Heisenberg and quantum mechanics

[DrChinese]

I really don't see how this EPR experiments disproves experimental uncertainty. How do we know for sure that even after the two particles are separated there is not some connection between them?

Well, there is, sort of - they are part in superposition of the same wave function. But are they mediated by a physical non-local force? That is certainly a possibility that cannot be absolutely ruled out. If you accept Bohmian Mechanics, then that is indeed the case... and now the HUP can be explained in different terms. I would say that many scientists do postulate that there is some sort of non-local physical mechanism (for lack of a better term) involved. But I would not say it is generally accepted as such.

 

[Locrian]

That's right the uncertainty principle doesn't allow you much predictions.
It is merely the root of quantum mechanics.
Further, it explains the most fundamental predictions.

Like the [blah blah blah]

... any more ?

Let's start a big list ...


Michel

Congratulations on misrepresenting what I wrote, confusing what the "root" of quantum mechanics is, and - best of all - missing the forest for the trees.

I'll say again: The uncertainty principle is not the primary barrier in "predicting everything," as the opening post suggests. On the contrary, we're more than capable of predicting many things even beyond the necessary precision and accuracy necessary, and yet are completely stumped at predicting other things (weather, turbulent fluid flow, economic shifts) within an order of magnitude of the precision we would prefer.

 

[MeJennifer]

But are they mediated by a physical non-local force?

Well to me it seems that all forces work non-local.
Locality seems only relevant when there is some sort of scattering, which I see as a space-time event where two (or more) particles happens to interact. The other forces kind of "hover" above space-time directing the probability of the location of the particle.

 

[ZapperZ]

Well to me it seems that all forces work non-local.

OK, could you point out to me an example of a "non-local" EM force at work?

Zz.

 

[MeJennifer]

OK, could you point out to me an example of a "non-local" EM force at work?

I would say pretty much every force that require some sort of wave function.

Could you point out to me an example of a force that is local?

 

[Locrian]

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

So what situation does the HUP actually prevent us from predicting something? The most obvious (and probably only) situation is one that fits the following criteria:

1) The prediction involves a system exhibiting quantum mechanical phenomena. More precisely, the system must require quantum mechanics to make predictions. I've had individuals in this forum try to argue that large objects (such as tennis balls) must be described as a wavefunction, but anyone with sense or a grasp of physics knows that most massive objects shouldn't be - at least if you plan to actually predict what will happen in the system.

2) The prediction involves taking two consecutive measurements whose operators don't commute. The HUP only affects something multiple consecutive measurments that are in some special way related. The addage about position and momentum isn't even entirely accurate: for instance, you can know the position in one direction and the momentum in an orthogonal one without violating the HUP at all.

3) The prediciton must require precision for multiple noncommuting measurables that is less than the HUP would allow. This alone removes just about any measurement ever made to predict some result. We don't need precision that low for most military, economic, physical or social issues that we would like to predict. The universe is one of many scales, and almost none require us to measure things to that small a degree.

It should be plainly obvious that the HUP doesn't prevent us from predicting what will happen in any but a select set of arenas.

 

[ZapperZ]

I would say pretty much every force that require some sort of wave function.

Could you point out to me an example of a force that is local?

You'll notice that I made no assertion one way or the other. You did. And your answer is very vague. Show me exactly one concrete example which clearly illustrates what you mean by a force that is "non-local".

Zz.

 

[MeJennifer]

You'll notice that I made no assertion one way or the other. You did. And your answer is very vague. Show me exactly one concrete example which clearly illustrates what you mean by a force that is "non-local".

Zz.

Well EM waves in the EPR experiment for instance.

 

[jbusc]

So what situation does the HUP actually prevent us from predicting something? The most obvious (and probably only) situation is one that fits the following criteria:
*snip*
It should be plainly obvious that the HUP doesn't prevent us from predicting what will happen in any but a select set of arenas.

In fact, the uncertainty principle allows us insight and predictions into fundamental questions which were proposed at the beginning of the 20th century - like why electrons are not found in atomic nuclei.

