Is There a Limit to How Fast We Can Accelerate Into an Incident Photon?

[Criticalmass]

Recently I heard someone make the assertion that the visible spectrum only makes up approximately 2% of the entire EM spectrum. That to me seems like a horrible statement to make since the bounds of the EM spectrum seem to be undefinable. But it brought this question to mind:

Is there a physical property that limits the highest theoretical frequency or is the highest frequency possible infinite.

The same question in a different form: Is there any reason why an infinitely small wavelength isn't possible? And if so, why?

Thanks.

 

[Chaos' lil bro Order]

Smallest Wavelength

Great Question.

The smallest possible wavelength is the Planck wavelength which is theorized to be 10*-34cm, and is also what String theory predicts as the length of its strings.

However, there are infinite wavelengths possible in the sense that wavelenghts do not have to be integer numbers, so theoretically even the visible spectrum of ~380-740nm contains within it, infinite wavelengths.

On the largest scale, gravitational waves which have been stretched (red-shifted) since 10*-42seconds after the 'big bang' are the largest wavelengths we can conceive of, although its quite possible there are longer wavelengths. LISA, a NASA probe consisting of 3 Laser Interferometers will be sent into space to measure if Gravity waves do exist. The 3 'LIs' will be in a triangular pattern separated by 5 million km, which is theoretically the length of gravitational waves.

 

[Claude Bile]

There is nothing in EM theory (as far as I know, I could be wrong) that specifically forbids frequencies above a certain value. There are however, other issues that prevent extremely high frequency waves from being generated, the most obvious of which is energy. Also, as you go to extremely high frequencies (beyond Gamma frequencies), energy tends to go into forming particles, rather than EM waves (a particle physicist may be able to elaborate a little here).

I agree though that saying the visible spectrum only makes up approximately 2% of the entire EM spectrum is a horrible way to put it. That is the kind of statement that will give a physicist seizures .

Claude.

 

[Criticalmass]

Thanks for the replies.

Chaos: What is it that defines the Planck wavelength (ie what reasoning generates 10^-34cm). Why does string theory use that size for its theoretical strings?

I'm no physicist but I have a technical background and exposure to basic physics up through Relativity and an introduction to string theory if that gives you a measure of how far you have to dumb the explanation down.

 

[Ivan Seeking]

I don't think we really know that the Planck length is the minimum wavelength. The Planck length is derived, or maybe it would be better to say contrived, from the physical constants. It is found that the constants can be arranged to produce a natural set of units. We have long suspected that these relate to min/max values, but I don't think that we actually know this.

 

[vanesch]

Recently I heard someone make the assertion that the visible spectrum only makes up approximately 2% of the entire EM spectrum.

As such, that sounds indeed as a ridiculous statement - so maybe it was just taken out of context or something, like, I don't know, the part of the spectrum emitted by the sun (with appreciable energy content) or something (even then, I don't know if the statement is correct).

But for sure the statement is absolutely not correct if seen as a "limit" to the spectrum: visible light is around 1eV, so that would mean that there are no photons above, say, 50 or 100eV ? What about gamma rays of several GeV that we observe in accelerators then ?

 

[Chaos' lil bro Order]

An excellent Question

The Planck length of 10*-34cm is a consequence of the Planck time of 10*43s, which is the time the Universe theoretically came into existence. Incidentally, the Planck length if thought of as a photon's wavelength would have an energy of 5.2x10*29 eV. This also implies a background energy density of p=10*125GeV/m*3 and a temperature of 6x10*31 Kelvin at the moment of creation.

I'm sorry if this does not explain the derivation of the Planck length, I simply don't know it and am as equally as curious as you are to hear a complete answer to your question since no one has posted one yet. My tentative answer is that a 'particle' cannot be smaller then the Planck Length because its energy would be greater then the energy that first theoretically created our Universe in the first place. So clearly this contradicts our best theories at present, perhaps it won't in the future (fingers crossed).

All of the above values can be calculated simply by using the 'Friedman Equation' and substituting in the 'Stefan-Boltzmann Law' to achieve a final formula that looks like the 'attachment' I've included.

Hope this helps a bit, try starting a new thread about the Planck Length's derivation, its a great question.

