# Definition of speed in relativity?

I had a physics question, but sufficient procrastination in posting the question has given me time to have possibly solved the question myself. But that led me back to an earlier question that just never seemed to have been answered adequately in anything I have ever heard (nor a quick search of the back logs.)

If, say, you have a question where you are talking about the comparitive effects of object A travelling at 1/2 c and object B travelling at 3/4 c…well, how do we know that A is going 1/2 c and B 3/4 c? Is this just a simple shorthand for saying “relative to the speed at which Earth/us/the third man is travelling which we will assume to be 0 c”? In which case there is really no such thing as 0 c except the speed at which “I” am travelling.
<brain fart>
Which, writing, makes me want to ask if, if I am at 0 c, then does this mean that everything travelling towards me is travelling more than 0 c and everything going away from me is travelling at negative something c? That is, stuff which is able to catch up with my relative speed, and stuff which can’t. Would this mean that the low end border of maximum travel speed is -1 c?
</brain fart>

Anyways, my original question was that given that a meter (metre) is defined as the distance light will travel over a certain period of time–whether that is only true given at the speed at which Earth is travelling, or if you were travelling “faster” than Earth, this distance would change.
My conclusion was that the distance would change, but that your perception of it wouldn’t (or, rather, that your perception would change equally)–so that so far as you (and everything travelling at the same speed as you) were concerned, it would the same distance.
Which of course brings us to the murky question of what speed is anyone travelling at–if at all?

## Ummm… 0c is not possible considering that all objects are in motion and shall remain in motion unless there are no frames of reference. As in: we are always traveling a fraction of c regardless of how tiny the fraction. Now, on the topic of negative c, one can not travel a negative speed. Speed is like distance and you can only have positive speed. (right?)

I have no idea what your last part means but I think I can make a little bit of sense from it. From www.webster.com:

Main Entry: 3me·ter
Function: noun
Etymology: French mètre, from Greek metron measure
: the base unit of length in the International System of Units that is equal to the distance traveled by light in a vacuum in 1/299,792,458 second or to about 39.37 inches – see METRIC SYSTEM table

## The greater the fraction of c you are traveling a peculiar thing begins to happen. It is known as time dilation. The faster an object you view travels (and the greater percentage of c it is) the shorter it will appear to you.

Just to throw it in: realitivistic speed is due to the fact that there must be something to compare the location of the traveler because with just the traveler there is no way to actually know what motion is occuring. There has to be something which will show that distance is being covered, a frame of reference.

I meant in terms of relative perception. You can’t say “half the speed of light” unless you have two values (zero and c) to find the midpoint of. You seem to be agreeing that I was right in saying that when one is talking about 1/2 c, they are assuming an imaginary third party, who (for the sake of simplicity) is assumed not to be moving (0 c).

I was thinking in terms of the two examples of person A who is travelling at half c, and person B who is travelling at 3/4 c, as viewed by the third man. So in this case, we know that the speed of B > A. But if that is so, then when the third man calls up person B and tells him he is running faster than person A, then how does person B view the situation? In a relativistic view, person B doesn’t think he is moving at all. So if he is not moving (speed = 0) and his speed–as reported by the third man is more than person A’s–then that would necessitate that person A is travelling a negative speed.
To person B, it would look like A was simply moving away from him–but if we must reconcile his perceptions to those of the third man, then we would have to say that A is moving a negative speed.

…But thinking about it a bit more, that doesn’t work, since to person A, person B would also be moving away, even though the third man would tell A that he was moving slower than B. if A == 0 and A < B then B > 0.
So I guess there is no way to reconcile their views. Le sigh.

To try and explain my original thinking about the meter a bit more clearly:

If I say I want a meter to be the amount of distance a particular train travels over a particular amount of time–1/8th of a second–well then this is pretty clear cut. But it is only clear cut because we have an accepted 0 speed.
If however I say that I want the length to be the distance the train will travel over 1/8th of a second minus the distance I will travel at a sprint.

