Are There Limits to Photon Wavelengths in the Big Bang Theory?

[GENIERE]

If the Big Bang Theory is valid, I would think the highest possible energy producing event took place during the first fractional second of our universe’s existence. Further it must have produced the highest possible energy photon. Is there a limitation to the shortest possible wavelength of a photon? Is there a limitation to the longest possible wavelength? As a photon travels through the universe its wavelength increases due to the red shift. Will its wavelength increase smoothly or by quantum increments? If it increases incrementally, does that imply that measurements of length increase incrementally?

 

[jcsd]

I've just answered a simlair question on this forum (and I've posted my answer below)some people think that the wave length may be quabtized in Planck lengths and therefore the smallest wavelength possible for a photon is one that corrsponds to the Planck length, however due to differing refernce frames I find this unlikely:

It is highly debatebale whether or not the Planck length is the smallest possible divison esp. when referring to wavelenghths. I mentioned this above but I'll now illustrate this exactly:

The relativistic Doppler shift is given by the following:

z = Δλ/λ = [(1 + v/c)/(1 - v/c)]^1/2 - 1

Where λ is the original wavelength, Δλ is the change in wavelength due to the Doppler effect, v is the relative velocity of the source and the observer and c is the speed of light in a vacuum.

This can be rearranged into the following:

λ' = (z + 1)λ

Where λ' is the observed wavelength (λ + Δλ ) and (z + 1) = [(1 + v/c)/(1 - v/c)]^1/2

Now consider two beams of light with wavelengths (for an observer sationery to the source) Λ₁ and Λ₂ and two observers one sationery to the source and one moving with velocity, v, relative to the source. These two equations can then be derived from the equation above:

λ₁' = (z + 1)λ₁

λ₂' = (z + 1)λ₂

For the observer sationery to the source the difference between the wavelengths of the beams will be:

dλ = λ₁ - λ₂

For the observer moving with velocity, v, relative to the source the difference between the two wavelengths will be:

dλ' = λ₁' - λ₂'

We can then relate these two differences:

dλ' = (z+1)dλ

This tells us that the difference between the wavelengths of two beams of lights will be different for different reference frames, therefore in one refernce frame a difference between two wavelengths may be less than or equal to the Planck length yet in another it may be greater.

 

[Loren Booda]

Intermediate (fractional) wavelengths do not seem to be observed thanks to the Heisenberg uncertainty principle. The HUP infers measurement to statistically justify "fractional wavelengths" as artifacts of probability.

 

[GENIERE]

Jcsd – Thanks for your response but does not the introduction of other reference planes require that all possible reference planes be considered? While mathematically possible to have an infinite number it may not be physically possible i.e., reference planes are separated by quantum increments or their number is physically limited. If those 2 statements have any validity, your equations would be constrained to a not quite infinite series and therefore support a quantum separated spectra.

Loren- Thanks for the link. I hope I can understand it,

 

[jcsd]

Well even if you try to quantize refernce frames you still get the same problem that a Planck length difference between wavelengths appears larger in other reference frames.

 

[Loren Booda]

GENIERE, the link you mention is my personal site. I post it on PF as part of my signature. Although I sometimes take it seriously, I suggest you study it cum grano salis. It's content may only help partially with the problem at hand, but includes many intriguing "out of the box" ideas in quantum mechanics and relativity.

 

[reilly]

I would suspect that an ultra-high energy photon traveling through the universe would be unstable. That is it would pretty much fry anything around, and lose energy in the process. Imagine a photon with mass equivalent energy of the moon's mass going through a gas, even a very sparse one. It, most likely, will get down to baseball mass energy very quickly.
Regards,
Reilly Atkinson