# Does light have a frequency limit?

1. May 5, 2004

### ShawnD

Are there any limits (or predicted limits) on what the frequency of light can be? It is possible to have waves with a frequency of 10^3000 Hz? How about 10^-3000?

2. May 5, 2004

### TeV

1.Yes, there are the limits (theoretical and experimental) of a free photon to be formed and to propagate.
2.No ,it's not possible to have photon with such a high energy and frequency."Particles" with corresponding energy level would be far in GUT range.Another consideration is limited to elementar quantum of Planck space lenght and vacuum speed of light.Finally there is a distance in "not shielded" universe which ultra high energy EM radiations could travel up to before interaction with relic cosmic radiation photons occurs.
3.No.Also more than one reason.Just to name one:The universe isn't infinitely "large".

cheers

3. May 5, 2004

### alpha_wolf

Not sure, but I think the minimum limit on the wavelength is on the order of planck's constant.. The maximum limit obviously has to do with the size of the universe (and maybe other factors...). The limits on frequency can then be calculated by $\nu = \frac{c}{\lambda}$

EDIT: Hmm, seems like TeV beat me to it . TeV - how do you know the universe isn't in fact infinitly large? Maybe it is (not the observable, but the entrie, or is only the observable size important here?)

Last edited: May 5, 2004
4. May 5, 2004

### TeV

Nothing in physics isn't infinitely large or small (sign of mathematical singularity in physical theory is a sign of sickness in theory).
I emphasize I'm not a cosmologist.The sense of meaning of the word "large" in my post should be looked for in the context of Einstein's GR.
Accordingly the universe is finitely old.At present how do you think the universe is old today?Rethorical (contra)question ,without * quantum theory of particles and fields to call in,:"How much time is classicaly needed to produce 1 cycle of 10^-3000 Hz EM radiation?"
Enjoy
______
* recognizing spacetime quantization in velocity range<0,c>, it can be shown that there is the lower frequancy limit at which electron/positron can emit EM radiation too.

5. May 5, 2004

### jcsd

No there's no known limit:

Isacc Asimov said the only limits on the frequency (well he said wavelength) of a photon was the size of the universe (mininumum frequency) and the total energy in the unieverse (maximum freqeuncy) but it's clear that in an expanding universe that will expand forever any photon given enough time may have an arbitarily small frequency and that in an infinite universe (which is certainly possible) a photon may have an arbitarily large freqeuency.

Some have speculated hat the maximum frequency of a photon may be limited by Planck scale physics, but until this physics is known this is little more than speculation.

6. May 5, 2004

### TeV

Well,let him just write good sci fi books.If he said that photon hasn't upper limit he knows very little about quantum physics and role of the observer in framework of GR.Even less he might know about modern view of high energy physics as concerns this issue.Be sure photon of 10^100 Hz isn't theoretical possibility for observer at any stage of our universe development.

7. May 5, 2004

### jcsd

I was merely quoting Asimov, but he is essentially correct, the known limits on photon energies are practical not theoretical.

I assure you in modern quantum physics there is absolutely no theoretical limit on the maximum and the minimum energies of a photon and in the unievrese there exist valid frames of reference in relativity where the photons coming from your screen have energies of about 10^100 Hz (due to blueshifting, it requires velocities though that I guesitmate at about (1 - 10^-40)c ).

I'll say it again, at the moment any theoretical limit to the allowable enrgies of photons is speculation.

8. May 5, 2004

### gnome

Just a thought, as my mind is reeling from these qm concepts:

If uncertainty requires that
$$\Delta p_x \Delta x \ge \frac{\hbar}{2}$$
and if the universe is not infinite, putting a maximum limit on $$\Delta x$$
(I don't know what that limit is, but presumably it's finite)
doesn't that require that there be some finite minimum momentum, and therefore a corresponding minimum energy, and a corresponding minimum frequency for a photon?

9. May 5, 2004

### jcsd

No gnome, because in the uncertainity principle Δpx can have arbitarily small values as Δx can be arbitarily large values.

edited to add: I should of read your post properly, I see what your saying but I'm not entirely if it &Deltax needs to have a maxima if the unievrse is finite, but it may.

Last edited: May 5, 2004
10. May 5, 2004

### Njorl

Consider a mundane lightwave of the visible spectrum. Is it not possible to pick a reference frame in which it has an arbitrarily high frequency? What prevents this?

Njorl

11. May 5, 2004

### jcsd

Nothing in relativity prevnts you from doing this, in my post before last I gave an guestimate (I estimated this as a conventional cacualtor, even one that can deal with the immensley large and small figures will round them up), for the relative velocity of a refernce frame in which a visible light photon (in our reference frame) appears to have a frequency of 10^100 Hz, my guestimate being about (1 - 10^40)c.

12. May 5, 2004

### gnome

Not sure, but doesn't arbitrarily high frequency mean arbitrarily high energy?

1. Where does "arbitrarily high energy" come from?

2. What happens when all of the energy in the universe is possessed by a single photon?

edit: i.e. what happens to "everything else"?

Last edited: May 5, 2004
13. May 5, 2004

### jcsd

That comes to other issues, such as limitations such as the possiblre mechansisms for concentrating all the matter of the unievrse into a single photon, whch brings in problems such as the conservation of momentum, angular momentum etc. (though in an infinite unieverse you don't have to worry about such considertaions).Of course any theoretical way do such a thing would be practcally impossible.

14. May 5, 2004

### gnome

Well, it's fun to speculate, but I should really be focusing on Friday's exam. Bye.

15. May 5, 2004

What happens if the universe happens to be curved in such a way that it has no real edge? Could not then an ultra-long wavelength exist? I'd wager it'd be very unlikely.

