# Infinity and beyond

October 19, 2007 9:12 PM Subscribe

What happens at either extreme of the electromagnetic spectrum?

What lies beyond gamma rays and radio waves? Is there a limit on frequency, either theoretical or practical? Can there be a radio wave with a wavelength nearly equal to infinity or a gamma ray with a wavelength nearly zero? What would be the properties of these waves?

What lies beyond gamma rays and radio waves? Is there a limit on frequency, either theoretical or practical? Can there be a radio wave with a wavelength nearly equal to infinity or a gamma ray with a wavelength nearly zero? What would be the properties of these waves?

Best answer: Is there an upper limit to the electromagnetic spectrum?

posted by Blazecock Pileon at 9:35 PM on October 19, 2007

posted by Blazecock Pileon at 9:35 PM on October 19, 2007

The theoretical limit on frequency at the high end is one such that the photon contains the energy of the entire universe.

The problem with producing low-energy photons with ridiculously long wavelengths is the size of the transmitting antenna. Its efficiency in producing photons is a function of its size relative to the wavelength of the photons it's trying to produce. (The ideal case is that it's half a wavelength.) If it was, for instance, a meter long and you were trying to produce a photon with a wavelength equal to the distance between us and the Andromeda galaxy, the efficiency of the antenna would be so low that it might take longer than there will be to produce even one. (Under the assumption that the universe is "open", there won't be a definable end as such, but for purposes of discussion we can assume that the "end" is when there isn't enough usable energy-imbalance left to power the transmitter.)

To produce a ridiculously long wavelength photon with any degree of certainty that you'd succeeded, the antenna would have to be ridiculously huge, at least a couple of percent of the wavelength. At a certain point when building the thing, you run out of available mass.

Andromeda is 4 million light years away. So it would require an oscillator that would produce one cycle every 4 million years to produce a photon with that wavelength. I guess the other limit on this would be that the photon cycle time would have to complete before we ran out of energy to produce it, even if we had an antenna large enough. (Enough silliness...)

posted by Steven C. Den Beste at 9:54 PM on October 19, 2007 [1 favorite]

The problem with producing low-energy photons with ridiculously long wavelengths is the size of the transmitting antenna. Its efficiency in producing photons is a function of its size relative to the wavelength of the photons it's trying to produce. (The ideal case is that it's half a wavelength.) If it was, for instance, a meter long and you were trying to produce a photon with a wavelength equal to the distance between us and the Andromeda galaxy, the efficiency of the antenna would be so low that it might take longer than there will be to produce even one. (Under the assumption that the universe is "open", there won't be a definable end as such, but for purposes of discussion we can assume that the "end" is when there isn't enough usable energy-imbalance left to power the transmitter.)

To produce a ridiculously long wavelength photon with any degree of certainty that you'd succeeded, the antenna would have to be ridiculously huge, at least a couple of percent of the wavelength. At a certain point when building the thing, you run out of available mass.

Andromeda is 4 million light years away. So it would require an oscillator that would produce one cycle every 4 million years to produce a photon with that wavelength. I guess the other limit on this would be that the photon cycle time would have to complete before we ran out of energy to produce it, even if we had an antenna large enough. (Enough silliness...)

posted by Steven C. Den Beste at 9:54 PM on October 19, 2007 [1 favorite]

(Small correction: The Andromeda galaxy is 2.5 million light years away. Doesn't affect what I said, but I thought I'd nitpick myself before anyone else did it.)

posted by Steven C. Den Beste at 10:00 PM on October 19, 2007

posted by Steven C. Den Beste at 10:00 PM on October 19, 2007

The key with light is the relation that Energy = hv (where v should really be the Greek letter nu). The h is Planck's constant and the v is the frequency. For any wave, frequency * wavelength = speed. Basically, the number of waves per second times the length per wave gives the distance per second. Since the speed of light is a constant, there is an inverse relationship between frequency and wavelength. Therefore long wavelength photons have very low energy and short wavelength photons have very high energy.

