Quantum Waves

2/25/2005

Using the space time energy triangle developed in the preceding papers (1) and assuming that the formula, (h is planks constant and f is the frequency) is true for all components. We get the figure below.

In Figure 1, the energy has been divided by h (planks constant).

From which we get:

But where is the space/time velocity. Also and

Hence we arrive at:

The wave length along the space/time axis of motion is:

And hence we arrive at: 1.0

Equation (1.0) is the wave length used in quantum mechanics. It was first used by Bohr to explain the energy levels in the hydrogen atom.

In this representation, the wave length is actually the vector subtraction of two very short wave length components. My motivation for this was an online document (2). For low velocity these high frequency components are virtually in the same direction. As high velocities it should be possible to see the effects of the high frequency components.

Wave Front method

Perhaps an easier way to describe this phenomenon is by considering the wave fronts of the particle and its motion in space/time. Refer to Figure 2 below.

In my previous paper (1), I showed that motion in space is always accompanied by motion in time. The motion in time is of course relative to the stationary motion in time or rate of time. A moving particle travels slower in time then its stationary twin and this can be depicted by a vector with spatial and time components.

In figure 2, a particle at To is emitting quantum waves at a frequency proportional to it’s total energy. . The wave length of these waves (distance between wave fronts) is: . These wave fronts are depicted in figure 2.

also equals .

Combining the above we get:

2.0

The moving particle encounters the wave fronts at an angle and the distance between them is . This is the wave length along the axis of motion

Clearly . But and hence we arrive at the well proven formula:

2.1

Conclusions:

A moving particle encounters the wave fronts that it emitted in the past. This encounter results in a frequency proportional to the momentum.

This theory clearly and simply resolves the issues that arise from the evidence suggesting that particle waves interfere at a frequency proportional to their momentum while other evidence suggest that all particles have a frequency proportional to their total energy.

Intrinsic Spin

In “Linear Motion ……….” (1), I showed a number of different ways to represent the total energy.

Two of these equations are written below:

3.0

3.1

Equation 3.0 is an exact formula where. In this exact formula the measurable component of rest mass decreases with velocity.

Equation 3.1 is an approximation based on the common notion that rest energy remains the same when a particle moves.

Converting these to frequency (dividing by h) we get:

4.0

4.1

is the frequency associated with the “immeasurable” amount of total energy. This is the true intrinsic spin of a particle in motion. It has a frequency proportional to its energy.

In present physics however, the particles frequency due to its rest energy doesn’t change. To be consistent with present theory then we must use the approximate formula 4.1.

Doing so results in the spin component being only half of its actual value.

A particle having measurable would have an angular momentum proportional to . Using the “constant rest energy” scenario we can only conclude that intrinsic spin is , and hence only half the angular momentum of an equivalent particle in a completely measurable orbit.

References

[ 1 ] David Barwacz, “Linear Motion in Space-Time, the Dirac Matrices,
and Relativistic Quantum Mechanics, ”, http://toe.sytes.net:65333/Theory_p041.pdf, 2003, Home page http://members.triton.net/daveb

[ 2 ] Jeffrey Lee, “The Complete Disproof of Relativity and Current Quantum Mechanics” http://www.realityphysics.com/, 2004.