Verified answer

The answer to both a) and b) is the speed of light.

Yes, it really is :)

Keep in mind that part of relativity involves the slowing of time as you approach the speed of light -- AT the speed of light, time appears to stand still for the observer. Since both photons are going the speed of light, when you pick one of them as an "observer", from that point of view time is standing still, but the it's NOT for the other photon -- from the observer's point of view, that other photon is really flying. It's the same whichever one you choose as the "observer."

Think about it :)

The problem with this question as posed is that it assumes that either proton A or B would even be able to measure the speed of any object, because in order to measure speed, one needs 1) a clock, and 2) a yardstick in which to measure the other's moving frame. Any massless entity cannot possess a clock or any other time-keeping means, and any moving frame moving at light speed would be contracted to a single plane, i.e. the entire universe would be contracted to a single plane. How do you even make sense of measuring velocities in such a context? You can't.

So let's use a couple of spacecraft A and B moving towards each other at near light speed. This time, each spacecraft can have the necessary measuring devices, and moreover, they take careful measurements as the spacecraft flash by each other, much like trains on parallel tracks. Now, how is spacecraft A really going to measure the speed of spacecraft B? The question isn't as obvious as you think, because more than one answer is possible, depending on how one measures the speed! Let's look at two imporant but different ways to do it:

1) Spacecraft A notes the time when the nose of spacecraft B lines up with the nose of spacecraft A, and then notes the time when the nose of spacecraft B lines up with the rear of spacecraft A. If the length of spacecraft A is L, and the time difference is t, then the speed is L/t. This figure never exceeds the speed of light.

2) Spacecraft A notes the time when the nose of spacecraft B lines up with the nose of spacecraft A, and then notes the time when the rear of spacecraft B lines up with the nose of spacecraft A. If it's already known (from public records, whatever) that the length of spacecraft B is M, and the time difference is t, then the speed is M/t. Surprisingly, this can EXCEED the speed of light, approaching infinity!

Part of the reason why we have such strange paradoxes is because if both spacecraft A and B have carefully synchronized all clocks along the lengths of the ships, should spacecraft A take a "snapshot" of all the clocks visible on spacecraft B, all the clocks would NOT appear synchronized. That is it say, to personnel of spacecraft A, it would appear that they're seeing spacecraft B in different time zones! This is a small but true fact that many people don't understand or leave out when trying to make sense out of these strange relativity problems. It makes problematic the job of measuring things, because one would literally be trying to measure a spacecraft that is existing in different time zones, for example. And, by the way, the method of using "public records" to find and use the value M for spacecraft B is a "no-no" in relativity theory, because this value M wasn't actually MEASURED, only known beforehand.

Relativity is the idea that the laws of physics do not change from one inertial reference frame and another. Any experiment that you can do in your laboratory at home should work equally well in a train coach or the stateroom of a ship (provided the train/ship is just cruising along and not accelerating, bumping, rolling, or turning). This was known since before the time of Galileo. Newtonian mechanics incorporates relativity. Specifically, Newtonian mechanics work under the following transformation (called the Galilean transformation) from one reference frame (x,t) to another (x',t') moving at a speed v. x -> x' - vt' t -> t' That's pretty straightforward. Everybody measures the same time and their positions are off by a reasonable, intuitive amount based on the relative motion. Everyone agrees on the time and distance between two events. Now the trouble is that the laws of electricity and magnetism (discovered by various folks and compiled by Maxwell) are NOT invariant under this transformation. Some folks thought that the old concept of relativity does not apply to electricity and magnetism--that the laws of E&M only work with respect to an ether. Einstein, however, assumed that relativity SHOULD apply to E&M and that Newtonian mechanics must be flawed. He thereby developed special relativity and derived new transformation laws (which had already been figured out by Lorentz, so they have his name). x -> gamma (x' - vt') t -> gamma (t' - vx' / c^2) Under these new laws, not everybody measures the same times and distances between events. That factor of gamma goes from one at slow speeds up towards infinity as you approach the speed of light. Moving clocks run slow and moving rulers are short!

A photon represents the energy of light received in one second. It is therefore not light but a mathemathical representation of the energy of a moving light flux. And this is where the cooky crumbles.

Relativity indicates that a moving light source moving relative to a zero point of reference will emit a light flux with a definte velocity relative to the zero point frame of reference, irrespective of the motion of the light source.

when particles of light collide with each other an interference pattern results.

According to the Galileo principle of relativity when two particles move at the same velocity the relative speed to each other is zero.

Take photon A,

Observing photon A from an external stationary frame of reference time has stopped for it in its frame of reference. However, in photon A's frame of reference, time is persevering as normal. It observes photon B moving away from it at the speed of light because photon A believes it is standing still and the whole universe is moving around it. The same is true if you consider photon B.

Importantly, it is because time doesn't exist for the photons that they both observe each other moving away from each other at the speed of light even though a stationary observer sees them moving in parallel. For the tiny snapshot of time we observe them (compared to infinite time it is technically zero time we observe them for in their respective frames of reference) there is no paradox.

There is a simple answer to your question, which is essentially the question einstein asked, "What would the universe look like from the point of view of a photon?" (paraphrased) In the special theory of relativity, his answer to this question, it says that you cannot be in the reference frame of a photon! Your question is often asked as a trick question to test one's understanding of relativity. Sorry, but that is the best answer physics can offer you.

THe photons, in reference to each other are stationary if they are both trvelling in the same direction and at the same speed.

If they are traveling the same speed and direction, they are in the same frame of reference. Relative to that frame, everything else in the universe is moving at the speed of light.

"God does not roll dice."

Also, light is not incoherent with itself.

The situation you describe is a stream of light photons. Hence, relative to each other, their speeds are -0-. Einstein's theory applies to objects that are NOT travelling at the speed of light.

.

Due to Lorentz contractions of space and time the velocity (if one could measure it under the given circumstances) would be c