Why does an observer affect the electron?

[Farsight]

I for one don't know, ron. But this Lamb Shift on a bound electron is pretty interesting.

http://www.llnl.gov/str/May06/Beiersdorfer.html

"The Lamb shift is a tiny difference in the energy of an ion’s electron between two quantum states that are otherwise identical except for the shape of the electron’s orbit around the nucleus. Because of this dissimilarity in the electron’s orbit in the two states, the electron interacts slightly differently with virtual particles—photons, positrons, and electrons—that appear and disappear in quantum fluctuations. The resulting energy difference, called the Lamb shift, can be measured when the electron jumps from one energy level to another..."

 

[Norman Albers]

How close do the slits have to be to get notable interference? Is this momentum-dependent? . . . . Results of my wave packet study: when you Fourier analyze the Gaussian packet, you do get a delta function in k at the propagation value. what you also get is a nice smooth spread in transverse stuff a la e^-(k_T^2)

 

[RandallB]

question. The double slit experiment is carried out in a vacuum so ... particles don't get in the way.
So what about the so called quantum foam, ...

The double slit is not always done in a vacuum, Light experiments do not use a vacuum, and even if glass is put in front of one, or the other, or both slits the pattern is still displayed.
(Note that since the glass is transparent no information is gained from it to say which slit was used either.)
So in the case of an electron one could assume that whatever ‘quantum foam’ is; it must be ‘transparent’ to the electron as far as the slit experiment is concerned.

 

[spinfusion]

Returning to the central question

Most laymen are interested in this question because they want to know whether or not the universe is fundamentally deterministic. I am a laymen with background in philosophy and debate, and it is sometimes frustrating to read scientific types debating this question, because they often miss each others’ arguments, use idiosyncratic definitions, shift ground, etc.

Essentially, I agree with JesseM. HUP is a measurement uncertainty built into the laws of physics for simultaneously knowing momentum and location of quantum particles, because “observation” alters one if not both of the measured properties.

I see no philosophical reason to conclude from this impossibility of simultaneous measurement that matter is fundamentally probabilistic. On the other hand, I would not want scientists to complicate their formulas by positing a fundamentally unknowable exact location and momentum for quantum particles (waves, whatever).

I can’t pretend to answer the determinism question. But I have my theory, and I’m trying to reconcile it with the facts of this dual-slit electron experiment.

Here’s how I understand the indeterminacy crowd’s explanation of the slit anomaly: The electron alters its state from indeterminate to determinate upon coming into contact with matter, photons, etc. In the absence of these constraints, it spreads in a probability wave.

Since I don’t believe in indeterminacy, I must believe that there is a wave-to-particle, deterministic explanation for why no interference pattern is produced when one slit is observed.

I can visualize why one slit does not produce a spread, and why two slits produces an interference pattern. But I don’t understand why one slit observed and one unobserved doesn’t produce at least some interference. Shouldn’t the electron begins spreading into waves again immediately after contact with the photons? Even if their momentum or frequency is different than the unobserved slit’s electrons, shouldn’t there still be interference?

Thanks in advance for your answers.

 

[spinfusion]

Update:

I began reading up on QM in the almighty Wikipedia. The debate between Einstein and Bohr was fascinating.

All my reading has not convinced me that any scientific data compels acceptance of the indeterminacy school. However, I have learned to accept the impossibility of visualizing quantum phenomenon, which I now realize have nothing to do with my "visual" understanding of time, space, and locality.

Wow, what a universe.

 

[ZapperZ]

Most laymen are interested in this question because they want to know whether or not the universe is fundamentally deterministic. I am a laymen with background in philosophy and debate, and it is sometimes frustrating to read scientific types debating this question, because they often miss each others’ arguments, use idiosyncratic definitions, shift ground, etc.

You are forgetting that when scientists debates, we base our definition and principles on well-defined, unambiguous underlying mathematical description. There's nothing "idosyncratic" here. It is up to you to make the effort in understanding the mathematics to be able to figure out what is being talked about.

For example:

I can visualize why one slit does not produce a spread, and why two slits produces an interference pattern.

This is wrong. There IS a spread when electrons pass through ONE slit - it's called diffraction, something that I have used to illustrate the HUP. You have confused and mixed two different aspect of quantum mechanics - the HUP and the superposition principle. One can use the single slit diffraction (which I have many times) as a manifestation of the HUP, but the double slit is a manifestation of superposition, in this case, superposition of paths!

You need to be able to understand the physics involved here, first and foremost, before coming up with a "theory".

Zz.

 

[wavemaster]

Though I'm aware of HUP is talking about standard deviation, I'm curious about one thing. So I'd like to raise this question: in what precision can we measure position and momentum of one, single electron. Feel free to talk in terms of eigenstates and wavefunction collapse.

 

[selfAdjoint]

Though I'm aware of HUP is talking about standard deviation, I'm curious about one thing. So I'd like to raise this question: in what precision can we measure position and momentum of one, single electron. Feel free to talk in terms of eigenstates and wavefunction collapse.

