The Single Hole and Relativistic Uncertainty

Read Blogs and Add Comments

The Single Hole and Relativistic Uncertainty

We shall now look at the effect of placing a barrier containing a single slit between a donor atom and a screen containing potential absorber atoms. This situation is illustrated in diagram 8. The size of the gap in the illustration is small compared to the potential response wavelength of the atoms.

In diagram 8a on the left of the barrier the wave-function determining where the donor may find an absorber is uniformly distributed over all solid angles radiating out from the donor atom. Some of the probability will therefore arrive at the hole and leak through to the side containing the screen. This probability will form a localised presence of the atom at the hole. The local presence of the donor atom will itself set up a wave-function on the far side of the hole. The probability of finding an absorber again has a uniform angular distribution radiating out from the hole. This means that the absorber atom may be placed any where on the screen. This degree of uncertainty is introduced not because of wave-mechanics but by special relativity. The constancy of the speed of light, the Lorentz transformation and space-time metric demand this level of uncertainty. Proper interval locality mechanics requires the wave-function to remove some of this uncertainty, depending on the experimental situation.

This is a remarkable result since special relativity is essentially a classical theory but it is the inevitable conclusion if the consequences of the constancy of the speed of light are fully explored.

We shall now examine how the angular probability distribution of finding an absorber atom is affected by making the size of the hole larger.

Diagram 10 shows how the localised presence of the donor atom is developed for point P on the diagram. Because our hole is relatively large we have many paths that link point P with the primary location of the donor atom. It is clear from the diagram that these paths will have different lengths, the path from R to P is shorter than the path L to P. This means that at any time at point P the localised presence of the donor atom is composed of the sum of the presences from all possible zero interval paths linking P with the donor atom. Because the paths have different spatial distances then the time components of the zero interval paths must also be different. The proper interval locality interpretation implies that an event at Point P on the screen properly touches the donor atom at many different times at once. Diagram 11 is a space-time diagram that illustrates how an event at point P on the screen properly touches the world-line of the donor atom over an extended period of time. The localised wave-form associated with a potential change in energy level in the donor atom at Point P will therefore consist of many super-positioned phases. It is the self super-positioning of the localised presence of the donor atom that will govern where on the screen the donor atom will find an absorber for its energy of excitation.

If we consider two events, event O1 and event P1 on the respective world-lines of the screen positions O and P.( Diagram 10). The period of time along the world-line of the donor atom touched by event O1 will be short compared with frequency of the wave-function associated with the expected change in energy level during interaction. The phases of the localised presences of the donor delivered by the many paths will be similar. The super-positioned wave-function presences of the donor atom delivered by the many paths from the donor to position O will reinforce themselves. On the other hand the period subtended by event P will be large and may cover one or more wavelengths. The super-positioned states of the donor at position P will therefore cancel themselves out. The intensity of the resulting wave-function of light at position O will be very much greater than that at position P. Thus with the hole size greater than the wave-length of the sine wave associated with the expected change in donor energy, the chances of the donor interacting with an absorber at position P is very low compared with it interacting with an atom at position O.

Note

The level of uncertainty introduced because of special relativity is modified by the presence of wave-functions associated with the expected change in energy levels of the participating quantum systems.

Index