Maximum photon energy?
- Thread starter mathman
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Not 100% sure on this, but I would suggest the wave length cannot be any smaller than the Planck length which is 10 to the minus 35th mtrs.
Tepid guesswork is not a satisfactory answer and is best ignored. For starters, the very concept of 'photon wavelength' has no clear meaning in QED. There is a spatio-temporal spread i.e. wavepacket nature that depends on particular details of the generation process. Better to talk about photon energy, which is a well defined concept. Then, if limited to the case of the rest frame of a hot plasma (BB say!), it's believed there is a maximum temperature therefore maximum particle energy known as the Planck temperature:
https://en.wikipedia.org/wiki/Absolute_hot
At such temperature, distinctions between different types of particles is lost so the limit equally applies to say photons, electrons, quarks etc. The idea is direct collisions at or above that temperature lead locally to black hole collapse (and presumed subsequent instant evaporation) thus setting a basic limit.
However, there is no obvious such limit if considering a single propagating photon. Suppose in a given frame S a photon has an energy corresponding to half the Planck temperature. Special relativity must continue to hold and in some other frame S' moving at arbitrary boost wrt to S, that photon may have an energy arbitrarily exceeding the Planck temperature 'limit'. Does this answer your question?
Because any photon near the planck-energy would have gravitational effects which are significant at the particle-physics level, current non-quantum gravitational theory cannot model phenomena reasonably. Therefore, we literally cannot answer such questions based on (unreliable) theory or (unevidenced) empirical observation.
Physics is simple when we can ignore that $$\frac{1}{c}, G, \hbar$$ are non-zero.
Ignore $$\frac{1}{c}$$ and you have Quantum Newtonian Gravity which has been tested in the lab with cold atoms.
Ignore $$G$$ and you have particle physics which has been tested in the lab with large machines.
Ignore $$\hbar$$ and you have General Relativity which has been tested in observations of the solar system and remote events, and most recently at LIGO.
But until we can deal with all three at once in a reliable way that had been vetted by empirical observation, we can't speak reliably on the behavior of particles near the planck energy.
Physics is simple when we can ignore that $$\frac{1}{c}, G, \hbar$$ are non-zero.
Ignore $$\frac{1}{c}$$ and you have Quantum Newtonian Gravity which has been tested in the lab with cold atoms.
Ignore $$G$$ and you have particle physics which has been tested in the lab with large machines.
Ignore $$\hbar$$ and you have General Relativity which has been tested in observations of the solar system and remote events, and most recently at LIGO.
But until we can deal with all three at once in a reliable way that had been vetted by empirical observation, we can't speak reliably on the behavior of particles near the planck energy.
exchemist
Valued Senior Member
A very elegant answer!
Planck time is ~ 5.4x10^(-44) s . Planck frequency is ~ 1.85x10^(43) /s
By limiting the minimum wavelength of photon to a finite value; its maximum frequency will also be limited. Its minimum time interval also will be limited. The concept of infinitesimal time interval or infinite frequency will become meaningless.
Well, thats the idea, to quantize the time..
The whole concept of calculus will then change.
You seem to be forgetting that the typical photon is an EM wave with hundred thousand or more cycles. Not much sense as I see it to be concerned with one wave length of it.
Can you comment on my following musings.....
In an expanding universe that will expand forever any photon given enough time may have an arbitarilly small frequency and that in any infinite universe (which is certainly possible according to WMAP) a photon may have an arbitarilly large frequency. So speculation that the maximum frequency of a photon may be limited by the Planck scale is reasonable?.
I don't see the logic there. Why should global cosmological models play a role in the reasonableness of discussion of Planck-scale physics when we have no local model for Planck-scale physics?
OK, I think I get the picture.........
"The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate." To me that does not imply that EM waves are not continuous regardless of how high their frequency, especially when even the shortest photon EM waves have many thousands of cycles. Am I missing something?