See https://www.physicsforums.com/showthread.php?p=1044897#post1044897" discussion by ZapperZ and others about that issue

 

[Prince of Quarkness]

But this doesn't mean that I have the ability to predict the outcome of the NEXT measurement, even when I have equipment to accurately determine both position AND momentum.

But isn't there a point to be made here that position and momentum do not commute, ie: are not compatible, and so there's no meaning to saying that 'particle A has position (x,y,z) and momentum (Px, Py,Pz) at time t'.

Now that isn't _quite_ the HUP, since the (necessarily statistical) concept of Uncertainty isn't used.

But surely it does still represent a fundamental incompatibility between position and momentum, which isn't present in classical theory? So although it's a mislabelling to call it the HUP, the HUP is a result of that non-commuting property and so the terminological mistake isn't all that heinous.

-Dave

 

[ZapperZ]

But isn't there a point to be made here that position and momentum do not commute, ie: are not compatible, and so there's no meaning to saying that 'particle A has position (x,y,z) and momentum (Px, Py,Pz) at time t'.

But not commuting does mean you can't measure them with some degree of accuracy. Again, I will point out to the single-slit scenario. The only thing that affects the accuracy of my measurement of the position of the particle is the slit width, and the only that that affects the accuracy of my measurement of the momentum after it passes through the slit is the pixel size of the CCD.

However, since the position and momentum do not commute, my ability to tell you the momentum of the particle that passes through the slit depends intimately on the slit size. The smaller I make the slit size (I know the position even more), the less certain I can tell you its transverse momentum. Why is this not the HUP?

Zz.

 

[selfAdjoint]

Zapper, the single slit is clear in these discussions but explanation of it it not sufficient to pin down the phenomena around position/momentum non-commutativity and uncertainty. See the discussion and links on the "Delayed Choice Quantum Eraser" in the thread on Brian Greene's Beam Splitter Experiments.

 

[ZapperZ]

Zapper, the single slit is clear in these discussions but explanation of it it not sufficient to pin down the phenomena around position/momentum non-commutativity and uncertainty. See the discussion and links on the "Delayed Choice Quantum Eraser" in the thread on Brian Greene's Beam Splitter Experiments.

I have been following that, but I don't see the relevance here.

Maybe everyone is seeing it from the perpective of the THEORY and trying to make physical sense out of it. I don't. I approach it from the IDEAL measurement/experimental angle. How would I measure the x-position of a particle, and then measure the x-momentum of the particle? All I see here is that the accuracy of my position is dictated by the size of the slit, and the accuracy of the momentum is dictated by how well I can determine where the particle hit my detector. I know this can be done because I've done it! Now the accuracy of my prediction of the momentum is an entirely different beast.

Now, is there an "explanation" to such a thing beyond the QM description? How does one do that without delving into the various flavors of QM formulation and interpretation, which inevitably boils down, at least for now, to a matter of tastes?

Zz.

 

[Prince of Quarkness]

However, since the position and momentum do not commute, my ability to tell you the momentum of the particle that passes through the slit depends intimately on the slit size. The smaller I make the slit size (I know the position even more), the less certain I can tell you its transverse momentum. Why is this not the HUP?

I must be getting confused about the flow of the debate.

I thought that you had asserted that the HUP is meaningful only when considering groups of particles, when here you've just said that if you measure the position of a single particle more accurately, you are less certain of it's momentum.

I think what I've missed is that you're saying that the HUP doesn't reduce the accuracy of measurements, simply the accuracy of _predicting_ the results of, say, the momentum of a particle whose position has been measured.

i.e: Would I be right in saying that your issue here is that people are conflating the width of a gaussian wavefunction in momentum space with the width of the gaussian produced by experimental accuracies?

Would I be re-wording your own statements if I said that an exact measurement of position is entirely possible within the theory, but it is subsequently impossible to _predict_ the momentum, though it can be _measured_ with arbitrary precision?

-Dave

 

[ZapperZ]

I must be getting confused about the flow of the debate.

I thought that you had asserted that the HUP is meaningful only when considering groups of particles, when here you've just said that if you measure the position of a single particle more accurately, you are less certain of it's momentum.

I think what I've missed is that you're saying that the HUP doesn't reduce the accuracy of measurements, simply the accuracy of _predicting_ the results of, say, the momentum of a particle whose position has been measured.

i.e: Would I be right in saying that your issue here is that people are conflating the width of a gaussian wavefunction in momentum space with the width of the gaussian produced by experimental accuracies?

Would I be re-wording your own statements if I said that an exact measurement of position is entirely possible within the theory, but it is subsequently impossible to _predict_ the momentum, though it can be _measured_ with arbitrary precision?

-Dave

In the other thread, I stated that there is a difference between measuring "x" and "p", and measuring \Delta(x) and \Delta(p). The latter is what is contained in the HUP. There's no ambiguity or even confusion here, correct?

