How slow does time become the closer you get to C?

[RichardE]

I might misunderstand this entirely, if so please disregard. From what I understand the closer you get to C the slower time becomes for you. Is there a accepted amount of reduction in the speed of time? Such as, at .75C time is reduced 30% type equation?

 

[Biftheunderstudy]

Without getting too far into special relativity, as you approach c time remains exactly the same for you. Where relativistic time dilation, length contraction and all that fun stuff comes into play is when you have someone else who is not in your "Frame of Reference". This means that if you are moving at .8c it has to be relative to something else...ie someone is watching you fly by in your spaceship at .8c relative to them.
When this happens, without getting into derivations, the observer at rest relative to the space ship travelling at .8c sees some funny things. For instance, he observes time on the space ship to be slowed down.
How much so?
Well, here's the equation, again without derivation.

delta_t'=gamma*delta_t

where delta_t' is the time seen by the observer
delta_t is the time seen by the astronaut
and gamma is 1/sqrt(1-v^2/c^2)
v is the velocity of the spaceship relative to the observer
c is the speed of light

In the example of the spaceship traveling at 0.8c, gamma becomes 1.666666 so the observer sees a clock on the spaceship moving 2/3 slower than his clock.

If any of this is wrong someone please correct me, it too early to be doing relativity here.

 

[racolvin]

I think I just sprained a neuron

but that's why I love ATHT .... its fascinating even if I don't understand a bit of it

 

[Foxery]

Short version: Time on the ship slows down exponentially (as seen by an observer) as its velocity increases. If you graph the difference between our clocks, it will form an asymptote.

Here's what Bif's forumla gives me:
% of c, ratio of time dilation
0.2500 1.03
0.5000 1.15
0.6670 1.34
0.7500 1.51
0.9000 2.29
0.9500 3.20
0.9900 7.09
0.9990 22.37
0.9999 70.71
0.99999 223.61
0.999999 707.11

 

[Foxery]

Y'know, I'm glad I wrote those out. Professors and sci-fi stories always make us think that the time difference gets out of control very quickly, but that's not the case at all. You can fly pretty damn fast before the dilation significantly impacts a human lifetime. TV shows where someone misses 1000 years in the blink of an eye seem a bit more silly now.

 

[TridenT]

Originally posted by: Foxery
Y'know, I'm glad I wrote those out. Professors and sci-fi stories always make us think that the time difference gets out of control very quickly, but that's not the case at all. You can fly pretty damn fast before the dilation significantly impacts a human lifetime. TV shows where someone misses 1000 years in the blink of an eye seem a bit more silly now.

Well that blink of an eye could be them traveling at like... 99.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 percent the speed of light.

 

[Onceler]

could someone tell me why nothing that has mass can accelerate close to c but electrons do and protons in accelerators it is supposed to require infinite energy right?

 

[Foxery]

Nono... reaching c takes infinite energy. Getting close to it only takes "a lot."

 

[hellokeith]

In relation to some very distance pulsars, Earth is traveling at 94% C.

If you think about it logically, two galaxies moving away from each other, the relative velocity of one could be up to 1.98 C. And if you take into account timespace expansion, it could be more though it would be difficult to prove since less and less light is reaching you from the other galaxy the further you go.

 

[kotss]

Originally posted by: hellokeith
In relation to some very distance pulsars, Earth is traveling at 94% C.

If you think about it logically, two galaxies moving away from each other, the relative velocity of one could be up to 1.98 C. And if you take into account timespace expansion, it could be more though it would be difficult to prove since less and less light is reaching you from the other galaxy the further you go.

In regards to objects moving relative to each other you will never get results that exceed c. To get a better definition of the current theories here is a link to The Metric Expansion of Space

 

[hellokeith]

Originally posted by: kotss

Originally posted by: hellokeith
In relation to some very distance pulsars, Earth is traveling at 94% C.

If you think about it logically, two galaxies moving away from each other, the relative velocity of one could be up to 1.98 C. And if you take into account timespace expansion, it could be more though it would be difficult to prove since less and less light is reaching you from the other galaxy the further you go.

In regards to objects moving relative to each other you will never get results that exceed c. To get a better definition of the current theories here is a link to The Metric Expansion of Space

From your very own link:

The metric expansion leads naturally to recession speeds which exceed the "speed of light" c and to distances which exceed c times the age of the universe, which is a frequent source of confusion among amateurs and even professional physicists.[1] The speed c has no special significance at cosmological scales.

Two flash lights pointed in opposite directions have photons moving away from each other at 2x c. In the same manner, two bodies of mass (2 spaceships) leaving the same body of mass (the earth) but in opposite directions, could each attain over time a velocity of 99% c with respect to the rest mass, and thus would be moving away from each other at 1.98x c. Add in timespace expansion, and it could be more than 2x c. Neither object violated any physics because it never exceeded c with respect to the rest object.

 

[Onceler]

Originally posted by: Foxery
Nono... reaching c takes infinite energy. Getting close to it only takes "a lot."

what about neutrinos?

 

[Foxery]

Neutrinos have mass, and therefore cannot reach c.
You may want to flip around a bit on http://en.wikipedia.org

 

[kotss]

Originally posted by: hellokeith

Originally posted by: kotss

Originally posted by: hellokeith
In relation to some very distance pulsars, Earth is traveling at 94% C.

If you think about it logically, two galaxies moving away from each other, the relative velocity of one could be up to 1.98 C. And if you take into account timespace expansion, it could be more though it would be difficult to prove since less and less light is reaching you from the other galaxy the further you go.

In regards to objects moving relative to each other you will never get results that exceed c. To get a better definition of the current theories here is a link to The Metric Expansion of Space

From your very own link:

The metric expansion leads naturally to recession speeds which exceed the "speed of light" c and to distances which exceed c times the age of the universe, which is a frequent source of confusion among amateurs and even professional physicists.[1] The speed c has no special significance at cosmological scales.

Two flash lights pointed in opposite directions have photons moving away from each other at 2x c. In the same manner, two bodies of mass (2 spaceships) leaving the same body of mass (the earth) but in opposite directions, could each attain over time a velocity of 99% c with respect to the rest mass, and thus would be moving away from each other at 1.98x c. Add in timespace expansion, and it could be more than 2x c. Neither object violated any physics because it never exceeded c with respect to the rest object.

Space itself can expand faster than c. Objects other than photons have not been observed to attain c. According to relativity you do not sum objects moving away from each other at speeds that become relativistic and attain results higher than c. They will measure each other as receding at no more than c. At cosmological scales you have to take into consideration the expansion of space itself which "frame drags" the matter along with it. There is a distinction between the scenarios though and your flashlight analogy is wrong. That was part of Einstein's relativity thought experiments. The thing with galaxies that are far enough away that space expansion is relevant, is that you will not be able to observe them if they are expanding away. The light from them will never reach us since space itself could be expanding faster than light is travelling.