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Directly measuring Wave-function?

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.
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There's nothing in there that's any different from what I said - you make many measurements on an ensemble of identically prepared particles, and use the results to reproduce the wavefunction. It's just that there are clever and efficient ways to do that, and not so efficient ways to do it - just as with any other type of measurement.
 
sol invictus said:
There's nothing in there that's any different from what I said - you make many measurements on an ensemble of identically prepared particles, and use the results to reproduce the wavefunction. It's just that there are clever and efficient ways to do that, and not so efficient ways to do it - just as with any other type of measurement.
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As for the differences between Quantum State Tomography (QST) and the method in the paper, they are very different. QST will work, from what I understand, on an ensemble of not identically prepared particles (course I would imagine they must all be the same type of particle), the method in the paper will not. The method in the paper allows one to 'scan' the wavefunction (for the specific case it covers), QST does not allow for scanning any kind of wavefunction. Oh, and QST gives a density matrix and not a wavefunction (although both hold the same info).

On the other hand, the Authors do note that the method they give is in accord with Quantum Mechanics... so differences are in a way only superficial in a much deeper sense.

Yet, if it was only a matter of efficiency that was at play, do you really think it would garner a Nature Journal Paper? I suggest reading the article before making too many more comments. It is on the news-stands right now. Barring that you can probably find it in a library (forget about paying the exhorbitent subscription fee unless you are an economic masochist or something).

In any case, it is interesting.

WARNING: the above is subject to my best understanding... I am new to QST and all the other Quantum Tomographies, and the paper is brand-new. Just covering my bases here.

p.s. I think the Nature Journal Paper has a typo in one of the equations! Brownie points for the first person to spot it!
 
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Reality Check said:
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!
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Yeah, fair enough. I guess I was referring to the fact that QM past say 1925 or something was thought of in pretty much a consistent way without much in the way of new comments (Even Quantum Field Theory is based primarily on good old fashioned QM). It was not until Bohm that people again tried questioning the basis of QM. The Nature Journal Paper is in that same vein I think.

Oh well, hope that makes sense.
 
tensordyne said:
As for the differences between Quantum State Tomography (QST) and the method in the paper, they are very different. QST will work, from what I understand, on an ensemble of not identically prepared particles (course I would imagine they must all be the same type of particle), the method in the paper will not. The method in the paper allows one to 'scan' the wavefunction (for the specific case it covers), QST does not allow for scanning any kind of wavefunction. Oh, and QST gives a density matrix and not a wavefunction (although both hold the same info).
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I'm not sure what you mean by QST - but you can reconstruct any wavefunction with repeated measurements on an (identical) ensemble of any observable. That's bog-standard QM; it's been well-understood since the very beginning (80 years ago or so).

On the other hand, the Authors do note that the method they give is in accord with Quantum Mechanics... so differences are in a way only superficial in a much deeper sense.
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There's nothing new or even slightly mysterious here.

Yet, if it was only a matter of efficiency that was at play, do you really think it would garner a Nature Journal Paper?
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Yes.

I suggest reading the article before making too many more comments. It is on the news-stands right now. Barring that you can probably find it in a library (forget about paying the exhorbitent subscription fee unless you are an economic masochist or something).
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I have free access to it, and I have skimmed it.
 
sol invictus said:
I'm not sure what you mean by QST - but you can reconstruct any wavefunction with repeated measurements on an (identical) ensemble of any observable. That's bog-standard QM; it's been well-understood since the very beginning (80 years ago or so).

There's nothing new or even slightly mysterious here.

Yes.

I have free access to it, and I have skimmed it.
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So from your responses the only thing I can say is you think the Journal paper is without merit, so that even if it is true (which I do not think you are contending it is not), it is not very interesting to you all the same, perhaps even being trivial in nature.

Or is it you do not like being shown how arrogant you are in your presumptions? It is no fun to me to try to psycho-analyse people but I wish RC wasn't so scholarly because then I would have probably been able to draw out a statement from you that the paper would definitely contradict.

Oh well, all the best to you all.
 
tensordyne said:
So from your responses the only thing I can say is you think the Journal paper is without merit
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Not at all. Experiments like that are very hard. But it's the experiment that is hard, not the theory.

Or is it you do not like being shown how arrogant you are in your presumptions?
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I may be arrogant, but I am also correct.
 
tensordyne said:
Yeah, fair enough. I guess I was referring to the fact that QM past say 1925 or something was thought of in pretty much a consistent way without much in the way of new comments (Even Quantum Field Theory is based primarily on good old fashioned QM). It was not until Bohm that people again tried questioning the basis of QM. The Nature Journal Paper is in that same vein I think.

