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Energy-Time Uncertainty

The relation between energy (E) of a particle and time (t) is obtained as follows:

Δ E Δ t ≥ ħ/2π
Δ E ≥ ħ / 2π*Δt

We pinpoint time zero as the moment when the particle-wave crosses the x-axis and initiates its wavelength in space-time. Around this point, changes in time are minimal. By the same token, according to our previous assumption, at the entering point changes of mass and therefore energy are at its peak.

The Heisenberg equation indicates that when the change in time is zero, the change in the particle’s energy can reach to its peak. At the peak of the curve Δt is maximal and changes in energy are minimal.

revisitingwaveparticle15-1

Therefore this particle-wave model is in line with the Heisenberg uncertainty principle for time and energy as well. This property exists because the particle in this model does not have a dual wave/particle nature; rather, it is a particle that oscillates along the way (pilot wave). Furthermore, it does not travel in a homogeneous motion; rather, it either decelerates or accelerates along its wavelength.

revisitingwaveparticle13-1

There are many complementarity relationships that follow the Heisenberg uncertainty principle. Interestingly, one of the pairs is comprised of tangible properties while the other pair is an abstract component that I have attributed to the proposed singularity. For instance, in the above examples, location in the first equation belongs to space-time, whereas momentum is an abstract and energy related factor. Similarly, in the second equation, time is a space-time element and we have related the energy to the singularity. Here we may assume that the uncertainty principle describes the gray interface between two entities. One can assume that at the boundary, there is a trade-off between the component of the space-time universe and that of the singularity. Any increase in one’s clarity comes at the expense of increasing the other’s haziness.


Particle’s Spin in This Model

Subatomic particles have a kind of spin specific to them. However, their spins are believed to be different from the spin of classical objects. The angular momentum of a classical object rotating about its axis is obtained by;

L = r X mv

Where r is radius of spinning object and mv is its regular momentum. Rotating a charge will generate magnetic field. We observe the electric fields around electron in experiments. However, if we apply classical angular momentum to particles like electrons, we face several problems.

If we liken an electron to a spinning top, the radius of the electron, coupled with the rate of its rotation, determines its angular momentum and therefore its magnetic field. Unfortunately, considering a reasonable size for an electron, while spinning, its edge would have to be moving faster than speed of light, which is not allowed in space-time.
In addition, classical physics cannot explain why all electrons have to have exactly the same spin regardless of the effect of external forces. In classical physics we can introduce different forces and alter an object’s spin. How do the spin of sub-atomic particles remain unaltered and constant?

Yet there is ample evidence that electrons have angular momentum. Although physicists believe that the intrinsic angular momentum of particles is real, they have concluded it has no resemblance to a classical spin because of problems like above.

Here is an example of where we observe an electron’s angular momentum. The conservation law dictates that the total angular momentum of an isolated system is preserved. When an electron orbits an atomic nucleus, the magnetic field it sets up combines with the electron’s own magnetic field, a process known as spin-orbit coupling. This interaction influences the energy of the atom. A thorough analysis of the possible orbital motions shows that you cannot conserve the angular momentum of the atom as a whole just by using orbital angular momentum, the electron spin has to be taken into account as well.[9]

9.
Jonathan Allday, Quantum Reality, CRC Press, Boca Raton. Fl, 2009 
   
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