The low energy side is not all that interesting, I would say. Extremely long wavelength light is similar to the tides in the open ocean. There is a very slow rising and falling in the height of water, but it is so slow and occurs over such a wide area that a floating object isn't affected. It can basically be thought of as a slowly varying, almost constant electromagnetic field over length scales much shorter than the wavelength. As a perk, though, the weak interaction with objects means that long wavelength light will pass through most things. Though low energy photons are still particles, this form of interaction makes them more wave-like.

High energy photons are quite the opposite. They have a very short wavelength, which makes them interact strongly with matter and makes them seem more particle-like (think billiard balls rather than water waves) than their low energy cousins. When people do quantum field theory, one of the things that is realized is that if something doesn't violate energy conservation (and several other restrictions), then an event is possible. Which is to say that if you have a photon zipping along, it will some small fraction of the time turn into a particle/antiparticle pair which then annihilate and create an identical photon again, so long as the total mass of the pair is less than the energy of the photon. This means that a high energy photon can have quite different behavior when it hits something than a lower energy, since these loop effects (as they are called, since the diagram contains a circle when the pair is created and destroyed) become more common and diverse.

As for restrictions, there can't be any theoretical ones. Relativity says that as you increase your velocity, lengths change and the rate of time changes, but the speed of light stays the same. If you increase your velocity against the direction of a photon, the wavelength shrinks arbitrarily small as your velocity approaches the speed of light. If you move away from the photon, its wavelength will become arbitrarily large as you approach the speed of light. Since each velocity is just as valid as any other, light can look like whatever you want. There are certainly some constraints when one gets down to the quantum nature of space itself or up to the size of the universe, but I don't feel we understand either well enough to know what those will be exactly.

posted by Schismatic at 10:00 PM on October 19, 2007

The low energy side is not all that interesting, I would say. Extremely long wavelength light is similar to the tides in the open ocean. There is a very slow rising and falling in the height of water, but it is so slow and occurs over such a wide area that a floating object isn't affected. It can basically be thought of as a slowly varying, almost constant electromagnetic field over length scales much shorter than the wavelength. As a perk, though, the weak interaction with objects means that long wavelength light will pass through most things. Though low energy photons are still particles, this form of interaction makes them more wave-like.

High energy photons are quite the opposite. They have a very short wavelength, which makes them interact strongly with matter and makes them seem more particle-like (think billiard balls rather than water waves) than their low energy cousins. When people do quantum field theory, one of the things that is realized is that if something doesn't violate energy conservation (and several other restrictions), then an event is possible. Which is to say that if you have a photon zipping along, it will some small fraction of the time turn into a particle/antiparticle pair which then annihilate and create an identical photon again, so long as the total mass of the pair is less than the energy of the photon. This means that a high energy photon can have quite different behavior when it hits something than a lower energy, since these loop effects (as they are called, since the diagram contains a circle when the pair is created and destroyed) become more common and diverse.

As for restrictions, there can't be any theoretical ones. Relativity says that as you increase your velocity, lengths change and the rate of time changes, but the speed of light stays the same. If you increase your velocity against the direction of a photon, the wavelength shrinks arbitrarily small as your velocity approaches the speed of light. If you move away from the photon, its wavelength will become arbitrarily large as you approach the speed of light. Since each velocity is just as valid as any other, light can look like whatever you want. There are certainly some constraints when one gets down to the quantum nature of space itself or up to the size of the universe, but I don't feel we understand either well enough to know what those will be exactly.

posted by Schismatic at 10:00 PM on October 19, 2007

The Heisenberg unncertainty principle would seem to set a lower limit to energy of a photon.

The uncertainty in the position of a particle times the uncertainty in its momentum is greater than or equal to h, Planck's constant, divided by 2pi.

