Naked Science Forum
General Discussion & Feedback => Just Chat! => Topic started by: Eternal Student on 21/02/2022 04:39:49
-
Hi.
This is the Just Chat section, so this is all informal. It's just a quiet evening and this has been worrying me:
Is there a maximum frequency for a photon? (I might call this thing a gamma ray elsewhere in this post).
There's a few reasons why you might think the frequency of EM radiation is limited, here's a few to start with:
1. Perhaps the wavelength can't meaningfully be less than 1 Planck length.
2. There should be some sort of energy density in space associated with a photon. If you keep pushing up the frequency then you have enough energy density to create a micro black hole.
3. Perhaps EM radiation is always ultimately generated as a result of charged particles like electrons moving and they can't be made to oscillate arbitrarily fast.
4. Quantum stuff instead of classical: Maybe photons always arise as a result of electrons changing orbitals around an atom or nucleons re-arranging themselves in a similar way inside the nucleus. Even the largest of jumps (from say n= ∞ to n=1) is still a finite energy change and there are only a handfull of different sub-atomic particles and only a finite number of ways of putting them together to make something with these energy states.
5. Some other reason.
Anyway, that's the first question: Is there an upper limit on the frequency of a gamma ray?
If you think that there could be (I'm about 71% inclined that way), then the follow up question has to be......
What if you change reference frames? Give yourself a boost to another frame and watch for the Doppler shift What's broken?
Best Wishes to everyone.
-
Isaac Asimov says that the photon energy of a gamma ray cannot exceed to the total mass-energy of the universe.
-
Isaac Asimov says that the photon energy of a gamma ray cannot exceed to the total mass-energy of the universe.
Great writer with lots of good ideas, but, although he’s right in principle I think the limit is much lower than this.
Most assessments I’ve seen on this suggest that the amount of energy needed to probe something at the plank length is around that needed to create a black hole.
This is one reason why we think that although plank length probably isn’t the smallest length that could exist, it might be the smallest we can investigate.
-
The Planck length has no physical significance apart from being, theoretically, the shortest length of an object that can be measured with a photon. That doesn't imply the converse that you can't have a photon with a shorter wavelength.
-
Is there a maximum frequency for a photon?
That's like positing a maximum reference frame speed, and not limited by 'awfully close to c but not closer'. All photons have an arbitrarily high or low frequency, depending on the frame of reference in which the photon is considered.
Perhaps the wavelength can't meaningfully be less than 1 Planck length.
The Earth is thinner than a Planck length in some frames. Does the Earth then not meaningfully exist?
There should be some sort of energy density in space associated with a photon. If you keep pushing up the frequency then you have enough energy density to create a micro black hole.
That's not how it works any more than a black hole forming by raising the relativistic mass of some object above the energy density threshold, again, something that is done to Earth all the time.
Quantum stuff instead of classical: Maybe photons always arise as a result of electrons changing orbitals around an atom or nucleons re-arranging themselves in a similar way inside the nucleus. Even the largest of jumps (from say n= ∞ to n=1) is still a finite energy change and there are only a handfull of different sub-atomic particles and only a finite number of ways of putting them together to make something with these energy states.
And yet a simple change of one H atom between the next-to-lowest state to lowest is enough to generate your arbitrarily high energy photon.
(I'm about 71% inclined that way)
Oddly specific :)
then the follow up question has to be......
What if you change reference frames?
Exactly
-
Hi and thanks for all your replies.
Isaac Asimov says that the photon energy of a gamma ray cannot exceed to the total mass-energy of the universe.
A very good point.
What's uncertain is if the universe has only a finite amount of energy. For example, the universe might be infinite in extent and have an infinite amount of mass-energy if the distribution looks the same everywhere as it is here in our local patch.
Most assessments I’ve seen on this suggest that the amount of energy needed to probe something at the plank length is around that needed to create a black hole.
Another good point. Also worth combining that response with Halc's :
(About forming a black hole) That's not how it works any more than a black hole forming by raising the relativistic mass of some object above the energy density threshold, again, something that is done to Earth all the time.
You don't even need to consider changing reference frames. Just staying in one inertial frame, if the energy of a photon is E = hf and f can go arbitrarily high then UNLESS the photon spreads out in spatial extent with increasing frequency, then surely you do have enough energy density to form a micro black hole. I don't know. One possibility is just that GR doesn't hold at these high energies and microscopic scales.