I think it was from Beiser's Modern Physics, he stated that the HUP was not a limitation of our knowledge, but a useful tool unto itself.

 

[ZapperZ]

Well EM waves in the EPR experiment for instance.

Er... what EM waves? The EPR experiment in which there is entanglement has no transfer of any kind of interaction when a measurement on one of the pair is made! There's no EM wave, no "strong" wave, no "weak" wave, no gravity wave of any kind going from one to another. Even the QM description shows no kind of EM "wave".

So how did EM wave became non-local here? You do know that the QM wavefunction is not the same as the EM wave, don't you?

Zz.

 

[moving finger]

I don't understand this "measuring position and momentum simultaneously" stuff.

Perhaps you should have said so earlier, when it was first mentioned in post #8, which you responded to but obviously ignored the reference to “simultaneously”.

You will note that the very fact that non-commuting operators, by definition, do not commute, means there is an ORDER in the measurement of the observables. You get one result when you measure A first, and then B, versus measuring B first, and then A. Where is this "simultaneous" measurement?

See the following for a paper on the Simultaneous Measurement of Noncommuting Observables :

http://prola.aps.org/abstract/PR/v152/i4/p1103_1

Since when does the HUP requires such a thing?

It has never been claimed that the HUP “requires” such a thing – but the HUP places limits on the precision with which such simultaneous measurements can be made.

As long as the system remains isolated and does not lose coherence, the HUP kicks in. In the example I mentioned, there is no "simultaneous" measurement, yet you STILL have a demonstration of the HUP.

The HUP applies all the way through, it does not mysteriously “kick in” just when you are about to make another measurement.

Can you point to me a "simultaneous" measurement that demonstrates the HUP? If you say one cannot make such a measurement, then you are implying that the HUP doesn't exist.

I have never said that a simultaneous measurement “demonstrates the HUP”, and I have never said that such measurements are impossible – you seem to misunderstand.

and take note that the original argument I was trying to correct was the fallacy surrounding the accuracy of a SINGLE measurement of position and a SINGLE measurement of momentum of a SINGLE particle. The accuracy of a single measurement of observable A and B are NOT goverened by the HUP. Have we settled this yet before migrating to this "simultaneous" issue?

I understand that you believe the OP was referring to sequential measurements – and I have no problem agreeing that two sequential measurements can provide you with information as precise as you would like – but I do not believe such was the intent of the OP.

Best regards

 

[ZapperZ]

Perhaps you should have said so earlier, when it was first mentioned in post #8, which you responded to but obviously ignored the reference to “simultaneously”.


See the following for a paper on the Simultaneous Measurement of Noncommuting Observables :

http://prola.aps.org/abstract/PR/v152/i4/p1103_1


It has never been claimed that the HUP “requires” such a thing – but the HUP places limits on the precision with which such simultaneous measurements can be made.


The HUP applies all the way through, it does not mysteriously “kick in” just when you are about to make another measurement.


I have never said that a simultaneous measurement “demonstrates the HUP”, and I have never said that such measurements are impossible – you seem to misunderstand.


I understand that you believe the OP was referring to sequential measurements – and I have no problem agreeing that two sequential measurements can provide you with information as precise as you would like – but I do not believe such was the intent of the OP.

Best regards

This is the OP:

Heisenberg showed that, even in theory with a hypothetical infinitely precise instrument, no measurement could be made to arbitrary accuracy of both the position and the momentum of a physical object.

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

And this was your response to me in post #8

To be fair to superweirdo, what he should have said is “we cannot simultaneously know to arbitrary precision both the position and the momentum”

Best Regards

I "ignored" the "simultaneous" aspect of it because QM and the HUP never require such a constrained in the first place. So I do not see the point of discussing a "special case" when the GENERAL case is equally valid. I don't have to make a "simultaneous" measurement of the non-commuting observable to detect the HUP. In other word, I don't have to go through all that difficult contortions to detect this. An ordinary one, such as from a single slit, will do just fine. This is why I said I do not understand why such a thing needs to be brought up in first place.

