# Why does time stop when we travel at the speed of light?

#### benzun_1999

Why does time stop when we travel at the speed of light?

Why does mass increase when we travel at the speed of light?

-benzun

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#### dumpy

For you, time always continues the same.

Mass doesnt increase at the speed of light. If you have mass, you cant get there!

#### HallsofIvy

Homework Helper
Basically, you are asking people to explain special relativity.

There have been whole books written on the subject!

In very rough terms, the problem is this:

Galileo, long ago, postulated that motion was "relative"- that is, that if you were in an enclosed cart, moving along a very smooth road at a constant velocity, there is no experiment you could perform that would tell you how fast you were moving (or if you were moving at all)- that is, that speed MUST be "relative to" some outside position.
Basically this is because of "f= ma": force, which is really how we "feel" the world depends on acceleration, not speed.

In the 19th century, it was discovered that a moving electron can be affected by a magnet depending on the speed of the electron (Galileo,of course, couldn't do electromagnetic experiments!). That meant that one could theoretically do some kind of electromagnetic experiment to determine an "absolute" speed.

In the late 19th century, Michaelson and Morley did exactly such an experiment using light (electromagnetic waves). They got a "null" result- their experiment showed no change no matter how they positioned their apparatus- there was no "absolute" speed. This is probably one of the most repeated experiments in history (certainly for one that reaches a null result) and always with the same result: there is no "absolute speed".

Lorentz suggested that perhaps the change in electromagnetic force in the direction of motion contracted the arm of the apparatus in that direction just enough to give an apparent null result (the kind of trick nature plays on us all the time!) and calculated what that contraction must be: l'= l sqrt (1- v2/c)

Other experiments showed that it can't be the electrons in the arm of the apparatus that do the contracting but Einstein made the extreme suggestion that it was space itself that contracted! The formulas are exactly the same as Lorentz (since they were derived directly from the Michaelson-Morley experiment) but Einstein showed that the contraction of space also implied that mass must increase:
m'= m/sqrt(1-v2/c), and time itself slow down
t'= tv2/c).

If you put v= c in those formulas, you will find that the length becomes 0, mass becomes infinite, and the time interval becomes 0.

Those are reasons why a body with mass CANNOT move at the speed of light!

Nicely put.
There is also the energy problem. As your velocity increases, so does your mass, so you put in more energy and get another mass increase as well as a velocity increase. It ends up like the law of diminishing returns. You would need infinite Energy to accelerate any mass up to the speed of light (if of course it were possible in the first place, which it isn't!)

#### HallsofIvy

Homework Helper
t'= tv2/c)
This was supposed to be "t'= t(1-v2/c2" but got butchered!

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