Undergrad Steven Weinberg on the interpretation of quantum mechanics

[bhobba]

If you need a human being to introduce the Born rule to nature and get classical outcomes, the interpretation is likely flawed.

That is not what he is saying. We need a human being to introduce any theory. His issue was a particular examination of Consistent Histories in that you started with the Born Rule and ended with a version of the Born Rule, so was circular. The Born rule as shown by Gleason depends mostly on non-contextuality. His issue against instrumentalist approaches, like Consistent Histories, is it says says if we measure a state and always find it has a position close to a certain value, then we can say it has a position close to that value. See:
http://quantum.phys.cmu.edu/CQT/chaps/cqt02.pdf
'It is sometimes the case, as in the examples in Figs. 2.2, 2.3 and 2.5, that the quantum wave
function is non-zero only in some finite interval x1 ≤ x ≤ x2, In such a case it is safe to assert that the quantum particle is not located outside this interval, or, equivalently, that it is inside this interval, provided the latter is not interpreted to mean that there is some precise point inside the interval where the particle is located. '

That is not what QM says - it is non-commital until it is measured and that required human intervention. He is ill at ease with a interpretation that has human beings in it's foundations. It can be made independent of that by accepting it as an assumption of the interpretation (or perhaps by just putting the Heisenberg cut there). Despite my high respect for Wienberg, I do not agree with him on that, nor on his conclusion all interpretations have problems. But his section on interpretations is well worth a read - it is very good - but beware - it would be wise to understand something about it first.

Thanks
Bill

 

[DrChinese]

I don't understand this one quote by Weinberg: "Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem - it just doesn't change the density matrix."

Where in the formalism of QT can one find this idea?

This is one of many things you have read about Weinberg that you simply dismiss. You are of course entitled to your opinions, no issue about that. You should take care to label your opinions as your own to provide suitable notice to the reader.

I.e. do that instead of labeling standard views of quantum theory as questionable (which you did here), and quoting yourself as an authority in the counter case. I would say, for example, that Weinberg's statements - as I quoted - are fairly innocuous... and they fall closely in line with what most physicists believe. The burden is on you, my friend, not on Weinberg. Show us where Weinberg is wrong by quoting SOMEONE ELSE.

 

[Morbert]

Worth noting that Weinberg, a few sentences later, says "the phenomenon of entanglement thus poses an obstacle to any interpretation of quantum mechanics that attributes to the wave function or the state vector any physical significance other than as a means of predicting the results of measurements."

I don't think he's saying anything to challenge mainstream interpretations of QM as a local theory.

 

[Morbert]

His issue against instrumentalist approaches, like Consistent Histories, is it says says if we measure a state and always find it has a position close to a certain value, then we can say it has a position close to that value. See:
http://quantum.phys.cmu.edu/CQT/chaps/cqt02.pdf
'In such a case it is safe to assert that the quantum particle is not located outside this interval, or, equivalently, that it is inside this interval, provided the latter is not interpreted to mean that there is some precise point inside the interval where the particle is located. '

That is not what QM says - it is non-commital until it is measured and that required human intervention.

Griffiths's claims here are consistent with his presentation of QM throughout that book. He presents a realist CH interpretation as opposed to a (more common) instrumentalist one. According to his account, the states illustrated in 2.2 and 2.3 imply any history that has the particle outside the interval would have probability 0, and so (according to his account) the particle is not outside that interval regardless of whether or not an observer comes along to check.

 

[vanhees71]

I meant the axioms as formulated in your QM lecture notes; they are your axioms, since different people formulate the axioms differently, and these differences may matter in logical arguments.

Yes, since in a manuscript about quantum physics I don't write about philosophical quibbles.

The axioms you stated work for an ensemble but say nothing about the interpretation of the state of an assembly (such as a microscopic system together with a single detector, or a single brick of iron) .
That's why Peres talks about 'mimicking' only.

As I wrote in this case you calculate expectation values and fluctuations of macroscopic coarse-grained (space-time averaged) quantities and see that the fluctuations are very small compared to the expectation values, which is compatible with what's measured by your "single detector". I don't know, what an "assembly" is. So I can't comment on this.

In our context we were not talking about these, or about the double slit, but about macroscopic quantum systems, which Peres calls assemblies.

But this is not covered by your axioms, where the average is over independent, identically prepared systems, not over interacting subsystems of a macroscopic system defined by a mesoscopic cell decomposition. The latter is the assembly of Peres. Born's rule - which is not about interacting subsystems of a quantum system - says nothing about assemblies.

