The speed of light, photon mass, and photon energy are discussed with long held hypotheses considered and a new approach presented.
KEY WORD AND PHRASES
light, photon, Einstein, Newton, velocity, mass, photopic, energy, wavelength, frequency, electromagnetic
KEY MATHEMATICAL EQUATIONS USED
f=1/λ, where f is frequency and λ is wavelength
e=1/2 mv2, (from Newton) where e is energy, m is mass and v is velocity
e=mc2 , (from Einstein) where c is the speed of light (using an approximate value of 300 km/s)
vn=, where vn, is the velocity using Newton’s equation
This work intends to look at much of the work done by many of our scientists in the past. It is an attempt to clarify some concepts and hypotheses that have confused many for a long time. Perhaps we can put some light on the subject.
Let’s begin with Max Planck whose work in black body radiation is of particular interest. He developed an understanding about the relationship of the energy level of light verses the “frequency” of that light. The prevailing idea at that time was that light was to be found as “waves”. He, on the other hand, allowed that perhaps it was discrete particles which have come to be known as photons in quantum theory.
Let’s take a broad range of wavelengths of light that we as humans particularly appreciate and that is the one we call the photopic region of the light range. This is the range where normal human vision is found. Let’s consider it to be from 400 to 760 nm in wavelength; which is our standard convention for identifying it.
If we consider light to be an electromagnetic form of radiation, which I don’t, then we would use the commonly used relationship of frequency being the reciprocal of the wavelength of the subject radiation.
This would lead us to have a frequency range therefore of 2.5 x 106 to 1.33 x 106 Hz. I wonder: if light was truly an electromagnetic form of radiation, would we be able to “see” radio transmitters sending out their messages in the range bounded by the aforementioned frequency range?
Let us for a while allow the conventional relationships to be considered valid and proceed. We have the relationship that is Planck’s constant. If we take that along with the range of light given above, we end up with an energy range of from 1.66 x 10-27 to 8.83 x 10-28 joules. We can just as easily use eV by changing the value of the constant we use thus yielding the range of from 1.034 x 10-8 to 5.514 x 10-0 eV.
Now if we remember back to the days of Isaac Newton we may recall that his relationship of energy to a body mass and velocity is given by e=1/2 mv2. If we wish to use Albert Einstein’s theory it looks like e=mc2 wherein the v in this case is restricted to what has been termed the speed of light or approx 300 km/s. We’ll speak more on this later.
If we solve for the mass of the photons using the median photopic velocity (the speed of light as given by Einstein) and the Einstein equation e=mc2 we get:
Or a nominal value for the quantum mass to be 1.339 x 10-44 g. Assuming for a moment that this is correct then we can determine the range of velocities that would satisfy the Newton approach wherein vn= where vn is the velocity according to Newton’s approach.
Using the “nominal” mass value, let’s find the range of velocities that will make up the photopic range of light. The range is found to be from 4.975 x 108 to 3.633 x 108 m/s.
Why did I move to the Newtonian approach where the velocities differ? Because if one looks at a solar orb at rest in the cosmos, it is emitting photons of a vast variety of wavelengths (or frequencies). The photons are emitted with their characteristic wavelengths assigned by the solar orb and the velocities at which they are being emitted.
I assign the mass of the photons to be of equal value since if they are not then the emission energies would have to be constant and the photon mass changed to allow for the spectrum we have so judiciously determined by decades of experimentation and study.
One can understand that if we were to approach this solar orb at a high velocity we would find the characteristic blue shift and conversely if receding from it find the appropriate red shift.
Since the solar orb is simply residing as rest in space and emitting photons in a most constant manner, the only thing changing to allow for these apparent shifts in spectrum is the relative velocity between the emission source and the mobile observer, us.
This certainly brings into suspicion the constancy of the speed of light that has been championed by so many “physicists” for these many decades since Einstein first floated his hypothesis. Not only does the speed of light vary but it is also does not define a speed limit within the Cosmos.
Light (photons) is not an electromagnetic form of radiation but particulate in nature. An intensive study concerning the proper form and structure of mathematical formulations must be undertaken to more precisely determine the true value of the photon range of velocities. A careful derivation without regard to or attachment to the rigor offered with regard to an association with those used in electromagnetic theory must be carried out. The wavelength to frequency relationship used within this paper is not presented as correct but only a means of bringing the idea of a variation of light velocity to the reader.
The speed of light in the Universe is not a constant. No relationship between the velocities of the photon spectrum and any other object of mass within the cosmos should be assumed. No fixed speed limit exists.
The photons appear to be a specific “color” or wavelength because that color and wavelength has been assigned as what is “seen” be the normal human visual process. We actually “see” the energy level of the particles of light and not a color or wavelength at all.