According to theory of relativity the speed of light in vacuum is ultimate. But since objects move relative to each other, with respect to what can't we travel at the speed of light?
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2This is a basic question, but it is a sensible one which is not clearly explained in discussions of SR. Down-voters should give reasons. – sammy gerbil Jul 06 '16 at 18:37
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I didn't d/v this but it's a kinda duplicate of this http://physics.stackexchange.com/questions/63555/why-cant-we-accelerate-objects-past-the-speed-of-light – Jul 06 '16 at 18:43
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Some good points made here also, but I'm not sure they quite answer the current question : If I run along the aisle of a bus traveling at (almost) the speed of light, can I travel faster than the speed of light? http://physics.stackexchange.com/q/7446 – sammy gerbil Jul 06 '16 at 18:51
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1@KrishWadhwana : If this is an answer to ayush's Question, please can you post it in an Answer box. I am not the person asking the question. – sammy gerbil Jul 06 '16 at 19:02
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1There is no expectation that voters explain themselves. No, not even for downvotes. More over, explaining a downvote isn't a good comment, except in so far as it offers a suggestion for improving the post. – dmckee --- ex-moderator kitten Jul 06 '16 at 21:49
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@dmckee I don't spend much time on this stack, but that seems like an odd thing to say, especially for a mod. Every other stack I've participated in says that downvoting without a comment is poor form, unless there's already a comment explaining a downvote for the same reason (which you should upvote). Is there a meta to that effect for this stack? – DCShannon Jul 07 '16 at 00:12
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@DCShannon It's a built in assumption of the system. The team has been turning down requests to force comments since the inception of the comment feature. Certainly a lot of people will encourage you to comment, but there is no onus to do so. Downvoters may explain themselves. Doing so can help improve a post. But the meaning of a downvote is given by the tool-tip. For questions it reads "This questions does not show any research effort; it is unclear or not helpful." – dmckee --- ex-moderator kitten Jul 07 '16 at 00:26
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@dmckee Being forced to comment is entirely different than being expected to. We're expected to, for sure. Further discussion would require a meta, which is why I asked if there was one. I guess I'll look for one myself next time someone claims that there's no such expectation. – DCShannon Jul 07 '16 at 00:49
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@DCShannon I'm with you on that one. What good would it be if a post obtained a large collection of downvotes, yet no explanations were given. Supporters upvote responses usually also appear in multiple words, sentences, paragraphs, yet it is recommended that non-supporters are required only to give one click of a mouse switch. That seems a bit biased to me. – Sean Jul 07 '16 at 02:40
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3@DCShannon Let's put it this way: it's polite and usually helpful to leave a comment explaining your downvote, but it is not and will never be required to do so. When we say "expected", we mean it in the sense of "forced", whereas mods on other sites may be using it in the sense of a cultural expectation. That being said, we do get a slow but steady trickle of posts which are, frankly, irredeemably terrible, in a manner such that it's fairly obvious why the post is bad (the reason is in the tooltip) and there's little to be gained by elaborating on it in a comment. – David Z Jul 07 '16 at 12:36
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This is the fundamental postulate of special relativity:
Light (in vacuum) moves at the same speed no matter what you measure it relative to.
Pretty much everything in SR is just a mater of figuring out the deductive consequences of this basic fact. It is an experimental fact that it is so, and it was so even before Einstein -- in particular, light had been found to have the same speed no matter whether we measure it relative to Earth-in-July or to Earth-in-January (at which times our planet moves in different directions along its orbit around the sun).
The fact that light has the same speed for everyone means that if a light signal is sent from one particular time and place (an "event" in relativity jargon) and is received at a different time and place, then two observers will agree what the speed of the signal was - even if the two observers move relative to each other. They will then disagree about how far the two events were from each other -- so, inescapably, in order to agree about the speed they have to disagee abouth how long it took for the signal to move. So two observers do not necessarily agree about how long intervals of time there is between the same two events.
Similar more involved thought experiments lead to the "classical" relativistic effects of time dilation, length contraction and so forth, as necessary consequences of the fact that all agree about what the speed of light is.
In particular, the fact that matter or information cannot move faster than light is one of those consequences -- so it doesn't depend on what we measure the speed relative to, because the premise of the entire fact is that light moves at the same speed no matter what we measure it relative to.
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1To the OP: if this doesn't bug you, reread it! Henning is correct, and it is incredibly counter intuitive. We observed this behavior in real life experiments and determined that the Lorentz transform does a good job of modeling it. Later, Einstein showed that you could explain that transform more elegantly by the constructs he put forward in relativity (the Lorentz transform made equations a bit ugly, so nobody really liked them). Later, some of his counterinutitive side effects of relativity were also tested, and we showed that they indeed happened. – Cort Ammon Jul 07 '16 at 01:32
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1Well, Henning is right but Einsteins postulate allows you easily to(in one or two handwritten pages, I saw it first as a freshman) derive the Lorentz transformations, and also the law of addition of velocities. You get a bus (but don't get hurt getting in) traveling at .99c and you try going at another .99c wrt the bus, you will still go at less than c wrt the street. Tfb below has a different example, same principle.Just get a SR chapter of a book, see the derivations, and understand why two velocities (nor a million of them) can add to c or more, if each is less. All else discussed is extra. – Bob Bee Jul 07 '16 at 04:38
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Light (in vacuum) moves at the same speed no matter what you measure it relative to because 'c' is given by the general cosmic field (result value of field overlap of all fields in space). Isolate it from that and 'c' will increase. – Overmind Jul 07 '16 at 09:13
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The simple answer is 'with respect to anything'.
