electromagnetic radiation - Are there any theoretical limits on the energy of a photon?

Is there any lower or upper limit on the energy of a photon? i.e. does the mathematical framework we currently use to study photons blow up when a photon surpasses a certain upper limit of energy? (or the same on the opposite side?)

My thoughts: If I let the energy of a photon tend to infinity, its wavelength would be tending to zero, and since it is thought that we cannot really distinguish things when they are on the scale of a Planck Length, would the photon have its maximum energy when its wavelength is equal to the Planck length? (Feel free to correct me, I feel I might not be.) and for the opposite end of the spectrum a photon with the least energy would have zero wavelength, implying no photon, which is a trivial case.

Answer

One of the main problems of Quantum Gravity is that Quantum Mechanics (in broad sense, including QFT) holds for arbitrary energies, i.e. there is no structural inner bounds to its validity nor there are known systems for which QM fails. In other terms, in the framework of QM, a collison between particles having Planckian energy has nothing special. On the other hand, at very high energy General Relativity holds and, as far it is known, its consequences must be taken in account. In particular, it is a theorem by Schoen and Yau that "[w]hen enough matter is condensed in a small region, gravitational effects will be strong enough to cause collapse and a black hole will be formed" (quoting the abstract of their article). So, there is a limit on the energy of a photon? Strictly speaking, I don't know. There is no physical evidence, as far as I know, for saying yes or no. If the answer was in the affermative however, QM has to be modified, in order to include an "inner blow up" at very high energies. Notice that one can't say for sure that a QG theory exists nor even that it is a physical necessity. The only persuading physical reason I know of to say that a more comprehensive theory ought to exist is that the cosmic microwave background, a specific GR-object, follows a black-body curve, a specific QM-behaviour.

At the opposite extreme, "soft" photons would not create any difficulty of this sort (provided that GR is "switched off", i.e., has no effects, otherwise picking sufficiently small regions the situation is in principle the same than above); interestingly, this limit is "fussy" for electrons, in the sense that, since electrons are very light but not massless, it is difficult to succeed in keeping them at nonrelativistic regime and check whether they behave according to nonrelativistic QM. Obviously, photons of too high energy are rather unuseful as probes, since annoying effects such as couple creation arise and most measurements become unsensible.

optics - Image formed in a compound light microscope

I am trying to understand whether the image formed in a compound light microscope is at infinity or not. I get conflicting answers everywhere I look.

homework and exercises - Calculation of tension in a loop with force acting outwards

I'm having a few problems with understanding how to calculate tension in a loop.

If I have a circular loop, and some force is applied uniformly radially outwards in such a way that the force acting on each element of the string is normal to the string at that point, then how will the string develop a tension?

My intuition tells me that some force must act by the string to prevent the string from expanding infinitely. However, how can the string apply such a force, when its only means is tension which acts perpendicular to the force always?

Any answers will be appreciated.

I suppose that this is analogous to asking why pumping air into a soap bubble will make it expand a certain amount (until the external pressure is equivalent to the excess internal pressure).

EDIT:

So, I can simply take the semi-circular half and apply Newton's Laws?

So $2 T = F $

Therefore, tension developed $= \frac F2$

Just want to clarify that by F I mean the total horizontal Force acting on the semicircle, not just the central element.

Is this correct? Just want to verify if I understood the concept.

Answer

The loop has a curvature. As a result, when you take a small element of the loop, the tension force applied to it from both the sides is at an angle, which results in a force component to the inside.

Since your question asks for a rationale behind the tension force, I'll leave it here. You can now try yourself to find the tension by equating the outward force with the inward force. Or, if you are given the total outward force, you can integrate the tension force over the loop and then equate the total outward and inward forces.

thermodynamics - How does mass leave the body when you lose weight?

When your body burns calories and you lose weight, obviously mass is leaving your body. In what form does it leave? In other words, what is the physical process by which the body loses weight when it burns its fuel?

Somebody said it leaves the body in the form of heat but I knew this is wrong, since heat is simply the internal kinetic energy of a lump of matter and doesn't have anything do with mass. Obviously the chemical reactions going on in the body cause it to produce heat, but this alone won't reduce its mass.

waves - Do photons occupy space?

Total noob here.

I realize that photons do not have a mass. However, they must somehow occupy space, as I've read that light waves can collide with one another.

Do photons occupy space? and if so, does that mean there is a theoretically maximum brightness in which no additional amount of photons could be present in the same volume?

Answer

However, they must somehow occupy space, as I've read that light waves can collide with one another.

That's not true. Yes, light waves can "collide" and interact with each other (rarely), but that itself doesn't imply that they need to occupy space.

It's not even entirely clear what it means for a subatomic particle to occupy space. A particle like a photon is a disturbance in a quantum field, and is "spread out" across space in a sense; it doesn't have a definite size in the same sense that a macroscopic material object does. But you'll probably agree that, if it's possible to make any sensible definition of "occupying space" for a subatomic particle, it should involve preventing other things from also occupying that same space. Photons don't do that. They're bosons, and as a consequence of that they are not subject to the Pauli exclusion principle, so if you have a photon occupying some space (whatever that may mean), you can in theory pack an unlimited number of additional photons into the same space.

electromagnetism - Distant bodies emitting photons

This comes from a discussion forum, where a friend of mine asked the following:

We can see objects in space billion of light years away, right? I started wondering about that.

If you take 2 objects in space, the other should be able to see the other no matter what angle in degrees you position it at. That would almost seem to imply that light is being sent out in an infinite number of degrees/angles from the source. But that cannot be true because energy cannot be infinite.

If the observer goes out far enough from the source, would there be gaps in the light? Could you pick a viewing angular degree (of extremely high angular precision) where there's no light?

I'm actually quite curious about this question myself and really have no answer, and the discussion hasn't really yielded a satisfying answer. So I figured I would bring it here on behalf of my friend and to sate my own curiosity.

Answer

Well, and in the two wave answers nobody considers the quantum mechanical picture.

Photons compose these classical waves.

Photons carry momentum equal to energy if we set c=1, p=hnu

When the distance from the source becomes large enough that individual photons can be counted in a counter, there will be a point where gaps will exist and no photons will be counted.

Taking this solution from Yahoo answers one can see that for a given wavelength and intensity, a delta(x) between two detected photons can be found where individual photons will be very rare.

So the answer depends on the original intensity,which falls with the distance as 1/r**2 ,the distance, the wavelength observed and the time available for the detection. If one waited an infinite time, the answer "there is no gap would hold probabilistically. For any reasonable delta(t) there will be gaps that cannot be predicted in r,theta,phi because they will depend on the probability function of the photons.

particle physics - Is it possible for quarks and charged leptons to 'oscillate' analogously to neutrinos?

In a hypothetical scenario where the coupling of the fermions to the gauge fields were extremely small, would it be possible to observe quark and charged leptons oscillate in the same manner as we observe neutrino oscillations today?

i.e. would it be possible for the flavour eigenstate of a quark/lepton produced in a weak interaction to be detected as a different flavour eigenstate at a distant detector due to the states propagating according to their mass eigenstates?

$$ \left| {\nu_{\alpha}(T)} \right> = \sum_iU^*_{\alpha i} \; e^{ip\cdot x} \left| \nu_i \right> $$