Secondly, recall what I am trying to do here. There is a very common fallacy that one cannot determine (be it simultaneous or not) the position and momentum with arbitrary precision of a particle. This is wrong. The HUP never says such a thing. The single measurement of a position is limited in accuracy only by the instrument. The same can be said of the position. The HUP is not about the value of p and x after a single measurement of each, but rather the spread in p and x and consequently, our ability to predict their values. This applies be it a simultaneous or non-simultaneous measurement.

And oh, aren't you curious that in the paper you cited, their definition of a "simultaneous" measurement is actually the same as my single-slit example? See Fig. 1.

Zz.

 

[MeJennifer]

Er... what EM waves? The EPR experiment in which there is entanglement has no transfer of any kind of interaction when a measurement on one of the pair is made! There's no EM wave, no "strong" wave, no "weak" wave, no gravity wave of any kind going from one to another. Even the QM description shows no kind of EM "wave".

So how did EM wave became non-local here? You do know that the QM wavefunction is not the same as the EM wave, don't you?

Zz.

So photons are not EM waves?

 

[ZapperZ]

So photons are not EM waves?

The EM waves are NOT the "wavefunction" of QM. You don't solve the Schrodinger equation for photons and get EM waves that you get out of Maxwell equations as the solution.

So again, where is the non-local interaction of EM?

Zz.

 

[MeJennifer]

The EM waves are NOT the "wavefunction" of QM. You don't solve the Schrodinger equation for photons and get EM waves that you get out of Maxwell equations as the solution.

So again, where is the non-local interaction of EM?

Zz.

Where did I say that the EM waves and the wave fuction are the same?

You were asking me about forces, electro-magnetism is a force.

 

[ZapperZ]

Where did I say that the EM waves and the wave fuction are the same?

You were asking me about forces, electro-magnetism is a force.

And you were claiming that EM forces are non-local. The "non-local" connection cannot be made using classical EM theory. And since you invoked the EPR experiment, then it must be quantum mechanical. But in such an experiment, no EM interactions is invoked upon measurement. QM entanglement may imply non-locality, but NOT EM interactions. No EPR papers that I've read have ever made such claims (and neither has QED)

You are being VERY terse in explaining yourself after each of my question. If this is how you wish to proceed with each of your claim, then I suggest you do not make such claims in the future since you appear to refuse to elaborate in detail, but rather make a specific citation of the paper that can back your claim. So in this case, please point out to me the EPR paper/s that have explicitly made the claim that the results imply a non-local EM force.

Zz.

 

[MeJennifer]

And you were claiming that EM forces are non-local. The "non-local" connection cannot be made using classical EM theory. And since you invoked the EPR experiment, then it must be quantum mechanical. But in such an experiment, no EM interactions is invoked upon measurement. QM entanglement may imply non-locality, but NOT EM interactions. No EPR papers that I've read have ever made such claims (and neither has QED)

Are you suggesting that photons are not EM interactions?

You are being VERY terse in explaining yourself after each of my question. If this is how you wish to proceed with each of your claim, then I suggest you do not make such claims in the future since you appear to refuse to elaborate in detail, but rather make a specific citation of the paper that can back your claim. So in this case, please point out to me the EPR paper/s that have explicitly made the claim that the results imply a non-local EM force.

Well I thought we had a friendly discussion about this. We don't have to discuss it, really. Sorry then!

One could clearly interpret the results of EPR as a non-local interaction which I do. This is not new at all. You may disagree but I don't understand what your problem is with me stating that.

 

[lalbatros]

Locrian,

By Locrian Congratulations on misrepresenting what I wrote ...

I did not try to represent your saying, I quoted them in full !
But english is not my native languange, maybe I misunderstood what you said (specially the word hurdle).

Now, let me note that what you quoted by "BlahBlah ..." from my post is what I consider the most interresting for a discussion: examples of how the HUP can make us understand the essentials of a quantum effect. Maybe not a hurdle ...

