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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:

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:

Now let us make a couple of modifications:

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

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.

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.

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

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