Sure, but they measure events, not states of the quantum field. The latter are unobservable, that was my claim. They are just theoretical tools for making predictions!

As I said, in the quantum many-body theory you have to go further and use these postulates to derive equations for macroscopic coarse-grained quantities. You end up in a hierarchy of semiclassical approximations (Kadanoff-Baym->non-Markovian transport->BUU->hydro) showing the emergence of classical laws for the said coarse-grained quantities.

What you measure related to "vacuum" QFT are squared S-matrix elements (transition probabilities), and that's what's measured in terms of cross sections. Of course, some mathematical tools like $n$-point Green's functions are not directly observable but a calculational tool to get the observable transition probabilities. Where is here a problem?

 

[vanhees71]

This is one of many things you have read about Weinberg that you simply dismiss. You are of course entitled to your opinions, no issue about that. You should take care to label your opinions as your own to provide suitable notice to the reader.

I.e. do that instead of labeling standard views of quantum theory as questionable (which you did here), and quoting yourself as an authority in the counter case. I would say, for example, that Weinberg's statements - as I quoted - are fairly innocuous... and they fall closely in line with what most physicists believe. The burden is on you, my friend, not on Weinberg. Show us where Weinberg is wrong by quoting SOMEONE ELSE.

Which standard views of QT did I label as questionable? I've not said that Weinberg is wrong. I said that I don't understand his argument. That's a big difference!

Again, I do not understand, how Weinberg comes to the conclusion that one needs a cut. This may have looked as a conclusion from the formalism, where thanks to Bohr and Heisenberg the collapse played an (in my opinion unjustified) important role. Today we are about 80 years further and have a much better understanding about open quantum systems, coarse-graining, decoherence and all that.

 

[A. Neumaier]

I don't know, what an "assembly" is.

Peres defined it in his book.

What you measure related to "vacuum" QFT are squared S-matrix elements (transition probabilities), and that's what's measured in terms of cross sections. Of course, some mathematical tools like nn-point Green's functions are not directly observable but a calculational tool to get the observable transition probabilities. Where is here a problem?

The only problem here is that you had erroneously claimed that the state of a quantum field is observable:

States of quantum fields describe many (if not all) phenomena. Why are you claiming they are unobservable?

Measuring transition probabilities is not the same as measuring a state.

By quantum tomography, one can measure to some limited accuracy the state of a single monochromatic photon modeled in the paraxial approximation, and perhaps in the future that of two entangled such photons (to even lower accuracy).

But the work grows exponentially with the number of degrees of freedom, and is already impossible for the state of an unrestricted photon, which has infinitely many degrees of freedom, so that quantum tomography would take more resources that the universe offers. Similarly, quantum tomography of the quantum states regularly used in many-body theory is impossible.

Therefore the state of a quantum field is not observable.

Of course, some mathematical tools like nn-point Green's functions are not directly observable but a calculational tool to get the observable transition probabilities. Where is here a problem?

In the same way, the state of the universe is not directly observable but a calculational tool to get observable coarse-grained approximations, such as Newtonian physics. Where is here a problem?

 

[Demystifier]

I don't understand this one quote by Weinberg: "Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem - it just doesn't change the density matrix."

By density matrix of the subsystem he means the object obtained by partial trace of the full unitary evolving state, while by state of the subsystem he means an object the evolution of which involves also something akin to the collapse. Does it make sense now?

 

[Demystifier]

Today we are about 80 years further and have a much better understanding about open quantum systems, coarse-graining, decoherence and all that.

Today there is a consensus among most (though not all) experts in open quantum systems, coarse-graining and decoherence that those things alone do not solve the measurement problem.

 

[Demystifier]

States of quantum fields describe many (if not all) phenomena. Why are you claiming they are unobservable?

The state (of quantum field) is a vector (or ray) in a Hilbert space. It is not observable in the sense that it is not a hermitian operator or an eigenvalue of a hermitian operator.

 

[DrChinese]

Which standard views of QT did I label as questionable? I've not said that Weinberg is wrong. I said that I don't understand his argument. That's a big difference!

How about what you picked on: " Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem ..."