Next, each of the Delta's require a statistical averaging. It includes the square of the average value, and the average of a square value. This explicitly implies a statistical ensemble. OK so far?

If things so far have not caused anyone to have any constipation, then I don't see why what I have said earlier on the HUP would rouse any curiosity. Because if we buy what the mathematical description of the HUP has to say, then we know that

the HUP is a statistical experession of how well we know about the values of a pair of non-commuting observables when we know one of them to a particular certainty.

I make a measurement of x. The uncertainty is the width of the slit, let's say, which is \Delta(x). Now, when I let it hit my detector, it will make a spot of a finite size. Since the location determines the momentum (such as that used in angle-resolved photoemission spectroscopy), then the CENTER of the spot is p, but the uncertainty in p is roughly the width of the spot. HOwever, and this is very important, this is NOT the uncertainty \Delta(p) that is in the HUP. Why? Because if I make my CCD and detection better, I could get a cleaner signal (that's what people do sometime, by cooling the detector to LHe temperature to reduce thermal fluctuation). So already we know that the instrument uncertainty can be reduced INDEPENDENTLY of the \Delta(x). This doesn't smell or look like the HUP, and it isn't!

So where is \Delta(p)? You make repeated measurement of the identical system. Shoot another, and another, and another, of the same particle prepared identically. Since your slit width doesn't change, your \Delta(x) remains the same. However, the value of p that you measure may not be identical. In fact, if you make the slit small enough, the value of p will scatter all over the place! If you collect enough sampling of the values of all these p's, you will find not only the average value, but also a spread in the statistical variance of this value. This is the \Delta(p) in the HUP!

If you apply this to what we know about statistics, the larger the value of \Delta(p), then the less are we able to predict with a reasonable accuracy the value of p that we will get when we shoot the next identical particle. In fact, go to the extreme where the slit width is a delta function and you'll get a flat distribution of the value of p, which means your \Delta(p) is infinite. The next value of p can attain any value imaginable.

This relationship is consistent with what we know of the HUP between two non-commuting observable.

Not sure if I've explained myself clearly enough, but I hope that is the last time I have to do that.

Zz.

 

[Prince of Quarkness]

Thanks for explaining that, and I'm now sorry to have put you to the trouble of saying it again. I quite agree with your stance.

-Dave

 

[ZapperZ]

Thanks for explaining that, and I'm now sorry to have put you to the trouble of saying it again. I quite agree with your stance.

-Dave

Well, if it makes just one person to finally understand what I was trying to get across, it was well worth it.

:)

Zz.

 

[gptejms]

Zz,tell me if
i) a single electron has a well defined x & p in your scheme of things?

ii)the wavefunction of a single particle has any meaning from your POV?--I mean do you believe that the wavefunction describes a multitude of particles or that it corresponds to a single particle?

 

[ZapperZ]

Zz,tell me if
i) a single electron has a well defined x & p in your scheme of things?

Before those are measured, no.

After they are measured, yes.

ii)the wavefunction of a single particle has any meaning from your POV?--I mean do you believe that the wavefunction describes a multitude of particles or that it corresponds to a single particle?

Note that in QM, you don't just write the wavefunction of a SINGLE particle - you have to know the potential geometry that it is in. I happen to know quite a bit about "single-particle" formalism, because in many-body systems, you reduce one intractable many-body problem into many one-body problem. This is where you get the single-particle spectral function.

So yes, you can write the "wavefunction" of one particle, or the wavefunction of a number of particles (assuming you have the ability to solve the Hamiltonian). I don't quite see how that relates to anything I have said.

Furthermore, I'm not so sure why this is my "POV". Can you point out to me which part of what I've said isn't consistent with the QM you get out of your textbooks?

Zz.

 

[Doc Al]

I think gptejms was asking if you thought the wavefunction describes the state of an individual particle or an ensemble of similarly prepared particles. (I don't think he was asking about many-particle systems.)

 

[ZapperZ]

I think gptejms was asking if you thought the wavefunction describes the state of an individual particle or an ensemble of similarly prepared particles. (I don't think he was asking about many-particle systems.)

Then I'm not sure if I understand that, because would that makes a difference?

For example, if I say that the probability of something to occur is 1/2, it means that if I perform it once, I would get a 50% chance of getting something. However, this could also mean that if I perform it on 100 identical system, I'd get half of them in the state that I want.

So is there any difference if it's just one or many, especially when they are non-interacting?

Zz.

 

[Doc Al]

Then I'm not sure if I understand that, because would that makes a difference?

For example, if I say that the probability of something to occur is 1/2, it means that if I perform it once, I would get a 50% chance of getting something. However, this could also mean that if I perform it on 100 identical system, I'd get half of them in the state that I want.

