# How does a photon able to store an arbitrary amount of energy?

"Regular" particles "accommodate" the energy they carry in their mass and velocity, and their frequency (or wavelength) is tied to those properties (e.g. de Broglie wavelength).

The energy of a photon, on the other hand, appears to be arbitrary, i.e. not tied to mass (which is zero) nor speed (which is the speed of light). Is there an intuitive way to understand how that magical particle is able to store an arbitrary amount of energy?

• Perhaps it's helpful for you to read this answer from the question Does photon absorb energ? – HolgerFiedler Mar 24 '17 at 5:03
• Don't you separate too much fields from energy ? All particles are actually "made" of fields. Any field has some energy. The more field is in a volume the more energy it has $K = \frac{1}{2}\epsilon_0 \iiint{\vec{E}^2}dV$ – Mihai B. Mar 24 '17 at 6:43
• @MihaiB. what about single photon emitters? – Sparkler Mar 24 '17 at 17:37

Photons , as quantum mechanical entities, have a wavefunction . This is a solution of a quantized form of Maxwell's equations, thus the continuity between the quantum level of photons that just have energy and spin when measured, to the classical electromagnetic wave is secured by the same differential equation solutions, in the two different frameworks, classical and quantized. the E and B in the equation are the electric and magnetic fields entering the classical too.

For the wavefunction when complex conjugate squared one gets the probability of finding the photon at a delta(volume ) at time delta(t).

For the classical electromagnetic wave the E field is connected to

the rate of energy transport S is perpendicular to both E and B and in the direction of propagation of the wave. A condition of the wave solution for a plane wave is Bm = Em/c so that the average intensity for a plane wave can be written To get the photon energy one has to operate with the energy operator on the wave function of the photon and will get a probability density of the energy, which will be the h*nu within a certain volume, according to the link above.

Thus the energy of the photon is as arbitrary as any other energy concept, and it is carried by energy=h*nu where nu is the frequency of the emergent classical wave by mathematical continuity of the Maxwell equations in both regimes.

I think that the main reason the photon wave function is not discussed is because the classical wave of Maxwell's equations is so successful that it is not necessary to delve into the intricate connection at the level of solving equations. In Quantum Field Theory it can be shown how the classical fields emerge from the underlying quantum mechanical, a demonstration here.

This link discussing the connection between the classical polarized EM wave and the photons that build it up might help the intuition.

It's stored in the electromagnetic fields, and it is intrinsically tied to the frequency of the photon.

Also, consider that "regular particles" also accommodate energy in many different forms besides mass/velocity. Consider nuclear power as an example, which is stored in a way that does not show up trivially in mass or velocity (technically it shows up in mass, but in a way which is far less intuitive than the energy of photons)

• Frequency of a photon is equivalent to (interchangeable with) energy, so that doesn't add to my understanding. Also, I'm not sure how the "field" plays a role in the case of single photon emitters. – Sparkler Mar 24 '17 at 3:36
• I think you've got a tricky question here, because the answer is "a photon stores energy in the way a photon stores energy." It's empirically well accepted that all photons can store energy. It is a property they have. If I flip this around, why do you believe they cannot store energy? What about your model of the universe prohibits photons from storing energy? – Cort Ammon Mar 24 '17 at 3:41
• It's still a good question, whether there is any limit to the energy or frequency. We have not seen any, the highest freq gamma rays/bursts from astrophysical processes are on the order of $10^{19}$ Hz. The limit might be where the photon wavelength reaches the Planck length, or thereabouts, where some Planckian theory must take over. It's not tricky, it's does seem to be the case that QED does not pose a limit to the energy or frequency. I've never seen a reason either way. As for massive particles, you can accelerate them as close to c as you can, and their energy also rises w/o bound. More – Bob Bee Mar 24 '17 at 5:18
• And they can interact or turn into each other if their characteristics allow it, and in fact in the early universe they were doing that. Of course for both freq and energy it depends on reference frames. – Bob Bee Mar 24 '17 at 5:21
• High energy photons are likely to split into lighter particle antiparticle pairs. So one might ask how does a massless particle generate two or more massive particles? The answer is simply because mass is a manifestation of energy just as frequency of a photon the manifestation of the energy of a photon. In qft all particles have wave equations with some frequency. In case​ of massive particles the dispersion relation has the mass term and so we can relate mass to energy. In case of photon there is no mass parameter and so we relate energy to frequency. I don't think there is anything confusin – Abhishek Pal Mar 24 '17 at 6:39