Dyson's View Of Wavefunction Collapse

  • #71
WernerQH said:
Quantum field theory does not say where the energy is localized between the emission and absorption events
It has not even a concept of emission and absorption events (as events in space and time)! So it seems that QFT says nothing about absorption and emission without being interpreted by what you consider to be metaphysical baggage.
 
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  • #72
Morbert said:
Why is this a problem?
Because we see extremely improbable things happen all the time. Tiny probabilities are not a good guide to living in the real world.
 
  • #73
A. Neumaier said:
For sufficiently long histories of consecutive measurements of continuous quantities (such as the particle paths measured at CERN), these probabilities become extremely tiny. Almost like the probability that a random generator for text produces a sonnett by Shakespeare....
People at CERN are experts at producing very unlikely events. :smile:
 
  • #74
A. Neumaier said:
Because we see extremely improbable things happen all the time. Tiny probabilities are not a good guide to living in the real world.
I recently read large parts of “Scientific Reasoning : The Bayesian Approach” by Colin Howson and Peter Urbach (2006). It made a similar comment regarding tiny probabilities, as an argument against Cournot's principle:
gentzen said:
One other interesting discussion point in that book was that Cournot’s principle is inconcistent (or at least wrong), because in some situation any event which can happen has a very small probability. Glenn Shafer proposes to fix this by replacing “practical certainty” with “prediction”. He may be right. After all, I mostly learned about Cournot’s principle from his Why did Cournot’s principle disappear? and “That’s what all the old guys said.” The many faces of Cournot’s principle. Another possible fix could be to evaluate smallness of probabilities relative to the entropy of the given situations. That solution came up during discussions with kered rettop (Derek Potter?) on robustness issues:
If an amplitude of 10^-1000 leads to totally different conclusions than an amplitude which is exactly zero, then the corresponding interpretation has robustness issues.
and was later used as an argument against counting arguments in MWI:
For me, one reason to be suspicious of that counting of equally likely scenarios is that this runs into robustness issues again with very small probabilities like 10^-1000. You would have to construct a correspondingly huge amount of equally likely scenarios. But the very existence of such scenarios would imply an entropy much larger than physically reasonable. In fact, that entropy could be forced to be arbitrarily large.
 
  • #75
A. Neumaier said:
Because we see extremely improbable things happen all the time. Tiny probabilities are not a good guide to living in the real world.
I would think coarse graining is what helps us make sense of these things. If I shuffle a deck and lay out the cards, I will observe an order that had a probability of about 1.24e-68. But the more coarse-grained outcome "first card is red" has a probability of about .5. It's these coarse-grained predictions that we care about.
 
  • #76
Morbert said:
If I shuffle a deck and lay out the cards, I will observe an order that had a probability of about 1.24e-68.
But it is fully determined by the way you shuffled it. So it is clear that the probability is an approximation.

But what should fundamental quantum probabilities of 1.24e-68 mean?
 
  • #77
A. Neumaier said:
But what should fundamental quantum probabilities of 1.24e-68 mean?
Even worse: The probability that a position measurement yields an irrational number is 1, but all actual position measurements produce rational numbers.
 
  • #78
A. Neumaier said:
Even worse: The probability that a position measurement yields an irrational number is 1, but all actual position measurements produce rational numbers.
Do they produce a number or an interval?
 
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  • #79
martinbn said:
Do they produce a number or an interval?
That depends on the definition what a measurement result is.

According to Born's rule in every formulation I know, measurement results are real numbers, not intervals.

But in my thermal interpretation, measurement results are uncertain numbers, so they have an intrinsic uncertainty.

I have never seen a definition of a measurement result that would define it as an (open or closed?) interval. Their boundaries would have to be uncertain, too.
 
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  • #80
A. Neumaier said:
but all actual position measurements produce rational numbers.
Wouldn't this require perfect resolution to be true? And perfect resolution would not be possible even in principle due to the Wigner-Araki-Yanase theorem.

Instead actual position measurements would be modeled with some POVM and yield a highly localized distribution.
 
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  • #81
Morbert said:
Wouldn't this require perfect resolution to be true? And perfect resolution would not be possible even in principle due to the Wigner-Araki-Yanase theorem.

Instead actual position measurements would be modeled with some POVM and yield a highly localized distribution.
Doesn't that also violate the uncertainty principle?
 
