Is there a limit to frequency?

[Starwatcher16]

Is there a minimum value for how small a wavelength can become?

 

[fleem]

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.

 

[Naty1]

Absolutely!
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.

 

[fleem]

Absolutely!
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?

 

[nnnm4]

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.

 

[Vanadium 50]

I agree with nnnm4.

 

[Civilized]

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.

 

[Naty1]

are the ideas that you express about the Planck length true enough to warrant such a confident answer?

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.

 

[Naty1]

...so I checked Wikipedia and found:(since I had no direct sources for my original reply)

http://en.wikipedia.org/wiki/Planck_scale

...At the Planck scale, the strength of gravity is expected to become comparable to the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown.

Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension, but it would be massive enough to immediately become a black hole (a.k.a Planck particle), thus completely distorting that region of space, and swallowing the photon.

and

At this (Planck) scale, the concepts of size and distance break down, as quantum indeterminacy becomes virtually absolute.

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:

...The wavelength of a photon (and therefore its size) decreases as its frequency or energy increases. The fundamental limit for a photon's energy is the Planck energy, for the reasons cited above.

These are the ideas I had in mind, maybe I did not express them clearly??

anyway, I'll stick with my answer for now.

 

[Civilized]

...so I checked Wikipedia and found:(since I had no direct sources for my original reply)

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:

...at the Planck scale, the strength of gravity is expected to become comparable to the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown.

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.

Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension, but it would be massive enough to immediately become a black hole (a.k.a Planck particle), thus completely distorting that region of space, and swallowing the photon.

Totally rubbish; half made up, half based on using classical reason in a quantum situation.

At this (Planck) scale, the concepts of size and distance break down, as quantum indeterminacy becomes virtually absolute.

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 are the ideas I had in mind, maybe I did not express them clearly??

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.

anyway, I'll stick with my answer for now.

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.

 

[Vanadium 50]

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.

Exactly.

OK, but then you are doing religion instead of science.

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.

 

[Naty1]

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.

Meantime

...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 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.

Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension, but it would be massive enough to immediately become a black hole

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

The problem with Quantum Field Theory (QFT) is that it is based on the idea that space and time (are continuous)...In fact most versions for QFT go haywire and produce nonsense...The remarkable fact is that string theory is quintessentially a holographic theory describing a pixelated universe...

So that's a STRONG indication supporting discreteness.

On the other hand Geradus 't Hooft has proposed (same source, pg 370)

The spectrum of particles does not terminate at the Planck mass. It continues on to indefinitely large mass in the form of black holes...like ordinary particles only discrete masses are possible.

So even here, where details might be hidden by an event horizon of a black hole, another great theoretical physicst implies continued 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.

 

[Naty1]

Some additional details:

From Fabric of the Cosmos, Brian Greene, 333-335

..on scales short than Planck distances and durations quantum uncertainty renders the fabric of the cosmos so twisted and distorted that the usual conceptions of space and time are no longer applicable...the smaller the scale of observation the larger the uncetainty and the more tumultous the quantum fluctuations become...Einstein's relativity (with) gently curving geometrical shape runs smack into the core principle of quantum mechanics, the uncertainty principle, which implies a wild turbulant...environment on the smallest of scales.

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

GR is background independent (bi)...this means spacetime is dynamical; nothing is fixed...a quantum therory of gravity should also be bi...space and time should arise from it, not serve as a backdrop for the actions of strings...string theory is not currently formulated as a bi theory...this is it's chief weakness...

Lee Smolin, pg 226-234:

The Planck length is in some sense the smallest thing that can be observed...will all observers agree on what this shortest length is?...there appears to be conflict between the idea of Planck length and special relativity...

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.
http://en.wikipedia.org/wiki/Doubly-special_relativity

 

[Naty1]

Two more sources, Paul Steinhardt and Neil Turok, The Endless Universe, 2007 with supporting interpretations discrete and limited frequencies/wavelengths:

pg76;

The concept of a photon was introduced by Max Planck in 1900...(existing theories)predicted a hot body would instantaneously radiate all its energy into light waves of arbitrarily high frequencies...Planck resolved this conflict...by introducing the assumption light is not a continuous wave but instead comes in discrete energy packets.

