Photons, particles and wavepackets

[OOO]

How then do you explain "interference" patterns from single slits?

I think you got me wrong. It's become a fairly long thread now so it's forgivable that you don't have the thread start in mind anymore. But jostpuur initially talked about putting a wall congruent to the plane between both slits so as to assure that no photon crosses the plane. If you have just one slit then of course you will have interference according to the circumstances of a one-slit experiment. Is that what you meant ?

 

[OOO]

Probability is a measure of the quality of information our mind has about reality, not a reflection of reality.

As far as quantum mechanics is concerned I guess most people would say you're wrong and probability amplitude in quantum mechanics does indeed reflect some physical reality independent of the observer. If this was simply probability in the sense of the maximum entropy compatible with observation then how would you explain the complex probability amplitude ? If you have some solution to this problem, I'd be grateful if you explained it to me.

 

[mn4j]

As far as quantum mechanics is concerned I guess most people would say you're wrong and probability amplitude in quantum mechanics does indeed reflect some physical reality independent of the observer. If this was simply probability in the sense of the maximum entropy compatible with observation then how would you explain the complex probability amplitude ? If you have some solution to this problem, I'd be grateful if you explained it to me.

Could you be kind to define the word "probability". Say the word slowly "probable...ity". There is no physical entity as a probability amplitude. Call it something else, so long as it is a probability amplitude, it is not a real "thing". The fact that the probable outcome of an experiment matches the physical outcome when dealing with an ensemble system does not mean the two are the same.

If you throw a die a single time, only one phase will show, yet you can talk of a probability for each phase showing (6 values). It does not mean the expectation value, which is a probability distribution (what you call a wavefunction or probability amplidue) is a real thing. It is a mathematical description of our uncertainty. The only situation in which it gets close to anything real is when you throw an infinitely large number of dice. You will find that the observed histogram matches the wavefunction of a single die. Even though each die only shows a single face. In other words, the wavefunction of a single particle, is a good mathematical description of how an ensemble of particles will behave, rather than a physical description of an individual particle.

That is why the double slit pattern appears one speck at a time but a large number of particles builds up the pattern. Interpreting the wavefunction as though it were the physical nature of individual particles is not science but metaphysics. That is why nobody has ever explained why the wavefunction collapses at point A and not point B

The first sentence of the wikipedia article on the subject of "probability amplitude" describes it quite well.

Have you ever seen a quantum explanation of a single-slit experiment?

 

[OOO]

Could you be kind to define the word "probability". Say the word slowly "probable...ity". There is no physical entity as a probability amplitude. Call it something else, so long as it is a probability amplitude, it is not a real "thing". The fact that the probable outcome of an experiment matches the physical outcome when dealing with an ensemble system does not mean the two are the same.

If you throw a die a single time, only one phase will show, yet you can talk of a probability for each phase showing (6 values). It does not mean the expectation value, which is a probability distribution (what you call a wavefunction or probability amplidue) is a real thing. It is a mathematical description of our uncertainty. The only situation in which it gets close to anything real is when you throw an infinitely large number of dice. You will find that the observed histogram matches the wavefunction of a single die. Even though each die only shows a single face. In other words, the wavefunction of a single particle, is a good mathematical description of how an ensemble of particles will behave, rather than a physical description of an individual particle.

That is why the double slit pattern appears one speck at a time but a large number of particles builds up the pattern. Interpreting the wavefunction as though it were the physical nature of individual particles is not science but metaphysics. That is why nobody has ever explained why the wavefunction collapses at point A and not point B

The first sentence of the wikipedia article on the subject of "probability amplitude" describes it quite well.

Have you ever seen a quantum explanation of a single-slit experiment?

I did know what probability is before you told me. Only I don't know what you're trying to tell me. Quantum mechanics describes physics by means of probability amplitudes. Period.

If you got some more clever way to describe nature but by using probability amplitudes then feel free to tell us.

By the way, what do you precisely mean by "quantum explanation of a one-slit experiment" ? Is that something different than a "quantum explanation of a one-slit-and-a-bump-on-the-edge-experiment" ?

 

[mn4j]

I did know what probability is before you told me. Only I don't know what you're trying to tell me. Quantum mechanics describes physics by means of probability amplitudes. Period.

