Here is the scenario. I am in Spaceship A and my friend is in Spaceship B. Each spaceship can accelerate to 99.99% the speed of light in seconds. If Spaceship A and Spaceship B start at the same point and travel in opposite directions what would I see if I looked in Spaceship B’s direction? It seems to me that any light coming from Spaceship B would never reach me and it would quickly disappear regardless of how good my telescope was. Is this accurate?
No, light from B will reach you. In your reference frame, the light emitted by B will travel toward you at c, but will be immensely red-shifted. In addition, if you could see B, the ship would look foreshortened, events on board would appear to happen very slowly, and the ship would appear to be traveling at some fraction of c. Incidentally, A and B are only traveling at 0.9999c relative to the starting point, or any point in the same frame of reference.
To expand upon that, using the normal intuitive addition of velocities formula, you in ship A would see ship B go away from you at nearly twice the speed of light. But addition of velocities formula doesn’t actually work that way. The reason for this is that light breaks all the rules. No matter how fast you’re going with respect to anything else, light will always be traveling at c away from you. So since ship B isn’t actually moving away from you faster than c, the light will reach you eventually.
Isn’t the answer basically that he already is traveling at 99.99% of C relative to something?
If, however, spaceship A is accelerating, then you would not be able to see spaceship B. In fact you would create a causal disconnect behind you (an event horizon) and you’d even get to experience some Hawking radiation.
I’m not sure where you’re getting this from. Accelerating, even when the relative velocity of the two spacecrafts is near c, would produce none of these effects.
Do you have a cite for this, or can you explain in more detail? I’m not disputing it; I just can’t remember this part of the relativistic-effects conversation very well. Mind you, it sounds familiar, but I can’t recall the details.
If I did the math correctly, their velocity relative to each other would be 0.99994999975c.
Maybe before you make a post like that you should check out “Rindler Horizon” and “Unruh effect.”
Ignorance fought. You are correct.
I believe such a large percentage of c would produce the following optical effect:
A circle of blue shifted stars…distorted as if photographed through a fish-eye lens…directly in front of you; another circle of red-shifted , equally distorted starlight directly behind; and to the sides…nothing. At your speed lateral photons would literally miss your retinas.
(half remembered from a 30 year old memory of Carl Sagan’s COSMOS)
Sorry about getting a little snippy earlier, I guess I just didn’t expect to be disagreed with.
I’ve always thought the Unruh effect is pretty nifty, because it shows the symmetry between gravitation and acceleration. An observer suspended outside the event horizon, with a local g value, will experience the same temperature radiation bath, as an observer accelerating through flat spacetme at that g.