If you are traveling at the speed of light away from the sun, and looking back at the sun, what would you see? Wouldn’t you see the unchanging features the sun had, the instant you left?
You aren’t.
The laws of physics do not allow for an observer to be traveling at the speed of light. There is no meaningful way one can speak of it happening within physics as we know it. If you wish us to answer in some other formulation of physics where it is possible, then you must first tell us what that formulation is.
That was basically the question that Einstein asked himself, which led to his development of the theory of Special Relativity. He considered that if you were traveling at the speed of light next to a beam of light, you’d see a stationary electromagnetic wave. Such a thing is not allowed by Maxwell’s equations. Further thought experiments along those lines led him to produce the theory of Special Relativity.
The simple answer to your question is you can’t travel at the speed of light. So what you would see is irrelevant. But given enough energy, you can travel arbitrarily close to the speed of light. Traveling at 99.9% of the speed of light, you would still see light from the sun reaching you at the normal speed of light. This is inconsistent with common sense, but nevertheless true. At low speeds it appears to us that velocities are additive, but actually they are not. Light always travels at the same speed, c, relative to any observer, no matter how fast he is traveling.
As you passed the Earth at c, looking at the sun you would see the same thing that observers on Earth see, except the light would be red-shifted. So the color would be different. As you passed the orbit of Mars (about 4 minutes later for someone on Mars or Earth, but faster for you due to relativistic time dilation), the sun would again look the same as it looks to someone on Mars, except for the red shift, and so on.
–Mark
OK, traveling at very close to c (relative to the Sun), that is possible, and we can address that. In that case, yes, you would see the Sun changing only very slowly. Redshift applies to any sequence of events, not just to wavefronts.
Can I, just for a moment, explore the impossible universe where you could travel at the speed of light? If you could, and you can’t, then I don’t think you would see anything at all in the direction that you are traveling away from, because no photons from that direction would enter your eye; they would be traveling in a parallel path right next to you. You would be bathed in them but unable to see them. This thought experiment requires suspending the laws of physics, in which case anything other arbitrary thing could happen as well. But I am providing this answer in the spirit in which the question was asked.
We now return to our regularly scheduled universe.
Most physics professors I have heard simply refuse to entertain the question.
Well, you have to decide whether relativity is still valid in this hypothetical universe. According to relativity, light travels at c relative to any observer. So in that case, light would still enter your eye normally. On the other hand, if relativity does not hold, then perhaps as you say and as Einstein originally considered, you might see the light sitting stationary next to you. But either choice, thoroughly explored, is going to result in inconsistencies and difficulties that are going to be hard (or impossible) to resolve. So, even if we’re just ignoring the “real” laws of physics and freely hypothesizing, we can’t easily come up with a good answer to this question.
–Mark
Wouldn’t the effects of length contraction cause the observer to notice that the sun is now ~22 times closer (at least initially), once traveling at .999c?
But if you were traveling next to a beam of light, at 99.9999999999% of the speed of light, which is theoretically possible, would you not see the electromagnetic wave mooing slowly enough that you could perceive and describe the phenomenon within its motion? And isn’t that close enough to the OP’s question to have relevance, and give one a glimpse of what would happen (not much differently, by inference) at the speed of light?
Hold on, so (0.9999…)c does not equal c?
No, if you were traveling at .9999999c, every electromagnetic wave you can detect would be moving at c from your perspective. That light beam traveling in parallel with you, that you might expect would appear to be moving at .0000001c, would in fact actually appear to you to be moving at c.
The speed of light is always constant to any observer, no matter what motion they have relative to other observers. Or to put it another way, how is it you know that you’re traveling at .999999c? The only way you can do that is by measuring your movement relative to other things. If you’re blasting off from Earth for Alpha Centauri, then you could say you’re traveling to Alpha Centuari at .99999c. Except why can’t you say that Earth is traveling away from you at .99999c and Alpha Centauri is traveling towards you at .99999c, and you’re just stationary?
And the answer is that you can. All the weird stuff about time dilation and red-shifting and such is just a consequence of the fact that you’ll always observe light traveling at c, no matter what. And if that requires things like two people traveling at different speeds to not be able to agree on what time it is, then that’s what happens.
And to add, suppose a rogue star was blasting through our galaxy at .99999c, relative to us. As it approached us, the light emitted from the star would be traveling towards us at c. And as it passed us and receeded, the light emitted from the star would be traveling towards us at c. Not 1.99999c, or 0.000001c. Always c. Our velocity relative to the star doesn’t change our measurement of the speed of light.
It is true that when the star is moving towards us, the light it emits will have higher energy…it will be what they call “blue shifted”. The higher energy isn’t detected as moving faster, though. And moving away we don’t detect the lower energy light as moving slower, it moves at c, but is “red shifted”.
If you don’t like this answer and think that it’s weird and impossible, welcome to all the people who hate Einstein and have been devoting the last 80 years trying to disprove relativity. Yes it’s weird and doesn’t make sense. The only thing is, every experiment we’ve been able to conduct shows that it is true.
As an aside,
…and there’s a recent speculative paper showing that massive black hole mergers might accelerate stars to as much as 1/3 the speed of light:
(Given what Randall said about a relativistic baseball, it would have to a be something of a concern if one of these were headed our way.)
In a little more detail …
In everyday life, we think that if an object A is moving with velocity v1 relative to you, and another object B is moving at velocity v2 relative to A, then B is moving at a velocity of v1+v2 relative to you.
This is wrong.
According to special relativity, the actual formula is
(v1+v2) / (1 + (v1v2 / cc))
When v1 and v2 are small compared to c (the speed of light), the denominator is close to 1, and the whole formula is almost equal to v1+v2, so we don’t notice the difference. When speeds get close to c, the difference becomes apparent. When v2 actually equals c, as when B is light itself, a little algebra shows you that the result of the formula always equals c, no matter what v1 is.
Here’s the wiki article.
–Mark
I think the best way to resolve that hypothetical is to state that you would see nothing not because no photons were fast enough to reach your eye, but rather, that they were redshifted down to zero
Well technically photons don’t experience time so …
Also, the aberration of light would cause your field of vision to “fold together” at speeds approaching c; so much so that objects behind you would appear in front of you.