It makes a difference if you are talking about interpretations of quantum mechanics, which was the point of the question (I think). Much electronic ink has been spilled in this forum on such issues, but I'll just say that one major division of interpretations could be:

"Copehagen" Interpretation: Here the wavefunction is interpreted as describing all there is to know about the individual systems that it describes: If a property (such as the position of the particle) is not described by the wavefunction, it doesn't exist or is meaningless to talk about.​

Statistical Ensemble Interpretation: This is a kind of minimalist interpretation wherein the wavefunction provides statistical properties only; the state vector applies (abstractly) to the ensemble, not the individual system.​

As I understand it, the ensemble interpretation is agnostic about the existence of properties of individual systems that go beyond what's described by the wavefunction. The main proponent of this interpretation today is Leslie Ballentine of Simon Fraser University. (L. E. Ballentine: The Statistical Interpretation of Quantum Mechanics. Rev.Mod.Phys. 42 (1970) 357) His textbook, "Quantum Mechanics, A Modern Development" (1998), is excellent. (You'd love his treatment of the uncertainty principle!)

My opinion: As a (former) experimentalist, I gravitate towards the statistical interpretation; it's lean, mean, and carries little metaphysical baggage. (Much of the nonsense written today about QM--even in textbooks!--is a direct result of taking the Copenhagen philosophy too seriously.) Of course, to attempt to go beyond "orthodox" QM and explain what's "really" going on you'll need more: That's where all the action is with regard to the many other interpretations out there. (Bell, Bohm, EPR, MWI, RQM, and many more...)

So is there any difference if it's just one or many, especially when they are non-interacting?

Again, that's not what's being referred to here.

 

[Prince of Quarkness]

I fail to see how the 'statistical interpretation' could have any hope of resolving the philosophical difficulties of QM.

If the wavefunction is merely a description of ensemble properties, then what are we to make of the single-photon diffraction experiment? It's true that we can't build up a picture of the probabilities involved until we've fired several photons through there - so are we talking about an ensemble constructed across time?

How does the individual photon know where it fits in the ensemble? Maybe there isn't an ensemble, and it's the only one that's going to pass through the slits. At which point we're back to saying that it has a certain probability of striking the screen at a certain point, and we're back in Copenhagen.

Am I missing the point completely?

-Dave

 

[ZapperZ]

It makes a difference if you are talking about interpretations of quantum mechanics, which was the point of the question (I think).

Ah, then that's why I didn't get it, because I wasn't doing anything remotely close to making any kind of interpretation. As you can see, I was describing the HUP from the "practical" standpoint - you measure one observable, and the next. My incursion into this thread was to clarify this fallacy that people continue to have regarding the HUP based upon what CAN be measured, not to make any kind of philosophical interpretation. I'm sure you are well aware of how much I dislike doing that.

Zz.

 

[Doc Al]

I fail to see how the 'statistical interpretation' could have any hope of resolving the philosophical difficulties of QM.

I encourage you to look at Ballentine's review article for a start.

If the wavefunction is merely a description of ensemble properties, then what are we to make of the single-photon diffraction experiment? It's true that we can't build up a picture of the probabilities involved until we've fired several photons through there - so are we talking about an ensemble constructed across time?

I think you misunderstand the meaning of "ensemble" in this context. An ensemble is a theoretical infinite set of all systems that could result from the same state preparation procedure. For the photon diffraction experiment, a system is a single photon going through the slits; the ensemble is the conceptual set of a zillion replicas of a photon going through indentical slits. An ensemble is not a "beam" of particles. (Of course, since the photons do not interact, for practical purposes we can treat a beam of photons as providing an ensemble. Certainly a collection of identical one-photon experiments done one at a time will be a good approximation to an ensemble.)

How does the individual photon know where it fits in the ensemble?

Good question! To answer that, you'll have to ask your interpretation. The statistical interpretation would say that the answer is beyond the scope of standard QM, since QM only describes ensembles of systems, not individual systems. Copenhagen would say, in effect, that the system is completely described by the wavefunction--that the particle has no location, for one thing, until the wavefunction "collapses" (for some reason) when a "measurement" is made--when the photon hits the screen. The statistical interpretation would say that there is no justification for the mysterious "collapse of the wavefunction" or for strange statements such as "the particle goes through both slits" (or neither slit) or perhaps doesn't even exist until it is "observed".

Maybe there isn't an ensemble, and it's the only one that's going to pass through the slits.

Again, an ensemble is a theoretical construct for predicting probabilities.

At which point we're back to saying that it has a certain probability of striking the screen at a certain point, and we're back in Copenhagen.

Again, Copenhagen wants to go beyond mere statistical predictions about ensembles. (See my comments above or look at Ballentine's paper or textbook.)

Note that I am not saying that the "statistical interpretation" is the final word--far from it! I think other interpretations that go beyond standard QM can do better. (But that's another story.)

 

[Pythagorean]

I fail to see how the 'statistical interpretation' could have any hope of resolving the philosophical difficulties of QM.

I gravitate towards the statistical interpretation; it's lean, mean, and carries little metaphysical baggage.