Train Speed = 8 U/s
Me = 1 U/s

So 1m = ((1/8) * 8) - ((1/8) * 1) = 7/8 U

Which gets us a definite value. But if we perform the same equation for my friend, Joe, who can run twice as fast as myself then we get:

Train Speed = 8 U/s
Joe = 2 U/S

1m = ((1/8) * 8) - ((1/8) * 2) = 6/8 U

That is, a slightly shorter meter.

But, of course, due to both the fact that it is very hard to say who is moving faster than who in relativistic terms and then the way that space and time trade off at varying speeds, my eventual conclusion was that this little bit of logic just doesn’t scale.
The person travelling “faster” may indeed appear to have a shorter meter as viewed by the third man, but once you get everyone moving the same speed, that meter will have “grown” and now be the same length as the meter that the slower runner had. …Which is I am sure not the optimal phrasing among people who know what they are talking about–but personally I’m happy if I can be confident of the general gist.

You hit the nail on the head. Not to be overly pedantic, but in special relativity everything is, well, relative. As long as I’m travelling at a constant velocity (not accelerating or decelerating), then my reference frame, in which I’m at rest and everything is moving around me, is jim-dandy to perform calculations in. Of course, the beauty of the theory is that if you zoom by me at half the speed of light, you’re perfectly justified in saying that you’re sitting perfectly still, and performing all the calculations in your frame; and everything will come out the same.

Um… no. Physicists talk about negative values of velocity all the time. Basically what it means is that you’ve defined one direction (say, towards Alpha Centauri) to be the direction of positive displacement; a negative velocity then means that you’re moving away from Alpha Centauri.

Yup. Things can move away from you in either direction, but only at a magnitude of c.

I’m assuming that you’re drawing an analogy between the movement of the train and the pulse of light. In what follows, assume that “the train” is, in fact, shorthand for “a pulse of light”:

This is where time dilation comes in. Essentially, when you start moving, your clock starts running slower relative to people sitting on the train platform. This means that your clock reads 1/8 of a second some amount of time after the clocks of the people sitting on the platform, so the train has gotten farther away from you and — hey presto — the extra time and the decreased relative velocity exactly cancel out to give you back the exact same speed for the train. Your friend’s clock slows down even more, but he has an even smaller relative velocity with respect to the train, and — hey presto — the same cancellation occurs. Everyone concludes that the train has travelled one unit after 1/8 of a second; it’s just that the amount of time people call “1/8 of a second” changes.

You got it. There is no absolute speed. We always just assume that the observer is “at rest” and the object being observed is moving, but that’s just a convention. One must just as well assume that the object is at rest and the observer is moving.

If by -1 c you mean [the speed of light]x[-1], then yes. But negative and postive speed are just conventions. You could switch the signs, and all the physics would be the same.

Relativistic physics tells us that if you observe an object at a certain speed, it will appear shorter than it would if it were “at rest” (ie, in the same reference frame that you are in). But the speed of light is always the same in all reference frames, so a meter would always come out the same.

You don’t need Einstienian relativity to determine this. Even Galilean relativity tells us that all speeds are relative. Speed only has meaning with reference to something else.

If all this is so, whence the story of the spaceship that zipped off into space at some high fraction of c and came back “right away” from the perspective of the space travellors, yet time on earth had gone centuries ahead.

If one frame of reference is as good as another, why is there an age difference in one and not the other?

This is called the “twin paradox”, and more than you ever wanted to know about it can be found here. The simplest resolution is that to “turn around and come back”, the spaceship has to do some acceleration, and thus its frame is no longer inertial.

And of course it had to accelerate to get out into space in the first place, not just when it turned around.

Mike, Zebra is correct, because speed != velocity, and distance != displacement.

Speed and distance are scalar quantities, and cannot be negative. (Another scalar quantity that cannot be negative is volume.) Velocity and displacement are vector quantities, and can be negative.