Michel

 

[Doc Al]

One could clearly interpret the results of EPR as a non-local interaction which I do. This is not new at all.

Absolutely.

You may disagree but I don't understand what your problem is with me stating that.

I don't think Zapper is disagreeing that entangled EPR pairs can imply nonlocality; he is only objecting to ascribing that nonlocality to the EM forces. (I would agree with that.)

Edit: I didn't intend to imply that Zapper was agreeing or disagreeing about whether EPR implies nonlocality, just that whatever is going on, no one is claiming that there exist nonlocal electromagnetic forces.

 

[selfAdjoint]

One could clearly interpret the results of EPR as a non-local interaction which I do. This is not new at all.

Absolutely.

You may disagree but I don't understand what your problem is with me stating that.

I don't think Zapper is disagreeing that entangled EPR pairs can imply nonlocality; he is only objecting to ascribing that nonlocality to the EM forces. (I would agree with that.)

I don't think the quantum correlation between the entangled particles can be described as an "interaction", much less a "force". For that matter "nonlocal" is a subject of much contention, on this forum and elsewhere. Experienced professional physicsts cannot all agree.

 

[ZapperZ]

Are you suggesting that photons are not EM interactions?


Well I thought we had a friendly discussion about this. We don't have to discuss it, really. Sorry then!

There's nothing wrong with "discussion". However, I don't consider terse, one-sentence responses as "discussion". Furthermore, if you have reviewed our guidelines, we clearly prohibit speculative discussion. Since "non-local forces" as derived out of EPR experiments are what I consider to be speculative (i.e. no EPR papers have ever concluded forces are non-local), it was why I asked to elaborate further since I do not understand your claim. This, you have refused to do.

One could clearly interpret the results of EPR as a non-local interaction which I do. This is not new at all. You may disagree but I don't understand what your problem is with me stating that.

You need to first understand how "entanglement" of a particular observable correlates to "non-locality". The problem you had was that you are assuming that just because that observable exhibit non-locality, then there MUST be a force that is transmitted that is non-local. There's nothing in QM that implies such a thing. There are no "non local interaction" here since there's nothing that "interacts". Look closely at ALL the EPR experimental paper if you don't believe me. You will notice that not one of them indicates that "forces" are non-local. So it is your interpretation of the results that is faulty here.

Try this one. I have an object A that is stationary, and has no angular momentum. At some time, it explodes into 2 separate pieces that fly off in opposite directions. At a later time, I capture one of the pieces and found out that it has an angular momentum L1. Immediately I know exactly the angular momentum of the other piece L2.

There's nothing quantum mechanical here. In fact, it is purely classical. Are you telling me that in this case, there is a "non-local" force that went from one of the pieces to the other? Everything after the instant of measurement here is identical to the EPR/QM experiment.

Zz.

 

[ZapperZ]

I don't think the quantum correlation between the entangled particles can be described as an "interaction", much less a "force". For that matter "nonlocal" is a subject of much contention, on this forum and elsewhere. Experienced professional physicsts cannot all agree.

Agreed. That's why *I* didn't make any assertion of something being local or non-local. However, to claim that EM forces are non-local based on the EPR experiment is erroneous. Even if the entanglement is non-local, there's nothing here that implies that it is due to EM interactions. MeJeniffer has made a faulty connection between two separate phenomena.

Zz.

 

[MeJennifer]

You need to first understand how "entanglement" of a particular observable correlates to "non-locality". The problem you had was that you are assuming that just because that observable exhibit non-locality, then there MUST be a force that is transmitted that is non-local.

I did not say that and that is not my position at all.
My interpretation is that there is communication at a distance as soon as a measurement is made on one part of the entangled setup. That is just a particular interpretation, and I am certainly not the only person in the universe who makes that interpretation. Are you suggesting that this is any more "speculative" than other interpretations? If so, feel free to demonstrate that.

