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comment by cousin_it · 2020-04-11T08:42:43.012Z · LW(p) · GW(p)

If the past is a cone of possible pasts, most of which have higher entropy than the present (due to time symmetry), that means your memories are probably fake, because they describe a past with lower entropy. This is known as Loschmidt's paradox.

One popular solution to the paradox is to assume that the distant past had very low entropy for some reason. If that's right, that means the past's nondeterminism is different from the future's nondeterminism: probabilities about the future are conditioned only on the present, but probabilities about the recent past are conditioned on both the present and the distant past.

Replies from: lsusr

↑ comment by lsusr · 2020-04-11T19:58:03.036Z · LW(p) · GW(p)

I suspect that entropy is more fundamental than time. This is my second post related to Loschmidt's paradox. The first one is here [LW · GW].

Update: See this comment [LW(p) · GW(p)] for a more complete resolution of Loschmidt's paradox.

comment by TAG · 2020-04-11T14:59:00.395Z · LW(p) · GW(p)

In the Born rule’s model of the universe, the future is non-deterministic.

That's more like the Born-rule-as-interpreted-by-the-Copenhagen-interpretation.

If you apply time-reversal symmetry to the Born rule then the past becomes non-deterministic. More accurately, the past always was non-deterministic.

What do you mean by "non-determinstic" ? The standard (single universe indeterministic) view is that past events occurred with a probability less than 1, ie they did not occur inevitably or necessarily. That is coupled with the idea that there is only one past state, and its can be assigned a probability of 1 for the purpose of calculating the probability of subsequent events .

But your past light cone is defined only in probabilities.

Huh? Whatever information you had about the past is observations, not uncollapsed wave functions.

You seem to be simultaneously appealing to time symmetry, and to Copenhagen (events occur probablistically as the result of WF collapse) whilst not noticing that the collapse postulate is not time-symmetrical.

Replies from: lsusr

↑ comment by lsusr · 2020-04-11T19:48:21.965Z · LW(p) · GW(p)

That's more like the Born-rule-as-interpreted-by-the-Copenhagen-interpretation.

Yes.

What do you mean by "non-determinstic" ? The standard (single universe indeterministic) view is that past events occurred with a probability less than 1, ie they did not occur inevitably or necessarily. That is coupled with the idea that there is only one past state, and its can be assigned a probability of 1 for the purpose of calculating the probability of subsequent events .

Yes. This is what I mean by "non-deterministic".

...the collapse postulate is not time-symmetrical.

I think the time-symmetry of the collapse postulate is the crux of our disagreement. In Chapter 4 of Principles of Quantum Mechanics, Second Edition by R. Shankar, the collapse postulate is stated as follows.

III. If the particle is in a state $| ψ ⟩$ , measurement of the variable (corresponding to) $Ω$ will yield one of the eigenvalues $ω$ with the probability $P (ω) \propto | ⟨ ω | ψ ⟩ |^{2}$ . The state of the system will change from $| ψ ⟩$ to $| ω ⟩$ as a result of the measurement.

According to in Chapter 11.5 Time Reversal Symmetry, time-reversal is performed by $ψ \to ψ^{*}$ . What happens if we plug this into postulate III?

$| ⟨ ω | ψ ⟩ |^{2} \to | ⟨ ω | ψ^{*} ⟩ |^{2}$

If we can show that $| ⟨ ω | ψ ⟩ |^{2} = | ⟨ ω | ψ^{*} ⟩ |^{2}$ then the Born rule is time-symmetric.

