Is there a minimum value for how small a wavelength can become?
As far as we know, there is no limit except that imposed by the total energy of the universe and/or the energy that could make the photon (specifically its emitter/absorber) a black hole IFF it is confined, but things get more complicated then--it has to do with the relativity of the photon position including the relativity of when the photon was emitted / absorbed, and the definition of relativistic mass. A free photon doesn't actually become a black hole, because a black hole has rest mass.
The limit on wavelength and frequency is limited by the discrete nature of space and time itself. Space and time are not continuous and that means some restrictions apply.
You can't get shorter than Planck time frequency nor shorter than Planck length wavelength, about 10-43 seconds and 10-35 meters.
There are energy limitations as well, a corollary to frequency/time stemming from de Broglie relationships...via E = hf for example....so frequency is proportional to kinetic energy...I assume Planck scale energy provides Planck scale wavelengths....
Another way to consider energy limits is via black hole formation: put too much energy into a finite particle, say accelerating a particle to Planck energy, and a black hole will form via mass energy equivalence.
So where does the extra energy go in a situation in which, for example, Doppler shifting or gravitational blue shifting would otherwise shorten a wavelength to less than the Planck length?
Naty1, are the ideas that you express about the Planck length true enough to warrant such a confident answer? It's my understanding that -some- theories of quantum gravity call for a discrete spacetime that is often characterized by the planck length, however not all theories call for it, and there is absolutely no experimental evidence for it whatsoever.
I agree with nnnm4.
I agree that Naty1 has created a highly misinformative post that is in conflict with the standard model and all mainstream extensions of the standard model. In mainstream physics, there is no upperbound on frequency and so there is no smallest wavelength either. The limit as frequency goes to infinity and wavelength goes to zero is called the UV limit.
Nothing in physics is "true enough" to warrant a confident answer!
Planck length, time and energy are certainly not confirmed experimentally. If you do not subscribe to Planck based physics, that's ok by me. I'm not selling anything here.
I look forward to reading better replies.
And by the way, my "Absolutely" comment posted previously was in no way a reflection about the question itself...It's an excellent question.
....so I checked Wikipedia and found:(since I had no direct sources for my original reply)
so with apparently all forces are unified, a black hole would be created by any photon energetic enough to get to that size, and quantum indeterminancy becomes absolute.....
So it sure does sound like a photon (electromagnetic wave) could not exist below Planck scale....
Under Theoretical Ideas:
These are the ideas I had in mind, maybe I did not express them clearly??
anyway, I'll stick with my answer for now.
Normally wikipedia is good for math and decent for physics, but there are several misleading/wrong statements in the particular article you linked.
First of all, let there be no doubt that spacetime in the standard model and in string theory is a smooth manifold --- which a layperson would call "continuous" --- and is no way made of discrete pieces (in mathematics manifolds always look locally like a "continuous shape" e.g. line, plane, ball, etc ). There is no sense in which spacetime is discrete in the standard model or in string theory.
I'll go through the statements one by one:
The above is an example of a theoretical speculation, but since it is a mainstream idea that is a part of string theory I agree with its inclusion in the wikipedia article.
Totally rubbish; half made up, half based on using classical reason in a quantum situation.
The phrase in bold is so vague the author could mean anything, but if they are correct they certainly don't mean that spacetime is discrete on this level, because in string theory spacetime is a smooth manifold.
These ideas are part of laymen's physics folklore, not mainstream theoretical physics e.g. string theory. The notion that spacetime is discrete is mostly found in unpublished manuscripts by amateurs, unreviewed web 2.0 writings e.g. wikipedia or comments on blogs etc. Discrete spacetime is not compatible with one of the best tested symmetries in nature, lorentz symmetry, and the only theory of quantum gravity which respects lorentz symmetry is string theory.
OK, but then you are doing religion instead of science. Look at any textbook on string theory and you will see that spacetime is a smooth manifold, not discrete.
And, by answering in that way, proselytizing.
In conventional, ordinary, non-science fiction physics, frequency is a frame-dependent quantity. An electromagnetic wave can have any possible frequency, depending on the coordinate system you use to describe it.
That's the only part of the prior two posts that makes possible sense to me...I had thought about it before my original post and am unsure what it portends....except to comment that any classical theory is likely to contain a number of characteristics inconsistent with quantum discreteness.
In string theory spacetime is not dynamic nor an output of theory...its a given input....string theory is background dependent....that's a major drawback. See below about string theory discretness.
Ok so you guys don't like that....yet it's ddd that these are almost the precise descriptions used by Leonard Susskind!
So that's two sources.
I'll take Leonard Susskinds interpretations instead: From the Black Hole Wars, 2008, pgs 331f
So that's a STRONG indication supporting discreteness.
On the other hand Geradus 't Hooft has proposed (same source, pg 370)
So even here, where details might be hidden by an event horizon of a black hole, another great theoretical physicst implies conmtinued discreteness.
Separately, the implications of the holographic principle clearly point to discrete spacetime structure. Too radical?
It clearly shows information in any volume of space is finite and that is a STRONG indication that all processes with are discrete....
Supporting references from Lee Smolin and Brian Greene next post.
Some additional details:
From Fabric of the Cosmos, Brian Greene, 333-335
and 349, 350
[QUOTE...the non zero size of gravitons (and everything else) in string theory sets a limit, at roughly Planck scale, to how finely a gravitational field can be resolved....by limiting how small you can get string theory limits how violent the jitters of the gravitational field become...what does this mean....it forcefully challenges the conventional notion that the fabric of space and time is continuous...if string theory is correct, the usual concepts of space and time simply don't apply on scales finer than the Planck Scale. [/QUOTE]
Lee Smolin, THE TROUBLE WITH PHYSICS, PG 182-183
Lee Smolin, pg 226-234:
And for anyone interested, this conflict is addressed, but not entirely solved, via "doubly special relativity", a subject covered in Wikipeda as well as by Smolin.
Two more sources, Paul Steinhardt and Neil Turok, The Endless Universe, 2007 with supporting interpretations discrete and limited frequencies/wavelengths:
Which of course brings up the nature of the double slit experiment if yet another example is required.
hmmmm...seems Civilized and Vanadium have stopped making accusatory comments.
excellent question(s) !!! I do not know the answer(s).
I'll keep your questions in mind and see if any insights pop up.....or you could post them in the quantum mechanics or relativity forums...I can never decide which forum to use....
maybe someone will be able to answer.
Interesting. Could you elaborate?
I am not good at the Plank scales. It seems to me no one loupe can help to see it.
I also think that the Plank scale (length) is highly artificial. I can take a0*(me/Mp)n→∞ limit, why not? Not all combinations make sense.
Moreover, the frequency shift in a gravity field is well described even in a plane (Minkowsky) geometry (see works of Eugene Stefanovich, for example). It is better than a curved space-time because in a curved space-time there is no energy-momentum conservation.
Concerning highest photon frequency, I think is it quite unlimited but highly highly suppressed, see, for example, the Plank black body radiation law. The highest frequency photon in any system carries a very small part of the total system energy.
hello- first post here
i have trouble to find the smallest and the longest wavelength ever measured/ produced
i'm just curious and i like to know the hystorical or related details where those records happends who/how made them etc.
I gave the answer. Electromagnetic wave frequency is a frame dependent quantity, so you can always find a frame where it's bigger. That's the answer, and it's not worth arguing about. You can either accept it, or not.
The de broglie wavelength,
suggests the wavelength can have as small a value as large the momentum. Since waves and particles are the same, you can have a conclusion.
Separate names with a comma.