# New Twist on Double Slit

1. Dec 25, 2006

### dtfroedge

Double Slit
For those who appreciate this experiment for being the simplest demonstration of the essence of quantum mechanics, I would like to throw a modification into the scheme that I haven’t seen before. I don’t know the answer to this or how to approach explaining it, in terms of conventional QM. It may have been noted earlier by others, if so my apologies. I’m hopeful this forum can elucidate the issue.

The content will also be posted on:
http://www.arxdtf.org/css/slit.pdf [Broken]
And if there are any good responses I’ll add them there also.
Preface:
Paul Dirac, The Principles of Quantum Mechanics, Fourth Edition, Chapter 1
Some time before the discovery of quantum mechanics people realized that the connection between light waves and photons must be of a statistical character. What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place. The importance of the distinction can be made clear in the following way. Suppose we have a beam of light consisting of a large number of photons split up into two components of equal intensity. On the assumption that the beam is connected with the probable number of photons in it, we should have half the total number going into each component. If the two components are now made to interfere, we should require a photon in one component to be able to interfere with one in the other. Sometimes these two photons would have to annihilate one another and other times they would have to produce four photons. This would contradict the conservation of energy. The new theory, which connects the wave function with probabilities for one photon gets over the difficulty by making each photon go partly into each of the two components. Each photon then interferes only with itself. Interference between two different photons never occurs.​

Let us consider not necessarily a slit. But a pair of radio dipoles being driven by a signal generator at a frequency of say, 100 k hertz. The radio pattern generated at a distant point perpendicular to the dipole being the classical double slit.

So as per Dirac The photons generated in the signal generator:

Note Dirac:
The new theory, which connects the wave function with probabilities for one photon gets over the difficulty by making each photon go partly into each of the two components. Each photon then interferes only with itself. Interference between two different photons never occurs.​

Now let us make a couple of modifications:

1) The signal 100 k hertz generator is being counted down from a cesium clock with a stability of 1 second in 20 million years so the phase is accurate and stable to one wave wavelength per 200 years.

2) The generator for second dipole is replaced with an identical generator with a cesium clock, that is in no way connected to, or coupled with the first.​

I think we all agree that there will still be a double slit pattern, rather than the single slit sum. One could disagree with this but I don’t think its really in question. Because of the time stability of the generators the pattern will be constant, at least for a period of many years.

The argument that a photon interferes with it self to create the pattern does not quite hold true in this system, since photons generated by the first generator have no opportunity or probability to exit through the second dipole. In no way are the photons correlated, but the double slit pattern exists. Photons going off at a particular angle from the first dipole cease going in that direction when the second transmitter is activated, yet the photons are not correlated.

Most of the usual arguments regarding the probability distribution including that by Dirac don’t apply.

So what your best explanation for this? DTF

Last edited by a moderator: May 2, 2017
2. Dec 26, 2006

### Hans de Vries

For recent proof of two photon interference see here:

http://arxiv.org/abs/quant-ph/0603048

Which was published in PRL 96, 240502 (2006) and mentioned in this thread:

I feel strongly that the outcome of this experiment is of essential importance
in finding the right interpretation of Quantum Mechanics. From the standard
result:

If one photon enters a beamsplitter it will be detected only at one
of the two outputs, either one but not at both outputs at the same time.

One finds in this experiment:

If two equal photons enter a beamsplitter at the same time, at
different inputs, (there are two inputs), there will only be something
detected at one of the two outputs, either one, but there won't be
detected anything at both outputs at the same time.

This is the so-called Hong-Ou-Mandel-type (HOM) interference.
The effect disappears if the two photons have different polarization.

Regards, Hans

Last edited: Dec 26, 2006
3. Dec 26, 2006

### dtfroedge

Hans:
I am in agreement with you. I was unaware of the paper and thread you cited, but the thought experiment in my original post, would obviously yield the same results as noted in paper by Kaltenbaek et al.