$\begin{matrix} ⟨ V | V ⟩ & = & \sum i | v_{i} |^{2} = & \sum i | v_{i}^{*} |^{2} = & ⟨ V^{*} | V^{*} ⟩ ⟨ ψ | ψ ⟩ & = & ⟨ ψ^{*} | ψ^{*} ⟩ (⟨ ψ | ψ ⟩)^{*} & = & (⟨ ψ^{*} | ψ^{*} ⟩)^{*} | ψ^{*} ⟩ ⟨ ψ^{*} | & = & | ψ ⟩ ⟨ ψ | ⟨ ω | ψ^{*} ⟩ ⟨ ψ^{*} | ω ⟩ & = & ⟨ ω | ψ ⟩ ⟨ ψ | ω ⟩ | ⟨ ω | ψ^{*} ⟩ |^{2} & = & | ⟨ ω | ψ ⟩ |^{2} | ⟨ ω | ψ ⟩ |^{2} & = & | ⟨ ω | ψ^{*} ⟩ |^{2} \end{matrix}$

Replies from: TAG, TAG

↑ comment by TAG · 2020-04-12T09:18:14.886Z · LW(p) · GW(p)

What do you mean by “non-determinstic” ? The standard (single universe indeterministic) view is that past events occurred with a probability less than 1, ie they did not occur inevitably or necessarily. That is coupled with the idea that there is only one past state, and its can be assigned a probability of 1 for the purpose of calculating the probability of subsequent events .

Yes. This is what I mean by “non-deterministic”.

The standard view of non-determinism is supported by the standard take on Copenhagen, which includes the time-irreversability of collapse. Yet you are arguing for the time-reversibility of collapse. Why would you want to put forward a novel premise, if you are not drawing a novel conclusion?

Replies from: lsusr

↑ comment by lsusr · 2020-06-21T23:34:25.378Z · LW(p) · GW(p)

This post about the time-reversibility of collapse sets the groundwork for a novel conclusion [? · GW].

↑ comment by TAG · 2020-04-11T23:18:50.547Z · LW(p) · GW(p)

time-reversal is performed by ψ→ψ∗

No, it's basically performed by t -> -t. Because what you are reversing is a dynamic process.

Complex conjugation is a bookkeeping thing you need to do in quantum mechanics alone. In classical physics, t -> -t is all you need to do.

then the Born rule is time-symmetric.

The Born rule shows how to get classical probabilities out of quantum amplitudes. It is not a dynamical process. Collapse is a process. The Born rule is not collapse (again), although both are involved in measurement.

It makes no sense to talk of reversing the Born rule, because its just a calculation. Collapse is a dynamical process, so it makes sense to talk of reversing collapse. But collapse cannot be reversed because it loses information. (There's a reason why collapse is also known as reduction!)

The collapse postulate (not the Born rule) says:

If the particle is in a state |ψ⟩, measurement of the variable (corresponding to) Ω will yield one of the eigenvalues ω with the probability P(ω)∝|⟨ω|ψ⟩|2. The state of the system will change from |ψ⟩ to |ω⟩ as a result of the measurement.

The state changes to one of the original eigenstates, and you cannot work back from that to get the original set of eigenstates and eigenvalues. In concrete terms, if a photon lands somewhere on a detector, you can't use that information to infer back to its probabilities of landing elsewhere.

comment by Richard_Kennaway · 2020-04-11T08:36:56.356Z · LW(p) · GW(p)

We have imperfect information about everything. But each of us has different information, giving different probability distributions. Leaving aside the hidden-variable/EPR issues, why should we not regard these distributions as expressions of our variously imperfect knowledge, rather that a nondeterminacy present in the things themselves?

Replies from: TAG, gworley

↑ comment by TAG · 2020-04-11T10:30:29.048Z · LW(p) · GW(p)

We always have Knightian uncertainty, lack of complete information, imperfect maps. The claim that there is also indeterminism in the territory as well is supported by arguments about EPR, hidden variables etc.

↑ comment by Gordon Seidoh Worley (gworley) · 2020-04-11T19:44:51.104Z · LW(p) · GW(p)

I was going to phrase my comment slightly differently but I think to make a similar point: all this post does is claim that we have subjective uncertainty about the past just as we do about the future, not that we need make any claims about determinism.