The uncertainty in position cannot be greater than the diameter of the universe. Therefore the uncertainty in its momentum must at least be h/2pi divided by the diameter of the universe. If the actual momentum of the photon were lower than this, that would violate the principle because the uncertainty of the momentum would then be between zero and that number.

This is a very low limit, and is ever decreasing as the universe expands.

posted by jamjam at 10:05 PM on October 19, 2007 [1 favorite]

The uncertainty in the position of a particle times the uncertainty in its momentum is greater than or equal to h, Planck's constant, divided by 2pi.

The uncertainty in position cannot be greater than the diameter of the universe. Therefore the uncertainty in its momentum must at least be h/2pi divided by the diameter of the universe. If the actual momentum of the photon were lower than this, that would violate the principle because the uncertainty of the momentum would then be between zero and that number.

This is a very low limit, and is ever decreasing as the universe expands.

posted by jamjam at 10:05 PM on October 19, 2007 [1 favorite]

Wouldn't Heisenberg set an upper limit on the frequency as well? As energy increases, frequency increases and the distance between wave crests becomes shorter. If this distance between wave crests becomes shorter than the Planck length, there is a probability that the photon would interfere with *itself*... and, well, I really don't know what would happen, but the math would be ugly.

You might hit that "more energy than the universe contains" practical limit first.

posted by Mozai at 6:46 AM on October 20, 2007

You might hit that "more energy than the universe contains" practical limit first.

posted by Mozai at 6:46 AM on October 20, 2007

'The uncertainty in position cannot be greater than the diameter of the universe.'

It's not at all obvious to me that this should be true. The horizon problem for one thing suggests to me you could be less certain about something's position, since it seems opposite sides of the universe were once in contact, so something uncertain enough at that time could in principle be beyond either side.

I suspect a much better way of thinking about it would be something to do with the age of the universe and relating that to the frequency somehow.

I think Schismatic sums it up well with his bit - 'I don't feel we understand either well enough to know what those will be exactly.'

posted by edd at 6:43 PM on October 20, 2007

It's not at all obvious to me that this should be true. The horizon problem for one thing suggests to me you could be less certain about something's position, since it seems opposite sides of the universe were once in contact, so something uncertain enough at that time could in principle be beyond either side.

I suspect a much better way of thinking about it would be something to do with the age of the universe and relating that to the frequency somehow.

I think Schismatic sums it up well with his bit - 'I don't feel we understand either well enough to know what those will be exactly.'

posted by edd at 6:43 PM on October 20, 2007

Edd, the universe doesn't have sides. There is no edge. It wraps around.

Tell me, where is the "end of the earth"? (Yeah, I know, it's in Idaho.) There isn't one. There's no edge to the surface of the earth, even though it is not infinite in size.

The universe is the same way. It wraps around. There's no edge. But it is still finite in size. Which means that it places an upper limit on the uncertainty in position of a particle, which therefore places a lower limit on the uncertainty in its momentum, and thus its energy, and its frequency, when it comes to photons as JamJam says.

(It's sort of the opposite of a Bose-Einstein Condensate.)

posted by Steven C. Den Beste at 7:22 PM on October 20, 2007

Tell me, where is the "end of the earth"? (Yeah, I know, it's in Idaho.) There isn't one. There's no edge to the surface of the earth, even though it is not infinite in size.

The universe is the same way. It wraps around. There's no edge. But it is still finite in size. Which means that it places an upper limit on the uncertainty in position of a particle, which therefore places a lower limit on the uncertainty in its momentum, and thus its energy, and its frequency, when it comes to photons as JamJam says.

(It's sort of the opposite of a Bose-Einstein Condensate.)

posted by Steven C. Den Beste at 7:22 PM on October 20, 2007

An interesting associated question is how these extrema can interact with matter. Are these very highs and lows even detectible?

