Run a two-particle, single-spatial dimension, time dependent sim of the Schroedinger equation, starting with a high level of quantum independence, and you will see decoherence as plain as day.
Please feel free to post a link to such a sim. I’m almost willing to bet real money against it. That you would even propose that decoherence can be observed without including the environment in the simulation tells me how much of QM you really understand.
The Collapse postulate breaks CPT symmetry, violates conservation the quantum hamiltonian, violates Liouvilles theorem, violates relativistic locality, is non-linear, is non-unitary, is non-differentiable, inherently stochastic, poorly defined, anthropocentric and formulated in deep confusion.
You mean, the straw collapse EY constructed and happily demolished. The windmill you are fighting has nothing to do with the orthodox formulation of QM, which is perfectly compatible with decoherence.
The orthodox formulation of QM (given in Griffiths and most other modern QM texts) is the following:
Time evolution of an isolated system is governed by the time-dependent Schroedinger equation (this includes einselection when the system is no longer isolated).
The Born rule: after a measurement is performed on a system in a given state, the probability of observing a given eigenstate is given by the square modulus of the system’s state’s projection onto the eigenstate.
Note that there is no mention of collapse. The Born rule is the miracle step in the orthodox approach (and is an open problem in physics), just like it is in any other approach, including the MWI (EY admitted as much, if you want an argument from authority).
The interpretational confusion starts once you try to invent the reasons behind the Born rule. A proper scientific way to address the issue would be to construct a model which explains the Born rule AND makes other testable predictions separate from the orthodox QM. This conjunction is essential. There is no way to simply “dissolve” the question.
The orthodox formulation of QM (given in Griffiths and most other modern QM texts)...
Here’s Griffiths on what he calls the “orthodox position” on quantum indeterminacy. This is from pages 3-5 of his text:
It was the act of measurement that forced the particle to “take a stand”… Jordan said it most starkly: “Observations not only disturb what is to be measured, they produce it… We compel [the particle] to assume a definite position.”… Among physicists it has always been the most widely accepted position. Note, however, that if it is correct there is something very peculiar about the act of measurement...
We say that the wave function collapses upon measurement, to a spike… There are, then, two entirely distinct kinds of physical processes: “ordinary” ones, in which the wave function evolves in a leisurely fashion under the Schrodinger equation, and “measurements”, in which [it] suddenly and discontinuously collapses.
Going by Griffiths’ own account (and I picked Griffiths because he’s the authority you cited), what Eliezer says about the orthodox interpretation is not a strawman. In fact, Griffiths explicitly discusses the view you call the “orthodox formulation”, except he doesn’t call it “orthodox”. He describes it as an alternative to the orthodox position, and labels it the “agnostic position”.
I think your flavor of instrumentalism is a respectable position in the foundational debate, but to describe it as the standard position is incorrect. I think there was a time when physicists in general had a more operationalist bent, but things have changed.
Hmm, I suppose my personal classification is slightly different. Thanks for pointing that out.
The agnostic position is “shut up and calculate”, which is basically resigning to one’s inability to model the Born rule with anything better.
The instrumentalist position is to admit that doing research related to the Born rule origins is essential for progress in understanding the fundamentals of QM, but to also acknowledge that interpretations are not interesting physical models and at best have only an inspirational value.
The realist position (hidden variables are fundamental, collapse is fundamental, or MWI is fundamental, or Bohmian mechanics is fundamental) is the one that is easiest to falsify, as soon as it sticks its neck out with testable predictions (Bohm and collapse do not play well with relativity, local hidden variables run afoul of the Bell theorem, MWI makes no testable predictions whatsoever).
I suppose the confusion is that last paragraph: “There are, then, two entirely distinct kinds of physical processes: “ordinary” ones, in which the wave function evolves in a leisurely fashion under the Schrodinger equation, and “measurements”, in which [it] suddenly and discontinuously collapses.” This is a realist position, so I don’t favor it, because it does not make any testable predictions.
I think your flavor of instrumentalism is a respectable position in the foundational debate, but to describe it as the standard position is incorrect.
OK, I will stop calling it standard, just instrumental.
I think there was a time when physicists in general had a more operationalist bent, but things have changed.
Okay, the Orthodox QM is an informal specification of anticipated experimental results, and acknowledges decoherence as a thing. That is good to know.
My base claim is that decoherence can and will become macroscopic given time. Some physicists seem to disagree. Why? To my best expertise it is obviously implied by the mathematics behind it.
I am well aware the Born Rule is a mystery. Where the Born Probabilities come from, idk. Mangled Worlds seems like it might have the structure of a good explanation, it smells right, even if it isn’t.
(EY admitted as much, if you want an argument from authority)
Okay, the Orthodox QM is an informal specification of anticipated experimental results, and acknowledges decoherence as a thing. That is good to know.
OK, as pragmatist pointed out, calling it orthodox is misleading. Sorry. From now on I’ll be calling it instrumentalist. As for “informal”, it’s as formal as it gets, pure math.
My base claim is that decoherence can and will become macroscopic given time.
That’s an experimental fact, you don’t need to claim anything.
Some physicists seem to disagree.
Really? Who?
Why? To my best expertise it is obviously implied by the mathematics behind it.
Feel free to outline the math. The best sort-of-derivation so far, as far as I know, is given by Zurek and is known as einselection.
In addition to these formal axioms one needs a rudimentary
interpretation relating the formal part to experiments.
The following minimal interpretation seems to be universally
accepted.