There's no need to let your imagination run too wild.... but who's to say that a high energy photon whizzing past you isn't actually a micro black hole racing past you? As you probably know micro-black holes aren't any more destructive (they create the same gravitational field) at a distance r from another particle as any other object with the same mass paramater at a distance r would. A photon doesn't have many important characteristics, the frequency tells you just about everything although perhaps you also have some interest in its direction of travel through your space. Anyway, a black hole has sufficient characteristics to describe a photon, it has a mass parameter and they can also sometimes be moving through your space. (It's not absurd to imagine photons can form black holes, there's a whole load of existing theory about black holes formed from radiation sometimes called "Kugelblitz", https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics) ).
The Planck length has no physical significance apart from being, theoretically, the shortest length of an object that can be measured with a photon. That doesn't imply the converse that you can't have a photon with a shorter wavelength.
Another good point.
There are some ideas that space and time are actually quantised or discrete variables rather than being continuous. The Planck length isn't necessarily the smallest unit of distance but there might be some limit, some unit of distance which is no longer divisible. I only suggested the Planck length because it's evocative of discrete limitations on things like wavelength for photons.
That's like positing a maximum reference frame speed..... (along with more stuff about reference frames and Special relativity)
I can completely see what you're saying, Halc (and it is exactly why I ended my original post by considering a boost). I'm not certain if there is an upper limit for the frequency of a gamma ray, or if space is actually discrete and not continuous etc. If any of these do apply then special relativity seems to break, although it could be something else that breaks. One easy get out is just to consider that the initial assumption is wrong - i.e. accept that a photons frequency can be arbitrarily high and then see what else might need some adjustment because of that (e.g. maybe GR just doesn't hold at these high energies and microscopic scales so that photons don't form black holes etc.)
Some relevance to another thread
Most of us were recently contributing to another post - "Why don't gamma rays have a higher speed?". I'm not going to mention any of this stuff in that post - but we did all just step around the possibility that if you push the frequency of the gamma ray higher then we could get outside the range of energy that most of the current scientific theories work with.
Best Wishes.
-
There are some ideas that space and time are actually quantised or discrete variables rather than being continuous.
Space and time are mathematical constructs that we usually define as continuous. Discretisation isn't founded in the definition of Planck units, any more than quantum mechanics is implied by the Imperial Furlong - they just happen to be a handy size for some discussions.
-
Most assessments I’ve seen on this suggest that the amount of energy needed to probe something at the plank length is around that needed to create a black hole.
Another good point.
But you seem to be conflating wavelength of a photon with its size. A photon doesn't have a size, and one would presumably not have any trouble measuring this super energetic photon with even the most trivial apparatus.
if the energy of a photon is E = hf and f can go arbitrarily high then UNLESS the photon spreads out in spatial extent with increasing frequency, then surely you do have enough energy density to form a micro black hole. I don't know.
I do know at least this much: That same photon is a low energy microwave in another frame. A simple change in choice of abstract frame cannot make a difference in objective reality. No particle lacking in proper mass can form a black hole. A black hole is formed under conditions as defined by the stress energy tensor, and I don't think there can be a normalized tensor for a system consisting of a single massless particle.
Anyway, a black hole has sufficient characteristics to describe a photon
A black hole has (among other properties) proper mass. A photon cannot.
I'm not certain if [ ... ] space is actually discrete and not continuous etc.
My argument had nothing to do with the discreetness of space, but I suppose if it was, Galilean relativity could be falsified. Planck lengths have to do with the limits of measurability (an empirical limit) and not some kind of actual metaphysical limit of reality.
Best Regards
-
At the lower end, there is a limit to the energy of a photon we can observe at Earth's surface, because a gamma ray with energy much greater than 1 MeV will produce an electron/positron pair if and when it passes near the nucleus of an atom, and lose a MeV or so.