There's nothing in QM that implies such a thing. There are no "non local interaction" here since there's nothing that "interacts". Look closely at ALL the EPR experimental paper if you don't believe me. You will notice that not one of them indicates that "forces" are non-local. So it is your interpretation of the results that is faulty here.

I think you misunderstand the forces part. For instance if we make a correlation on photon observables we are dealing with electro-magnetic forces correct? Or are you suggesting that a photon as a particle has unique properties that are not related to electro-magnetism?

Try this one. I have an object A that is stationary, and has no angular momentum. At some time, it explodes into 2 separate pieces that fly off in opposite directions. At a later time, I capture one of the pieces and found out that it has an angular momentum L1. Immediately I know exactly the angular momentum of the other piece L2.

There's nothing quantum mechanical here. In fact, it is purely classical. Are you telling me that in this case, there is a "non-local" force that went from one of the pieces to the other? Everything after the instant of measurement here is identical to the EPR/QM experiment.

Well in my interpretation, at the quantum level, we don't deal with objects at all. It s not "Newtonian" mechanics, and trying to make it look like that will obviously give "paradoxes".

In EPR we make a statistical correlation of the measurements of different observables. The superposition "knows" the result of the first measurement.
However there is no "force" involved as you suggest I claim. I do not claim that at all. But the complete quantum state is spread out over space, it is therefore non-local.

 

[ZapperZ]

I did not say that and that is not my position at all.
My interpretation is that there is communication at a distance as soon as a measurement is made on one part of the entangled setup. That is just a particular interpretation, and I am certainly not the only person in the universe who makes that interpretation. Are you suggesting that this is any more "speculative" than other interpretations? If so, feel free to demonstrate that.

"communication" at a distance is FAR from being able to be connected to "forces". You have made that connection between the entanglement of observables with "forces". Somehow, you continue to ignore this connection that isn't made in all the EPR papers. That is why I continue to ask you to show this explicit connection.

I think you misunderstand the forces part. For instance if we make a correlation on photon observables we are dealing with electro-magnetic forces correct? Or are you suggesting that a proton as a particle has unique properties that are not related to electro-magnetism?

No, I measure an observable. The fact it happens to be the polarization of a photon is irrelevant. I could easily measure the momentum of a neutrino if I can make that observable in that system be strongly entangled. So then what? What's the "force" you are dealing with here?

Look again at the description of an entangled system. WHERE is the "force" mediating between the entangled particles?

Well in my interpretation at the quantum level we don't deal with objects at all. The is not "Newtonian" mechanics.
In EPR we make a statistical correlation of the measurements of different observables. The superposition "knows" the result of the first measurement.
However there is no "force" involved as you suggest I claim. I do not claim that at all. But the complete quantum state is spread out over space, in it therefore non-local.

Then why in hell did you say these?

Well to me it seems that all forces work non-local.
Locality seems only relevant when there is some sort of scattering, which I see as a space-time event where two (or more) particles happens to interact. The other forces kind of "hover" above space-time directing the probability of the location of the particle.

I would say pretty much every force that require some sort of wave function.

Well EM waves in the EPR experiment for instance.

So you now claim that I am the one who suggested this? You made an explicit connection that there are "EM waves" in EPR experiment, and now you are saying that there's no such forces in such a scenario?

Oy vey.

Zz.

 

[MeJennifer]

It simply seems that we have a fundamentally different interpretation about what those elementary particles are.

To me they are waves, they are not little "balls".
So to explain paths by some sort of Newtonian mechanics does not make sense, and it actually does not work.
Look at momentum, can anybody with a straight face explain to me how a particle could have a momentum that is an imaginary number in space-time? Or a fractional spin?

I think a wave interpretation makes more sense, waves that spread out over time and operate non-locally.

 

[ZapperZ]

It simply seems that we have a fundamentally different interpretation about what those elementary particles are.

To me they are waves, they are not little "balls".
So to explain paths by some sort of Newtonian mechanics does not make sense, and it actually does not work.
Look at momentum, can anybody with a straight face explain to me how a particle could have a momentum that is an imaginary number in space-time? Or a fractional spin?

