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russ_watters

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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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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; thats 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.

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; thats 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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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?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; thats 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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russ_watters

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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.So you’re saying that dilation does “kick-in” at the last minute...

Whether time dilation is an

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.and doesn’t evenly occur as a straight line on a graph?

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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I meant "stationary observer" as the thing that the clock is moving relative to. Not that the observer is stationary to the clock.

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Doc Al

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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.

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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 aproach 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.

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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 travelling at a huge velocity, but it makes no difference to you, you are stationary in your own frame.

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

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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