Which of course brings up the nature of the double slit experiment if yet another example is required.

pg 78

The short wavelength photon behaves as if it were a particle and the impact on electrons is similar to what happens when one billard ball; strikes another...Long wavelength light...is ineffective (in ejecting electrons)... because each photon carries too little energy

hmmmm...seems Civilized and Vanadium have stopped making accusatory comments.

 

[Naty1]

fleem posted:

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?

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.

 

[Phrak]

Discrete spacetime is not compatible with one of the best tested symmetries in nature, lorentz symmetry, ...

Interesting. Could you elaborate?

 

[Bob_for_short]

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.

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*(m_e/M_p)^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.

 

[karl_greifenk]

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.

 

[Vanadium 50]

hmmmm...seems Civilized and Vanadium have stopped making accusatory comments.

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.

 

[vin300]

Is there a minimum value for how small a wavelength can become?

The de broglie wavelength,
l=h/mv
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.

 

[Naty1]

PHRAK...I addressed your post #16 via source references at the end of my post #13...doubly special relativity... the poster has a valid point...this IS a contradiction between relativity and quantum...

Both Lee Smolin and the wikipedia write up acknolwedge that conflict: how can one supposedly discrete, absolute fixed minium distance, Planck length, appear fixed (the same) rather than continuous in all reference frames ...

It IS a conflict between relativity and quantum...but the theory of relativity also fails to to address double slit (valid) quantum (photon) effects...there is apparently no resolution yet...

 

[Vanadium 50]

Doubly special relativity is far, far from established science - much less the "current status of physics as practiced by the scientific community".

Doubly special relativity asserts that the most tested theory in physics today, SR, is right by accident. It does so without evidence. Further, its own internal contradictions are far worse than the problems it purports to solve (and doesn't). In particular, two objects of different masses but the same velocity in one frame have different velocities in another.

 

[Naty1]

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.

No, you gave the (correct) CLASSICAL answer. Anyone who thinks all there is to physics is classical relativity will miss a lot.

i have trouble to find the smallest and the longest wavelength ever measured/ produced...

Related, but not definitive, not experimentally confirmed, for perspective: here is an interesting excerpt from Renate Loll's July 2008 Scientific American article, which gives some perspective on the wide application of classical physics, THE SELF ORGANIZED QUANTUM, pg 49...Marcus posted this source in another thread:

Down to about 10^-34 meter the quantum universe at large is well described by classical...geometry...althought quantum fluctuations become increasingly significant. That one can trust the classical approximation to such short distances is rather astonoishing. On still shorter scales quantum fluctuations of spacetime become so strong that classical, intuitive notions of geometry breakdown...the number of dimensions (appears) to drop from four to ABOUT two.

(appears) is my addition.
This work shows partial dimensions, that is, fractals, at sub Planck lengths!

 

[Vanadium 50]

No, you gave the (correct) CLASSICAL answer. Anyone who thinks all there is to physics is classical relativity will miss a lot.

And anyone who thinks doubly special relativity is the "current status of physics as practiced by the scientific community" is mistaken.

You stated as a fact that there is an upper limit to frequency, and again, as a fact that space and time are discrete. Neither is a fact.

 

[Naty1]

I came across a related but somewhat different perspective: Leonard Susskind, THE BLACK HOLE WAR 2008, page 103:

..In quantum mechanics it turns out energy comes in little, indivisible steps...the size of a quantum unit depends on the frequency...Planck and Einstein discovered for light quanta the quantum of energy is E = hf...you will never notice the quantization of energy in orfinary experience...increasing the the energy of an electromagnetic wave by one step is the same as adding a single photon to a light beam...the fact that energy can be added only in indivisible quanta seems illogical (to a classically wired brain) but that is what quantum mechanics implies..

Sounds like Susskind is saying frequency f is a restricted, quantized entity??

 

[DrGreg]

Sounds like Susskind is saying frequency f is a restricted, quantized entity??

No, he's saying light comes in the form of discrete photons rather than a continuous wave. He's saying that, for monochromatic light of a given frequency f, the energy comes in integer multiples of hf.