I'm really not sure why you keep pushing a contrary position to this simple statement, when I have challenged you repeatedly to provide authoritative quotes. Stop quoting yourself! Your question is really not a question, it is a statement of your opinion. You want to attack the answer. Well, here you go:

ANY (of many) measurement on a component of an entangled system throws the distant subsystem into state in which the outcome of another measurement can be predicted with certainty. This is not a "coincidence", as Weinberg is saying. One measurement "causes" the other outcome, although causal direction is not certain (the reason we have interpretations).

 

[vanhees71]

This contradicts the microcausality condition fulfilled by QFT. It's also in Weinberg's QFT books as it is in any other book on QFT: There is no causal influence over space-like distances by construction! That's why I'm very surprised that Weinberg seems to claim the contrary in his newer QM book.

 

[martinbn]

This contradicts the microcausality condition fulfilled by QFT. It's also in Weinberg's QFT books as it is in any other book on QFT: There is no causal influence over space-like distances by construction! That's why I'm very surprised that Weinberg seems to claim the contrary in his newer QM book.

That is not what they are saying. Consider the usual example, two spin one half particles in a state |10>-|01>. The statement is that if you measure the left particle along an axis and you get the result 1, then the right particle will be in the state |0> for that axis. Are you saying that this is not correct?

 

[vanhees71]

Of course it's correct, but this correlation is not caused by the measurement but by the preparation of the entangled state, you have written down in the beginning, i.e. before (!) the measurement is done. There is no instantaneous change of the state due to the measurement.

 

[martinbn]

Of course it's correct, but this correlation is not caused by the measurement but by the preparation of the entangled state, you have written down in the beginning, i.e. before (!) the measurement is done. There is no instantaneous change of the state due to the measurement.

The point is that prior to the measurement you cannot say that the right particle was in the state |0>. Because it has to be true for any axis and there are no states like that.

 

[vanhees71]

Of course, I can't say this before the measurement, because the single-particle states are given by the partial traces and thus $\hat{\rho}_1=\hat{\rho}_2=\frac{1}{2} \hat{1}$.

Of course, it's true for any axis, because you have prepared a spherically symmetric state (total spin $S=0$). Now doing a local measurement at particle 1 Alice knows that Bob will find (or has already found) with certainty the opposite result when both are measuring in the same spatial direction, but that she knows because this 100% correlation of measurement results is due to the preparation of the two particles in this state. Alice's measurement has no instantaneous influence on Bob's spin and vice versa.

At least that's what's commonly agreed upon when interpreting all the Bell tests of recent experiments, i.e., when the measurement events at A's and B's place the common understanding is that there cannot be a causal effect of one of the measurements at the other (or are there refereed physics papers claiming otherwise?).

 

[Lord Jestocost]

....but by the preparation of the entangled state,...

Does it mean, as your are focusing on "preparation", that each particle emerges from the singlet state with, in effect, a set of pre-programmed instructions for what spin to exhibit at each possible angle of measurement?

 

[vanhees71]

No, there's nothing "pre-programmed". The two-spin state is just the singlet state you prepare it in. You can get such a state by, e.g., decaying a spin-0 particle to two spin-1/2 particles.

 

[Lord Jestocost]

Of course it's correct, but this correlation is not caused by the measurement but by the preparation of the entangled state, you have written down in the beginning, i.e. before (!) the measurement is done. There is no instantaneous change of the state due to the measurement.

J. Bell in "Bertlmann's Socks and the Nature of Reality"

“Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of quantum mechanics. So we cannot dismiss intervention on one side as a causal influence on the other.”

 

[martinbn]

Of course, I can't say this before the measurement, because the single-particle states are given by the partial traces and thus $\hat{\rho}_1=\hat{\rho}_2=\frac{1}{2} \hat{1}$.

Of course, it's true for any axis, because you have prepared a spherically symmetric state (total spin $S=0$). Now doing a local measurement at particle 1 Alice knows that Bob will find (or has already found) with certainty the opposite result when both are measuring in the same spatial direction, but that she knows because this 100% correlation of measurement results is due to the preparation of the two particles in this state. Alice's measurement has no instantaneous influence on Bob's spin and vice versa.

At least that's what's commonly agreed upon when interpreting all the Bell tests of recent experiments, i.e., when the measurement events at A's and B's place the common understanding is that there cannot be a causal effect of one of the measurements at the other (or are there refereed physics papers claiming otherwise?).

So, you agree that before and after Alice's measurement the state of Bob's particle is different, but you disagree with saying that the measurement changed it.

 

[EPR]

Lots of physicists think in terms of broken realism akin to 'everything is a field'(the 'particles' are approximate, momentary notions).