[quote="ZapperZ]...not to make any kind of philosophical interpretation. I'm sure you are well aware of how much I dislike doing that.[/quote]

as you can see, philosophical questions (about physics) are generally irrelevant to physicists.

 

[gptejms]

Before those are measured, no.

So,it's meaningful to talk of uncertainty for a single particle.Though,the single particle's uncertainty is quantified by studying an ensemble of identically prepared particles(or by doing a calculation).

After they are measured, yes.

Isn't this somewhat like collapse--uncertainty before making a measurement,no uncertainty after the measurement?

Let me point out one more thing here.In your single slit experiment,you measure the momentum of the particle not at the same time as you measure its position.You get to know the delta x at the slit itself,while you get to know the delta p later when the particle hits a certain spot on the screen.This does not mean that the particle has uncertainties delta x and delta p at the slit.At the slit delta p is much bigger where the particle could have gone to any of the (bright) spots on the screen.

 

[ZapperZ]

So,it's meaningful to talk of uncertainty for a single particle.Though,the single particle's uncertainty is quantified by studying an ensemble of identically prepared particles(or by doing a calculation).

Yes, why not?

When you solve the simple harmonic oscillator problem in undergrad QM class, how many particles did you think you were solving for? What does that "m" in the Schrodinger equation represent? An ensemble of particle?

Isn't this somewhat like collapse--uncertainty before making a measurement,no uncertainty after the measurement?

I've always illustrated my HUP via a measurement. I do, however, note that our ability[/b\] to predict the next measurement is strictly governed by the HUP.

Let me point out one more thing here.In your single slit experiment,you measure the momentum of the particle not at the same time as you measure its position.You get to know the delta x at the slit itself,while you get to know the delta p later when the particle hits a certain spot on the screen.This does not mean that the particle has uncertainties delta x and delta p at the slit.At the slit delta p is much bigger where the particle could have gone to any of the (bright) spots on the screen.

In the Heisenberg thread, I have already addressed this issue of "simultaneous" measurement. Can you tell me how, in an ideal measurement, it would change had I made my detector to be 1 micron after the slit, 1 cm after the slit, 1 meter after the slit, etc..? Can you also tell me how you would make a "simultaneous" measurement and where exactly is this necessary in the HUP in such a way that it does make a difference?

Zz.

 

[gptejms]

Yes, why not?

When you solve the simple harmonic oscillator problem in undergrad QM class, how many particles did you think you were solving for? What does that "m" in the Schrodinger equation represent? An ensemble of particle?

I had the impression that you thought that the (Heisenberg)'uncertainty of a single particle' was meaningless--and that it was meaningful only if it were a measurement/instrumentation uncertainty.If that's not the case,then fine--no problem!

(as a side remark---I don't differentiate between the two uncertainties)

In the Heisenberg thread, I have already addressed this issue of "simultaneous" measurement. Can you tell me how, in an ideal measurement, it would change had I made my detector to be 1 micron after the slit, 1 cm after the slit, 1 meter after the slit, etc..? Can you also tell me how you would make a "simultaneous" measurement and where exactly is this necessary in the HUP in such a way that it does make a difference?

Zz.

Since I have not understood your question(s) or what you are driving at,I leave it for you to answer.

 

[ZapperZ]

I had the impression that you thought that the (Heisenberg)'uncertainty of a single particle' was meaningless--and that it was meaningful only if it were a measurement/instrumentation uncertainty.If that's not the case,then fine--no problem!

(as a side remark---I don't differentiate between the two uncertainties)

It is meaningless in the sense that people apply it blindly no matter what the situation is. Refer again to the single-slit example that I have described

https://www.physicsforums.com/showpost.php?p=1046959&postcount=64

Here the uncertainty in position is dictated by the slit width. But the uncertainly in momentum is not apparent from just ONE single measurement of one single particle going through the slit. You need to do this for many particles. However, even when one particle goes through the slit, your ability to accurately predict its momentum does depend on the HUP. So even when you do not have a quantitative value of the momentum uncertainty simply from measuring one single momentum from that one particle, the HUP still plays a role here even without you knowing it. It is only apparent to you after you see the particles hitting not at the same spot all the time.

The point that I've been trying to get across all along is that you can have definite value of position, and you can have definite values of momentum, for a single particle. There's nothing physically to prevent me from making the slit as small as I can so that I know at some point, a particle passed though that slit (so I know the position of that particle very well), and then after the particle has passed though the slit, to measure where it hits the detector and get the momentum value. These are all technologically possible. Both x and p are WELL-DEFINED AFTER MY MEASUREMENT for this single particle, having accuracies that only depends on my instrumentation (my slit width, and the pixel density of my CCD camera).

Zz.

 

[gptejms]

The point that I've been trying to get across all along is that you can have definite value of position, and you can have definite values of momentum, for a single particle. There's nothing physically to prevent me from making the slit as small as I can so that I know at some point, a particle passed though that slit (so I know the position of that particle very well), and then after the particle has passed though the slit, to measure where it hits the detector and get the momentum value. These are all technologically possible. Both x and p are WELL-DEFINED AFTER MY MEASUREMENT for this single particle, having accuracies that only depends on my instrumentation (my slit width, and the pixel density of my CCD camera).