Oh well, hope that makes sense.
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It does make a bit of sense. It looks like you are concentrating on Bohm for some reason. You are forgetting about all of the other people who have questioned the basis of QM since ~1925. There are many interpretations of QM including De Broglie–Bohm theory.

IMO which interpretation you use does not matter since they give the same predictions. I tend to the Copenhagen interpretation since it seems to meet Occam's razor critera (no extra worlds, no extra pilot wave, etc.).

The Nature paper (at least according to the abstract) is not in the same vein. It is basically using well-known techniques (weak measurements) to provide a better understanding of QM. There is no mention of new QM interpretations in the abstract.
 
So, does quantum tomography, or other methods of being able to completely measure a wave function invalidate the Heisenberg Uncertainty principle?
 
Vorpal and Sol gets my vote :)

A weak measurement is always statistical as I understands it. And if you want to it to become 'statistically significant' you will have to repeat it, a lot. It's about what 'nature' is. If you define 'reality' as something following strict mathematical laws of probability, it's not a long shot to expect 'reality' to adhere to those ideas, even when impossible to measure, as with HUP in its original form.

I don't know there, somehow all this probability, or if you like Feynman, all this 'quenching' and 'reinforcing' of 'paths' (interference) leaves us with a reality that I can touch and feel. What I think there though, is that if you adhere to this idea, then I'm not sure discrete events, quanta, will satisfy the idea it builds on?

And Dave seems correct to me? His link describes a similar idea, in that it builds on the same proposition. That weak measurements is a acceptable (factual?) description of 'reality'.
 
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Reality Check

So the only way to invalidate the Heisenberg Uncertainty principle would be if you could measure wave function and position/speed simultaneously?
 
INRM said:
Reality Check

So the only way to invalidate the Heisenberg Uncertainty principle would be if you could measure wave function and position/speed simultaneously?
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INRM
Firstly the Heisenberg Uncertainty principle has nothing to to with the wave function.

The Heisenberg Uncertainty principle is a statement about uncertainty in measurements (perhaps you should read the linked article).

If you can measure position of a particle to a certain accuracy and at the same time it's momentum to a certain accuracy and the product of the uncertainties violates the Heisenberg Uncertainty principle then the Heisenberg Uncertainty principle is invalidated.
 
davefoc said:
I wonder if somebody could take a shot at this question. What do you know after you have directly measured a wave function about the wave you just measured?
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The only way to 'measure a wavefunction' is to measure many particles, and reconstruct a wavefunction from the distribution you get.

Measuring a particle tells you it's eigenvalue, and from that point on you know the particle is in an eigenstate with that eigenvalue, (though there may be many states with that eigenvalue, and the particle may be in a combination of some or all of those states).
 
Reality Check said:
INRM
Firstly the Heisenberg Uncertainty principle has nothing to to with the wave function.

The Heisenberg Uncertainty principle is a statement about uncertainty in measurements (perhaps you should read the linked article).
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I disagree entirely. The Heisenberg Uncertainty principle (as is used today, not necessarily as it was formulated) is a mathematical statement about waves. It's far more useful when describing things that aren't being measured.

For example, suppose we think about an electron in an orbital a nucleus. Classically we know that the electrostatic energy goes infinitely low as we get closer (remember the electron will want to lose as much energy as possible, like a ball rolling down a hill). Even with the electron described as a wave we can simply make a very small wave, and by this should allow the electron to drop down to an arbitrarily low energy. We have the same problem classical physics had: the electron should spiral into the nucleus, release a huge amount of energy and everything should collapse into a very small volume.

The uncertainty principle tells us what's wrong with this: as the electron gets closer to the nucleus, it's position gets more and more exact, so it's momentum must get less exact. We started with zero-momentum (so the electron doesn't fly away from the nucleus), so we have to add larger and larger values of momentum. Larger value of momentum implies more kinetic energy. Now we know why electrons won't spiral into the nucleus: orbitals need to balance the loss of electrostatic energy with a gain of kinetic energy.
 
Dilb said:
The only way to 'measure a wavefunction' is to measure many particles, and reconstruct a wavefunction from the distribution you get.

Measuring a particle tells you it's eigenvalue, and from that point on you know the particle is in an eigenstate with that eigenvalue, (though there may be many states with that eigenvalue, and the particle may be in a combination of some or all of those states).
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What are the units of this eigenvalue? What is knowable about a wave when one knows its eigenvalue? What kind of tool does one measure waveforms with? When one measures a waveform by measuring particles how are the particles affected?
 
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