Hi, first of all, I would like to apologize if this question is very very trivial or completely stupid, but it's something that was bugging me for a long time. Let's have a look at an example where a cosmic ship travels at a speed of light from Earth to Sun. Known fact is that for a photon, judging from a point of view of a human positioned on Earth, it takes about 8 minutes to travel from Sun to Earth. So from this point of view, it would take about 8 minutes for the ship to travel to sun as well. But from the point of view of the pilot of that ship, it should take considerably less time than 8 minutes as the relativity theory claims.. So it wouldn't take years for us to travel to nearest stars other than in our solar system (eg. To Alpha Centauri, it wouldn't take about 5 years to travel to, but from a point of view of the pilot, it would take much much less time...)? Now, if the latter is true, what bugs me is if the pilot ages slower than we do, every atom on that ship traveling at a light speed is slowed down? Should the atoms be slowed, the pilot shouldn't perceive time differently as we do on earth, though. Right? Does that mean, that even if the atoms of his body are slowed, the brain, slowed too, perceive time normally? Again, considering the latter is true, doesn't that mean the time is not relative? Only the speed of movement of atoms is relative to the speed of framework they are in, right? But judging from that this sounds strange, I guess I'd made a mistake or am completely of point, please... help me solve my dilemma. Thanks in advance
It's neither of those things, but it's been asked many, many times. So you could try searching for similar threads. Massive objects can't travel at the speed of light. See e.g. this post, so I'm going to have to assume that it travels at a slower speed. (I don't mind trying to answer questions that start with unrealistic assumptions, like "if I just ate 5 billion hamburgers for dinner...", but I can't answer questions that assume something that contradicts the theory that I'm supposed to use to answer the question). That's right. All clocks on the ship, including the pilot's body (which can be considered a really crappy clock), will measure less time than 5 years. That's right. Nothing inside the ship looks funny to him. Not sure I follow you here. Different observers will definitely measure different times between the same two events (because they're actually measuring different things; they're measuring a property called "proper time" of two different curves in spacetime).
I would understand it only the perception of time is relative. As it could take 8 minutes for us to watch the ship arrive at sun, and as it could take eg. seconds to arrive at sun for the crew, it would happen at the same point - the only and utter change would be the age of atoms in either of the frameworks - thus the different perception of time by the different subjects. But this perception only originates from the variation of the speed of the movement of their atoms which was caused by the speed of the framework, not because of some change of the timeflow, wouldn't you agree? This can even lead to the assumption there is no time, only space.
FAQ: What does the world look like in a frame of reference moving at the speed of light? This question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers. The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light. Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)
Hi Norzog. One of the easy way to escape from being taught the theoretical impossibility and contradiction related with travelling with the speed of light rather than being answered what you want, is to begin your question by saying that the ship don't travels at c but very very very very close to c.
Yea, I wanted to imply that the ship doesn't have to fly at light speed but I also wanted to simplify the question and thought it wouldn't matter... But you could also exchange the ship with photon, which age as well and travel at c.
A photon doesn't have any sort of internal clock that would tell us how it is aging, so it isn't physically meaningful to talk about how photons age. If you're just talking about an astronaut moving close to the speed of light then your question can be addressed: Time is relative--it's true that in the Earth's rest frame all the astronaut's bodily processes are slowed down, but in the astronaut's rest frame his bodily processes are running normally while we on Earth (and any observers on Alpha Centauri) are the ones whose bodily processes are slowed down. Both perspectives are equally valid in relativity, there's no objective way to say whose bodily processes are "really" running slower. And despite the disagreement about who is aging more slowly, all frames agree about local events happening at a single point in space and time, like how old the astronaut is when he lands on a planet circling Alpha Centauri. Also, in the astronaut's frame the reason he can get to Alpha Centauri quickly has nothing to do with time dilation, it has to do with length contraction which means that the distance between Earth and Alpha Centauri is much less in his frame than it is in our frame.
I always thought that from the Astronaut's frame the earth would look sped up, not slowed... ?? Or at least, they taught us that.
Assuming the astronaut's frame is an inertial one, then they taught you incorrectly--in his frame Earth clocks would be running slow. The relation between a clock's velocity in a frame and its rate of ticking in that frame has to work the same in all inertial frames, otherwise all frames could not be considered equal and the first postulate of relativity (that the laws of physics work the same in all inertial frames) would be violated.
this is a fun question, and worth contemplating a bit. however, since no mass can travel at "c", let's modify the question just a bit, by assuming that our space ship can travel at 0.99999999 C, and then ask how long it takes to get to alpha centauri, for example. at that speed, the rate of time passage for the ship, as measured by a stationary viewer on earth, will be extremely retarded, and the ship's clock will indicate that it only took about 1 year to travel to alpha centauri. then you face the dilemma of either the ship just traveled faster than the speed of light (by going 4LY in one year), or that the star is really not 4 LY way. oye vey!
It's not really a dilemma, the answer is definitely going to be the latter if you are analyzing things in the ship's inertial frame, the smaller distance in this frame is just a straightforward consequence of length contraction.
jesse - indeed. so, how far is it exactly to alpha centauri? and if i can get there in a spaceship traveling at .99999c in one year, why does it take light 4 years to get there traveling at c? :-)
Well, there's no frame-invariant definition of distance, or of the time it takes something to get from Earth to Alpha Centauri. In the rest frame of Earth and Alpha Centauri the distance is a little over 4 light-years, so it takes anything (including light) at least 4 years to travel from one to the other in this frame. In the rest frame of a ship traveling at 0.99999c relative to the Earth, the distance is only about 0.0045 what it is in the Earth's frame, so about 0.018 light years, which means the ship goes from one to the other in 0.018/0.99999 years in this frame. Light takes even less time in this frame since the light is moving to the right at 1c while Alpha Centauri is moving to the left at 0.99999c in this frame, for a "closing velocity" of 1.99999c (the distance between two objects can shrink faster than light in a given frame, even though neither object individually can be traveling faster than light in this frame), so it would only take 0.018/1.99999 = about 0.009 years for light to get from Earth to Alpha Centauri in this frame. We can't ask how long it takes light to get from one to the other from light's own perspective, since light doesn't have an inertial rest frame of its own.
This question is the very reason that I have joined physicforums.com. My understanding is this so far: If I am standing on earth, watching the spaceship heading for Alpha Centuri, to me it will take the spaceship four years to get there. However, for the astronaut, who is actually on the spaceship, it will seem to him mentally that the trip actually took just one year. His body would only age one year too, right? How? Sorry still not clear. Also Jesse, how did you figure out 0.0045 distance, and 0.018 light years?
That's right. From his point of view the distance is length contracted, so he's traveling a shorter distance.
Not sure what "on the astronaut" means. I'm talking about the length contraction of the distance between the astronaut and the star. If you are too, then yes, this length contraction is what solves this particular mystery.
I hope that you can bear with me on this, as I till cannot grasp: 1. Does length contraction only affect the astronaut and his spaceship? 2. How is 4 light years actually 1 light year if traveling at .99999c? 3. Why does time contract for the astronaut but not for a beam of light?
It affects anything that is travelling relative to something else. From Earth, the astronaut and his spaceship are travelling near c, and thus are length contracted. From the astronaut's point of view, the entire universe is travelling with respect to him, and thus the entire universe is length contracted. See above. When travelling near c, the astronaut measures Alpha Centauri as much closer than we would. It is also flattened. Photons do not experience time.