Zz.

Re your last statement:Are both x and p really well defined after the measurement?I don't think so--one measurement(that of x) is made at the slit,the other(that of momentum at the screen)--so are they really well defined at any stage?

 

[ZapperZ]

Re your last statement:Are both x and p really well defined after the measurement?I don't think so--one measurement(that of x) is made at the slit,the other(that of momentum at the screen)--so are they really well defined at any stage?

But that's what I asked you in that previous post that you said you didn't understand. I asked would it make any difference if I had my detector 1 micro after the slit, 1 cm after the slit, 1 meter after the slit... etc?

Note that if you think it does matter, then all those ARPES measurement that measure the momentum of the photoelectrons after they leave the material's surface would be inaccurate, because they place their detector at various distances away from the photoemitter. This means that my avatar (which has appeared in PRL) is wrong in showing the electron's momentum in the horizontal axis.

Zz.

 

[gptejms]

Note that if you think it does matter, then all those ARPES measurement that measure the momentum of the photoelectrons after they leave the material's surface would be inaccurate, because they place their detector at various distances away from the photoemitter. This means that my avatar (which has appeared in PRL) is wrong in showing the electron's momentum in the horizontal axis.

Zz.

Is this your argument:-

From the spot where the particle hits the screen,we conclude that the particle would have had 'such and such(definite) momentum' at the slit.We use this to build the argument that since different particles hit at different spots,the uncertainty at the slit is \Delta p(for a particle that is yet to pass thru the slit).

If the above argument is correct,then it is justified to extrapolate the momentum measurement at the screen back to the slit and say that 'this' particle really had a well defined(almost) x as well as p at the slit.

 

[ZapperZ]

Is this your argument:-

From the spot where the particle hits the screen,we conclude that the particle would have had 'such and such(definite) momentum' at the slit.We use this to build the argument that since different particles hit at different spots,the uncertainty at the slit is \Delta p(for a particle that is yet to pass thru the slit).

If the above argument is correct,then it is justified to extrapolate the momentum measurement at the screen back to the slit and say that 'this' particle really had a well defined(almost) x as well as p at the slit.

I don't know about that last part. All I can say is that unless there's something weird going on, the particle that hit the detector to allow for momentum measurement has a well-defined momentum at the moment of measurement. Could I then say that if I had put the detector closer to the slit, it would have had that same momentum? I don't see why not, or why this would matter. This is because if I were to do this for many particles, the end result (i.e. getting p and \Delta(p)) would yield the same answer no matter where I put the detector.

Zz.

 

[gptejms]

I don't know about that last part.

What last part?

 

[ZapperZ]

Last part of your message - the last paragraph, the last point, the last whatever...

Zz.

 

[gptejms]

But I built up the whole argument in post 82 to come to a conclusion which I thought you held(the last part).After all you said 'Both x and p are WELL-DEFINED AFTER MY MEASUREMENT for this single particle, having accuracies that only depends on my instrumentation (my slit width, and the pixel density of my CCD camera)'.

'AFTER MY MEASUSEREMENT' is implied in my last part.

 

[ZapperZ]

But I built up the whole argument in post 82 to come to a conclusion which I thought you held(the last part).After all you said 'Both x and p are WELL-DEFINED AFTER MY MEASUREMENT for this single particle, having accuracies that only depends on my instrumentation (my slit width, and the pixel density of my CCD camera)'.

'AFTER MY MEASUSEREMENT' is implied in my last part.

Not in between the slit and the detector. The measurement of p isn't complete, which is what you were asking when you said:

"If the above argument is correct,then it is justified to extrapolate the momentum measurement at the screen back to the slit and say that 'this' particle really had a well defined(almost) x as well as p at the slit."

Till I measure it at the detector, there are no well-defined momentum. However, a subtle but slightly differernt issue is, AFTER I measure that momentum, would it (that particle+system) have given me a different value had I had the detector in a different position? This is where I hazzard a guess as being a yes, or not a meaningful question that can make a difference.

Zz.

 

[gptejms]

Not in between the slit and the detector. The measurement of p isn't complete, which is what you were asking when you said:

"If the above argument is correct,then it is justified to extrapolate the momentum measurement at the screen back to the slit and say that 'this' particle really had a well defined(almost) x as well as p at the slit."

There are two parts to post no. 82 which I've numbered below:-

"1. From the spot where the particle hits the screen,we conclude that the particle would have had 'such and such(definite) momentum' at the slit.We use this to build the argument that since different particles hit at different spots,the uncertainty at the slit is 'such and such'(for a particle that is yet to pass thru the slit).

2. If the above argument is correct,then it is justified to extrapolate the momentum measurement at the screen back to the slit and say that 'this' particle really had a well defined(almost) x as well as p at the slit."