See: https://en.wikipedia.org/wiki/Pair_production
Chinese astronomers claim to have observed gamma rays of 1 PeV by looking for photon showers as thegamma ray enters the upper atmosphere.
https://en.wikipedia.org/wiki/Gamma-ray_astronomy
-
At the lower end, there is a limit to the energy of a photon we can observe at Earth's surface,
True-ish of cosmic radiation, but we've been generating bucketloads of 15 MeV photons for radiotherapy for as long as I have been in the business, and AFAIK work is proceeding on a high-brightness 6 GeV source in China.
-
....we did all just step around the possibility that if you push the frequency of the gamma ray higher then we could get outside the range of energy that most of the current scientific theories work with.
As this is informal, otherwise much would go into new theories, although the new theorists proposing these ideas are orders of magnitude brighter than the ones we get here. There is interesting work being done at CERN, some on photon/photon collisions which don’t happen at low energies. Some work on questioning whether high energies might reveal extra dimensions via Kaluza-Klein states, or might reveal gravitons which wouldn’t be detected, but could be lost into the extra dimension leaving an energy momentum imbalance.
Don’t worry about the discussions on the very short wavelengths/high energies needed to make measurements near planck length creating a black hole. As you’ve no doubt realised, the energy needed to create John Wheeler's kugleblitz put it out of being a credible possibility. However, it’s still a lot less than Asimov’s suggestion.
-
Hi again.
But you seem to be conflating wavelength of a photon with its size.
Well, I'm actually very cautious of that. I agree photons don't have a well defined size. As a consequence it may be impossible to produce a stress-energy tensor for a photon since you just don't have a particlular volume in space you could say that mass-energy is definitely all contained in. Photons are really a quantum model and General relativity...... well it just isn't, it's a classical field theory only.
However, you are completely ignoring the theory that already exists for Kugelblitz, black holes that were formed entirely from radiation and not from any particles with some rest mass.
No particle lacking in proper mass can form a black hole. A black hole is formed under conditions as defined by the stress energy tensor, and I don't think there can be a normalized tensor for a system consisting of a single massless particle.
You probably can't have a stress-energy tensor for a photon, as discussed above. However, we can generate a stress-energy tensor that includes energy density from an electric and magnetic field, i.e. treating light as a classical electro-magnetic wave.
See https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor
If that energy density exceeds a critical value then a black hole forms (according to conventional GR anyway). Although this is all theory, once formed the black hole is indistinguishable from any black hole that was formed from particles with a more conventional non-zero rest-mass (which I think you're describing as the proper mass of a particle).
There is existing theory for the formation of a black hole when a shell of light (or just some rays of light from mutilple sources scattered around the circumferance of a circle) is directed inward and made to converge at one central point in space. I'm going to call this a shell of incoming photons, although you don't actually have to assume the light is quantised during the application of the theory. However, you can describe it however you wish after the result is in your hands. Most Pop Sci articles will describe it as an incoming shell of photons because I suppose people prefer to imagine little incoming particles instead of a continuous stream of e-m radiation. (Side-note: the light never actually reaches that central point instead an event horizon starts to form at that central point and grows to meet the incoming shell of photons).
Wikipedia has some more information about Kugelblitz: https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics) but it's not a very good explanation. The best or shortest explanation of how light could form a black hole that I've seen came from ... roughly lecture 7 of 11 available on YouTube and called something like "General Relativity" by Stanford University presented by Leonard Susskind. (Obviously that's not a very helpful reference, sorry).
A black hole has (among other properties) proper mass.
I'm going to strongly disagree here. Maybe you're using the term "proper mass" is some special way, I'm not sure.
A Black hole has a parameter M, which we call the Mass parameter but it's just a parameter not the mass of a black hole, at best it's the equivalence of the mass required to generate the same gravitational field. (I feel reasonably certain you (Halc) would already know this, I'm just leaving the next part here in case anyone else reads this: At a big distance (something outside the surface of the equivalent ordinary spherical mass, so that has to be outside the Schwarzschild radius) the gravitational field from a black hole is identical to that from an ordinary (not collapsed) spherical object of mass M placed an equivalent distance away from the observer).
To say this another way, a black hole doesn't care if it eats particles with rest mass; objects with a hybrid of rest mass and thermal energy; objects like photons with no rest mass or even other black holes with just a mass parameter. If it eats any kind of mass, energy or mass parameter thing, then the mass parameter of the black hole will increase.
I'm seriously wondering if you (Halc) had something else in mind when you said "proper mass" for a black hole.
