What happens to photons when they collide?
Does light have garvity? And all other particles?
Photons are massless, and as such they don't bend space-time themselves. As for "photons colliding", the simplest process I can think of that matches what you're talking about would be this:
Photon A and Photon B pair produce into two electron-positron pairs. Positron A and Electron B annihilate, as do Positron B and Electron A, and this results in two photons coming out. This is an extremely high-order effect, though, and light generally doesn't scatter off of itself.
If there is enough energy, a particle-antiparticle pair may form.
Light is subject to gravity, like anything else. I am not sure what your second question means?
Photons have energy and momentum and thus they do bend space-time. The source of gravitation in Einstein's theory is not just rest-mass but rather the whole of the stress-energy tensor. Assuming a quantum theory of gravity is developed wherein we can actually say what a graviton is or if they exist, then in principle photons could scatter off each other by exchanging gravitons.
Photon-photon collision would produce one particle-antiparticle pair. Electron-positron is the easiest, but others are possible if the photon energies are high enough. These processes are extremely rare nowadays, but right after the big bang they were very common.
Ok, the stress-energy tensor also contains energy, momentum and pressure. But if a single flying photon bent space-time, how could it be that the amount of this bending depends on the frame of reference in which you observe the photon?
(Since a photon's energy and momentum depends on that, see Doppler effect).
Because the components of the "bending of spacetime" a.k.a. curvature tensor also depend on the frame, as do the components of the energy-momentum 4-vector of the photon (and in general, the components of the stress-energy tensor of the EM field).
Are photon-photon collisions without the presence of matter possible? If yes, have they been ever detected?
Ok, but does it implies that the space-time curvature caused from a single photon depends on the frame? So, in some frames, we see almost no curvature; in others we see a black hole ? This can't be true.
Possible? Certainly they have not and cannot be ruled out empirically. As far as detection goes, one cannot practically eliminate all matter in an experimental apparatus so the question is somewhat moot.
Again hypothesizing a quantum theory of gravity one may suppose a photon-photon interaction mediated by the exchange of a graviton. However I'm certain we do not have the resources to observe such an effect empirically. The scale of time and space required to observe such a phenomenon for photon energies we can reasonably achieve are likely on the same scale as the size/age of the observable universe.
There are other mechanisms by which two photons might be predicted to interact, e.g. virtual fermionic particle-antiparticle pairs. But in the absence of some catalyzing medium such phenomena are well beyond laboratory verification.
The only empirical experiments which can come close to this order of phenomena are astronomical observation of high energy cosmic radiation or of gamma ray bursts. This gets really speculative as one must first propose an astrophysical theory which predicts a certain frequency of events and then utilize photon scattering to explain a deficit in the observed frequency.
Cosmic radiation is problematic as their energies are so high it is as yet impossible to identify the species of particle. I do recall however reading some abstracts investigating the opacity of the universe to high energy photons which might be relevant. Try searching the pre-print archives, but pay close attention to whether a given pre-print has been submitted to or accepted by a credible peer reviewed journal. Pre-prints are not themselves peer reviewed as yet.
Let me add to the other reply in saying this. First since we're talking General Relativity and there's as yet no quantum theory of gravitation lets stick to the classical realm and talk about classical light bending space.
Remember that "photon" means quantized light and not "quantized plane-wave constant frequency light". Take any classical solution of Maxwell's Equations in whatever curved or flat (fixed) space-time you like and then remember that
you can resolve the classical wave as a number (or superposition of numbers of) photons each of which are scaled copies of the same solution. For example you may consider a single photon whose wave function is in the form of the radiation field for a dipole radiator. Just because we find it convenient to resolve photon fields in a momentum basis (i.e. plane-wave Fourier spectrum) don't think this is a physical requirement. So work in the classical realm and just consider waves of amplitude low enough to be approximately one photon's worth if that is your concern.
That having been said... to get the full exposition of the phenomena you must simultaneously solve Einstein's equations and Maxwell's equations in curved space-time. As this is a sticky problem you might then try a weak field approximation. I would imagine such an approximation would show say the beam emitted by a laser producing gravity waves of comparable wave-length but with an oscillating and dissipating solution where both the light and gravity waves are dispersed. (I would imagine also that it might be necessary to take into account the loss of mass-energy and relative motion of the source including the thrust produced by the emission and how that too affects the shape of space-time.)