The energy would get so vanishingly small that quantum uncertainty would start to affect it methinks.

16. May 6, 2004

### TeV

Remember what your Assimov said,and calculate the energy of single photon with frequeny 10^100 Hz.Than calculate just for comparation the same $$E=mc^2$$ for the Milky way galaxy when you find estimate for m of the galaxy.
In answer to qustion how about change of refference frame I answer that SR isn't preceise and GR is must used in such cases.The photon of extremly high energy induces gravitationa fields in its neighborhood which aren't insignifican't any more and one have to deal with mix of relativistic Dopler wavelenght shifts and Gravitational shifts.
From the aspect of quantum physics or even better high energy physic one can present specualtion on reaction of positron electron anihilation in super high energy range which is unknown what would happen.The authority-much more eminent is S.Hawking (oh too bad he doesn't write sci fi books) who gave some speculation what could be expected (but don't take me for words it was him for sure).

17. May 6, 2004

### ShawnD

So basically there is no limit, thanks.

18. May 6, 2004

### TeV

Just on the contrary ,I'm saying there must be.In other words,it is not just nonsense to talk about 10^3000 Hz photon,but there's no sense even to talk about 10^100 Hz photon after the Planck time of Big Bang .The upper limit is lower than that . Not just becouse of problematic universe energy resources issues to achieve that,but becouse of ultrahigh energy physics unknown land where quantum field theory and gravity are in the mix.
I can give many examples related to this problem.
Consider the reaction of classical electron-positron anhilation where they travel in oposite directions with same antiparallel velocities (the simple case):$$e^+e^-\rightarrow\gamma\gamma$$
At normal energy levels this reaction is valid.But now,Hawking asked himself what would be if electron and positron are given velocities very very very close to the speed of light that reaction is at say 10^50 eV?Is the reaction still valid?What should be expected?

19. May 6, 2004

### jcsd

As I said before there is still no known theroretical barrier, any barrier is just the result of speculation on the nature of Planck scale physics.

Yes 10^100 Hz is a ridculously high energy to havefor a photon, but there's still no theoretical barrier preventing a photon having such energies which is the point I'm making.

Yes I was aware that general relativity does come into play, but by having the phtoon local to the obsever, you wouldn't have to worry about the curvature of spacetime.

Two gamma rays is usually the low energy (as opposed to high energy) example of electron-positron anhilation anyway, though while being untypical at high energies I don't think there's any known mechanism to exclude them as products.

20. May 6, 2004

### jcsd

btw, as I said before, I was just quoting Asimov, not citing him.

21. May 6, 2004

### TeV

Relationships between observer and gravity field experienced in different refference frames are of the high importance in this example.As well as the curvatore of spacetime if one wants to consider proper spacetime transformations.But the point is after certain gravity field strenght and gradient of the same theories go nuts.
It is even of more relevance to consider border where quntuum interactions with vacuum state virtual particles take its tool on ultahigh energy travelling photon.Today ,nobody knows for sure how to take all these effects togather in mix with GR.
...though,I don't think there's mechanism to exlude them as products too (he cosmic rays in the reaction),according to Hawking the most of 10^50 eV will go in creation of mini black hole(s). Giving enough time they will evaporate giving the energy away in form of EM radiation.EM radition of much less frequency.

cheers
P.S.I think it was Hawking's or Penrose's preprint of lecture I saw few years ago.I was merely citing from memory this part.

22. May 6, 2004

### jcsd

Yes curvature would be important, though the point I'm trying to make is that it wouldn't matter as long as the observer and the photon are occupying the same spatial psotion, or have an arbitarilty small seperation as metrics in GR tends to the Minowski metric locally.

I think it's certainly fair to say there may be a limit on the allowable energues of a photon or even there probably is a limit on the allowable energies of a photon,. it's just at the moment no-one can say with any real assurance as the theory does not exist do describe these situations.

23. May 7, 2004

### TeV

Finally you seem to understand what I'm saying,even without issue of allowable energies of the photon.From both aspects (ie GR and quantum physics) sense of talking about 10^100 Hz photon frequency (or the frequency of any particle for that matter) losses meaning.
In simple terms ,energy of gravitional field and local curvatore that accompanies "photon" 10^100 Hz would create after certain point event horizont,very similar to that of black hole.(That's why I gave you to compare the energy with energy of Milky way.The photon energy turns to higher,and if you start think what kind of object is in very center of our galaxy..well it gives you some indications ).That's just from aspect of GR.
From aspect of quantum physics,who gives one right to talk about meaning of word frequency in "space" lenghts of 10^-90 m?That's the unknown teritory for current physics.

Cheers

24. May 7, 2004

### jcsd

No, I'm pretty you wouldn't create an event horizon, after all do neutron stars suddenly become black holes, if your travelling with a relativistic (but not unrealistic) velocity.

At the moment there's nothing that specifically prohibits you from talking about wavelengths of 10^-90 m, though it's a definite possibilty that quantum gravity will say that you can't talk about such wavelengths.

25. May 7, 2004

### TeV

The situation is very similar to the even horizon of black hole (not identical though).Gravity field gradient induced by photon will be creating event border to the observer.For instance, any material particle will experience huge nonlinear acceleration- tidal forces in vicinity of photon beam of sufficiently high energy becouse field is not uniform.From the observers' standpoint any particle or other photons that come too close will dissapear preventing him for even knowing what generates the gravity field (speed of light varies-due to same reason :gravity field ).
And don't complicate the things with neutron star.Neutron star will stay a neutron star.Gravity fields created by moving nonzero rest mass objects does not change spacetime geometry in the same manner as gravity field induced by "light" (Tolman et al).

You're right about last statement.Nothing prohibits as from talking about happenings at 10^-90 m distances.But I have no idea what's there.