Given is a body that has a constant acceleration. Let the acceleration be . Let us assume that the body starts at rest. If so then the travelled distance is given by and the velocity is given by . So there is a critical time for what the velocity becomes the speed of light. This critical time is given by . However, to maintain the constant acceleration , energy is required. By definition, the amount of energy is given by

(1)

The force is given by , valid both for *Classical Mechanics* and *Special Relativity*. The difference is however, that the momentum is different for both *Classical Mechanics* and *Special Relativity*. For Classical Mechanics, the momentum is given by and for Special Relativity, the momentum is given by . Let us assume that the force is acting in the direction of the velocity, then we obtain

(2.1) and

(2.2)

Then it is clear that

(3.1) and

(3.2) .

Using that and we obtain

(4.1) and

(4.2)

Then we obtain a special time for *Special Relativity* – where the amount of energy goes to infinity. It is clear that this time is given by . Then we see that , meaning that the critical time is reached when an infinite amount of energy is required to maintain the constant acceleration of the body . Therefore in Special Relativity, a body can have a constant acceleration during some time-interval that is given by ; assuming that the body starts at rest. Since an infinite amount of energy is already required to maintain this interval, exceeding the time is not possible. In *Special Relativity* a body can have a constant acceleration, but not for ever.

### Like this:

Like Loading...

*Related*