Matter essentially is an antenna, with certain frequencies interacting on different scales of matter: radio frequencies interact with nuclear-electronic coupling (NMR/MRI), microwaves rotate molecues, IR stretches chemical bonds and so on. Use a wavelength that doesn't strongly interact with matter and those frequencies effectively become invisible light: the terrahertz band for example. At very low energy long-wavelengths, free electron (or plasmon, etc..) distance becomes a significant problem. At very high energies, the target the photon has to hit becomes so small that interactions are vanishingly unlikely.

posted by bonehead at 8:12 PM on October 20, 2007 [1 favorite]

Matter essentially is an antenna, with certain frequencies interacting on different scales of matter: radio frequencies interact with nuclear-electronic coupling (NMR/MRI), microwaves rotate molecues, IR stretches chemical bonds and so on. Use a wavelength that doesn't strongly interact with matter and those frequencies effectively become invisible light: the terrahertz band for example. At very low energy long-wavelengths, free electron (or plasmon, etc..) distance becomes a significant problem. At very high energies, the target the photon has to hit becomes so small that interactions are vanishingly unlikely.

posted by bonehead at 8:12 PM on October 20, 2007 [1 favorite]

*The universe is the same way. It wraps around. There's no edge. But it is still finite in size.*

To be fair, that's a hypothesis that makes a lot of sense, but has no experimental proof. It is one of the simplest hypotheses, but it's not unique or proven.

posted by bonehead at 8:17 PM on October 20, 2007

*To be fair, that's a hypothesis that makes a lot of sense, but has no experimental proof. It is one of the simplest hypotheses, but it's not unique or proven.*

I had a brief email conversation with J. Richard Gott III about this back when

*A Map of the Universe*was published, and if I recall correctly from that thread, I believe he would confirm that we are still trying to verify this experimentally.

posted by Blazecock Pileon at 8:46 PM on October 20, 2007

The observable universe has limits. That's what I mean. If you read what I said again, you'll see that by implying something could be beyond the edge, I didn't mean it in the same sense you thought I did.

Otherwise bonehead and Blazecock Pileon got there first. There's as yet no evidence for the wraparound idea. It's possible we'll get some later, but only if the wraparound scale is small enough (smaller than the size of the observable universe).

The fact that the true universe could be considerably larger than the observable one is precisely why I raised the issue. The

posted by edd at 6:02 AM on October 21, 2007

Otherwise bonehead and Blazecock Pileon got there first. There's as yet no evidence for the wraparound idea. It's possible we'll get some later, but only if the wraparound scale is small enough (smaller than the size of the observable universe).

The fact that the true universe could be considerably larger than the observable one is precisely why I raised the issue. The

*age*of the universe however is pretty well known for sure, and that's why I think it's likely that if something like jamjam's argument could be used here then basing it in the time-domain is likely to be a better approach.posted by edd at 6:02 AM on October 21, 2007

As for the low end, you'll want to read up on bremsstrahlung. The above comments about needing a huge antenna to produce very low energy photons are wrong. In accelerator experiments, for example, you can scatter an electron of known energy off a photon of known energy. Before or after that interaction, but before you detect the electron at the end, it can emit low energy photons. These photons are not detected because the experimental apparatus can't detect them. However, there is an observable effect on the energy spectrum one measures in such an experiment. In quantum electrodynamics, you must allow for the possibility that photons of arbitrarily small energies are created. In doing calculations, you typically cut off the effective lowest-possible energy by putting in your experimental resolution by hand so that cross-sections don't diverge.

As for high energy photons, the short answer would be that the Planck mass provides a solid upper limit. This is

Well before this point, you run into the problem that other forces dominate, and you should really focus on them, because your photons will be splitting into other particles that experience the weak and strong interactions.

posted by dsword at 11:40 AM on October 21, 2007

As for high energy photons, the short answer would be that the Planck mass provides a solid upper limit. This is

*well*below the energy of the Universe. While the theory of electromagnetism itself has no energy scale associated with it (and you can in principle go up as high as you want), when you do calculations you end up finding that you have to introduce an energy scale by hand. The effect, in the end, is that predictions of the theory relate measurements at one energy scale to those at another. This is fine for all accessible experiments. Eventually, you run into the Landau Pole, where things break down.Well before this point, you run into the problem that other forces dominate, and you should really focus on them, because your photons will be splitting into other particles that experience the weak and strong interactions.

