# Wouldn’t time dilation govern a speed limit?

swerdna
As well as time dilation slowing the rate that clocks run and things age etc, wouldn’t it also slow the rate of the very speed that was causing the time dilation? Isn’t time dilation effectively speed dilation? In other words, the faster you go the slower you go, and if you could ever reach the speed of light you would stop completely as time stops. As you were constantly increasing your speed to reach the speed of light however, wouldn’t time dilation reduce your ability to constantly increasing your speed, and at a certain point of speed/time dilation couldn’t you only travel at a constant speed? In other words, wouldn’t the maximum speed that a thing could travel be governed by the amount of time dilation that the speed creates? If so, could time dilation be what governs the speed of light?

## Answers and Replies

Mentor
Time dilation and length contraction are two sides of the same coin, yes, and together, they limit the speed of an object to arbitrarily close to C.

lzkelley
Swerdna, you're completely correct... but note that dilations happen BECAUSE of the speed limit, not the other-way around.

swerdna
Time dilation and length contraction are two sides of the same coin, yes, and together, they limit the speed of an object to arbitrarily close to C.
I would have expected that it would be a speed substantially less than C. Surely dilation doesn’t “kick-in” at the last minute

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lzkelley
Dilation starts effecting things at any velocity. The effects are very small until you get close to C. This is the factor by which things are dilated (time and space):
http://en.wikipedia.org/wiki/Lorentz_factor
Graph it on your calculator with C = 1; as V -> 1 (becomes the same as C), the lorentz factor approaches infinity; that's the speed limit.

I'm not sure what math level you're at, but the derivation for that formula isn't too complicated - you just have to assume that the speed of light is constant, then do some clever geometry, i think the wikipedia article links to a derivation.

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swerdna
Dilation starts effecting things at any velocity. The effects are very small until you get close to C. This is the factor by which things are dilated (time and space):
http://en.wikipedia.org/wiki/Lorentz_factor
Graph it on your calculator with C = 1; as V -> 1 (becomes the same as C), the lorentz factor approaches infinity; that's the speed limit.

I'm not sure what math level you're at, but the derivation for that formula isn't too complicated - you just have to assume that the speed of light is constant, then do some clever geometry, i think the wikipedia article links to a derivation.
Unfortunately my math level is somewhere near the bottom rung so I tend to see thinks more mechanically. So you’re saying that dilation does “kick-in” at the last minute and doesn’t evenly occur as a straight line on a graph?

Mentor
So you’re saying that dilation does “kick-in” at the last minute...
No, he said explicitly that time dilation (and length contraction) effect things "at any velocity". It's a critical factor in GPS satellite operation, for example, ai]nd they move around the Earth at roughly .000026 C. But at that speed, the time dilation is only miliseconds per day.

Whether time dilation is an important factor depends on the level of precision required in a measurement.
and doesn’t evenly occur as a straight line on a graph?
Well, yes - it is not linear, it is hyperbolic. You didn't say what level of math you are in (algebra 1 really should do it), but an equation that is related to y=1/x (from the wik link) is hyperbolic.

The equation is really easy to use. Try either graphing it or just plugging in a few values. For example, entering B=.1 (10% of the speed of light, or 67 million miles per hour) gives you a factor of 1.005 or 0.5% dilation.

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swerdna
Sorry to back-track, but I would like to check that I have the correct answer to this question - Would time dilation not only slow the relative time of a clock, but also slow the relative speed that the clock is traveling from a “stationary” observer?

CSherman
Time dilation only takes effect on objects that are moving relative to the observer. A stationary observer will see no effect on the clock because the clock is not moving relative to the observer, regardless of how fast it is moving relative to anything else.

swerdna
Time dilation only takes effect on objects that are moving relative to the observer. A stationary observer will see no effect on the clock because the clock is not moving relative to the observer, regardless of how fast it is moving relative to anything else.
I meant "stationary observer" as the thing that the clock is moving relative to. Not that the observer is stationary to the clock.

