# Maximun energy of a photon

• JAL
In summary, the conversation revolves around whether there is a minimum wavelength for electromagnetic radiation and if it is equal to the Planck length. Some argue that there is no limit to the energy a photon can carry, while others suggest that a photon with a wavelength smaller than the Planck length would collapse under its own gravitational field. However, this argument is deemed fallacious as the wavelength of a photon would appear different in different reference frames. Additionally, it is suggested that a photon at the Planck length would be unstable and likely form into massive particles after an interaction. The concept of the Planck length as the maximum length for a virtual photon is also discussed, but is met with skepticism due to the uncertainty principle.

#### JAL

Please explain the error in this logic (if any):

E = hc / &lambda;

Where
h = Planck Constant = 6.62606876 x 10-34 Js
c = Speed of light = 299792458 m/s
&lambda; = Wavelength

The wavelenght can't possibly be smaller than Planck Length (1.6160 x 10-35 m) yields:

Maximun Energy = 12292360398.7464 J
Maximun Energy = 7.6722887211823E+28 ev

Is this valid? Is there a limit on how much energy an photon can carry? I've never heard of that...

Woops

What's you argument for a phton's wavelength not being smaller than the Planck length? I mean the compton wavelength of a flea is about the same as the Planck length. Are you saying that a photon with a wavelength of the pPlanck length would be unable to escape it's own gravitaional field, cos I believe that's been theorized, but I'm unsure.

Originally posted by jcsd
What's you argument for a phton's wavelength not being smaller than the Planck length? I mean the compton wavelength of a flea is about the same as the Planck length. Are you saying that a photon with a wavelength of the pPlanck length would be unable to escape it's own gravitaional field, cos I believe that's been theorized, but I'm unsure.

Actually I was just wondering if there is a minumum wavelength for EM radiation and if so if it is the Planck Lenght? This would mean that there is a limit to the energy of a photon can carry.

All I can say is probably not, the idea that a photon will collapse under it's own graviational field is fallacious (it forgets blue-shifting), unless there's something I'm unware of I don't see why a photon can't have a wavelength > the Planck length, though such a photon would be unstable with any interaction probably forming an electron-positron pair. In fact Isaac Asimov (I don't like quoiting sci-fi authors but anyway) said that the maximum energy of a photon was the energy of the cosmos and the minimum energy was the enrgy corresponding to a photon with a wavelength the same as the size of the cosmos.

I'm not sure what gravity has to do with this, jcsd - JAL din't mention it. Planck's constant is the "size" of quantum uncertainty. I don't think a photon can have a wavelength shorter than that.

Well I would suggest doing some simple quantum calculations with escape velocity as well.

However, it does seem that a photon of that small wavelength would be extremely energetic for a photon, and hence would be very unstable.

Originally posted by russ_watters
I'm not sure what gravity has to do with this, jcsd - JAL din't mention it. Planck's constant is the "size" of quantum uncertainty. I don't think a photon can have a wavelength shorter than that.

Yep, but it has been suggested in a physics report that the Planck length is the maximum length for a virtual photon as any photon with a wavelength greater than this would collapse in it's own graviational field like a black hole. This logic is obviously fallacious as from a different reference frame the photon's wavelength would be blue-shifted above the Planck wavelength so following this logic it wouldn't collapse in this reference frame, so we must reject it collapsing in a refernce frame where it's wavelength is below the Planck length.

Macroscopic objects, including yourself, generally have Compton wavelengths below the Planck length, why not a photon? There is no comopelling reason to think that photons with wavelengths smaller than the Planck length could at exist in theory.

Originally posted by jcsd
Yep, but it has been suggested in a physics report that the Planck length is the maximum length for a virtual photon as any photon with a wavelength greater than this would collapse in it's own graviational field like a black hole. This logic is obviously fallacious as from a different reference frame the photon's wavelength would be blue-shifted above the Planck wavelength so following this logic it wouldn't collapse in this reference frame, so we must reject it collapsing in a refernce frame where it's wavelength is below the Planck length.
confused. Did you mean that photon with wavelength 'shorter' than Planck's would collapse, and that redshift would 'avoid' that? Shouldn't frame of photon be the only one that matters (if such q makes sense)?

There is no comopelling reason to think that photons with wavelengths smaller than the Planck length could at exist in theory.
Photon at Planck length would have mass of 1.5E+23 Me. Shouldn't such 'thing' condense into matter?

SST says the photon will grow instead of becoming
smaller, I think.

Live long and prosper.

Originally posted by wimms
confused. Did you mean that photon with wavelength 'shorter' than Planck's would collapse, and that redshift would 'avoid' that? Shouldn't frame of photon be the only one that matters (if such q makes sense)?

Photon at Planck length would have mass of 1.5E+23 Me. Shouldn't such 'thing' condense into matter?

No, as I said before the premise behind it is faulty, as considering a differen refrence frames the wavelength would be different.

Photons don't have mass, but yes, such a high energy phton is unstable and would after nearly any interaction change into massive particles.

Originally posted by jcsd
Macroscopic objects, including yourself, generally have Compton wavelengths below the Planck length, why not a photon?
Isn't that just a mathematical average? Analagous to the idea of light "slowing down" when traveling through a medium?

There is no comopelling reason to think that photons with wavelengths smaller than the Planck length could at exist in theory.
You mean could NOT exist, right? There is no compelling reason to think they could NOT exist? I still think HUP is a pretty compelling reason (not that I necessarily understand it all that well).

Originally posted by russ_watters
You mean could NOT exist, right? There is no compelling reason to think they could NOT exist? I still think HUP is a pretty compelling reason (not that I necessarily understand it all that well).