---- Ended this post, it's getting too long and many other people have now written something which shifts the balance of what is relevant. -----
Best Wishes.
-
Black holes are completely characterised by only three parameters: mass, rotation (angular momentum) and charge. But does proper mass mean solar masses? Can mass equivalence be done with energy? Or an electromagnetic mass (https://en.wikipedia.org/wiki/Electromagnetic_mass) relation?
... If it eats any kind of mass, energy or mass parameter thing, then the mass parameter of the black hole will increase.
As much as the black hole loses a small amount of its energy and therefore some of its mass by evaporation. Hawking radiation reduces the mass and rotational energy of black holes.
-
Hi again. I'll try and be quicker responding to the other posts.
Evan_au said this stuff:
At the lower end, there is a limit to the energy of a photon... (because of pair prduction)....
I hadn't thought of that much. It's a good point.
I was partly motivated by the the changes to our perception of the e-m spectrum at the high frequency end. When I was at school it was common enough to talk about "cosmic rays" as a part of the e-m spectrum with frequency higher than gamma rays. However, more recently it has been noticed that most of these extremely energetic particles were not really e-m radiation at all but were instead more likely to be things like protons and Beta particles with high velocity. There are some discussions that suggest that it is unlikely that any high energy gamma rays in what was previously called the cosmic ray region were ever really detected. Instead high energy charged massive particles were fooling or triggering the detections. The general idea being that maybe Cosmological events cannot create these high frequency e-m radiations at all.
Chinese astronomers claim to have observed gamma rays of 1 PeV
Thanks, I'll also check the wiki link later (Late editing: done... it looks like 1.4 PeV is the current record).
alancalverd said this stuff...
....but we've been generating bucketloads of 15 MeV photons for radiotherapy for as long as I have been in the business, and AFAIK work is proceeding on a high-brightness 6 GeV source in China....
Yes.
Our ability to generate a gamma ray is limited. It's not clear if there are materials and resources on this planet capable of generating gamma rays of arbitrarily large frequency. This begs the question... in what sort of process are the high energy cosmic rays being created or indeed... is there any such process? (Perhaps most cosmic gamma rays were just mis-identified high energy charged particles as discussed earlier).
If you (alancalverd) get a moment, is there a useful link to some information about how the latest high energy gamma rays are actually generated? X-rays are easy enough... just accelerate some electrons into a tungsten target inside an x-ray tube - but can you really push those frequencies up higher to the gamma range just by increasing the velocity of those electrons? Are your machines producing medical gamma rays directly from nuclear decay these days? Even if they are produced directly from nuclear decay, where are you (we) going to get even higher frequency gamma rays from after that?
Colin also said some good stuff:
...As this is informal, otherwise much would go into new theories...
I think I understood what you were saying. My main reason for not putting any of this (contents of this thread) into that other discussion is the usual two sensible reasons: 1. The original poster doesn't need to be confused.
2. There is value in keeping excessive speculation out of the main sections and where it is done it should be flagged or declared.
As you’ve no doubt realised, the energy needed to create John Wheeler's kugleblitz put it out of being a credible possibility. However, it’s still a lot less than Asimov’s suggestion.
I agree but those calculations were for creating a black hole with a mass parameter in the region of 1 solar mass. Creating micro back holes is not so energy demanding (if indeed micro black holes are possible) and the general theory for creating a Kugelblitz with small mass parameter isn't completely throw-away absurd.
We also now have some theory for black hole evaporation and Hawking radiation, which does seem to link in nicely. A micro black hole would evaporate quickly and produce radiation in the gamma ray region while doing so.
As such it's possible to imagine that a very high energy gamma photon might form a micro black hole because ... it's not like it matters or changes anything you'd observe.... The micro black hole would evaporate (almost) instantly and release a gamma ray in the process. In effect much the same gamma ray photon emerges from the evaporation as the gamma ray that went in.
Speculation: If gamma rays have a maximum frequency then maybe the formation of micro black holes is the frequency limiter: try and go above this frequency and a micro black hole forms and just releases a photon of the maximum frequency. Anyway, I'm not that interested in connecting theories and wild speculation. To start with I would just consider the possibility that maybe gamma rays have an upper limit for their frequency.
