Relativity and Cosmology

Hello! This is and was interesting to me. I am not a physicist and this sort of thing interests me to no end. Let me think up another experiment. We are in a lab. You are on one photon and I am on another. We both are in a coherent light beam side by side. Sam the lab tech sends our beam of light into a splitter. You are riding on one photon going one way while I am split off riding the photon going the other way. We bounce off a series of mirrors arranged in a circle so to speak and we each hit every mirror in the same place, just going in opposite directions. We meet at the point where we were split apart and pass each other. What is the combined passing or collision speed? What would Sam see? Would the see two photons passing each other at the speed of light or double that speed. If only at the speed of light where does the extra velocity go?

As you can see I know nothing about this sort of thing but sure am interested!

mayf, way off and far out in pahrump

Who is SAM? from the perspective of an outside observer the collision speed would be 2x the speed of light, from the perspective of either person on the photon the collision would be at the speed of light but the incoming photon would be blue shifted alot. There is no extra velocity, the velocity is relative to the observer, as is the frequnecy of the approaching photon.

Guest1, you asked: "What would Sam see? Would the see two photons passing each other at the speed of light or double that speed. If only at the speed of light where does the extra velocity go?"

I assume Sam is an laboratory observer. Sam cannot measure the relative speed between the two photons. He can measure each photon's speed and then add them using the relativistic addition of velocity rule:

v =(v₁ + v₂)/(1 + v₁v₂/c²)

Plug in v₁ = c and v₂ = c and we have v = c. So where did the "extra velocity" go? It's there, Sam just cannot measure it!

Photons cannot measure speed, but say we have two observers traveling past each other in opposite directions, each at 0.99c, both relative to Sam's laboratory (the reference) frame. Can you work out how fast the one observer would measure the other? Where did the 'lost' velocity go here?

I know this reply is almost 3 years after the fact, but does the relativistic addition of velocity hold true for all speeds or only ones near the speed of light? I understand that the effect is negligable, but is it still considered scientifically true? Also, if the two beams of light are directed at each other is the "true" closing speed between them 2c and c is the "observed" speed or are they physically approaching each other and only the speed of light.

Sorry, I generally understand all the concepts that you talk about, but its a whole other battle getting myself to believe or accept them fully.

Dan

Hi Dan,

No problem - these threads are not time limited (for as long as the authors live and CR4 exists!).

The relativistic addition of speeds rule holds for all speeds, as far as can be established. It must, otherwise Special Relativity (SR) must be wrong - so far it has withstood 100+ years of testing with flying colors, so what reason do we have to doubt it?

'True closing speed' is meaningless, since speed is a coordinate dependent concept (coordinate distance traveled divided by coordinate time elapsed). Every inertial observer measure a different coordinate distance and time and hence a different speed for the same object - except for light, where the coordinate differences 'cancel out' and every inertial observer get the same speed for light.

Einstein's relativity is concerned with what is observed (and measurable) and how they relate. It tells us little (if anything) about the 'true nature' of light or gravity.

-J