If point 1 is right then so must 2 be--that's what one would expect.But yes,it's more subtle than that.It's as if the measurement at the screen forces the particle to have had a certain momentum at the slit(kind of delayed choice!).Had I made a measurement at another point,the answer could have been different.

 

[eep]

I just wanted to point out that Feynman says pretty much the same thing that ZapperZ's saying in the Feynman Lectures, as I think he was mentioned in this thread earlier. He says something along the lines that yes, you can make the momentum measurement after the particle passes through the screen and hits the detector, and you can say this particle must have had such-and-such a momentum after it passed through the slit in order to arrive at the spot on your detector. But that doesn't matter, because the HUP concerns predictions about the future - you're not predicting anything after you've already measured the position of the photon on the screen and gotten your momentum. Thank you ZapperZ for clearing away some misconceptions about the HUP - it's easy to get confused!

 

[ZapperZ]

There are two parts to post no. 82 which I've numbered below:-

"1. From the spot where the particle hits the screen,we conclude that the particle would have had 'such and such(definite) momentum' at the slit.We use this to build the argument that since different particles hit at different spots,the uncertainty at the slit is (for a particle that is yet to pass thru the slit).

2. If the above argument is correct,then it is justified to extrapolate the momentum measurement at the screen back to the slit and say that 'this' particle really had a well defined(almost) x as well as p at the slit."

If point 1 is right then so must 2 be--that's what one would expect.But yes,it's more subtle than that.It's as if the measurement at the screen forces the particle to have had a certain momentum at the slit(kind of delayed choice!).Had I made a measurement at another point,the answer could have been different.

Here's the problem with #1. You have 2 non-commuting operators A and B. If you measure A, you have only "collapsed" the wavefuction only for that observable. The value of B could still be in superposition. This is what is going on in the Schrodinger Cat-type experiments such as those done in the Delft/Stony Brook experiments. You measure a non-commuting observable in other to detect the superposition in the other.

Or use something out of a QM textbook. Lz does not commute with Lx and Ly. You make a measurement of Lz, but Lx and Ly are still undertermined and still in a superposition of all the various states.

This is why I said that the momentum is undertermined until you measure it at the detector/screen. But once I measured it, I make the assumption that this particular particle made a classical trajectory from the slit to the detector to be able to calculate its momentum (more precisely, its transverse momentum).

Zz.

 

[gptejms]

Let me just add that the measurement at the screen is that of position i.e. the spot where the particle hits---from this we infer that the momentum of the particle was 'this' at the slit.

Here's the problem with #1. You have 2 non-commuting operators A and B. If you measure A, you have only "collapsed" the wavefuction only for that observable. The value of B could still be in superposition. This is what is going on in the Schrodinger Cat-type experiments such as those done in the Delft/Stony Brook experiments. You measure a non-commuting observable in other to detect the superposition in the other.

Right, and that's why the uncertainty principle is for simultaneous measurements.

This is why I said that the momentum is undertermined until you measure it at the detector/screen. But once I measured it, I make the assumption that this particular particle made a classical trajectory from the slit to the detector to be able to calculate its momentum (more precisely, its transverse momentum).

Zz.

At the end of it all,I don't know where we differ and where we agree!

I guess the only difference is that you seem to differentiate between Heisenberg uncertainty and measurement uncertainty whereas I don't--for me all uncertainties are measurement uncertainties.Unmeasured is anyway uncertain.

 

[ZapperZ]

Let me just add that the measurement at the screen is that of position i.e. the spot where the particle hits---from this we infer that the momentum of the particle was 'this' at the slit.

Right, and that's why the uncertainty principle is for simultaneous measurements.

But I don't understand this "simultaneous" stuff. The momentum is measured AFTER the particle passed through the slit, i.e. after the position measurement.

Can you show me an example of a "simultaneous" measurement, and why this is necessary between AB or BA?

At the end of it all,I don't know where we differ and where we agree!

I guess the only difference is that you seem to differentiate between Heisenberg uncertainty and measurement uncertainty whereas I don't--for me all uncertainties are measurement uncertainties.Unmeasured is anyway uncertain.

Because I can have a perfect detector that has zero uncertainty in where the particle hits it and still have a spread of statistics as I do this repeatedly. Furthermore, and this is the major distinguising factor here, the measurement uncertainty are independent of each other. I can make them arbitrarily accurate without caring what the other is doing, because it depends on my technology.

So the instrument uncertainty and the HUP are not of the same beast.

Zz.

 

[gptejms]

But I don't understand this "simultaneous" stuff. The momentum is measured AFTER the particle passed through the slit, i.e. after the position measurement.

Momentum was not measured,but the position at which the particle hit the screen.From that it was calculated that the particle would have had 'this' momentum at the slit.So the measurement(s) refer to x & p (simultaneous)values at the slit.Because the spot on the screen that's hit varies from particle to particle(there is a \Delta p) uncertainty at the slit.