Yes, quantum mechanics is a mathematical model of the behavior of nature. Yes you can solve a lot of problems in nature by using probability amplitudes. But it doesn't mean the probability amplitudes are physical entities. That is what I'm trying to tell you. Probability means just that -- probability: a mathematical tool for doing inference from incomplete information. Period.

If you got some more clever way to describe nature but by using probability amplitudes then feel free to tell us.

No I don't. But questioning the establishment is a step in the right direction. All progress in physics starts with a critical look at the establishment. If we are expected to form new theories before questioning existing ones, there will never be progress. Besides I don't question QM. It is a great mathematical tool. I question the prevailing physical interpretation of the mathematics. The fact that the mathematics works does not validate any interpretation of it.

By the way, what do you precisely mean by "quantum explanation of a one-slit experiment" ? Is that something different than a "quantum explanation of a one-slit-and-a-bump-on-the-edge-experiment" ?

However you choose to call it, do you have any pointers to a quantum explanation of single-slit experiments with photons/electrons etc.

 

[jostpuur]

Just because you don't know the source of a photon does not mean it does not come from a particular source.

I agree to some extent, and understand the confusion.

merely saying "you cannot know where the photon came from" doesn't make the whole point clear, pedagogically ...

... The symmetry of the wave function, according to the Bose statistics, makes the explanation complete.

If you are interested to understand why independently emitted photons interfere, which you seemingly do not yet understand because you don't yet seem to believe in the probability concept of QM, you can find the explanation in my post #37

This thread was about one particular kind of experiment, its outcome, and its explanation. There is no point in leading the discussion to the foundations of the QM.

 

[OOO]

Yes, quantum mechanics is a mathematical model of the behavior of nature. Yes you can solve a lot of problems in nature by using probability amplitudes. But it doesn't mean the probability amplitudes are physical entities. That is what I'm trying to tell you. Probability means just that -- probability: a mathematical tool for doing inference from incomplete information. Period.

No I don't. But questioning the establishment is a step in the right direction. All progress in physics starts with a critical look at the establishment. If we are expected to form new theories before questioning existing ones, there will never be progress. Besides I don't question QM. It is a great mathematical tool. I question the prevailing physical interpretation of the mathematics. The fact that the mathematics works does not validate any interpretation of it.

However you choose to call it, do you have any pointers to a quantum explanation of single-slit experiments with photons/electrons etc.

I guess I didn't claim anywhere that a probability amplitude is a sort of physical entity. But on the other hand I believe it is a valid point of view to think of the wave function as a physical entity the square of which is "accidentally" a measure for the probability for what happens in a certain context.

In this sense, one day, we could probably find the reason why there is such parallelism between the actual physical field (the wave function) and the fact that it can trigger a stochastic process with well defined transition probabilities. (we need not extend the discussion to the relation between the terms "physical field" and "wave function", I know about gauge invariance and probably there are some other issues with it, but I think that's not relevant here)

So I think we are not so far apart regarding our skepticism against quantum mechanics. It seems you're tending more towards particles as the fundamental reality whereas I'd prefer the field and collapse viewpoint. But arguing about these views is futile as long as nobody of us has a mathematical formulation that expresses one of these views clearly.

It's fine to question the establishment but one always has to keep in mind that every alternative must be at least as powerful in explaining reality as the established theories.

 

[Demystifier]

I guess I didn't claim anywhere that a probability amplitude is a sort of physical entity. But on the other hand I believe it is a valid point of view to think of the wave function as a physical entity the square of which is "accidentally" a measure for the probability for what happens in a certain context.

In this sense, one day, we could probably find the reason why there is such parallelism between the actual physical field (the wave function) and the fact that it can trigger a stochastic process with well defined transition probabilities.

We already know (a possible) reason for that: Bohmian mechanics.

 

[OOO]

We already know (a possible) reason for that: Bohmian mechanics.

I like Bohmian mechanics but I think it is a bit optimistic to say that it solves the problems discussed here. I guess that was the reason why you put "possible" in parentheses.

For example I know of no consistent relativistic formulation of Bohmian mechanics. So how do you explain particle creation and annihilation with it. And by the way it doesn't explain the collapse of the "guidance field" either. As far as I know it just serves to demonstrate that quantum mechanics does not contradict permanent localization of particles.