What is HUP?

HUP=Heisenberg Uncertiantiy Priciple.

Originally posted by jcsd
For some reason I can't open that page, could you quote the relevant sections?

The Question
(Submitted April 12, 1997)

At the upper end of the electromagnetic spectrum are Gamma-rays. These "Gamma-rays" have the highest energy content in the electromagnetic spectrum. What is never discussed by the High-Energy astronomers is the following: Is there a an upper limit (frequency) to the electromagnetic spectrum? To wit: What is the "highest frequency" Gamma-ray ever detected and is there reason to believe that there are Gamma-rays with even higher levels of energy and if so...does the electromagnetic frequency spectrum have an upper limit...or does it go out to infinity?

The Answer
Thank you for your very good question about the highest energy gamma-rays. Historically, all particles with frequencies greater than about 1019 Hertz (or about 50,000 electron Volts (5x104 eV) where a typical optical photon carries 2-3 eV) are called gamma-rays. Theoretically, there is no hard limit to the energy that a gamma-ray can have. However, there are a number of practical considerations that one needs to take into account involving both astrophysical sources and basic physics.
Before we address this, however, let's tackle the question about the highest energy gamma-rays yet detected. The highest energy measurements of gamma-rays are accomplished using ground-based instrumentation which also measure cosmic rays. Reliable detections of very high energy gamma-ray radiation from individual astrophysical sources, specifically from a couple of active galaxies and from the Crab Nebula, have extended up to about 1027 Hz (5 x 1012 eV). Aside from these individual sources, there is also expected to be a diffuse emission of gamma-rays which accompany the isotropic flux of cosmic rays. This diffuse gamma-ray emission is well measured below around 1024 Hz (109 eV) or so, and is expected to extend up to at least 1030 Hz (1015 eV). There have been reports of measurements of diffuse gamma-ray emission above 1029 Hz, but many other groups have only reported upper limits to emission at these energies. The measurement is exceedingly difficult since cosmic rays can outnumber gamma-rays at these energies by a factor of 10,000 to 1 or more! So you have to sift through a lot of cosmic rays to try to find the gamma-ray signal - a very difficult task.

The truth is we may never actually know to how high an energy nature sees fit to produce gamma-rays. As the gamma-ray is making its way to our telescopes, it has to traverse through space, where there are photons and particles all around us, for example the microwave background. At the highest energies, these photons will scatter down to lower energies before they arrive at Earth. In addition, many sources could produce very high energy gamma-rays which are absorbed and re-processed within the source. As a result, at the most extreme energies, we should see only those gamma-rays produced by relatively nearby sources. In addition, while we expect diffuse gamma-rays up to 1030 Hz, at energies beyond this the basic physics of particle interactions and gamma-ray production is less clear. There could be many surprises.

Nevertheless, from the distribution of gamma-ray energies observed we know we should be able to detect gamma-rays with energies higher than those stated above. There are currently a number of projects being developed that will collect ultra-high energy gamma-rays from cosmic sources, such as OWL and MILAGRO. See

http://lheawww.gsfc.nasa.gov/docs/gamcosray/hecr/owl_new.html [Broken]

for details on these exciting gamma-ray astronomy projects.

Thanks for you interest,

Padi Boyd and Daryl Macomb,
for the Ask a High-Energy Astronomer Team

Last edited by a moderator:

Originally posted by JAL
Theoretically, there is no hard limit to the energy that a gamma-ray can have.
I wish he'd coverd that part in more depth than the practical astronomy part. Ie, why doesn't HUP put a theoretical cap on the minimum wavelength

Originally posted by JAL
Theoretically, there is no hard limit to the energy that a gamma-ray can have.
This sounds like opinion rather than fact to me.. Sounds much like old times 'Theoretically, there is no hard limit to the velocity in space'.

In addition, while we expect diffuse gamma-rays up to 10e30 Hz, at energies beyond this the basic physics of particle interactions and gamma-ray production is less clear. There could be many surprises.
Planck length photons would be 10e43Hz, or 'mere' 10e13 times beyond where physics is 'less clear'.

Wavelength is product of c and Planck time 10e-43sec. Question comes down to whether there can be shorter meaningful measure of event time, or whether velocity c is constant. Interestingly, wavelength depends on frame of reference, meaning also energy depends on frame, and so does Planck time?

Seems to me that if there exists finite limit on velocity c, then there also exists some finite limit on frequency and energy. no?

## What is the maximum energy of a photon?

The maximum energy of a photon is determined by its frequency and is given by the formula E = hf, where E is the energy in joules, h is Planck's constant (6.626 x 10^-34 joule seconds), and f is the frequency in hertz.

## How is the maximum energy of a photon related to its wavelength?

The maximum energy of a photon is inversely proportional to its wavelength. This means that as the wavelength decreases, the energy of the photon increases.

## Can the maximum energy of a photon ever exceed a certain value?

According to the theory of relativity, there is a limit to the maximum energy of a photon, known as the Planck energy. This limit is equivalent to about 1.22 x 10^19 GeV (gigaelectronvolts).

## What factors can affect the maximum energy of a photon?

The maximum energy of a photon can be affected by the material it is passing through, as different materials can absorb or scatter photons at different frequencies. Additionally, the energy of a photon can be altered by the presence of strong gravitational fields or intense magnetic fields.

## How is the concept of maximum energy of a photon important in fields such as astronomy and quantum mechanics?

The maximum energy of a photon is crucial in understanding the behavior of light and electromagnetic radiation in various phenomena, such as the emission of light from stars and the photoelectric effect. It also plays a significant role in quantum mechanics, where the energy of a photon is used to describe the behavior of particles on a subatomic level.