To address your question about Lorentz transformations keep in mind that once space-time gets bent you must consider General Covariance and not just Lorentz covariance. It is true that in SR you can transform a monochromatic plane wave to arbitrarily low frequencies but remember that a similar transformation on non-plane-waves will decrease the frequencies in one direction for one part of the wave while increasing the frequencies elsewhere. (Imagine in the extreme case the Lorentz transformation of spherical waves).
Since a plane-wave extending over all of space would have infinite energy it is not physically reasonable. Rather you must consider at best a beam of finite cross section. Said beam will already disperse due to diffractive effects and if you add the dispersion due to gravitational coupling it will further loose its unidirectional behavior. In the end you should find that any physically meaningful case will have a sensible and consistent interpretation in all frames.
As I see it you are improperly thinking in absolute terms while invoking relativity. Specifically you consider an absolute "bent" vs "not bent" question about space-time while Lorentz transforming a "photon". The question should be "how bent" given a "photon" of "what frequency" at a given space-time point. And the answer is of course "its all relative" but relative in a consistent way to the choice of frame.
Curvature is a frame independent and a coordinate independent property of spacetime.
A photon does, albeit extremely little, curve spacetime. All objects with a non-vanishing stress-energy tensor are sources of spacetime curvature.
First of all, thank you for your answers.
Yes. I wonder how could we be so sure about the photon generating curvature without such a quantum theory of gravitation.
Say a laser source fixed in the origin of a coordinate system emits, in his frame, 1 photon every minute with wavelenght 500 nm in the +x direction. How will those photons bend spacetime as seen from that frame? Is it also necessary to specify the coherences of the source? Make all the simplifications you need.
How will those photons bend spacetime, seen from a ref.frame moving in the -x direction at v = 299,792,457.9999999999 m/s?
And if v is in the +x direction?
I admit not to know very much about the stress-energy tensor, but I wonder how is it possible to construct a non-zero invariant quantity (or set of quantities) for a photon, since a photon's energy depends on the frame and there isn't any proper frame for a photon.
The stress energy tensor is not a constant: it's a covariant rank-2 tensor. That means that its components aren't constant. Instead they transform under a change of coordinates, but under a very specific fashion. See the tensor transformation rule for more details.
Sorry if I keep asking, of course I will look for the tensor transformation rule, but is it possible to explain it in a simple way?
In the case of a 4-vector of a non-zero rest mass's particle, we know that, even if its components (energy and momentum), are not invariant, the 4-vector square modulus is invariant (because it's the proper or rest mass square).
But how is it possible to make something similar with a photon? What exactly is (or are) that (different from zero) invariant quantity?
Perhaps reading this section in Wikipedia's SR article and Wikipedia's Lorentz covariance article might help.
We can only be sure about what GR says should happen given we can speak meaningfully about the stress-energy of a photon.
To answer your question:
First take the weak field approximation to GR and calculate the first order gravity waves generated by the light.
Second solve Maxwell's equation for the propagation of that light through the space-time curved by said gravity waves.
Repeat step one using weak field approximation on the curved space-time you get from the previous cycle. Then repeat step two using this additionally curved space-time.
Lather rinse repeat and hope the sequence converges.
If you work it out carefully it will be quite a publication... I'll be anxious to read it. It would make a great PhD thesis. I've already done a PhD thesis so I'll leave it to you or someone else.
What I think you will get is that over a length scale much larger than our observed universe and a time scale much larger than its current age as asserted by most Big Bang theories... that the light will slowly disperse and decay into gravity waves. The other possibility I see is that there will be an oscillation between gravity waves and E-M waves. But until you do the math (I'm not going to attempt it any time soon) all that can be said is that it won't yield simply E-M waves propagating through flat space-time.
Certainly these gravitational waves generated from the photon (if they exist) will be in the form of a wave packet, which will have a group velocity. This velocity should be equal to light's velocity; so will this wave packet be stationary with respect to the photon? It doesn't seem possible, but if it is, then the photon shouldn't find any curvature in its path. If it's not possible, which will arrive first to a specific distance, the gravitational wave packet or the photon? Everything seems absurd to me.
Separate names with a comma.