[Physics] the maximum time dilation between two objects, if one is standing still and the other is moving at $c$

observersreference framesspecial-relativityspeed-of-lighttime

What is the maximum ratio in the rate of change in time in reference to object $A$ which is standing still and object $B$ which is moving at the speed of light?

Best Answer

Objects, defined as things with mass, don't move at the speed of light. The time dilation factor is

$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

and it has no limit - it diverges at $v\to c$. For speeds very close to the speed of light, we could define $\epsilon = \frac{c - v}{c}$, then we'd have $\gamma \sim \frac{1}{\sqrt{2\epsilon}}$ This shows how much time slows down for speeds very near the speed of light. Here's a picture

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As gamma shoots up to infinity, the time dilation factor becomes arbitrarily large. If you want the clock to go 1/100 as fast, or one millionth as fast, or one quadrillionth, that can be done by going very close to the speed of light (just solve for $\epsilon$ in the above).

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