It may not always be possible however to infer the momentum in an indirect way and if you do that by some other means later,you would be disturbing the original value--in that case it would not qualify as a simultaneous measurement(measurement of simultaneous values may be a better terminology)

A gamma ray microscope may be better qualified for the job of simultaneous measurements in the literal sense.

Because I can have a perfect detector that has zero uncertainty in where the particle hits it and still have a spread of statistics as I do this repeatedly. Furthermore, and this is the major distinguising factor here, the measurement uncertainty are independent of each other. I can make them arbitrarily accurate without caring what the other is doing, because it depends on my technology.

So the instrument uncertainty and the HUP are not of the same beast.

Zz.

I see your point for 'measurement of simultaneous values' case in the sense described above.

For a simultaneous measurement(in the literal sense) as in gamma ray microscope,x & p values are uncertain (even) after measurement.

 

[ZapperZ]

Momentum was not measured,but the position at which the particle hit the screen.From that it was calculated that the particle would have had 'this' momentum at the slit.So the measurement(s) refer to x & p (simultaneous)values at the slit.Because the spot on the screen that's hit varies from particle to particle(there is a \Delta p) uncertainty at the slit.

But this is rather dicey in calling it a "simultaneous measurement". I certainly won't. I would be more comfortable in simply calling it what it is, a measurement of position, and then a measurement of momentum. That description accurately reflects what is being done, rather than what one likes it to be.

Zz.

 

[Prince of Quarkness]

as you can see, philosophical questions (about physics) are generally irrelevant to physicists.

Thanks for that, but two years of undergraduate physics here at Imperial has clued me into the vast prevalence of cool-headed empiricism in the physics community.

There's a lot to be said for your direct Popperian science - examine observations, make hypothesis to explain observations and predict new ones, test hypothesis, rinse, repeat. Indeed, this is the meat and potatoes of scientific work and I wouldn't dream of criticising scientists for not wanting to get bogged down in questions of 'reality', 'philosophy' and all the rest.

On the other hand, at the time I posted we were discussing 'interpretations' of quantum mechanics, which are inherently philosophical creatures. One day one of them might produce a testable mathematical ramification, but at this point they are on the level of 'does the good of the many outweigh the good of the few?' rather than the level of 'what result do I get if I make my laboratory setup look like this . . .'

The answer to the latter question is provided by the QM theory itself, to an enormous degree of accuracy. Philosophical questions are left to the interpretations. And yes, even Copenhagen _is_ an interpretation, because it makes an unspecified and presently untestable distinction between 'classical-like' measuring apparatus and quantum systems themselves.

Very common among physicists is a sort of empirical 'super-Copenhagen' typified by the phrase: Shut Up And Calculate.

As I have said, there is a vast amount to be said for just getting your head down and working on the actual theories, predictions et cetera without weeks of navel-gazing in the labyrinth of Quantum Conundra that so occupy popular science writers and people wanting to look smart down the pub.

On the other hand, as Roger Penrose argues in 'The Road to Reality', some physicists are willing to take a dose of philosophy along with their empiricism, and address questions of Reality rather than just the Popperian bones of hypotheses and observations. He contests that this is a useful method, and I'd recommend the book for anyone. Particularly those who have issues with quantum mechanics, because it's very entertaining to read a man who has grave doubts about quantum ontology that aren't just based on the ever-popular cliched Schrodinger's Cat/Observer Effect pseudophilosophy.

-Proteus

 

[selfAdjoint]

Proteus, may I just inject a small belief of my own. The present state of the quantum formalism, whether in it's non-relativistic or in its most extended form, does not give us enough data to base any philosophical conclusions on.

"So geographers, o'er Afric Downs
Draw elephants, for want of towns"

 

[Prince of Quarkness]

Proteus, may I just inject a small belief of my own. The present state of the quantum formalism, whether in it's non-relativistic or in its most extended form, does not give us enough data to base any philosophical conclusions on.

Aye, and that's a common and sensible opinion.

The question then becomes, might philosophical considerations be the factor that actually leads to the required development of the formalism?

The Principle of Relativity, for example, is an expression of the idea that physics 'should' be the same in all inertial reference frames. That to me sounds like a philosophical consideration (with the required empirical backup that any consideration in physics requires), and it was one of the cornerstones that led to the eminently Popperian and empirical theory of relativity.

And perhaps its a similar consideration, treated as irrelevant by Copenhagenists and those who shun 'interpretations' altogether, that will light the way in developing quantum theory.

I will admit that this path has shown few if any results thus far - QFT seems in my limited understanding to be based on practical not philosophical concerns - ie: not worrying too much about the infinities, simply making sure that one gets rid of them mathematically before trying to make an actual prediction.

So at the moment it looks to be 1-0 to the utilitarians, with the interpretationists lagging behind. :-)

-Dave (sorry for signing out with the wrong handle last post, these things become instinctive after a few years online!)