I think a wave interpretation makes more sense, waves that spread out over time and operate non-locally.

This seems completely irrelevant to the current discussion.

*I* can tell you how "particles" can have fractional spin via emergent properties. That is how we set up the Laughlin wavefunction in describing the fractional charge and fractional quantum hall effect.

You still have not produced a single citation on how you are justified in connecting the non-locality of quantum entanglemnt with non-locality of "forces", or are you adament in insisting that (i) you never made such claims or (ii) you no longer want to make that connection?

Zz.

 

[MeJennifer]

You still have not produced a single citation on how you are justified in connecting the non-locality of quantum entanglemnt with non-locality of "forces", or are you adament in insisting that (i) you never made such claims or (ii) you no longer want to make that connection?

When we talk about EPR with photons for instance we talk about forces. photons represent forces!
It seems you misunderstood me, I don't claim that some unknown forces communicate at the non-local level.

So what are your thoughts about the matter, do you think photons are particles, little balls? Are they point sizes? Do they really spin? How can they have fractional spin?

I think the whole particle approach that started with Einstein was a mistake, sure we can make the math work and create any emerging property or virtual particle to "explain" it.

To me the wave approach makes much more sense. But of course I cannot prove it, but on the other hand you cannot prove it is a particle either. But I don't claim, and I suppose you don't either that we have an answer for all the questions in QM.

So then we can simply discuss this fascinating topic and even agree to disagree in a friendly and respectable way as far as I am concerned.

 

[MeJennifer]

You still have not produced a single citation on how you are justified in connecting the non-locality of quantum entanglemnt with non-locality of "forces", or are you adament in insisting that (i) you never made such claims or (ii) you no longer want to make that connection?

When we talk about EPR with photons for instance we talk about forces. photons represent forces!
It seems you misunderstood me, I don't claim that some unknown forces communicate at the non-local level.

So what are your thoughts about the matter, do you think photons are particles, little balls? Are they point sizes? Do they really spin? How can they have fractional spin?

I think the whole particle approach that started with Einstein was a mistake, sure we can make the math work and create any emerging property or virtual particle to "explain" it.

To me the wave approach makes much more sense. But of course I cannot prove it is really just waves, but on the other hand you cannot prove it is a particle either. But I don't claim, and I suppose you don't either that we have an answer for all the questions in QM.

So then we can simply discuss this fascinating topic and even agree to disagree in a friendly and respectable way as far as I am concerned.

 

[ZapperZ]

When we talk about EPR with photons for instance we talk about forces. photons represent forces!

Really?

What is the difference between the photons that you see as ordinary light, and the "photons" that are carriers of EM interaction in QED? Are you seriously telling me you see ZERO difference between the two?

It seems you misunderstood me, I don't claim that some unknown forces communicate at the non-local level.

The statements you have made that I quoted indicate otherwise.

So what are your thoughts about the matter, do you think photons are particles, little balls? Are they point sizes? Do they really spin? How can they have fractional spin?

Can you give me a citation of "fraction spin" for photon?

Secondly, please do a search on photon sizes on here. It has been discussed ad nauseum. Look in Einstein's papers, and even in QM and tell me where the property of "size" was ever associated with a photon. You might as well ask if it has a degree of saltiness.

I think the whole particle approach that started with Einstein was a mistake, sure we can make the math work and create any emerging property or virtual particle to "explain" it.

To me the wave approach makes much more sense. But of course I cannot prove it is really just waves, but on the other hand you cannot prove it is a particle either. But I don't claim, and I suppose you don't either that we have an answer for all the questions in QM.

Fine. IF you can explain qualitatively AND quantitatively (i) resonant photoemission (ii) angle-resolved photoemission and (iii) multiphoton photoemission experiments, then come talk to me that the wave picture can explain everything and as well as the photon picture. You are not the first to come this way touting such claims. But each time I asked for these people to put their money where their mouths are in coming up with a description that matches those 3 phenomena, they ran with their tails in between their legs. So I now ask you to do the same and come up with such a description to justify your claim that the wave picture is as good.