 

[Demystifier]

For example I know of no consistent relativistic formulation of Bohmian mechanics. So how do you explain particle creation and annihilation with it. And by the way it doesn't explain the collapse of the "guidance field" either. As far as I know it just serves to demonstrate that quantum mechanics does not contradict permanent localization of particles.

Bohmian mechanics DOES explain the EFFECTIVE collapse of the guidance field, provided that environment induced decoherence is also taken into account.

Concerning relativistic formulation and particle creation/destruction, there are several inequivalent approaches, so the things are not yet settled. In my opinion, the most promising approach is the one pushed forward in
http://xxx.lanl.gov/abs/0705.3542
See also Refs. [16] and [3] for other approaches.

 

[OOO]

Bohmian mechanics DOES explain the EFFECTIVE collapse of the guidance field, provided that environment induced decoherence is also taken into account.

Concerning relativistic formulation and particle creation/destruction, there are several inequivalent approaches, so the things are not yet settled. In my opinion, the most promising approach is the one pushed forward in
http://xxx.lanl.gov/abs/0705.3542
See also Refs. [16] and [3] for other approaches.

I have started to read this paper (I assume it is yours ?) but I get drowned in scepticism when I read such things as "there is no position operator in QFT". How can you have a position operator in a field theory ? If you want to describe a position measurement then you have to define position in terms of the fields, i.e. find some state that represents localized fields. Is it that what you mean with "there is no position operator in QFT" ?

 

[OOO]

In my opinion, the most promising approach is the one pushed forward in
http://xxx.lanl.gov/abs/0705.3542

As far as I can see this paper doesn't do much more than define trajectories from currents. That's of course what the Bohm approach always does and it is ideed interesting. But nothing is said about the coupling between gauge fields and fermions.

So where is there any justification for the claim that this is a promising approach for replacing QFT ?

 

[OOO]

Bohmian mechanics DOES explain the EFFECTIVE collapse of the guidance field, provided that environment induced decoherence is also taken into account.

There seems to be no support for such a claim. Can you cite some references where it is explained in detail how such a collapse should work ?

 

[rewebster]

Do you know the story I mentioned in my post #106 in the “cat in a box paradox” session?

I am not sure about his name (I think P.Wood; my first book on ED at high school was written by him). He was in the middle of the measurements. The performance severely degraded due to dust on the internal surfaces and the tubes were about 11-14 m long. Project! He took the cat, put him inside, thus to show the completely deterministic way out. After 10 min he continues the measurements.

Regards, Dany.

Those DARN dust bunnies!----ahh, maybe there's a dust bunny in the box with the 'cat'

 

[Anonym]

Yes, quantum mechanics is a mathematical model of the behavior of nature. Yes you can solve a lot of problems in nature by using probability amplitudes. But it doesn't mean the probability amplitudes are physical entities. That is what I'm trying to tell you. Probability means just that -- probability: a mathematical tool for doing inference from incomplete information. Period.

I don’t agree with you. QM is not a mathematical model of the behavior of nature; QM is the adequate physical theory in the non-relativistic limit. The probability amplitudes are just unsuccessful terminology pushed through by N.Bohr and you clearly explained why in your posts #129 and #151 “cat in a box paradox” session.

But the terminology is not a matter, call it as you wish. Your problem is that you should obtain the image of the extended object and you have only the points available to do that (it is possible, C.Monet demonstrated that). The nature uses the repeatability and indistinguishability. There is no correlation between the individual samples; they are integral inseparable part of the overall picture.

Using the standard QM terminology I would say that the particle density is the real and therefore observable quantity. And I see no essential difference between the electron wave function and the electromagnetic potentials.

Regards, Dany.

 

[Demystifier]

So where is there any justification for the claim that this is a promising approach for replacing QFT ?

In this paper, I argue that a Bohmian description of particle creation/destruction requires strings. It is well known that strings can replace QFT.

 

[Demystifier]

I have started to read this paper (I assume it is yours ?) but I get drowned in scepticism when I read such things as "there is no position operator in QFT". How can you have a position operator in a field theory ? If you want to describe a position measurement then you have to define position in terms of the fields, i.e. find some state that represents localized fields. Is it that what you mean with "there is no position operator in QFT" ?

No. Nonrelativistic QM should be derivable from relativistic QFT. Therefore, there should exist a position operator that corresponds to localized PARTICLES, not localized fields. See Ref. [1] in the paper for more details.