More accurately: can have negative values for their components relative to a given (noncanonical) basis. Einstein wasn’t really happy with “relativity” as a descriptor of his theory, since it’s more about what stays the same under various transformations. The components of a vector change as you change the basis (say, the Gauss normal coordinate vector fields for two different observers) but the vector itself – the geometric object – stays the same. The principle of relativity could be well stated that the objects of physics are geometric, and behave independantly of the arbitrary coordinate systems imposed by different observers.

Except for the Speed of Light itself. That one is absolute, which is the big difference between Lorentzian Relativity (the basis of Einstein’s work) and Galilean Relativity. Any observer in any reference frame whatsoever will measure the same speed for a beam of light.

And in any properly-stated relativity problem, speeds will always be specified in some frame of reference. That is to say, you should never see something like “Particle A is moving at 3/4 c and particle B is moving at 1/2 c”. It should always be, for instance, “Particle A is moving at 3/4 c relative to the laboratory, and particle B is moving at 1/2 c relative to the laboratory”. Actually, there should probably be directions for A and B specified in there, too.

You can only talk about velocities being “positive” or “negative” if you’ve established some convention for which direction is positive. Anyone with a different convention will disagree about which are which. So if A, B, and the unlabeled observer in your example all use the same convention, in which A and B are moving in a positive direction relative to the unlabelled observer, then yes, B would say that A is moving at negative speed. But they might well choose different conventions.

No, the whole point of the development of the equations of relativity theory is that all views are reconciled. You just have to be careful how you apply them.

Any inertial reference frame. The usual caveat is that in a non-inertial reference frame, you can still find a way to measure it in an inertial reference frame, and so you do “measure the same speed”.

I have heard that we have successfully accelerated small particles (or something) to light speed. If, to the particle, it always appears that light speed is still the same relative speed faster than what it is travelling…how does it ever reach light speed?
Other posts seem to be indicating that acceleration fiddles around with things a bit… I am assuming this has some part in it?

It’s impossible to accelerate anything with mass to lightspeed. Only massless particles like photons can go that fast.

However, we have accelerated particles to a speed very close to lightspeed. Greater than 99% of the speed of light, as a matter of fact.

It’s kind of counter-intuitive to realize that an observer moving at nearly the speed of light would still perceive light itself as moving at full speed. If you imagine yourself being in a locomotive steaming forward at 99% of lightspeed and you shine a flashlight straight ahead, it seems like the logical result would be for the beam of light to creep away from you at 1% of the speed of light, slowly edging ahead of the locomotive. The fact that it moves away at 100% of lightspeed seems weird and broken. But that’s what it does.

What actually happens is that time behaves differently when you’re moving at very high speeds. As you approach the speed of light, time slows down for you. The amount that time slows down exactly cancels out the perceived lower speed the beam of light.

Both time and space act weirdly when comparing reference frames moving at a large fraction of c relative to each other, and both the time and space weirdnesses contribute to keeping c constant. It should be noted that in any one reference frame, everything seems normal, time and space included. If you were on that train, you would have no indication that you were moving at all.

Particles with mass can (in principle) go at any speed less than c. Neutrinos, for instance, (which have a very small but nonzero mass) have been measured to go at least about 99.9999999999% of c (that should be twelve nines, unless I miscounted). There’s also the matter that c is the speed of light in a vacuum, and that light slows down travelling through other materials. For instance, visible light will travel at about 3/4 c through water. It is quite possible for other particles to travel through water at speeds greater than 3/4 c (but less than 1 c), in which case they’re travelling faster than the speed of light in that medium. When this happens, you get something called Cherenkov radiation, which is analagous to the wake of a boat or a sonic boom.

Occasionally, one also hears about experiments where something (usually light) is alleged to be travelling faster than c. In all cases, this is a misreporting. The most common cause of the misunderstanding is that different parts of a wavefront are examined entering and leaving the aparratus. Suppose, for instance, that I walk through a doorway: If I hold my arm out in front of me as I do so, then my arm will leave the far end of the doorway before the rest of me enters the near end of the doorway. Nothing at all weird about that. But when a physicist does the same thing with a wave pulse, some popular-press reporter will pick up on the experiment as “the pulse leaves the apparatus before it enters”, or some such nonsense.