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I've been pondering the implications of time dilation. Is it right to assume that if a craft was travelling at a speed very close to the speed of light (>= 0.9999c for example), that to an external observer it would appear to be moving very much slower?

Example: at 0.9999c, time dilation is 70.71, so while the craft is travelling at 186,263.37 miles/s, doesn't that mean to a (stationery) observer it's only moving at 2,634.10 miles/s?

And at 0.99999c, time dilation is 223.61, so while the craft is now travelling at 186,280.14 miles/s, doesn't that mean to the observer it's now only moving at 833.07 miles/s?

The obvious implication is that as the craft approaches the asimptote of the speed of light, external observations (beyond around 0.9c) see it decrease in velocity towards the asimptote of being stationary.

Is this reasoning correct?

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no, the reasoning is not correct. You do not take into account spatial contraction. Because of this, the 0.99999c would be the speed an outside observer sees. Ignoring contraction the speed the traveller thinks they are travelling at is well above c. –  Jim Jul 8 at 12:52

3 Answers 3

No.

Time-dilation is the slowing of time as experienced by the fast moving craft, not the 'stationary' observer.

Remember that light moves at c, and we see it move at c, not some slower or stationary speed.

As the craft approaches c, it appears to accelerate increasingly slowly; from 0.99999c to 0.999999c is only a difference of 2.7 km/s, but it is still an increase in speed and thus an acceleration.

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Time-dilation is the slowing of time as experienced by the fast moving craft I'm not sure I understand the distinction. If I'm moving near-c relative to you, then you're moving near-c relative to me. –  Cruncher Jul 8 at 16:48
    
True, and this is the basis of many 'paradox' explanation articles. The question, however, was how it would appear to an observer, not to the traveller. To the observer watching someone accelerate near c, it is still an acceleration. Just because you move at some speed relative to me, it does not change my experience of time. –  Phil H Jul 9 at 9:26

that to an external observer it would appear to be moving very much slower?

I don't understand the reasoning here. When you write

assume that if a craft was travelling at a speed very close to the speed of light

I take that to mean that the craft is travelling very close to the speed of light according to an external observer.

Keep in mind that the craft is at rest with respect to itself and the specified velocity of the craft is the relative velocity between the craft and another inertial reference frame, i.e., an external observer. In other words, according to someone inside the craft, it is the external observer that is moving very close to the speed of light.

So, when you specify the many speeds in your question, your actually specifying the speed of the craft according to this external observer.

To summarize, you're:

(1) asking us to assume that a craft is travelling at a speed very close to the speed of light [according to some observer]

(2) and then asking if it would appear to be moving much slower to this same observer

to which the answer is, of course, no.

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Sorry if my question wasn't clear. No - i'm assuming the craft is travelling at a speed very close to the speed of light according to someone inside the craft, & considering how the time dilation affects how its speed is perceived by an external observer. –  user53047 Jul 8 at 12:04
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@user53047, according to someone inside (say, seated within) the craft, the craft is stationary. –  Alfred Centauri Jul 8 at 12:07
    
Yes, you're right - i'm clearly getting myself confused here - thanks! Can we use a different example? A craft travelling at 0.9999c has time dilation of ~70, so if it travels a distance of 1 light year, to someone in the craft this would last roughly a year, whereas an external observer would see the journey take ~70 years. Is that correct? –  user53047 Jul 8 at 12:11
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@user53047, to those on the craft, the craft isn't travelling a distance. Imagine that, in our frame of reference, we have set up 'mile' markers 1 light-year apart (according to us) and we observe that the craft is travelling between the mile markers with speed 0.9999c. According to someone on the craft, it is the mile markers that are moving and, further, they are much less than 1 light-year apart. So, think a little more carefully about your scenario and then repose it being careful to specify in which frame of reference any specified distance is measured. –  Alfred Centauri Jul 8 at 14:27
    
@user53047 Its the other way round. To an external observer you take just over a year to travel a light year, but from your point of view it takes around 1/70th of a year to travel the same distance (but you would measure that distance as far less, so you are not breaking the c limit from your perpective either). As an extreme example; a photon that left a star a million years ago hasn't "experienced" even a second of time, from its point of view all points in the universe are in the same place and it moves between them instantly –  Richard Tingle Jul 9 at 9:20

"I've been pondering the implications of time dilation. " - thar be dragons! :)

The answer to the question is no, of course. Per the previous answers you have to consider frame of reference which in space time is arbitrary. Time dilation is how you resolve the problem of two objects traveling directly towards each other at > .5C per a 'stationary' third reference point. If each is traveling at > .5C then Newtonian physics says that the speed of one relative to the other must be > 1C. That's not possible because of the time dilation.

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