So then we can simply discuss this fascinating topic and even agree to disagree in a friendly and respectable way as far as I am concerned.

then create your own thread and not hijack an existing one. This appears to be nothing more than a diversion away from you having to justify what you have said earlier.

Zz.

 

[MeJennifer]

You are not the first to come this way touting such claims. But each time I asked for these people to put their money where their mouths are in coming up with a description that matches those 3 phenomena, they ran with their tails in between their legs.

Well frankly I am not surprised if you treat everybody the way you treat me.

then create your own thread and not hijack an existing one. appears to be nothing more than a diversion away from you having to justify what you have said earlier.

Ok, now you are simply rude, the floor is yours.

 

[ZapperZ]

Well frankly I am not surprised if you treat everybody the way you treat me.

I only treat people like that who have no qualm in making outrageous claim while being ignorant of the current understanding. To thnk that the photoelectric effect, in its primitive form, is the ONLY standard bearer for "photons" is ridiculous. The QM description has been used, and used successfully, to describe all those experiments that I've described. Where are the wave picture descriptions?

Without such a thing, how can one even begin to claim that the photon description is wrong and the wave picture is correct? It makes no rational sense.

Ok, the floor is yours.

Thank you. And you continue to ignore any of my request for citation to back any of your claims. You still don't see any difference between the QED photons and ordinary photons?

Zz.

 

[Mickey]

Light is much more likely to take a straight path. QED photons have an equal probability of taking any path to any destination (but not an equal probability of reaching any specific destination). http://jhunix.hcf.jhu.edu/~blee27/software/qedlens/index.htm

I give the floor back to whomever. :)

 

[yossell]

I think the point that momentum OR position can be made as accurately as you like is correct, but I still have some uncertainties about how the HUP should be interpreted.

This is from Feynmann, Lectures in Physics, vol III, section 1.8

"This is the way Heisenberg stated the uncertainty principle originally: if you make the measurement on any object, and you can determine the x-component of its momentum with an uncertainty dp, you cannot, at the same time, know its x-position more accurately than dx = h/dp, where h is a definite fixed number given by nature...The uncertainties in the position and momentum of a particle at any instant must have their product greater than Planck's constant".

In this version, the question as to whether the measurements are made simultaneously or at the same instant seems to be important, supporting moving finger's take on things.

Feynmann goes on to say that it is a special case of a more general uncertainty principle that 'one cannot design equipment in any way to determine which of two alternatives is taken, without, at the same time, destroying the pattern of interference'.

I'm not sure what to make of this second version (it seems pretty vague to me), but again 'at the same time' appears in its statement.

Could it be that there are variations on the uncertainty principle in the phyiscs literature and that different members have different versions in mind?

 

[ZapperZ]

I think the point that momentum OR position can be made as accurately as you like is correct, but I still have some uncertainties about how the HUP should be interpreted.

This is from Feynmann, Lectures in Physics, vol III, section 1.8

"This is the way Heisenberg stated the uncertainty principle originally: if you make the measurement on any object, and you can determine the x-component of its momentum with an uncertainty dp, you cannot, at the same time, know its x-position more accurately than dx = h/dp, where h is a definite fixed number given by nature...The uncertainties in the position and momentum of a particle at any instant must have their product greater than Planck's constant".

In this version, the question as to whether the measurements are made simultaneously or at the same instant seems to be important, supporting moving finger's take on things.

But your interpretation contradicts QM. How do you explain the significance of the commutating relations of observables in QM? Why would it matter if A or B operates on a wavefunction FIRST?

The very fact that AB is not identical to BA implies that the "order" of operation is crucial. If A and B can be determined simulaneously in a single measurement, then A and B commutes! You have this for non-degenerate plane wave states and you measure the momentum and get the energy at the same time, because p and E commutes! But tell me how you would measure p and x "simultaneously". In the paper that moving finger cited, you'll notice that they are using the same single-slit scenario where the momentum is determined AFTER the slit. Is this what we are all calling "simultaneous"?