  • #82
jbergman said:
Doesn't that also violate the uncertainty principle?
No. A very narrow position distribution will be a very wide distribution in momentum space.
 
  • #83
PeterDonis said:
No. A very narrow position distribution will be a very wide distribution in momentum space.
Right, but we were talking about perfect resolution. My point was that we can only measure position up to some range because of the uncertainty principle. A delta function at a single position is an unphysical state that violates the uncertainty principle.
 
  • #84
jbergman said:
My point was that we can only measure position up to some range because of the uncertainty principle.

No, that's quite popular misconception. Uncertainty has nothing to do with this, it tells you about statistical spread of your measurements, not how precise each measurement can be - standard deviation for single measurement is 0.
 
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  • #85
jbergman said:
we were talking about perfect resolution.
Perfect resolution means infinite precision in position space and infinite spread in momentum space. The Fourier transform of a delta function is a complex exponential with equal amplitude at every value of momentum. All perfectly consistent with the uncertainty principle, as long as you're okay with things like delta functions. (There are other formulations for those who are squeamish about such things, but they end up at basically the same place.)

jbergman said:
My point was that we can only measure position up to some range because of the uncertainty principle.
No, as @weirdoguy has pointed out, that's not correct.

Physically, the reason real measurements can only have finite precision has to do with the finite size of the measuring tools, but that's not something that's driven by the uncertainty principle. It's driven by the fact that measuring tools have to be made of something, and every possible "something" has a finite size.
 
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  • #86
PeterDonis said:
Perfect resolution means infinite precision in position space and infinite spread in momentum space. The Fourier transform of a delta function is a complex exponential with equal amplitude at every value of momentum. All perfectly consistent with the uncertainty principle, as long as you're okay with things like delta functions. (There are other formulations for those who are squeamish about such things, but they end up at basically the same place.)
I don't take that as a real state as that would imply infinite energy. This is essentially a mathematical formalism for computation. Just because the delta functions are the eigen-basis for position space doesn't imply that any real particle is in such a state.
PeterDonis said:
No, as @weirdoguy has pointed out, that's not correct.

Physically, the reason real measurements can only have finite precision has to do with the finite size of the measuring tools, but that's not something that's driven by the uncertainty principle. It's driven by the fact that measuring tools have to be made of something, and every possible "something" has a finite size.
I broadly agree with this which is why I stated my original post as a question. I will have to read @A. Neumaier 's work and others, though, to convince myself that this isn't related to the original question.
 
  • #87
jbergman said:
I don't take that as a real state
It's not. A delta function state is not physically realizable. But that doesn't prevent it from having the necessary mathematical properties to satisfy the uncertainty principle.

jbergman said:
as that would imply infinite energy.
No, it doesn't. An infinite spread in momentum is not the same as infinite energy. The particle has some finite momentum, and therefore some finite energy; we just have complete uncertainty as to which finite momentum it is.
 
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  • #88
weirdoguy said:
No, that's quite popular misconception. Uncertainty has nothing to do with this, it tells you about statistical spread of your measurements, not how precise each measurement can be - standard deviation for single measurement is 0.

Yes. That is one reason I like Ballentine so much.

He explains this clearly.

Thanks
Bill
 
  • #89
Demystifier said:
But QM as it is has collapse.

I read somewhere that Schwinger's version of QFT had no collapse. I will see if I can dig up the source.

Added later:
Only Rodney Brooks paper. While Rodney is a qualified physicist, I look at him more as a populist:
https://arxiv.org/vc/arxiv/papers/1710/1710.10291v4.pdf

'Quantum collapse was not included in Schwinger’s formulation of QFT'


Thanks
Bill
 
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  • #90
bhobba said:
'Quantum collapse was not included in Schwinger’s formulation of QFT'
The full sentence (at the bottom of page 4) is:
Quantum collapse was not included in Schwinger’s formulation of QFT, but it became an important part of the source theory that he developed later.
 
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  • #91
Morbert said:
Wouldn't this require perfect resolution to be true? And perfect resolution would not be possible even in principle due to the Wigner-Araki-Yanase theorem.

Instead actual position measurements would be modeled with some POVM and yield a highly localized distribution.
Born's rule in all its textbook forms claim that measurements produce eigenvalues, and don't say anything about resolution. This shows that Born's rule is an idealization, but people talk as if it were a universal basic law. Real measurement is something quite complicated,
 
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