posted by dsword at 11:40 AM on October 21, 2007

Edd, when I first thought of trying to use the HUP to answer this question at the lower limit (it bears a family resemblance to the zero-point motion question around absolute zero) it seemed more natural to use the HUP in its alternative formulation in terms of energy and time rather than position and momentum. However, I didn't see how to get a grip on an individual photon with that version, but now I'm thinking something Steven CDB said in his first answer may point the way.

In the energy/time HUP, the uncertainty in energy times the uncertainty in time must be greater than h/2pi. With SCDB's answer in mind, it might be possible to use that version by focusing on the emission of the photon. If the emission of a single photon took from the beginning of time (the big bang) until the present moment, that would seem to give you maximum uncertainty in the time of the event. The uncertainty in energy would then be at an absolute minimum, and would equal h/2pi divided by the age of the universe at that moment. The actual energy of the photon then could not be lower than that uncertainty without violating the HUP.

You can substitute any event for the emission of a photon in this discussion, and that turns it into an argument which tends to claim that the smallest energy an event can have depends on the age of the universe at the time it happens. This looks a lot like saying the size of the minimum possible quantum of energy at any given moment depends on the age of the universe, and that the quantization of energy gets finer as the universe ages.

By the same token, if you substitute any other particle for photon in the argument I originally used, it remains equally valid (however valid that may be), and thereby seems to establish a minimum amount of momentum (in absolute value) which can exist in the universe at any instant in its history, depending on the size of the universe at that instant.

This is not quite the same, perhaps, as saying that the size of the universe establishes the size of the steps by which momentum is quantized in the universe, but it appears to me to come close to that.

In qualitative terms, one of the implications of this argument is that the universe gets finer grained as it expands and ages.

posted by jamjam at 12:13 PM on October 21, 2007

In the energy/time HUP, the uncertainty in energy times the uncertainty in time must be greater than h/2pi. With SCDB's answer in mind, it might be possible to use that version by focusing on the emission of the photon. If the emission of a single photon took from the beginning of time (the big bang) until the present moment, that would seem to give you maximum uncertainty in the time of the event. The uncertainty in energy would then be at an absolute minimum, and would equal h/2pi divided by the age of the universe at that moment. The actual energy of the photon then could not be lower than that uncertainty without violating the HUP.

You can substitute any event for the emission of a photon in this discussion, and that turns it into an argument which tends to claim that the smallest energy an event can have depends on the age of the universe at the time it happens. This looks a lot like saying the size of the minimum possible quantum of energy at any given moment depends on the age of the universe, and that the quantization of energy gets finer as the universe ages.

By the same token, if you substitute any other particle for photon in the argument I originally used, it remains equally valid (however valid that may be), and thereby seems to establish a minimum amount of momentum (in absolute value) which can exist in the universe at any instant in its history, depending on the size of the universe at that instant.

This is not quite the same, perhaps, as saying that the size of the universe establishes the size of the steps by which momentum is quantized in the universe, but it appears to me to come close to that.

In qualitative terms, one of the implications of this argument is that the universe gets finer grained as it expands and ages.

posted by jamjam at 12:13 PM on October 21, 2007

I'd be wary of going from saying there's a lowest practical energy you could have to saying that has some effect on quantisation. I really don't know enough QM to say much more though.

posted by edd at 3:02 AM on October 22, 2007

posted by edd at 3:02 AM on October 22, 2007

*I really don't know enough QM to say much more though.*

I'll have to rely on your word for that, edd, since it's clear from previous posts that you know much more than I do.

posted by jamjam at 9:12 AM on October 22, 2007

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Also, who can name the bigger number.

posted by Chuckles at 9:32 PM on October 19, 2007