Best Wishes.
-
Hi. I can't believe how fast people write. @Kartazion has written something before I finished the earlier post.
Black holes are completely characterised by only three parameters: mass, rotation (angular momentum) and charge.
yes.
Can mass equivalence be done with energy? Or an electromagnetic mass relation?
That wiki reference is a bit new to me - but in general, yes mass-energy equivalence applies. If a black hole absorbs something with energy than its mass parameter goes up.
As much as the black hole loses a small amount of its energy
See earlier post. The rate of evaporation is not constant for a black hole. Smaller mass black holes emit radiation like a black body of higher temperature. Solar mass black holes will take 1067 years to evaporate (source: Wikipedia), meanwhile micro black holes should be gone in a flash and shoud emit a shower of high energy gamma rays in that flash.
Best Wishes.
-
However, you are completely ignoring the theory that already exists for Kugelblitz, black holes that were formed entirely from radiation and not from any particles with some rest mass.
But not from one photon, or for that matter, any number of photons all going the same way.
I'm all for photons of sufficient energy suddenly undergoing pair production, but again, only for pairs of photons meeting from different (not necessarily opposite) directions. The resulting matter must preserve the energy and momentum of the original photons, and that isn't possible for one or more photons going in just one direction.
If that energy density exceeds a critical value then a black hole forms (according to conventional GR anyway).
Sorry, but no. Physics is about invariants (the existence of a black hole, or the lack of it), and not about the abstractions (the energy of the system say), and pulse of light has high energy only in selected frames and not others. The energy is an abstraction, not an invariant. That's the logic from which I'm working.
Once you have photons meeting from different directions, there is suddenly a minimum energy of the system that no abstraction can reduce below some fixed value. Suddenly there's a real energy density and not just an abstract one.
-
A black hole has (among other properties) proper mass.
I'm going to strongly disagree here. Maybe you're using the term "proper mass" is some special way, I'm not sure.
I'm using it the same way you're using 'mass parameter', and only using it at a distance where the two are not distinct. The thing has a meaningful velocity and mass. It takes X amount of force to accelerate it. It has a meaningful velocity relative to coordinate space, even if the coordinate system goes to hell if you get too close. I'm talking about a black hole that's no different than say a dark star, at least outside of a certain radius.
A Black hole has a parameter M, which we call the Mass parameter but it's just a parameter not the mass of a black hole, at best it's the equivalence of the mass required to generate the same gravitational field.
Maybe mass-parameter is a better term. Functionally, it does the same thing. It gives the black hole a proper coordinate frame, which would be a violation of conservation laws if one photon (with say the mass-energy of Earth) suddenly became a black hole.
At a big distance (something outside the surface of the equivalent ordinary spherical mass, so that has to be outside the Schwarzschild radius) the gravitational field from a black hole is identical to that from an ordinary (not collapsed) spherical object of mass M placed an equivalent distance away from the observer).
But at a big distance is all I'm considering here. A photon cannot suddenly morph into something that can be meaningfully stationary. It would violate conservation of momentum. That's why all the cases you describe with a BH forming from just light require light coming in from multiple (at least two anyway) directions.
-
Hi again.
@Halc presented some ideas about momentum and the requirement of conservation.
I've taken a bit of time and ......
.....I don't think there's anything I can do about it. You've made quite a good point, Halc. I'm going to (more or less) concede that point.
Well... maybe we can can consider an accelerated frame where a photon appears to be stationary but that's getting a bit desperate.
I'll agree that if an observer was stationary in a typical or sensible frame of reference (one where photons do seem to travel at the speed of light) then it shouldn't be possible for a single photon to form anything that looks or behaves like a black hole for the observer. You are going to need a pair or a few of them coming together as Halc suggested. There's still the possibility that in some weird frame, a single photon could look like a black hole - and this does absolutely require the existence of a black hole to be a subjective or frame dependant phenomena (which is why it's a bit of weak argument).
I do quite like your (Halc) approach of considering Physics in a manifestly objective and co-ordinate independent way. I'm not saying that you can actually do that but it is useful to try.
