& some thoughts about the double slit experiment

by Jeffrey H. Boyd

Abstract

This web page has two aims. First, it will sketch some ideas about the double slit experiment. There is a video on this website which also sketches the same ideas. Second, I will propose an experiment which will produce different results depending on which way the waves travel.

Those readers who are unfamiliar with the conventional explanation of the double slit experiment should click on the following link: Dr. Quantum on YouTube. That YouTube video starts out, “And here we are, the grandaddy of all quantum weirdness . . . .” With one glaring exception, that video presents all possible explanations of the double slit experiment. The exception is that Dr. Quantum does not mention the possibility that waves and particles do not necessarily travel in the same direction. In this essay we will assume that  you know the ideas that Dr. Quantum teaches.

Copyright © Jeffrey H. Boyd, 2012

I. Introduction

Consider two theories. According to Einstein, de Broglie, and their followers, waves travel in the same direction as particles. We will call that the “conventional viewpoint.” According to the Theory of Elementary Waves (TEW) that is not necessarily true. One would think it would be easy to devise an experiment that would produce different results depending on which theory is correct. That is precisely what this essay proposes to do. In the process I will also sketch some ideas about the double slit experiment.

The central concept behind the experiment I propose is that the timing of wave interference differs between the two theories. According to the conventional viewpoint interference occurs during or after the emission of the particle. According to TEW interference occurs before or as the particle is emitted. In TEW no interference that occurs after the particle is emitted has any effect on that particle and its trajectory.

Therefore it should be possible to build a gate that is open before the particle is emitted, and rapidly closes at precisely that instant when the particle is emitted. This should isolate the two forms of interference from one another. It is important that, when the gate is “open,” is must not be a source of its own elementary waves.

Figure 1

Design of the Experiment

Figure 1: This is a double slit experiment, with a laser added above the right hand slit. Particles would be emitted one at a time. Prior to a particle being emitted the laser would be “OFF” so that elementary waves from the target screen would be able to come through both slits and those waves from the left and right slit would interfere at the particle source. At that nanosecond when a particle is emitted, the laser would switch “ON.” The laser should be sufficiently powerful to knock the particle out of its trajectory, if the particle tries to go through the right-hand slit. This idea was suggested to me by Jeff Ausfeld (jeffausfeld@gmail.com).

This experiment will produce different results depending on which theory is correct. According to TEW there should still be some interference fringes on the target screen, because those particles that go through the left hand slit would previously have been affected by interference that occurred at the particle source. According to the conventional view there should be no interference fringes visible, because of complementarity: we know which slit the particle goes through, therefore we cannot see interference fringes.

II. TEW explanation

As discussed elsewhere in this website, we are immersed in an invisible sea of elementary waves. There are elementary waves of all wavelengths going from every point on the target screen, in all directions, 24 hours a day, seven days a week. These waves convey no energy. We will restrict our attention to those waves that have these characteristics: the wavelength corresponds to the energy of the particle which will be emitted at a later time. And we are interested in only those waves which penetrate the two slits. There are no plane waves. Waves from each point of the target screen are independent of waves from other points on the target screen.

Figure 2

Waves from the Target Screen Interfere at the Source

 

Figure 2: For each point “P” on the target screen there are waves penetrating the two slits. The rays through the upper and lower slit interfere at the particle source, as shown.

So far there is not a particle involved. In fact, the scientists are at home sleeping or partying, and they have not yet turned on the electricity for the experiment. Because of wave interference waves from one point P will arrive at the particle source with greater amplitude than waves from another point P’. That is why, in the final data, one sees an interference fringe pattern.

When the scientists come to work, flip on the power switch, a particle is about to be emitted from the source. The source is built in such a manner that only one particle at a time will be emitted. When a particle is emitted, it is in response to a specific elementary wave (i.e. ray) from one particular point P. The probability of a wave triggering a particle is proportional to the intensity (amplitude squared) of that ray impinging on the particle source.

You might ask how a wave with zero energy could trigger such an event? That subject is discussed, and experimental data is presented, elsewhere in this web site (see: excited Rydberg atoms in a resonant cavity).

In the double slit experiment, if a particle is emitted in response to one particular wave, it follows that wave backwards with a probability of one. The ray (wave) is the trajectory. Once the wave and particle are joined, any wave interference that takes place after that has no affect on the particle. The particle goes through one and only one slit; it doesn’t matter which slit it is. The particle strikes the target screen at precisely that point “P” from which its wave originated. (Of course the wave didn’t “originate” at the target screen but penetrated the screen from behind.)

What pattern would we expect on the target screen, if this is what was going on? To answer that, we turn to Figure 3.

Figure 3

Formula for Wave Crests

 

Figure 3: The black line is orthogonal to the upper red line. The green arrow shows the difference in the path length of a wave going from P, through the upper slit, to the particle source; versus a wave from P, through the lower slit, to the particle source. We assume that the distance between the barrier and the target screen is large, compared with “d” which is the distance between the two slits (in this detail, the diagram is misleading). The length of the green arrow is (d sin θ). Depending on the relationship between the wavelength λ and the length of the green arrow, the interference at the particle source will be constructive, destructive, or somewhere in between.