 

[Naty1]

Post # 3 here implies one type of frequency constraint in ultra dense conditions:

https://www.physicsforums.com/showthread.php?t=376810

which relates to the Pauli exclusion principle and likely the Heisenberg uncertainty principle in less dense states...

 

[Orion1]

Naty1, that is not a frequency constraint, it is a General Relativity principle regarding Equation of State (EOS) called causality.

Basically, no two interacting EOS differential functions in an Equation of State can cause an event to occur faster than $c$.

For example, the change in differential_pressure and differential density cannot cause an event to occur faster than $c$:

$$\sqrt{\frac{\partial P}{\partial \rho}} \leq c$$

Current theoretical physics regarding Maxwell's equations, QED and the Standard Model do not set a theoretical limit on a minimum wavelength.

I also have a theoretical problem using Planck scales to define the limits of a photon.

For example, the Planck scale spatial definition for particles with mass for the Equation of State is established by setting the gravitational radius equivalent to Compton wavelength:
$$r_G = \overline{\lambda}_C$$

$$\frac{G M(r_G)}{c^2} = \frac{\hbar}{M(r_G) c}$$

Setting M(r_G) = 0 for a photon in this equation results in a zero on the LHS and a infinity on the RHS of the equation, therefore Planck scale dimensions cannot be used to define the wavelength limit of a massless photon.

The principle of mass-energy_equivalence cannot be invoked here because the photon does not have any rest mass, therefore a photons energy density cannot cause space-time to curve and absorb itself into its own Schwarzschild radius.

Reference:
http://en.wikipedia.org/wiki/Causality_%28physics%29"

 

[Naty1]

Naty1, that is not a frequency constraint, it is a General Relativity principle regarding Equation of State called causality.

you say potato, I say potato...

But i agree it is GR related...which leads to frequency and hence energy limitations.

I posted #27 not because it gives a final unequivocal answer to this thread, but because the thread has no precise answer, another viewpoint to a closely related phenomena is relevant...or at least may offer interested readers a different perspective...

 

[Orion1]

The Equation of State establishes the frequency limits of a bosonic photon confined within a such a limited system prior to collapse of such system, but not on the frequency limits of a free photon itself governed only by a smooth space-time manifold under General Relativity, Maxwell's_equations and QED and the Standard Model.

The only known limit to a free photon's frequency is the amount of energy available to generate a photon.

$$E_U = \hbar \omega$$

$$E_U$$- the total sum of all energy and_mass-energy equivalence in the Universe.

Maximum free photon frequency:
$$\omega = \frac{E_U}{\hbar}$$

Basically an entire General Relativity spatial universe with a smooth space-time manifold composed of only one free photon.

 

[Vanadium 50]

This thread does have a precise answer. It's simply that you refuse to accept it. Electromagnetic wave frequency is a frame dependent quantity, so you can always find a frame where it's bigger.

 

[Orion1]

Vanadium 50, I have a theoretical disagreement with this Wikipedia statement:

Very high-frequency photons, which cycle at once per Planck time or faster, could potentially swallow themselves up in black holes from their own energy density, which would make it difficult or impossible to probe this time scale. In the quantum theory, this would mean that the Planck time should be the smallest unit of time physics can reason about in a meaningful way.

The principle of mass-energy_equivalence cannot be invoked here because the photon does not have any rest mass, and a Planck mass is not a particle in the Standard Model, therefore there is no QED channel available for a photon to generate a Planck mass, therefore a photons energy density, regardless of photon energy magnitude, cannot cause space-time to curve and absorb itself into its own Schwarzschild radius as a Planck mass particle.

I also disagree that Planck time is the smallest unit of time quantization, it is merely a product resulting from the criteria of defining the gravitational radius equivalent to Compton wavelength for mass particles. The General Relativity space-time manifold is still smooth at Planck scales.
$$r_G = \overline{\lambda}_C$$

What are the PF Science Advisors theoretical position regarding these statements?

Reference:
http://en.wikipedia.org/wiki/Planck_time#Physical_significance"

 

[pgardn]

I had also wondered about this, limits for f or wavelength.
But unfortunately do not have the background to understand it fully.

So my general physics is lacking... SchnIkes.

I will stick with the frames of reference answer in case I get asked.