 

[Demystifier]

There seems to be no support for such a claim. Can you cite some references where it is explained in detail how such a collapse should work ?

See any paper on Bohmian mechanics that includes the THEORY OF MEASUREMENT.
Perhaps this is best explained in the P. Holland's book "The Quantum Theory of Motion". But even the original Bohm's paper (part II) contains it. An even better explanation is provided also in the review
D. Bohm and B. J. Hiley, Phys. Rep. 144, 323 (1987).
Note that these works do not use the word "decoherence", as this word become popular only later. But if you are familiar with the theory of decoherence, you will recognize it in these papers.

 

[OOO]

No. Nonrelativistic QM should be derivable from relativistic QFT. Therefore, there should exist a position operator that corresponds to localized PARTICLES, not localized fields. See Ref. [1] in the paper for more details.

In QFT particles are described by fields. So where is the difference between localized fields and localized particles ? They're just two different names for the same underlying theoretical description. At least if you are referring to QFT and not to some other theory.

 

[OOO]

In this paper, I argue that a Bohmian description of particle creation/destruction requires strings. It is well known that strings can replace QFT.

In this age it seems to be that strings can predict almost anything you want. If this is what you're looking for then you are certainly going to be a happy fellow compared to all those nerds who try to explain the outcomes of experiments. Nevertheless, just mentioning the buzzword strings doesn't help in clarifying anything.

 

[Demystifier]

In QFT particles are described by fields. So where is the difference between localized fields and localized particles ? They're just two different names for the same underlying theoretical description. At least if you are referring to QFT and not to some other theory.

This is not that simple. For example, in nonrelativistic QFT, you CAN introduce a state that corresponds to a localized particle. You can also introduce a state that corresponds to a localized field. However, these two states are VERY different. In particular, the former is a 1-particle state, whereas the latter is a coherent state with an indefinite number of particles. So no, particles and fields are NOT just two different names for the same thing.

 

[Demystifier]

In this age it seems to be that strings can predict almost anything you want. If this is what you're looking for then you are certainly going to be a happy fellow compared to all those nerds who try to explain the outcomes of experiments. Nevertheless, just mentioning the buzzword strings doesn't help in clarifying anything.

Now you shifted your original objection to a (common) objection against string theory. I will not dwell into a discussion for and against strings, because it would belong to the "Beyond the Standard Model" subforum, not this subforum. Let me just note that, in my paper, I indicate how, with a Bohmian-like reformulation of quantum theory, string theory could be tested at low energies, at the level of Standard-Model particles.

 

[OOO]

This is not that simple. For example, in nonrelativistic QFT, you CAN introduce a state that corresponds to a localized particle. You can also introduce a state that corresponds to a localized field. However, these two states are VERY different. In particular, the former is a 1-particle state, whereas the latter is a coherent state with an indefinite number of particles. So no, particles and fields are NOT just two different names for the same thing.

I don't know why you're so keen on nonrelativistic theory, it's just an approximation.

Let's talk more specifically about "relativistic" gauge theory. You have a wave functional that assigns to every gauge field configuration a complex number which you could consider as defining the probability density for having that gauge field configuration:

\Psi: A\to \Psi[A] with \Psi^*[A]\Psi[A]= probability density to find configuration A

So if you have detected a grain of silver on your photographic plate, you know definitely that the gauge field must have been in some configuration A_0 that was localized around the site of your grain of silver somewhere during or immediately after producing the latter.

So your wave functional \Psi[A] which has originally contained the possibility for many different gauge field configurations has now collapsed to a wave functional \Psi_0[A] such that

\Psi[A] = \left\{ \begin{array}{cr} \infty &amp; \qquad A=A_0 \\<br /> 0 &amp; \qquad otherwise \end{array}\right.

where I have introduced a symbolical definition of a "delta-function over function space".

Now where is the need to define something like a position operator here ? If you like to, you may define position as the weighted average of the usual position operator "x" over the electromagnetic energy of your localized gauge field configuration A0:

\bar{x}[A_0]=\frac{\int x T^{00}(F(A_0)) d^4 x}{\int T^{00} d^4 x}

You will not be surprised that this provides you with the position of your grain of silver. So what further insight does this give you ?

