Interpretations of the No Communication Theorem

[PeterDonis]

In order to disagree, you must be able to name one fact about a quantum system that that is accessible for humans but not predicted by the Born rule.

You have it backwards. My point is that there are many situations (like the orbit of the Moon 4 billion years ago) to which the Born rule can perfectly well be applied but which don't involve human measurements or observations.

 

[Nullstein]

Wikipedia is not a valid reference. You need to reference a textbook or peer-reviewed paper. (You do that for Boltzmann so that part is fine, although I don't have those books so I can't personally check the references.)

Fine, check Tolman (The Principles of Statistical Mechanics). Can you now explain what point in the last paragraph of post #125 you disagree with?

You have it backwards. My point is that there are many situations (like the orbit of the Moon 4 billion years ago) to which the Born rule can perfectly well be applied but which don't involve human measurements or observations.

But so what? The orbit of the moon is in principle measurable by humans, so it's not a counterexample. If nobody measured it 4 billion years ago, it's only because there were no humans at that time, not because it's not in principle measurable.

 

[PeterDonis]

The orbit of the moon is in principle measurable by humans

Then what isn't in principle measurable by humans? Your basic rule seems to be that anything to which the Born rule applies is "in principle measurable by humans" by definition, which is arguing in a circle.

 

[Fra]

in principle measurable by humans

Are you literally talking about humans(=physicists?) Or do you by human metaphor for any "observer/agent/meausurement device" ?

If the former do you refer to single human, or humans as in the whole scientific community? (ie intercommunication presumed? This would imply that invidivual observations by single human/physicists would not count, unless consensus is attained)

/Fredrik

 

[CoolMint]

Then what isn't in principle measurable by humans?

Systems isolated from the environment.

 

[Fra]

The no communication theorem is about measurement, which is an anthropocentric notion.

Reflecting again on this, my reaction is here, why the reference to humans. This is IMO introducing some fog, as was always the case in QM since the days of Heisenberg. If we can rephrase this to measurement beeing defined relative to a material observer/agent, then I would agree with this. The "external" view of the measurement process would rather be a normal interaction (following the laws of physics). It's only the inside observer that talks about it's own "measurement" of course. Other observers "measurements" are denoted as normal interactions.

From my perspective, the no communication theorem tells us something about the nature of causality in the laws of physics (that we do not yet understand btw). But I do not see why we need to bring "humans" into discussion? It gets confusing. Unless one actually refers to it as the "scientific consensus", it what is the communityes current "state of knowledge" of the laws of physics. But I do not think that is what is beeing discussed here?

/Fredrik

 

[jbergman]

Okay, let me try differently: Are there any entities in the universe, other than humans, that make use of the Born rule? The role of the Born rule is to extract relative frequencies from the state of the system. Relative frequencies are something that humans have ascribed meaning to. The system would evolve just fine if we didn't ascribe meaning to the relative frequencies. They play no role in the evolution laws of the system. All the universe needs is the wave function and the Hamilton operator. We could also decide to ascribe meaning to the value $\xi:=\psi(3)+\psi(8)$, but we don't because we are not interested in it, because it never appears as a result on any of our measurement devices. It is inaccessible to us. What we find interesting is the value $P([1,2]) := \int_1^2 |\psi(x)|^2\mathrm d x$. That's just a definition made by humans, just like my definition of $\xi$ earlier. But it is accessible to us by clever measurement setups.

As an analogy, think of temperature in classical statistical mechanics. The system is made of particles that evolve just fine according to Hamiltons equations of motion. There is no fundamental need for a quantity like temperature. It's invented by humans to quantify an aggregate property of the system. We could also define the variable $\eta:=x_{29} + x_{10^{23}+8}$, but it is of no interest to us, so we don't.

Thought experiment. Imagine instead of the Schrodinger's cat experiment, we set up a similar setup but the two outcomes are to either fill a bowl with dog food or water.

Then if a dog goes in there it will either eat the food or drink the water. You seem to be suggesting that without human observation, the dog is in a superposition of doing both.

Somehow this bothers me.

 

[DrChinese]

1. [The no communication theorem] says that no local operation at Bob's distant system (in the sense of separation by tensor products) can cause any disturbance of measurement results at Alice's local system...

2. The Born rule obeys locality. So if there was non-locality, then there would be non-local effects everywhere, but the theory would prohibit them from being observable even in principle (not just due to insufficient equipment).

3. If the facts about a quantum system that can in principle be measured by humans are in 1 to 1 correspondence with the facts that are predicted by the Born rule (which they are), then the predictions of the Born rule are anthropocentric.

1. This leaves out a critical component of the theorem: it's not that there can't be a change in the measurement results for Alice, because there might be... we don't currently know if that is the case or not (since that is an interpretational issue). I can always assert that the choice of measurement basis by Bob "causes" Alice's state to a very specific one (obviously randomly, at least as it appears to human observers). For the theorem itself: it's that Alice alone cannot detect a disturbance of those results - which is not an interpretational issue.2. To the extent that there is a question about locality or non-locality related to the Born rule: the Born Rule should not be considered local. Obviously, once Bob knows his measurement result, if he knows what distant Alice is measuring, he knows information about Alice's result - according to the Born rule. I don't see locality really applying one way or the other, but there is certainly nothing (random) limited here to c. But maybe someone has a good reference that says exactly otherwise. (Again, it is easy to fall into interpretational issues.) 3. But more importantly: I don't believe it is fair to say that there is some special connection between the Born Rule and human observers (anthropocentric). For example, Zurek (2002) derives the Born Rule from other quantum principles, and skips the idea of measurement:

"This is Born’s rule. We have derived it from the most fundamental properties of quantum physics, including in particular these embodied in envariance. In contrast with the other derivations, it relies on the most quantum of foundations – the incompatibility of the knowledge about the whole and about the parts, mandated by entanglement. It explains how Born’s rule arises in a purely quantum setting, i.e., without appeals to “collapse”, “measurement”, or any other such deus ex machina imposition of the symptoms of classicality that violate the unitary spirit of quantum theory."