MI. Upon measuring at times t_l (l=1,...,n) a vector X of observables
with commuting components, for a large collection of independent
identical (particular) systems closed for times t<t_l, all in the same
state
rho_0 = lim_{t to t_l from below} rho(t)
(one calls such systems identically prepared), the measurement
results are statistically consistent with independent realizations
of a random vector X with measure as defined in axiom A5.
Note that MI is no longer a formal statement since it neither defines
what ‘measuring’ is, nor what ‘measurement results’ are and what
‘statistically consistent’ or ‘independent identical system’ means.
Thus MI has no mathematical meaning—it is not an axiom, but already
part of the interpretation of formal quantum mechanics.
[...]
The lack of precision in statement MI is on purpose, since it allows
the statement to be agreeable to everyone in its vagueness; different
philosophical schools can easily fill it with their own understanding
of the terms in a way consistent with the remainder.
[...]
MI is what every interpretation I know of assumes (and has to assume)
at least implicitly in order to make contact with experiments.
Indeed, all interpretations I know of assume much more, but they
differ a lot in what they assume beyond MI.
Everything beyond MI seems to be controversial. In particular,
already what constitutes a measurement of X is controversial.
(E.g., reading a pointer, different readers may get marginally
different results. What is the true pointer reading?)
So what is the orthodox formulation of QM, which is perfectly compatible with decoherance and doesn’t resemble the straw man? I’m sorry if you’ve posted this elsewhere, but I’d really like to know what you think.
Please feel free to post a link to such a sim. I’m almost willing to bet real money against it. That you would even propose that decoherence can be observed without including the environment in the simulation tells me how much of QM you really understand.
You mean, the straw collapse EY constructed and happily demolished. The windmill you are fighting has nothing to do with the orthodox formulation of QM, which is perfectly compatible with decoherence.
What is the orthodox formulation of QM? Link?
The orthodox formulation of QM (given in Griffiths and most other modern QM texts) is the following:
Time evolution of an isolated system is governed by the time-dependent Schroedinger equation (this includes einselection when the system is no longer isolated).
The Born rule: after a measurement is performed on a system in a given state, the probability of observing a given eigenstate is given by the square modulus of the system’s state’s projection onto the eigenstate.
Note that there is no mention of collapse. The Born rule is the miracle step in the orthodox approach (and is an open problem in physics), just like it is in any other approach, including the MWI (EY admitted as much, if you want an argument from authority).
The interpretational confusion starts once you try to invent the reasons behind the Born rule. A proper scientific way to address the issue would be to construct a model which explains the Born rule AND makes other testable predictions separate from the orthodox QM. This conjunction is essential. There is no way to simply “dissolve” the question.
Here’s Griffiths on what he calls the “orthodox position” on quantum indeterminacy. This is from pages 3-5 of his text:
Going by Griffiths’ own account (and I picked Griffiths because he’s the authority you cited), what Eliezer says about the orthodox interpretation is not a strawman. In fact, Griffiths explicitly discusses the view you call the “orthodox formulation”, except he doesn’t call it “orthodox”. He describes it as an alternative to the orthodox position, and labels it the “agnostic position”.
I think your flavor of instrumentalism is a respectable position in the foundational debate, but to describe it as the standard position is incorrect. I think there was a time when physicists in general had a more operationalist bent, but things have changed.
Hmm, I suppose my personal classification is slightly different. Thanks for pointing that out.
The agnostic position is “shut up and calculate”, which is basically resigning to one’s inability to model the Born rule with anything better.
The instrumentalist position is to admit that doing research related to the Born rule origins is essential for progress in understanding the fundamentals of QM, but to also acknowledge that interpretations are not interesting physical models and at best have only an inspirational value.
The realist position (hidden variables are fundamental, collapse is fundamental, or MWI is fundamental, or Bohmian mechanics is fundamental) is the one that is easiest to falsify, as soon as it sticks its neck out with testable predictions (Bohm and collapse do not play well with relativity, local hidden variables run afoul of the Bell theorem, MWI makes no testable predictions whatsoever).
I suppose the confusion is that last paragraph: “There are, then, two entirely distinct kinds of physical processes: “ordinary” ones, in which the wave function evolves in a leisurely fashion under the Schrodinger equation, and “measurements”, in which [it] suddenly and discontinuously collapses.” This is a realist position, so I don’t favor it, because it does not make any testable predictions.
OK, I will stop calling it standard, just instrumental.
How?
Okay, the Orthodox QM is an informal specification of anticipated experimental results, and acknowledges decoherence as a thing. That is good to know.
My base claim is that decoherence can and will become macroscopic given time. Some physicists seem to disagree. Why? To my best expertise it is obviously implied by the mathematics behind it.
I am well aware the Born Rule is a mystery. Where the Born Probabilities come from, idk. Mangled Worlds seems like it might have the structure of a good explanation, it smells right, even if it isn’t.
Now that was uncalled for.
OK, as pragmatist pointed out, calling it orthodox is misleading. Sorry. From now on I’ll be calling it instrumentalist. As for “informal”, it’s as formal as it gets, pure math.
That’s an experimental fact, you don’t need to claim anything.
Really? Who?
Feel free to outline the math. The best sort-of-derivation so far, as far as I know, is given by Zurek and is known as einselection.
Perception of groups are often skewed. Mine was.
That update out of the way, why are we arguing? We do not disagree.
Aumann ftw!
I wouldn’t call it “orthodox”, but see this:
[...]
[...]
So what is the orthodox formulation of QM, which is perfectly compatible with decoherance and doesn’t resemble the straw man? I’m sorry if you’ve posted this elsewhere, but I’d really like to know what you think.
See my reply to MagnetoHydroDynamics.