How do you calculate change in time at the speed of light?
You don't because (1) you can't GO at the speed of light and (2) there IS no change in your time as you speed up, so even if you are talking about an achievable .999999c, your clock still ticks at one second per second.
You are probably thinking of time dilation, which is not an experienced phenomena but rather something that is perceived by remote observers, not the one being observed.
For example, you, right now as you are reading this, are MASSIVELY time dilated according to an accelerated particle at CERN and mildly time dilated relative to a passing comet and not at all time dilated according to your chair. Do you feel any of these effects? Do you feel all of them at the same time? (that would be a good trick).
That is exactly what I am talking about so you would observe everyone else moving slower? while your watch keeps ticking 1 second per second? and if you're traveling at .9 c for one hour how much time would have passed for people observing you? Would they be able to even see you? Would you appear frozen in time?
At .9c, the time dilation factor is about 2.3. So you would each see the other as moving at a little less than half speed.
At .995c, you'd be seeing a factor of 10.
Play with this calculator:
Cool thank you!
And keep in mind that "traveling at .9 c" is a meaningless statement by itself. You have to specify what you are using as a frame of reference. The assumption is that you mean .99c relative to an observer, but it's best to specify that.
so if you're moving .99c away from the galaxy it would appear to be rotating slower?
Yes. When you are moving relative to something that something always looks slower. At normal (human "normal" that is) the difference is negligible but at relativistic speeds you can use the Lorentz Transform to see the relationship
The time affecting your body at speed of light is in relative to the observer for you your time is just normal for you but relatively slower for an observer.
"your body at speed of light" is ridiculous. Have you not read the rest of the posts in this thread?
"...your body near the speed of light..." and it's sensical.
The OP's question was about the calculated speed, so strictly speaking the time dilation formula is the right one to use. OTOH the words "seeing" and "appearing" have crept in to the discussion at various points, so I'm just pointing out that if you want to know what you would actually see you should use the relativistic doppler formula, not the time dilation formula. The time dilation formula does not tell you what you would see as it does not take into account the light travel time to the observer. In particular, although traveling away from a galaxy at high speed you would see it rotating more slowly (also it would appear to be much closer/larger), whereas if you were traveling towards it you would see it rotating more quickly (and it would appear to be further away/smaller).
Well, of course it is, but I'm trying to help him see that sloppy terminology lead to (or stems from) sloppy thinking.
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