 

[JDBB]

Curious threat, however improblable

By Plank's equation E = hf it is imposible to attain an infite frequency, for as Einstein has shown in E = mc2 that energy cannot be infinite for its directly proportional to mass.

Hypothetically speaking, say you were able to attain an infinite frequency. Then by v= wavelength * frequency , you would only be able to choose from values whose product would equal c (the speed limit of the universe). Thus you can't have an infitely small or infinetly big wavelength and/or frequency,

 

[Chaos' lil bro Order]

jobb

But you can have an infinite # of frequencies between 1-2 hZ since frequencies are not integers.

 

[kmarinas86]

A gamma ray of 1.24 MeV that is blueshifted to a 4.52386226*10^26 times higher frequency has the energy equivalent to 1 gram of mass. To do this, photon of this energy in free space would have to approach to 1 Planck length from the event horizon of a black hole of about 1000 light year in diameter, it will have this amount of energy (.001 kg * c^2), and that's just one photon!

Verification:

1 Planck length is approximately 10^-35 meters
1000 light years is approximately 10^19 meters

Thus you can get the factor by which the frequency increases:
1/sqrt(1-1/(1+10^-54)) = almost exactly 1E+27

If you have precise caculator such as the PowerToy Calculator, you can get the value.

 

[Claude Bile]

By Plank's equation E = hf it is imposible to attain an infinite frequency. By Plank's equation E = hf it is imposible to attain an infite frequency, for as Einstein has shown in E = mc2 that energy cannot be infinite for its directly proportional to mass.

Hypothetically speaking, say you were able to attain an infinite frequency. Then by v= wavelength * frequency , you would only be able to choose from values whose product would equal c (the speed limit of the universe). Thus you can't have an infitely small or infinetly big wavelength and/or frequency,

Yes, but these equations do not explicitly give a finite upper limit for possible frequencies. Saying the upper limit is infinity is fairly meaningless, not to mention a logical contradiction since something that has a limit of infinity, would, in fact, be limitless.

Claude.

 

[imoatama]

Sorry to revive an ancient thread but I was wondering about whether there was a highest possible frequency too, and this was the top google result, and after doing more research the answer here didnt fully satisfy me.

In fact there is no theoretical upper limit to possible electromagnetic frequency. Wavelengths can be made arbitrarily small by accelerating the observer in the opposite direction to the wave's direction of propagation. The resulting Lorentz contraction will shorten the wavelength, and can do so arbitrarily depending on the speed of the observer.

Of course in the real world, if the observer had mass, it's unlikely we'd be able to accelerate them to any significant fraction of c, but to me this is a 'real-world' limitation rather than a theoretical one. This real-world limitation also seems to be basis of JDBB's post/claim.

Anyway some of the difference in answers may just be differing definitions of theoretical, but I hope this helps anyone that was similarly wondering, as I was. Corrections/debate welcome.

 

[vanesch]

Sorry to revive an ancient thread but I was wondering about whether there was a highest possible frequency too, and this was the top google result, and after doing more research the answer here didnt fully satisfy me.

In fact there is no theoretical upper limit to possible electromagnetic frequency. Wavelengths can be made arbitrarily small by accelerating the observer in the opposite direction to the wave's direction of propagation. The resulting Lorentz contraction will shorten the wavelength, and can do so arbitrarily depending on the speed of the observer.

Of course in the real world, if the observer had mass, it's unlikely we'd be able to accelerate them to any significant fraction of c, but to me this is a 'real-world' limitation rather than a theoretical one. This real-world limitation also seems to be basis of JDBB's post/claim.

Anyway some of the difference in answers may just be differing definitions of theoretical, but I hope this helps anyone that was similarly wondering, as I was. Corrections/debate welcome.

What you are saying is correct, but you should specify something extra:

*in the frame of special relativity*, you can use arbitrary boosts, and hence Doppler-shift any *classical radio wave* to any arbitrary real number for frequency.

