The relativistic speed limit is measured relative to...?

Question

I know that special relativity throws up problems with accelerating towards the speed of light due to the presence of the Lorentz factor in the calculations for things like mass and length. What I find myself having difficulty understanding though is why this does not place limitations even lower than c.

For example; say that from rest, one object leaves location A and accelerates to 0.5c. Once it reaches that velocity, another object leaves A in the opposite direction and also accelerates to 0.5c. Now, are the two objects not travelling at the speed of light relative to each other? Why should they then be able to accelerate further?

Obviously this limitation does not exist in real life, or else particle accelerators and so on would have problems, but I would like to know - what am I missing?

Answer 1

you raise a good question, but one that is well answerable within relativity

you are adding velocities according to the galilean non-relativistic transformation...let me ask you to read up on the relativistic addition of velocities, sometimes called the Einstein velocity addition rules

if you search for relativistic velocity addition, you will get lots of returns, one such is listed below

good luck

Answer 2

If I understand your setup, then the stationary observer originally left behind by A measures A and B to separate at a rate c, but they do not measure each other to separate that quickly. A and B can continue to accelerate for as long as they have fuel, and to their heart's content, and neither will ever reach speed c as measured by anyone. At most, an observer not A or B can measure them separate by nearly 2c (as each can go at nearly c in opposite directions), but neither ever measures the other travelling faster than c.

Answer to the title question: c is not measured relative to anything. It is absolute. c is identical in all reference frames.

Please try to eliminate thoughts of mass increasing near c. Relativistic mass is a deprecated concept that leads to severe misunderstandings of the theory.

Answer 3

kuiperbelt2003 is exactly correct.  The short answer is that, under relativity, relative velocities add as follows:

If two objects travel in opposite directions at speeds v1 and v2 (relative to some "stationary" observer), then their speed relative to each other is:

(v1 + v2) / (1 + (v1)(v2)/c²)

If you experiment with this formula you'll see that:

a) if v1, v2 are small compared to c, the formula gives approximately the same answer as the "classical" relative speed (v1 + v2);

b) if v1, v2 are each less than c, then their relative speed is also less than c.