I presume that others may have noted it, but Kaltenbaek e tal, seem to have missed the point as to the basis of the Dirac quote, which is conservation of energy. If two photons can interfere, energy is destroyed and energy is only conserved in the average, a concept flatly rejected by the founders of quantum mechanics. In addition it certainly complicates the two slit diffraction of massive particles.

Explaning this is going to take someone a click or so, above my skill level. If it is acceptable with you I would like to add your comment to the pdf I am keeping at:
http://www.arxdtf.org/css/slit.pdf [Broken]
DTF

Last edited by a moderator: May 2, 2017
4. Dec 26, 2006

### Hans de Vries

Dirac is talking about the so called "Old quantum mechanics" which did not
use the concept of probability:

This energy conservation argument does not apply to any theory which
interprets the wave function as a probability amplitude. He then goes on
to introduce the "New quantum mechanics"

The statement that a photon can only interfere with itself was still an
(unproved) assumption by the time Dirac wrote his book. Experiments
such as the one by Kaltenbaek et al. indicate that it is not so likely to
be true.

Regards, Hans.

P.S. Feel free to add anything from this discussion to your document.

Last edited: Dec 26, 2006
5. Dec 26, 2006

### cesiumfrog

In this situation you still consider only one photon at a time, but it could have come from either generator, and so you see that corresponding interference. I personally wouldn't really call it two-photon-interference. If you turn the intensity down until only one photon (not two) is measured per minute (say), I think we'll agree the pattern is still there.

I'd personally call a phenomena two-photon interference if it demonstrably occured only when two photons are both propogating through at the same time. I'm not aware of any such phenomena (in fact, I don't know if linearity of the SE prohibits it), despite the titles of several published experiments. Or maybe it is only a choice of interpretation/semantics?

6. Jan 7, 2007

### dtfroedge

Double Slit
Good Elf:
I don't see how photons coming from separate generator can be "born in the same causal event". The generators can be built independently, located separately, and so long as the phase relation between the generators is constant, which will be true if their frequencies are exact, a two slit pattern will be generated . From the dipole there will be an angle, where there is a photon flux, when one generator is on, but is absent a photon flux, when both generators are on. If at a given angle there is never a flux it seems to me that the photons didn't just add up, but added out
To me this is just magic. non local action at a distance is easy to say but is just a word substitute for "I don't have a clue". I don't think this is what Dirac had in mind when he stated that photons only interfere with themselves. How two generators potentially miles apart can conspire to generate a single photon that interferes with itself in a slit pattern does not make sense.

What it says is to me is as in the Bell experiment, we understand the math, we don't understand the phenomena. Like the Bell inequality, and the "Aharonov-Bohm Effect" the math is simple, but thats all that is simple.

The essence of responsive posts to this thread are being posted on:

http://www.arxdtf.org/css/slit.pdf [Broken]
DTF

DTF

Last edited by a moderator: May 2, 2017
7. Jan 8, 2007

### Hans de Vries

The claim of the author that the Aharonov Bohm effect is
something "entirely non-local" is incorrect. In fact
there's absolutely nothing special with this effect.

The Aharonov Bohm effect states that a charged particle
will acquire extra phase (or less phase) in a potential
field V or magnetic vector field A.

We can see this if we combine pre-Quantum Mechanical
relativistic electrodynamics, which gives for the energy
and momentum of a classical electron in potential fields
V and A: (Jackson 12.33)

$$E\ =\ mc^2 + eV, \qquad p\ \ =\ mv + eA/c$$

With the most elementary expressions in QM, relating energy
and momentum with the de Broglie frequency and wavelength:

$$E\ =\ hf, \qquad p\ \ =\ h/\lambda$$

The origins of these erroneous "non-local" ideas come from the
fact that V and A can be non-zero even though E and B are
zero on the path of the electron. The phase shift caused by
V or A will cause visible effects in interference experiments.
The claim is then that the effect is determined non-locally by
E and/or B from a distant location where they are not zero.
This is of course wrong. V and A are more fundamental in QM
as E and B.