Suppose the wave is catching up to me while I travel at 0.999999... of C in front of it. For me the wave length could be 10 microns, (near IR) even though in the frame of its source the wave length is at the planck length. Near IR waves sure seem continuous. If discontinuous in the source frame, how do these tiny bites get connected up for me to see as IR?
Suppose the wave is catching up to me while I travel at 0.999999... of C in front of it. For me the wave length could be 10 microns, (near IR) even though in the frame of its source the wave length is at the planck length. Near IR waves sure seem continuous. If discontinuous in the source frame, how do these tiny bites get connected up for me to see as IR?
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You wish to challenge me on the logic and validity of anything presented in #3? It covered the two relevant limit cases.
1: Head-on c.o.m collisions - which is the situation where Planck energy considerations actually do limit things (details depending on whether or not GR is the correct theory of gravity). And naturally therefore limits the maximum energy of quanta thermally generated in a given frame. [but would not be an in-principle limit as to energies attainable by a super-duper particle accelerator]
2: Unidirectional motion of a single photon or directed stream of such (e.g. laser beam), where Planck energy in a given frame is simply NOT an in-principle limitation. As to whether relative frame boosts as per mentioned in #3 are practically attainable has no bearing on the principle involved. To imply otherwise is to claim there is a universal preferred frame setting some absolute limit, thus invalidating the universality of SR kinematics. Current, to date universally failed, searches for deviations from Lorentz invariance afaik have no bearing whatsoever on above considerations.
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Considering this fact only I made my statement.
One photon wavelength x Frequency of the photon( or cycles as you say) = Speed of light or photon, which is c and is constant. So, by limiting the photon's wavelength, its frequency will be limited or not?
Schneibster
Registered Member
You got it backwards; I can tell you're not an EE. That scenario would require a minimum frequency, not a maximum, it's a maximum wavelength you're thinking of (and there isn't any). Remember that wavelength is the inverse of frequency. This will help you get it right the next time!
No, the Planck scale might limit the maximum frequency, and therefore the minimum wavelength. The Planck scale is very, very small.
Off goes my head and on goes a pumpkin! That of course is what I did mean.
Thanks for tidying it up.
Schneibster
Registered Member
Sure. I kind of do that automatically; spotting what someone's been thinking when they wrote something (for me, a piece of code generally, sometimes a comment if they're not an arrogant #%$& who don't need no stinkin' comments) is something I'm usually fairly good at.Off goes my head and on goes a pumpkin! That of course is what I did mean.
Thanks for tidying it up.
Limited; but why is the wavelength, which often is less than 1/1,000,000 of the photon's length, limited? The fact that man does not have an adequated theoretical understanding of very small (Planck) lengths, does NOT means nature is equally ignorant - can not make photons with shorter wave lengths.
Also think a little about other half of my post 13: viewing that photon over taking an observer in a very fast moving frame where it is observed to be an IR photon. Why in that frame could it not even be a UV photon, with a still smaller wavelength in the frame of its source?
From a practical POV, the highest photon frequency relatively easy to generate would be with a high atomic number atom that has been hit by a high energy particle, perhaps an electron from an acelerator, and that particle stripped / knocked out one of the two inner most shell electrons, follow by capture of one of the outer most electrons into that innermost shell.
This is a possible, but not probable event. More common following the knock out of an intermost shell electron is that that "created hole" will "bubble up" thru the shell structure with many lesser energic photons produce in a sequential cascade.
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Take a look at some pictures of the electromagnetic spectrum and there's two things worthy of note. One is that the depictions only go up to wavelength of about 10$$^{-17}$$m. The other is that the wave height is always the same regardless of frequency. If you think about a wave in a rubber mat, you will appreciate that the wave propagates at some speed c, and that the rubber mat can't move up or down at some infinite speed. If you tried to shake the mat too fast it would break apart instead of propagating a wave. I can't see how the same general principle doesn't apply to electromagnetic waves in space. IMHO there's some kind of upper limit to photon frequency.
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