Feynmann goes on to say that it is a special case of a more general uncertainty principle that 'one cannot design equipment in any way to determine which of two alternatives is taken, without, at the same time, destroying the pattern of interference'.

I'm not sure what to make of this second version (it seems pretty vague to me), but again 'at the same time' appears in its statement.

Could it be that there are variations on the uncertainty principle in the phyiscs literature and that different members have different versions in mind?

Again, this is a confusion between HUP and superposition principle. When you have the ability of a particle to go through a number of paths, QM description describes this as a superposition of all possible paths. This is not the HUP. HUP and superposition are two different, but connected, phenomena of QM.

Zz.

 

[yossell]

Dear Zz

"Your Interpretation contradicts QM"
Well, I didn't mean to endorse any particular interpretation in my post (I was trying to be very non-confrontational. Apologies if I seemed rude). I was merely quoting Feynman about HUP, and his words do seem to support this interpretation. But it may be that Feynman has mis-spoken here or that there are different versions of the principle in the literature.

But it's not just Feynmann: A.I.M. Rae, Quantum Mechanics (Undergraduate Text book): "This relation is known as the Heisenberg Uncertainty Principle. According to quantum mechanics it is a fundamental property of nature that any attempt to make simultaneous measurements of position and momentum are subject to this limitation". p.12.
Bohm: Quantum Theory, section 3 "On the Interpretation of the Uncertainty Principle", says "the momentum and position cannot even exist with simultaneously and perfectly defined values".

This isn't meant to tell against your own interpretation of HUD at all - but there's an indication that, at least in some of the serious literature, the explanation of the principle does seem to be sympathetic with the thought that it's the simultaneous possession or discovery of such quantities that is ruled out by the HUP.

Indeed there are parts of these books that support Zz's view: when Rae enters into a more mathematical discussion in terms of commutators (pp 71-2), he talks of a series of measurements rather than individual measurements, and simultaneity seems to disappear from his discussion. He introduces something called 'the generalised uncertainty principle', but the generality seems to come from the fact that it involves observables other than position and momentum - which wouldn't wholly explain the difference.

I agree that there's no experiment to measure p and x simultaneously - if there were, QM would be in trouble - but that's completely compatible with the version of HUP in terms of simultaneity. Indeed, if there were such an experiment, then that version of HUP would be untenable. Certainly, this version of the HUP seems compatible with the experiments you cite earlier showing that we can find the position and then the later momentum of an object with arbitrary accuracy. Since the object has these properties at different times, there is no conflict.

I do take your point that the signficance of the commutation relations needs explaining on the earlier view and it's not obvious what the right thing to say here is. Could it be that there is a difference between the time at which an experiment takes place and the information the experiment tells us about the time at which an object possessed a particular property? For instance, in the case of two compatible physical observables, if one quantify is measured a subsequent measurement of the other quantity will have a completely predictable result and will leave the wave function unchanged (or so my textbook tells me). Since the quantities are compatible, the later measurement merely reveals the property the system had all along. Indeed, the later measurement was actually unecessary since the quantity could have been predicted from the original measurement. In this case, Quantum mechanics allows us to know the simultaneous possession of the two observables. In cases of non-commuting operators, however, since the wavefunction changes on the second measurement we no longer have reason to think suppose that the measurement is non-disturbing and thus that we are merely revealing a property that the system had all along.

If this makes sense, then it may well be that different interpretations of HUP sit with different interpretations of QM itself. If one has something like a collapse interpretation, and one thinks that the only properties that an object determinately has are the ones given by the eigenfunctions of that state, then it may be that the interpretation of HUP involving simultaneity makes sense. If one has something like an ensemble interpretation of QM, which some comments of yours suggested you held, then it may be that the best way to make sense of HUP is in terms of repeated experiments on similarly prepared systems.

But I say this with no great confidence, and your challenge on how to interpret non-commuting observables is a good one.

Best