 

[Demystifier]

OOO, I think you do not understand what I am talking about. But I will give you a hint. You said that nonrelativistic theory is an approximation. Fine! Now how would you DERIVE nonrelativistic QM as an approximation from your (correct) equations above?

 

[OOO]

OOO, I think you do not understand what I am talking about. But I will give you a hint. You said that nonrelativistic theory is an approximation. Fine! Now how would you DERIVE nonrelativistic QM as an approximation from your (correct) equations above?

There was another thread recently where someone cited a reference on that topic. Unfortunately I can't find it, maybe you can.

Of course my equations above are by no means complete.

But thinking about it in terms of path integrals I'd say you have to take the limit of classical field theory (h to 0) where you obtain the condition that the classical action becomes stationary (the usual thing about phases oscillating rapidly except for the classical path). So you haven't got a wave functional anymore but classical fields.

From the classical field equations it gets quite easy I think, see Bjorken Drell. Sketch: approximate frequency by compton frequency + delta, drop second order terms, redefine the electric potential by absorbing rest mass. Et voilà, you got the Schrödinger equation. So the classical fields described by it define your position in the same sense as the (probabilistically distributed) fields did in the full quantum field theory.

 

[jostpuur]

where I have introduced a symbolical definition of a "delta-function over function space".

btw. wouldn't notation

<br /> \delta^{\mathbb{R}^3}(A-A&#039;) = \prod_{x\in\mathbb{R}^3} \delta(A(x)-A&#039;(x))<br />

be logical? It would work like this

<br /> \int\mathcal{D}A&#039;\;\delta^{\mathbb{R}^3}(A-A&#039;)\Psi[A&#039;] = \Big(\prod_{x\in\mathbb{R}^3} \int dA&#039;(x) \delta(A(x)-A&#039;(x))\Big)\Psi[A&#039;] = \Psi[A]<br />

It could help to use notation A_x = A(x) also.

 

[Demystifier]

There was another thread recently where someone cited a reference on that topic. Unfortunately I can't find it, maybe you can.

Of course my equations above are by no means complete.

But thinking about it in terms of path integrals I'd say you have to take the limit of classical field theory (h to 0) where you obtain the condition that the classical action becomes stationary (the usual thing about phases oscillating rapidly except for the classical path). So you haven't got a wave functional anymore but classical fields.

From the classical field equations it gets quite easy I think, see Bjorken Drell. Sketch: approximate frequency by compton frequency + delta, drop second order terms, redefine the electric potential by absorbing rest mass. Et voilà, you got the Schrödinger equation. So the classical fields described by it define your position in the same sense as the (probabilistically distributed) fields did in the full quantum field theory.

In this way, you will obtain the Schrodinger equation. But how will you recover the probabilistic interpretation of the solutions of the Schrodinger equation? You should not postulate it, but derive from the probabilistic interpretation of QFT. So, how exactly you will do that?

 

[OOO]

btw. wouldn't notation

<br /> \delta^{\mathbb{R}^3}(A-A&#039;) = \prod_{x\in\mathbb{R}^3} \delta(A(x)-A&#039;(x))<br />

be logical? It would work like this

<br /> \int\mathcal{D}A&#039;\;\delta^{\mathbb{R}^3}(A-A&#039;)\Psi[A&#039;] = \Big(\prod_{x\in\mathbb{R}^3} \int dA&#039;(x) \delta(A(x)-A&#039;(x))\Big)\Psi[A&#039;] = \Psi[A]<br />

It could help to use notation A_x = A(x) also.

Yes of course, that's what I meant to say with my short hand notation.

 

[jostpuur]

I would very much like to see how to derive the one particle wave function

<br /> \Psi:\mathbb{R}^3\to\mathbb{C},<br />

its equation of motion, and its probability interpretation, by starting from the field wave functional

<br /> \Psi:X^{\mathbb{R}^3}\to\mathbb{C},<br />

its equation motion, and its probability interpretation. (X defines what is the value of the classical field. It can be X=\mathbb{R},\mathbb{C},\mathbb{R}^4,\ldots or something else.)

 

[jostpuur]

Yes of course, that's what I meant to say with my short hand notation.

Have you seen this notation a lot already? If so, you wouldn't bother mentioning some sources? I mean, I have not seen this anywhere yet.