From (14) of: https://arxiv.org/abs/quant-ph/0211037

 

[Nullstein]

Then what isn't in principle measurable by humans? Your basic rule seems to be that anything to which the Born rule applies is "in principle measurable by humans" by definition, which is arguing in a circle.

In standard QM, this would e.g. be the phase of the wave function. Humans cannot measure it. But this really becomes relevant as soon as you introduce any additional entities such as hidden variables. No facts about the hidden variables are accessible to humans. The facts that are accessible to humans is still in 1 to 1 correspondence with the facts that are predicted by the Born rule.

 

[Nullstein]

Reflecting again on this, my reaction is here, why the reference to humans. This is IMO introducing some fog, as was always the case in QM since the days of Heisenberg. If we can rephrase this to measurement beeing defined relative to a material observer/agent, then I would agree with this. The "external" view of the measurement process would rather be a normal interaction (following the laws of physics). It's only the inside observer that talks about it's own "measurement" of course. Other observers "measurements" are denoted as normal interactions.

From my perspective, the no communication theorem tells us something about the nature of causality in the laws of physics (that we do not yet understand btw). But I do not see why we need to bring "humans" into discussion? It gets confusing. Unless one actually refers to it as the "scientific consensus", it what is the communityes current "state of knowledge" of the laws of physics. But I do not think that is what is beeing discussed here?

/Fredrik

You are right, a better word would be agentocentric if there is such a thing. It's not solely about humans, but about agents.

 

[Nullstein]

Thought experiment. Imagine instead of the Schrodinger's cat experiment, we set up a similar setup but the two outcomes are to either fill a bowl with dog food or water.

Then if a dog goes in there it will either eat the food or drink the water. You seem to be suggesting that without human observation, the dog is in a superposition of doing both.

Somehow this bothers me.

This is in fact observer dependent. There is such a scenario was Wigner's friend and you don't even need to replace humans by dogs in order to arrive at it.

 

[Nullstein]

1. This leaves out a critical component of the theorem: it's not that there can't be a change in the measurement results for Alice, because there might be... we don't currently know if that is the case or not (since that is an interpretational issue). I can always assert that the choice of measurement basis by Bob "causes" Alice's state to a very specific one (obviously randomly, at least as it appears to human observers). For the theorem itself: it's that Alice alone cannot detect a disturbance of those results - which is not an interpretational issue.

Well, yes, this is basically the point I'm making. If there were non-local cause and effect relationships, the no communication theorem shows that they cannot even in principle be detected or exploited by humans (agents). This makes any non-local theory that reproduces QM anthropocentric (agentocentric).

2. To the extent that there is a question about locality or non-locality related to the Born rule: the Born Rule should not be considered local. Obviously, once Bob knows his measurement result, if he knows what distant Alice is measuring, he knows information about Alice's result - according to the Born rule. I don't see locality really applying one way or the other, but there is certainly nothing (random) limited here to c. But maybe someone has a good reference that says exactly otherwise. (Again, it is easy to fall into interpretational issues.)

I think this is just a terminology issue. When we say something is local, we usually mean that all cause and effect relationships obey the speed of light limit. The Born rule just predicts probabilities, it can't be local or non-local. The underlying theory can be. In the same sense, the classical probability assignment e.g. in the Bertelmann's socks scenario isn't local or non-local either, just because it predicts correlations between spacelike separated events. Correlations between spacelike separated events don't necessarily require non-local cause and effect relationships. Whether there are such non-local effects can only be decided by looking at the concrete underlying theory, not just at the predicted probabilities.

3. But more importantly: I don't believe it is fair to say that there is some special connection between the Born Rule and human observers (anthropocentric). For example, Zurek (2002) derives the Born Rule from other quantum principles, and skips the idea of measurement:

"This is Born’s rule. We have derived it from the most fundamental properties of quantum physics, including in particular these embodied in envariance. In contrast with the other derivations, it relies on the most quantum of foundations – the incompatibility of the knowledge about the whole and about the parts, mandated by entanglement. It explains how Born’s rule arises in a purely quantum setting, i.e., without appeals to “collapse”, “measurement”, or any other such deus ex machina imposition of the symptoms of classicality that violate the unitary spirit of quantum theory."

From (14) of: https://arxiv.org/abs/quant-ph/0211037

Zurek's derivation of the Born rule is universally acknowledged to be flawed though.

 

[PeterDonis]

Zurek's derivation of the Born rule is universally acknowledged to be flawed though.

Enough is enough. This kind of claim is one you cannot possibly substantiate with references. You've had more than enough opportunity to state your views and you seem unable to consider different viewpoints.

Thread closed.