Have been really struggling for some considerable time to understand the universal limitation of speed i.e. it is not possible to travel faster than the speed of light. In particular – what is the limiting factor? Is it something physical that can be understood (e.g. is there an equivalence to terminal velocity of a falling body, which can easily be understood by a layman of balancing the wind resistance against the force of gravity).
Firstly, in trying to understand this I have learned that speed is only a relativistic quantity, everything can be considered to be at rest or in motion in makes no difference? So the limitation is only between two (or more) bodies. But if there was nothing in existence other than two independent particles separated by some arbitrary distance (let's say 10 light years for example) how can one influence the other? By which I mean the (relative) speed between the two is limited, so they must somehow influence each other? And if so how do they influence each other? Or is it the space-time vacuum between them that marks the relative distance & speed? What is the limiting mechanism and the reference??
Asked another way, in trying to understand this problem I have learned from various sources that the universe is expanding at an incredible rate…at more than half light speed in one direction, and more than half light speed in the opposite direction. I have learned that this is "allowed" since the two opposite ends are outside of each others sphere of influence…no information can ever be communicated between, neither can have cause or influence over each other (or are even aware of each others existence, and could perhaps be considered to be independent realities), yet it does seem possible that something could exist in between the two to observe that, relative to each other they are travelling faster than light…
So if we imagined just three particles in space, A moving "left" of B and C moving "right" of B (and saying B is "stationary" for the sake of argument). Let's say that initially A & C are within a sphere of influence (i.e. close enough to each other) so that they are limited in not being able to travel more than 0.5c away from each other. Let's say they are going 0.49c relative to B (in opposite directions). Over time they get further and further away…Suddenly, they reach the event horizon (the A-C event horizon) and they both increase speed to 0.9c relative to B. Particle B sees that A and C are now suddenly moving away from each other at 1.8c, almost as if they've hit a turbo switch. They have suddenly been allowed to increase speed by the universe.
When they fall off each others causality event horizon, what is it that allows them to increase speed? What is the limiting factor just before they reach the horizon? And finally, in going over that horizon would they experience any acceleration?
Best Answer
Either the structure of space-time has no speed limit (unbounded relative velocities would then be possible), or the structure of space-time has a maximum speed (limitation on the maximum relative speed possible).
The first case corresponds to Newtonian space & time. We know that this is incorrect for fast moving objects, and evidence has been accumulating since before Einstein's work of 1905.
The second case, where there is a speed limit, is explained by Einstein's Special Relativity. Here the maximum speed is c, which also happens to be the speed that light travels.
To consider the cosmological case of the expanding universe, one needs Einstein's General Relativity. Here we have a dynamic space-time, which responds to local density of matter and energy. From observation it is known that the cosmos is expanding, and the further away (in time and space), the faster it is moving away from the observer, such as us. There are two elements to this motion: one is ordinary motion, the other is due to the expansion (stretching) of space.
The stretching of space is not limited by the speed of light, and thus there are elements of the cosmos which used to be observable, but which now have attained speeds, due to the expansion of space, such that they can no longer be seen.
For details, see How Can the Universe Expand Faster Than the Speed of Light?