)

In a similar way, all preparable and all measurable information give little bits of information about the state of the universe, and from this information, one can draw theoretical conclusions.

This is actually what's lacking with RQM although almost similar, dumb-down version of it . Absolute relativization of quantities, namely the relativization of the possession of values (or definite magnitudes) to interacting physical systems is mute with respect to realism. It doesn't care any of the information in comparison to TI. It stay true to available formalism--Special Theory of Relativity. “The real events of the world are the "realization" (the "coming to reality", the "actualization") of the values q, q′, q″, … in the course of the interaction between physical systems. This actualization of a variable q in the course of an interaction can be denoted as the quantum event q.”

https://arxiv.org/ftp/arxiv/papers/1309/1309.0132.pdf

A. Neumaier
This is actually what's lacking with RQM although almost similar, dumb-down version of it . Absolute relativization of quantities, namely the relativization of the possession of values (or definite magnitudes) to interacting physical systems is mute with respect to realism. It doesn't care any of the information in comparison to TI. It stay true to available formalism--Special Theory of Relativity.
What is RQM?

Relativistic quantum theory is quantum field theory. In the standard model nothing is relative except the local gauges and the choice of the Lorentz frame.

vanhees71
Gold Member
What is RQM?
Relational Quantum Mechanics, the interpretation of QM (and QFT) proposed by Rovelli. It is inspired by relativity theory, but is logically independent on it.

vanhees71
Gold Member
In the TI, ##\rho## is a beable, since it is uniquely determined by the collection of all q-expectations. It is just not easily macroscopically interpretable, and hence has a subordinate role in the interpretation.
How can ##\rho## (assuming it's what's called the statistical operator in the standard interpretation) be a "beable", if it depends on the picture of time evolution chosen? The same holds for operators representing observables.

What's a physical quantity (not knowing, what precisely "beable" means, I rather refer to standard language) are
$$P(t,a|\rho)=\sum_{\beta} \langle t, a,\beta|\rho(t)|t,a,\beta \rangle,$$
where ##|t,a,\beta## and ##\rho(t)## are the eigenvectors of ##\hat{A}## and ##\rho(t)## the statistical operator, evolving in time according to the chosen picture of time evolution. In the standard minimal interpretation ##P(t,a|\rho)## is the probability for obtaining the value ##a## when measuring the observable ##A## precisely at time ##t##.

Now, before one discuss or even prove anything concerning an interpretation, one must define, what's the meaning of this expression in the interpretation. I still didn't get, as what this quantity is interpreted in the thermal interpretation, because you forbid it to be interpreted as probabilities.

Also it doesn't help to discuss about a fiction like the "state of the universe". This is something which is not observable even in principle.

On the other hand, I think it's pretty save to say the universe, on a large space-time scale, is close to local thermal equilibrium, as defined in standard coordinates of the FLRM metric, where the CMBR is in local thermal equilibrium up to tiny fluctuations of the relative order of ##10^{-5}##.

This is actually what's lacking ...
https://arxiv.org/ftp/arxiv/papers/1309/1309.0132.pdf
This is just an off-topic aside more suited to BTSM and regards whether this is despite considerations involving LQG, as I think with that it can be seen like QM with some adaptations as probabilistic relations between values of variables evolving together, not variables evolving just with respect to a single time parameter.

A. Neumaier