For instance if I am standing somewhere and you are in a spaceship then we will always measure our relative speeds to be less than $c$. Equally, if I am standing somewhere and two spacecraft are passing me in opposite directions, then I will always measure the speeds of the spacecraft to be less than $c$, and they will also measure their speed relative to each other to be less than $c$ (as well as their speeds relative to me of course). This is true even if, for instance, I measure the speed of each spacecraft to be greater than $c/2$, in opposite directions.
What this means is that velocities do not add in the simple way that we expect from everyday life: if I stand by the side of the road and observe two cars approaching me from opposite directions, both at 30 mph, then I know that their speed relative to each other is 60 mph and when they collide the drivers will almost certainly be killed. If, however, I am standing on a spaceport and I observe two space-cars approaching in opposite directions at, say, $0.8c$ then I know that their speed relative to each other is still less than $c$: it is in fact about $0.98c$. I'm still pretty confident the drivers will be killed though.
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I like this because it posits the answer in a way to help further the question - if two spaceships are moving away at .9c and one turns on his spotlight SR says that the other spaceship will see the light. Their relative velocity without SR would be 1.8c so how fast are they really moving with respect to each other and how far does the light 'travel'? – CramerTV Jul 07 '16 at 02:12
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The Lorentz transformation may shed some light on this... $$\gamma = \frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}$$
Assume one body is, dare I say, "stationary" and the other is traveling away at velocity v. If the relative velocity between these two bodies moving apart is equal to the speed of light, then the denominator in the Lorentz transformation would be equal to zero. Then gamma would be equal to one divided by zero which is utterly absurd. Nor is it possible for two bodies moving apart to travel faster than the speed of light, because then the denominator would consist of taking the square root of a negative number which introduces complex numbers.
Michael Lee
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The square root of a negative number is straightforward - not absurd. Perhaps all we need is a little imagination... – CramerTV Jul 07 '16 at 02:13
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@CramerTV Taking the square root of a negative number is not "absurd", but a velocity equal to the square root of a negative number is. Well, if not "absurd", at least it doesn't appear to have any meaning in the real universe. Like, it makes good sense to say there are 2 or 3 or 4 people in a room. If you said there are 2 1/2 people, I'd wonder what you meant. An axe murderer has cut someone in half and left one part of the body here and the rest somewhere else? If you said there are 4i+7 people in the room ... umm, no. – Jay Jul 07 '16 at 05:26
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I agree, so I changed "absurd" to "without introducing complex numbers." – Michael Lee Jul 07 '16 at 12:34
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@Jay - Interesting conjecture - what is an example of a negative number in the real universe? – CramerTV Jul 07 '16 at 17:01
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@CramerTV There are lots of meaningful uses of negative numbers in the real universe. A change in velocity could be positive or negative. Actually a change in almost anything. Altitude relative to sea level, where plus is above and minus is below. Etc. And I didn't say there are no applications of imaginary numbers in the real universe. A 2D surface can be interpreted as a complex plain, for example. I just said that velocity isn't one of them. – Jay Jul 07 '16 at 20:58
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@Jay, I was offering that our creation of numbers, math, etc. have been wonderful ways for modeling the universe but they also fail us at times. We say charges are positive and negative and use numbers similarly. What if we had chosen colors (black for positive and white for negative) and never had a negative square root to deal with in the first place? Maybe this other type of construct could actually model the universe perfectly with no discontinuities for division by zero, imaginary numbers, etc. The universe works perfectly. Perhaps our construct of numbers and math is what's wrong. – CramerTV Jul 07 '16 at 22:52
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Does this mean I must at least admit it is possible to go faster than the speed of light if introducing complex numbers into the Lorentz transformation is no problem what so ever? – Michael Lee Jul 08 '16 at 00:53
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@CramerTV As you've stated it, "maybe there's some alternative that would work better", one can only say, "sure, it's possible, or at least conceivable". There's no way to evaluate such a speculation until someone actually proposes an alternative and works out the details. – Jay Jul 08 '16 at 13:17
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@MichaelLee Maybe. But that's a big "if". What if I could count to infinity? What if I could travel north past the north pole? – Jay Jul 08 '16 at 13:21
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@Jay, "there's no way to evaluate such a speculation" - so we're back to my original statement, "Perhaps all we need is a little imagination..." It was Einstein himself who said a "leap in consciousness" - not intellect - is how we make discoveries. :) – CramerTV Jul 08 '16 at 18:17
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Lets imagine for a moment that for some reason or other only one object was left existing within the universe, and it was a spaceship. It can accelerate and decelerate, thus movement is in effect here, movement across space. However, whether it is alone in the universe or not, it has a maximum speed of which it can move across the vacuum of space. That being of course, the speed of light.
Light itself has no control of the spaceship. In fact, no matter what speed the spaceship moves across the vacuum of space, those on board the spaceship would still measure the speed of light as being 300,000 km/s.
Thus if they tossed a light beacon out of the spaceship, and moved toward or away from the beacon, and did so at a variety of different speeds, they would still measure the speed of light being emitted from the beacon to be the very same 300,000 km/s.
This consistent outcome of the measuring of light speed can only happen if the spaceship itself was constantly in motion across the 4 dimensional space-time environment, and did so with the very same magnitude of motion that is also known as the spatial magnitude of motion of light, a.k.a. the speed of light.
And so overall, the spaceships spatial speed is relative to the 4D space-time environment. Meaning, the spaceships velocity of motion across space only, is merely determined by the spaceships direction of travel across the 4D space-time environment.
Sean
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