I mean, going off on a sideline, even just special relativity can be interpreted in many ways: Trying to define everything in a co-ordinate independent way is sensible but it's also very human and just clinging to the belief that there is an objective reality. An alternative view is just to give up on objective reality and accept that if you change your motion then you do seem to have changed the universe around you. For example, there are some things, like the mass of a planet, where you can choose to have it defined objectively (e.g. as the mass you measure in a frame of reference where the planet is stationary). However, there are some things that you just can't objectively define: For example some pairs of events that are spatially separated cannot be put into chronological order in any objective, co-ordinate independent way (if the distance of separation between them, Δx, is greater then c.Δt in any co-ordinate frame).
Objective reality takes more of a bashing for accelerated reference frames: For example, the Unruh effect implies that even the existence of some particles is subjective. An inertial observer (we'll call them "inertial" because they would see light moving at the speed c) in flat empty Minkowski observes nothing much - it's empty space. Meanwhile an accelerated observer in the same space would see a thermal bath of particles exist. Hawking radiation is similar, it exists for an observer outside the event horizon who is constantly accelerated so as to avoid falling into the black hole. It may* not exist for an observer who is in free fall towards the black hole. (NOTE: I'd really like to say it does not exist for an observer in free fall but QFT on a background of curved space is a bit tricky and a bit beyond me, the Unruh effect is the simple man's version of what seems to be happening with Hawking radiation. It seems that Hawking radiation must exist for accelerated observers outside the event horizons, while it's not required to exist for observers in free fall. See section 9.5, page 402+ in Spacetime and Geometry, Sean Carroll for a better discussion).
Anyway.... I've almost completely lost track of what was being discussed. Oh, yes, the bit about changing the universe when you change your motion. That actually links with something we've recently been discussing in another thread "Musings on Newton" where Mach's principle was one of the main topics.
I'm also going to give @Halc the best answer award this time (because the argument about momentum was good and I was quite wrong to suggest a single photon could form a black hole - or at least in any sensible reference frame).
Best Wishes to everyone and thanks for all your time and consideration.
-
If you (alancalverd) get a moment, is there a useful link to some information about how the latest high energy gamma rays are actually generated? X-rays are easy enough... just accelerate some electrons into a tungsten target inside an x-ray tube - but can you really push those frequencies up higher to the gamma range just by increasing the velocity of those electrons? Are your machines producing medical gamma rays directly from nuclear decay these days? Even if they are produced directly from nuclear decay, where are you (we) going to get even higher frequency gamma rays from after that?
Sorry I missed the question earlier!
Nuclear decay isn't terribly useful for tele-radiotherapy applications. By the time you have enough gamma flux to be useful, you have a very large radionuclide source that you can't switch off, can't modify the spectrum, and its output is continually decreasing and probably being contaminated with decay product gammas and betas. AFAIK all existing 1.3 MeV cobalt teletherapy units (apart from a few exotic "gamma knife" systems) are being phased out.
Linear accelerators are very useful up to about 15 MeV, producing a large controllable flux of electrons which we do indeed bash into a target to make x-rays (same as gammas, but man-made rather than of nuclear origin).
Betatrons can produce small fluxes of 300 MeV electrons and x-rays which are useful for industrial radiography, and synchrotrons currently go up to 15 TeV (CERN LHC source) but I'm unaware of any routine medical use of photons above 15 MeV.
-
Hi.
Sorry I missed the question earlier!
Not a problem. I forgot to check back on this thread for late replies.
Anyway thanks for the info.
It looks like you (the medical physics community) do produce ever more enegetic x-rays just by increasing the velocity of electrons that bombard a target. I'm surprised it continues to work to be honest. I thought the electrons would eventually reach energies where they are just going to go straight through the target and woldn't interact to produce X-rays. I guess you can make the taget thicker but then I would have guessed the electrons are slowed and you could get multiple interactions (some from just slowing down the electron) and not just the production of 1 very high energy x-ray.
Best Wishes.
-
Just bashing the electron into a target is technically simple up to about 15 MeV but not very efficient: you produce a broad spectrum of x-rays, most of which you don't want, and a lot of heat, none of which is useful.
At higher energies you use various forms of magnetic wiggler or undulator. Remember a photon is emitted when an electron accelerates, so if you keep the speed constant but bend the track, you will generate photons tangential to the bend. A good wiggler or undulator will give you a very intense beam of near-monochromatic x-rays.