Mentor
Sorry to back-track, but I would like to check that I have the correct answer to this question - Would time dilation not only slow the relative time of a clock, but also slow the relative speed that the clock is traveling from a “stationary” observer?
The notion of "time dilation" as slowing the relative speed of the clock seems obscure and unproductive to me. Better to think that spacetime has a structure which limits the speed of material particles and information to sub-light speeds. That same structure also gives rise to effects such as time dilation and length contraction.

yuiop
Sorry to back-track, but I would like to check that I have the correct answer to this question - Would time dilation not only slow the relative time of a clock, but also slow the relative speed that the clock is traveling from a “stationary” observer?

I think time dilation of accelertion is slightly better picture. Say you have a missile that is capable of accelerating to 0.8c before it burns up all its fuel. Say the missile is placed on a mother ship that accelerates to a speed of 0.8c relative to you before firing the missile. When the missile is fired from the mother ship the fuel is burned up slowly due to time dilation and the missile accelerates much more slowly and only reaches a top speed of about0.976c relative to you or 0.176c faster than the ship it was fired from.

The equation used to calculate the additive speed (0.976) is the relativistic velocity addition equation v = (u+w)/(1+u/c*w/c) where u is the velocity of the ship and w is the velocity of the missile.

Earlier you asked "if you reached the speed of light would you stop due to time dilation?". It would be slightly better to say that as you approach the speed of light relative to another observer your acceleration relative to the other observer tends towards to zero no matter how much fuel you burn up. Of course, to you onboard the ship it would look like you were always accelerating at the same rate and your onboard accelerometer would indicate that. However, because no physical object can get exactly to the speed of light your relative acceleration would never reach exactly zero.

campal
i posted this in another forum but want feed back please help, and thanks for your time! I've been told that as a person approaches the speed of light, time relative to others being viewed slows. when you make the speed of light ( if possible, I’m aware of distance change and mass increase and of the immense amount of energy needed to possibly reach this speed to push that mass) time for others stops and past the speed of light time goes back wards. Does this huge mass increase make an objects gravitational force so immense that it drops through space time and can continue traveling at higher speeds then light? Such could be possible in the even of a star becoming too heavy and dropping through space time to create a black hole. BUT what happens as you slow down? As in all the particles in your body slow down to absolute zero, where your temperature and kinetic motion would be zero. Would this result in forward time travel? Does mass decrease?

Mentz114
Hi Campal,
you've been told wrong. All motion is relative, and there's no absolute velocity. So it does not make sense to say ' as a person approaches the speed of light' unless you say who is measuring them. Relative to someone in a distant galaxy you may be traveling at a huge velocity, but it makes no difference to you, you are stationary in your own frame.

M

campal
THE OBSERVER IS TRAVELING AT LIGHT SPEED WATCHING A SYSTEM TRAVELING AT SPEEDS WE NORMALLY TRAVEL AT. but if you alter the E+MC(^2) EQUATION and sub in the rate of time won't you find that as velocity increases to the constant of "c" (the speed of light), the rate of time pasage (for others, not moving at your speed) decreases and if light speed was acheived their time would no longer pass, and if you passed the speed of light their time relative to you would go backwards?

yuiop
THE OBSERVER IS TRAVELING AT LIGHT SPEED WATCHING A SYSTEM TRAVELING AT SPEEDS WE NORMALLY TRAVEL AT. but if you alter the E+MC(^2) EQUATION and sub in the rate of time won't you find that as velocity increases to the constant of "c" (the speed of light), the rate of time pasage (for others, not moving at your speed) decreases and if light speed was acheived their time would no longer pass, and if you passed the speed of light their time relative to you would go backwards?

If you imagine a particle traveling at twice the speed of light its time dilation factor would be $$1/\sqrt{(1-v^2/c^2)} =1/\sqrt{(1-(2c)^2/c^2)} = 1/\sqrt{-3}$$

The square root of a negative number is an imaginary number. That tells you are not looking at a real physical situation. We can only "imagine" it. Some mathematical models in physics involve intermediate imaginary numbers in the calculations, but they only have physical significance if the imaginary parts cancel out and a real answer is obtained.

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