When the length of the green arrow is a multiple of the wavelength λ there will be constructive interference:

d sin θ = m λ where (m = 0, ±1, ±2, ±3, . . .)        (1)

Similarly there will be destructive interference when m = ±½, ± 3/2, ± 5/2, etc.

If the angle θ is such that there is constructive interference, that means that the amplitude of the wave impinging on the particle source will be at a maximum, compared with waves coming from other points on the target screen, which have a different angle θ’. If the amplitude of the impinging wave is at a peak, then the intensity will be at a peak, and the probability of a particle being emitted in response to that wave will also peak. If a particle is emitted then it will end up at point P, from which its wave came. Thus equation (1) tells us where to expect dark areas on the target screen, because of an increased number of particles striking the screen. This is why there are interference fringes in the final data.

Figure 4

TEW’s Prediction of the Interference Fringes

 

Figure 4: Using formula (d sin θ = m λ where (m = 0, ±1, ±2, ±3, . . .)) to predict where we would expect maxima and minima in the number of particles emitted (and therefore the number of particles striking the target screen), we predict interference fringes as shown here.

Nonlocality dominates the conventional view of the double slit experiment. If the waves travel as wave packets in the same direction as the particles, then wave interference occurs after the particle is emitted, and somehow the entire volume of the area between the double slit barrier and the target screen determines the particle’s ultimate behavior after wave function collapse. We have taken that non-locality and given it a name: “elementary waves.” In our model it is possible to understand exactly how and why there is wave interference. Our model uses only local cause-and-effect. We call this T2LR (type 2 local realism) to distinguish it from the way 99.999% of people, including Einstein) view the real world. Unlike the conventional view, it is possible to draw a picture that can be understood by the human mind.

To restate that last paragraph: the conventional view is that quantum mechanics explains things better than does local realism. However, that idea is false for the simple reason that there are two kinds of local realism, and they are as different from one another as night and day. What scientists should say is that QM explains things better than type 1 local realism. Both type 2 (T2LR) and QM are able to explain the double slit experiment. So how could we distinguish those theories? That is why we proposed the experiment with a laser above the right hand slit.

Ours is the only interpretation that has ever been offered, which explains the double slit experiment using local cause-and-effect. Non-locality is intrinsic to the QM view of the double slit experiment, and to David Bohm’s quantum potential model, and it is intrinsic to all the so-called “interpretations” of QM. But we claim that local cause and effect prevails in the quantum world (i.e. no entanglement).

Figure 5

A Test for Which Slit the Particle Goes Through

 

Figure 5: When scientists put in a detector to find out which slit the particle goes through, that detector itself sends out elementary waves to the source. Therefore there is no wave interference at the source, because the green ray and red ray in this diagram don’t match and cannot interfere. They are not partners. Therefore there are no interference fringes in the final dataset. Our claim is that interference fringes in the final dataset mean there was wave interference at the particle source, and vice versa, that no interference fringes means there was no interference. This means that, according to us, the Principle of Complementarity is unnecessary. That principle says that if you know which slit the particle came through, you cannot see the interference fringes, and vice-versa. While that is true, the reason it is true is because of what is shown in Figure 5 above.

Here is a restatement of what was said in the last paragraph: Someone might ask how we could account for the Complementarity Principle with our model of the double slit experiment. Why, if we observe which slit the particle goes through, do the interference fringes vanish? The answer is that the elementary wave situation is now entirely different (see Figure 5). Through one slit comes an elementary wave from the target screen (shown in red). Through the other slit comes an elementary wave from the observer (shown in green). There would, therefore, be no interference. Therefore no evidence of interference would appear on the target screen.

Our proposed experiment

Having now presented a TEW explanation of the double slit experiment, we can now discuss the experiment we propose, with a laser above the right hand slit. Our proposed experiment separates the two theories by means of timing. With the conventional theory (presented by Dr. Quantum on YouTube) no interference occurs prior to the emission of the particle. Indeed, the conventional view is that the quantum waves don’t even exist prior to the particle emission, so there could not possibly be wave interference. With our theory, no wave interference (relevant to the trajectory of that specific particle) occurs after the particle emission. Therefore, if we take a knife and divide time into “before” and “after” segments, it should be possible to determine when the wave interference occurs.

The knife in question is any gate that can close one of the two slits at that instant when a particle is emitted. We propose a laser (as in Figure 1) as the gate. Both slits are open to elementary waves from the target screen impinging on the particle source, before particle emission. Only the left slit is open after particle emission. Therefore there would be wave interference at the particle source, as manifest by interference fringes in the final dataset, if and only if there is truth to the TEW theory.

References

1. Selleri, F., “On the direct observability of quantum waves,” Foundations of Physics, vol. 12, no. 11 (1982), pp. 1087 – 1112.
2.  Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, M. O. Scully, “A delayed choice quantum eraser,” Phys. Rev. Lett. 8: 1–5, 2000; arXiv:quant-ph/9903047v1 (DOI: 10.1103/PhysRevLett.84.1