Regards, Hans

Last edited: Jan 9, 2007
8. Jan 9, 2007

### dtfroedge

Hans:
Thanks for the correction, sometimes we engage our keybord before our mind. DTF

9. Jan 10, 2007

### Hans de Vries

Hi, DTF

I hope there's no misunderstanding here. I wasn't referring to you but to the
one who wrote these rather bold claims of non-locality in regards with the
Aharanov Bohm effect on PhysOrg forums.

Regards, Hans.

10. Jan 10, 2007

### hellfire

In the paper "Understanding Electromagnetism" that can be found http://www.pitt.edu/~gbelot/Papers/papers.htm#_Papers_1 [Broken], it is mentioned that to describe the Aharonov-Bohm effect it is need anyway a non-local theory. This is argued more or less as follows. Two different positions outside the solenoid are only differentiated by the value of the vector potential. On the one hand, one cannot adscribe physical reality to every different value of the potential, because this would differentiate between values related by a gauge transformation and this would make the theory indeterministic. On the other hand, there is actually some physical effect going on in the B = 0 region so that the vector potential can produce somehow observable effects. Starting from the requirement to put gauge orbits and physical states in a one-to-one relation, one wants therefore to find out the right configuration space. This turns out to be the set of holonomies of the potential around closed curves, which are non-local objects.

Last edited by a moderator: May 2, 2017
11. Jan 10, 2007

### Hans de Vries

The author of this philosophy paper makes the following claim:
What he calls interpretation no.1: The vector potential as a physical field.
(The common interpretation) is then claimed to be both indeterministic
AND nonlocal....... The non locality claim is based on this:

Well, It was already shown in 1900 by Lienard & Wiechert who calculated
the potential and electromagnetic fields of an arbitrary moving (accelerating)
charge that:

The V&A (vector) potential is to be taken as more fundamental as the
E&B fields. To obtain the correct E&B fields one must presume that V&A
propagate away with speed c from the originating charge. By differentiating
the so obtained V&A potentials in the usual way they derived the correct
fields. (They did so in the Lorentz gauge)

The V&A potentials as derived by Lienard & Wiechert are always single valued.

Now V&A always uniquely determine E&B, but not the other way around.
E can be both the result of dV/dx or dA/dt. One could induce an electric
field E in a loop with a changing vector field (dA/dt) and then claim a
potential V which is multivalued (indeterminate) by integrating over the loop
one or more times.

This is what led to the indeterminate claim. However, as said, The V&A
potentials as derived by Lienard & Wiechert are always single valued.

Regards, Hans

Last edited by a moderator: May 2, 2017
12. Jan 10, 2007

### hellfire

So you say that you take the interpretation 1, assuming physical reality of the potential field, and eliminate the indeterminism by fixing the Lorenz gauge, that you take as the "correct" one, plus some boundary conditions. Did I understand right? By the way, I did not cite the paper as an authority to support any claim, sorry if I gave that impression. I just read it some days ago and was a bit confused about it.

Last edited: Jan 10, 2007
13. Jan 10, 2007

### Hans de Vries

Indeed

That's OK. Well, It's rather long, 36 pages in "philosophy" style, There are
many reasonable remarks in the paper as well but I highlighted the point
which is in conflict with mainstream physics: The instantaneous propagation
of the potentials.

The multivalued issue of the potentials is more often seen, sometimes
in relation with "not simply connected vacuum topologies" With Lienard
& Wiechert there is no need for this. Interesting note is that the field
outside the long solenoid is small but never totally zero:

http://en.wikipedia.org/wiki/Solenoid#Derivation_of_magnetic_field_around_a_long_solenoid

Regards, Hans

Last edited: Jan 10, 2007