how does special relativity deal with time dilation & length contraction?

Answer 1

Special Relativity doesn't deal with time dilation, length contraction and mass increase. Rather, these are experimentally proven consequences of Special Relativity.

However, the mathematical relationships that describe these effects is the Fitzgerald-Lorentz ratio.

(1 - v^2/c^2)^.5

Apparent length is related to rest length according this ratio as its a relation of velocity increase vs. length decrease.

Apparent time is related to rest time according to the inverse of this ratio as its a relation of velocity increase vs. dilation increase.

Apparent mass is related to rest mass according the inverse of this ratio as its a relation of velocity increase to mass increase.

In the case of mass, E=mc^2 is the derivation of the relationship between mass and energy for masses at rest because velocity can be canceled out.

This formula is also the reasoning as to why its impossible to travel faster than light. If you do, you end up with a value for v^2/c^2 that is greater than one which leads to a square root of a negative number which is an imaginary number which means its a mathematically valid answer yet nonsensical answer from a physical perspective.

On the other hand, when you consider than Relativity theory's math has so accurately predicted and agreed with experiment and observation, I wonder if it is reasonable to question the math - it has over time proven itself to be quite accurate.

Answer 2

All medical experiments played thus far, together with particular determined movements that people handiest become aware of, and are not able to manipulate, verify the relativity proposals through Einstein and others. Consider the lowly muon as a made of a cosmic ray putting the higher surroundings. Its very brief lifetime implies that it are not able to achieve the outside of the earth to turn on a detector. But it does besides. Its lifetime is multiplied therefore of its very prime pace. Only time dilation can account for this. And handiest relativity thought can give an explanation for time dilation.

Answer 3

Relativity says that as your approach the speed of light:

You have an increase in mass
You experience a shortening of length and
you experience a slowing of time

Heres more on time dialation if you're looking for a more in-depth answer http://en.wikipedia.org/wiki/Time_dialation

Answer 4

I have no clue. I don't have the same book you do. Because i know you are not smart enough to ask a question like that on your owen

Answer 5

It uses tensors.

The key tensor is the metric, which acts on vectors to give their magnitude in effect. The metric tensor is frame dependent.

Answer 6

By deriving the appropriate formulas: How else?

Answer 7

Dunno, but your pic is fun.