Then nonseparability comes out 'naturally' - hence your misunderstanding.

 

[DrChinese]

Of course it's correct, but this correlation is not caused by the measurement but by the preparation of the entangled state, you have written down in the beginning, i.e. before (!) the measurement is done. There is no instantaneous change of the state due to the measurement.

Quote someone to back up your position. Other than yourself. As requested too many times to count.

 

[EPR]

We can say that because we have evidence that realism and determinism are broken in the quantum world, everything there is fields.

This notion once accepted, there is no issue with entanglement. There certainly are no causal inflences between Alice and Bob.
Only when one thinks in terms billiard balls, do classical issues arise.
There is nothing wrong with vanheesh71's statements - some people need to adjust their worldview. The billiard balls do not exist.

 

[PeterDonis]

this correlation is not caused by the measurement but by the preparation of the entangled state, you have written down in the beginning, i.e. before (!) the measurement is done.

the common understanding is that there cannot be a causal effect of one of the measurements at the other

You have been focusing on the easy case, where Alice and Bob both measure spin in the same direction, so there is perfect anti-correlation and a "Bertlmann's socks" type of argument, which is the argument you are making, is workable.

However, such an argument is not workable for the hard cases, where Alice and Bob measure spin in different directions, at angles for which the correlations violate the Bell inequalities. For those cases, I don't think you can claim that "it's all just due to the previously prepared state", since the whole point of the Bell inequalities being violated is that there is no possible "previously prepared state" (no set of local hidden variables) that can account for the correlations. The QM "state" can do it, but only by being nonlocal, i.e., giving correlation probabilities that do not factorize as described in Bell's paper.

 

[PeterDonis]

There certainly are no causal inflences between Alice and Bob.

That's not what is "certain". The only thing that is "certain" is that Alice's and Bob's measurements must commute; but that does not require that there are no causal influences between them. It only requires that any such influences must not have a preferred direction, i.e., that the "Alice to Bob" and "Bob to Alice" causal directions must both be consistent with the results.

 

[A. Neumaier]

the whole point of the Bell inequalities being violated is that there is no possible "previously prepared state" (no set of local hidden variables) that can account for the correlations.

This is not quite cogent. Bell showed that there is no possible "previously prepared state" with classical hidden variables - but a quantum state is of course not covered by the argument. (Bell's argument are purely classical and assume nothing at all about quantum mechanics.)

 

[DrChinese]

We can say that because we have evidence that realism and determinism are broken in the quantum world, everything there is fields.

This notion once accepted, there is no issue with entanglement. There certainly are no causal inflences between Alice and Bob.

Not what Weinberg said. Again, if you want to contradict him, perhaps you’d care to provide a suitable reference that says different.

And your first statement does not follow anyway. Realism and determinism may indeed be broken. And we might throw in locality as well. That says absolutely nothing about QFT. And as everyone should know, QFT must respect Bell, regardless of one’s spin.

 

[PeterDonis]

Bell showed that there is no possible "previously prepared state" with classical hidden variables - but a quantum state is of course not covered by the argument.

Yes, that's why I said later in the same post that a quantum "state" can account for the correlations (but only by violating the Bell locality assumption).

 

[DrChinese]

That's not what is "certain". The only thing that is "certain" is that Alice's and Bob's measurements must commute; but that does not require that there are no causal influences between them. It only requires that any such influences must not have a preferred direction, i.e., that the "Alice to Bob" and "Bob to Alice" causal directions must both be consistent with the results.

Exactly, there is no clear causal direction. And there is nothing that explains the random outcome prior to measurement. That these confusing elements are present but not solved by any theory is why Weinberg would express dissatisfaction (which most of us share in some respect).

 

[EPR]

We can say that because we have evidence that realism and determinism are broken in the quantum world, everything there is fields.

This notion once accepted, there is no issue with entanglement. There certainly are no causal inflences between Alice and Bob.
Only when one thinks in terms billiard balls, do issues arise.

Exactly, there is no clear causal direction. And there is nothing that explains the random outcome prior to measurement. That these confusing elements are present but not solved by any theory is why Weinberg would express dissatisfaction (which most of us share in some respect).

Without realism/determinism, how can there be causal influences?

This is essentially the epr debate started anew.

A new, bigger theory superceded qm of single objects(qft) as a more comprehensive explanation of reality.
You will likely struggle forever with the ingrained notion of particles and billiard balls like thousands other physicists do.