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Directly measuring Wave-function?

tensordyne

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tensordyne
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May 12, 2010
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Do you think it is possible to directly measure the wave-function of quantum mechanics?
 
No.

For starters, I can't think of many measuring devices that return complex results.
 
tensordyne said:
Do you think it is possible to directly measure the wave-function of quantum mechanics?
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Given many instances of the same wavefunction, one could perform a measurement on each and reconstruct the wavefunction with arbitrary accuracy. But you can't have a "wave-function meter" that measures the wavefunction in one shot.

If you knew the wavefunction was a single eigenstate of some Hermetian operator, then a single measurement of that observable suffices (although you're still not exactly measuring the wavefunction - you're measuring the value of some observable and then using your knowledge to reconstruct the wavefunction from the result). But in general, you don't know that - which means you will not be able to reconstruct the wavefunction accurately from one measurement.
 
tensordyne said:
Are you really sure of that sol invictus?
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He's right. Given enough identical copies of a wavefunction, you can figure out what it was. (Except for the arbitrary complex phase multiplying the whole function; you can't figure that out AFAIK.)
 
tensordyne said:
Are you really sure of that sol invictus?
Click to expand...

Yes, Sol is correct. When we make a measurement on a wavefunction, the wavefunction "collapses" (in the Copenhagen view of QM) which leads to the value of position, momentum, energy, whatever being read on whatever detector you are employing. All that measurement tells us is what value the wavefunction collapsed to, not what the overall form of the original wavefunction was in the first place.

To get that information, you would have to make multiple repeated measurements on identical wavefunctions, as ben_m stated.
 
+1 to 'Sol is obviously right', for whatever that's worth.

In the ordinary case of a particle and position as our observable, for example, the wavefunction has an absolute value determined by the probability density (up to overall normalization) and a phase by the probability flux (up to some global constant).
 
This is why interpretations are so much philosophical fun. Some people claim but cannot prove that all states exist in reality and so on hence MWI a deterministic approach. It's a frustrating limit on human understanding, but as yet no experiment has ever really shown any exact value that is deductive. Ie the wave equation is inferred from results of an experiment and induced form probability statistics of a series, thus they do not come from first principles, a classical particle assumption. Although some would contest this, they are not considered reliable.

If God does not play dice with the universe, they are strangely inconsistent with reality even to God. ;)
 
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MattusMaximus said:
I'm going to read the entire article in detail, but at first glance it seems they've even teased out a method of measuring the imaginary part of the wavefunction. Wowser.
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Why is that surprising? If you can measure the real (well, amplitude) part of the wavefunction, then the imaginary (or rather, phase) part corresponds to how the former changed with time.
 
So there is something you all should know, I asked the question in the OP knowing that the paper in nature

http://www.nature.com/nature/journal/v474/n7350/full/nature10120.html

shows how to measure at least one kind of wavefunction in a direct way. What I find interesting about the paper myself is the use of "weak" measurements (read paper if you want to know exactly what that means). So RC did not fall for my ruse but I think some others kind of did. Oh well, it would be interesting to see if the measurement in the paper could be used to measure multi-particle wave-functions and other cases.
 
Well that's impressive, although I'm not 100% sure about how much an actual weak measurement affects the wavefunction, and given that you need multiple measurements still how good a measurement you can end up getting in practice - it's that bit about the coupling vanishing that bothers me.
 
tensordyne said:
So there is something you all should know, I asked the question in the OP knowing that the paper in nature

http://www.nature.com/nature/journal/v474/n7350/full/nature10120.html

shows how to measure at least one kind of wavefunction in a direct way.
Click to expand...
I've been vaguely aware of weak measurements, but I don't see how they're relevant to this disagreement. You're still dependent on having an ensemble of identically prepared particles, so while it may be more elegant than a brute-force statistical reconstruction, the basic issue of having to do multiple measurements over many instances is unchanged.
 
Vorpal said:
I've been vaguely aware of weak measurements, but I don't see how they're relevant to this disagreement. You're still dependent on having an ensemble of identically prepared particles, so while it may be more elegant than a brute-force statistical reconstruction, the basic issue of having to do multiple measurements over many instances is unchanged.
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To be honest, I wish I had the article (read it first in a magazine store). The idea is that they have shown how to measure the wavefunction of a photon, given certain conditions, in a direct way, so that if you want to know what the wavefunction value is (up to normalization) at say position x, then it can be done by simply reading values from various instruments (this shows my ignorance on how these measurements work, but from what I have read, one measurement for amplitude and one for phase).

The normal method of measuring the wavefunction is with quantum state tomography. With that method you have to sample over and over again.

Even so, this might just turn out to be another interesting "corner" case. Since Bohm, Quantum Mechanics keeps on giving out nice surprises.
 
tensordyne said:
Even so, this might just turn out to be another interesting "corner" case. Since Bohm, Quantum Mechanics keeps on giving out nice surprises.
Click to expand...
To be more exact, Quantum Mechanics has been giving out nice surprises due to many scientists work since it was first formulated. Just look at the subject of this thread!
 
tensordyne said:
To be honest, I wish I had the article (read it first in a magazine store). The idea is that they have shown how to measure the wavefunction of a photon, given certain conditions, in a direct way, so that if you want to know what the wavefunction value is (up to normalization) at say position x, then it can be done by simply reading values from various instruments (this shows my ignorance on how these measurements work, but from what I have read, one measurement for amplitude and one for phase).

The normal method of measuring the wavefunction is with quantum state tomography. With that method you have to sample over and over again.

Even so, this might just turn out to be another interesting "corner" case. Since Bohm, Quantum Mechanics keeps on giving out nice surprises.
Click to expand...

Any chance this might be the paper from Canada, where they were using a Two-Slit Interferometer and a Calcite crystal, getting a series of "weak" measurements, then reconstructing the Photon's trajectory after-the-fact?

If so, this thread is currently discussing SOME details, but the signal/noise ratio is not the best.;):D

It may help if you are able to ignore the Moron.:D

Dave
 
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