So in the theoretical frame of special relativity and classical electromagnetism for instance, there is no upper limit to frequency. But that is *within that theory* and we don't know if the real world is still well-described by that theoretical framework at those boosts. In other words, we don't know whether almost infinite boosts (which are clearly "present" in special relativity) are sensible in nature.
Or, in other words, whether that part of the theory is still within its scope of applicability to nature.

Like you can go to very high velocities in Newtonian mechanics, many times the velocity of light. Within the theoretical framework of Newtonian mechanics, that is easily possible. However, the applicable scope of Newtonian mechanics stops short of that mathematically accessible domain.

 

[Chaos' lil bro Order]

This thread is hilarious. The original question was: IS THERE A LIMIT TO THE HIGHEST POSSIBLE [ELECTROMAGNETIC] FREQUENCY? Look, the answer clearly is yes. If you have a photon, which IS known to be the force carrying particle of the electromagnetic force, you can never increase its energy frequency infinitely. You would have to pump its energy up infinitely and the Universe would rift a black hole way long before that. Hell, Supernovae produce black holes. If you take a point particle like a photon, you must realize that, if you get the particle beyond a critical energy density, it creates a black hole, well long before you are on your way to infinity. That my friends, would be the old proverbial infinite c ckblock.

Put another way. Buy a blender. Buy an infinite power supply (future shop has em). Plug in the blender to the supply. Increase the speed on your blender to infinite and wait. Know what will happen? Well, assuming its a blender built by god and will last all the way to infinity if it gets the chance. So what happens? The blender spins so fast and its blades cause so much turbulence and friction in the air that it sets the Earth's air on fire. That analogy was a stretch, but seriously, frequencies are limited when you are talking about a photon's frequency as in the Electromagnetic force.

 

[DaveC426913]

This thread is hilarious.

Not sure why you're being so derisive; it's a perfectly serious and valid question. The blender analogy is clumsy, beneath you.

So I'll just skip to the end, where you get serious.

This seriously, frequencies are limited when you are talking about a photon's frequency as in the Electromagnetic force.

No one doubts that there may be practical limits. The question is whether there are theoretical limits.

One example is that you could theoretically doppler shift incoming radiation infinitely, "simply" by accelerating into it forever. Yes, ultimately you will be getting the **** kicked out of you by cosmic rays, but that's a practical problem. There's no equation that says "this is the highest frequency, beyond this thyere be dragons".

 

[Antiphon]

To put the Planck photon in perspective, it's equivalent to 17,000 Kg of TNT.

A single photon with the energy of an atomic bomb!

I would NOT want to be hit by that photon.

 

[singhvi]

I think that if one has an idea of the mass of the universe, it would be safe to say the equivalent energy (mc^2) would definitely be the upper limit on the energy of a photon.

 

[Chaos' lil bro Order]

I think that if one has an idea of the mass of the universe, it would be safe to say the equivalent energy (mc^2) would definitely be the upper limit on the energy of a photon.

Sing, that is precisely right and very well said.

Dave, sorry, I get frustrated when people talk about 'frequencies'. Its a word so often abused and rarely properly differentiated, so it makes answering questions about it, very difficult. Dave, how do you accelerate infinitely into an incident photon? This assumes you CAN accelerate infinitely, but that would be limited by C. Which you could approach but never reach. So you run into a paradox. The half room paradox, so to speak. You will never get there. Never blue shift the the incident photon into infinity, but you sure as hell will get close to approaching it. That is my logic. I think it is correct.

 

[DaveC426913]

Dave, how do you accelerate infinitely into an incident photon?

By applying your propulsion continuously. Say, with a ramjet.

This assumes you CAN accelerate infinitely,

You can.

but that would be limited by C. Which you could approach but never reach.

True, you would never reach c - from the frame of rerfernce of an external observer. Yet that would not stop you from accelerating for an arbitrarily long time. Nor would it stop the photons from blue-shifting arbitrarily high.

So you run into a paradox.

There is no paradox, there is only relativity.

You will never get there. Never blue shift the the incident photon into infinity,

Inasmuch as you may never get to infinity, that may be true, but the question was: is there a limit? No. You could accerelate without limit, and blue-shift the photons without limit.



I think once you give this some thought you will realize the error in your logic. Blue shifting is with respect to the observer in the craft, who experiences acceleration continuously.