Speed of Light Barrier

This is a question to all the physics gurus (Sylas, Eta, etc) on this board. I have a good background in physics, so try not to dumb down answers too much.Why can't we exceed the speed of light? I've heard two explanations but I am not sure which one is right.The first explanation is that mass increases as matter approaches the speed of light, so it would take more and more force to further accelerate an object as it approaches the speed of light. This seems wrong to me for some reason. One's mass doesn't objectively (from all reference frames) increase, does it? Only from a second observers. So why would the fact that there is a second observer affect how I can accelerate?The second is the reason I think is correct, but I'm having trouble articulating it. Basically, it's a fundamental property of space-time. Velocities aren't additive according to special relativity. In order to add velocities, you use the equation:u= (v1 + v2)/(1+ v1v2/c^2)So from your referece frame you may add 2000 m/s on to your original velocity, but the second observer won't see it add that way due to the above equation.Are these mutually exclusive explanations? Are they related?

Thanks for the analogy. I never heard it put that way, though I like to think I'm pretty well read on the subject. That "time-velocity" does really clarify what's going on. I'm having trouble understanding the "length-contraction" in that analogy.

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Hold a second ruler perpendicular to the first, so it starts pointing in a purely sideways / spatial direction. As we start moving spatially, we rotate and now our spatial vector is pointing slightly downwards. The important point is that the ruler does not now point as far in the spatial direction because of its rotation. Rotate 90 degress to "the speed-of-light" and the spatial ruler no longer points spatially at all. This is length-contraction.

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Is the first ruler pointed up? Why does the vector point downwards, wouldn't that be going backwards in time? I'm missing something.Back to the original question, though. I'm not sure you guys really answered it.Chiroptera showed that mass will increase as velocity increases, but only by assuming there is a limit to the speed of light. I took that post as "mass will increase since there is a speed of light limit," not "there is a speed of light limit because mass increases."You gave me a good way of visualizing special relativity concepts, but only by assuming a fixed length to the ruler.Is the answer just: Assuming there is a speed of light limit, various predictions would be made such as time dilation, etc. These have been observed or inferred by experiments, supporting the assumption.Another way I like to think about it, though I'm not sure it is correct, is similar to how Einstein first thought about the problem.Based on Maxwell's equations, light is a self-propogating E-Field and B-field. The only way it is self propogating is for it to be moving, but if you were traveling at the speed of light it wouldn't be moving relative to you, so it wouldn't exist. Then if you slowed down, it would either: 1.) reappear (something from nothing) or 2.) continue to not exist, although from another persons reference frame (whose was moving slower than c the whole time) it would still be there, right next to you. These scenerios seem pretty illogical, and it seems intuitive to assume one simply can't go faster than c.

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Ok, that was a little vague... the horizontal vector simply represents a length, say of the ruler itself. As the ruler's "velocity increases" its 4-velocity vector starts to tip out of the vertical as decribed above. But the horizontal vector tips with it, so now the spatial extent of the ruler is pointing slightly through time and slightly less through space. So from a spatial perspective it is shorter. Hold a ruler out in front of you from left to right. Now rotate it slightly into the front-back direction so you now see it obliquely. Does it not look shorter? This is length-contraction except instead of front-back, you are rotating into time. Does that help?

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Yes, that helps alot. The length that is projected into the space direction is less and less as you you rotate more.

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Yes, that is right. The "mass" increase is just another optical effect, as with the length contraction.

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Actually, in many ways so is the speed limit: You do realise that if you travel to another star, you will have no max velocity... you can travel there as fast as you like... have I just confused everything

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Why yes, yes you have. Can you maybe expound that a little.

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It's not that the length of the ruler is fixed... it doesn't have to be... the point is that its length doesn't change by rotating it!

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Ah yes!

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Sure As you travel towards a distant star, the star is moving towards you, as is the length or distance between you and the star. So the length contracts, firstly because you are moving towards the star, and secondly becasue of length contraction. We measure speed as distance over time. Well, the distance is shrinking at a much higher rate than expected... so we must have a much greater speed, so V_effective >> V. In the limit of V=C, the distance shrinks to zero and we have traversed the distance in zero time implying infinite V_effective. So as far as you are concerned, given a spacecraft with sufficient thrust and fuel, you can visit any part of the universe in as short a period of time as you like. Just don't expect anyone to be around when you get home...

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So what is the difference between V effective and V? Why can V effective go above c but not V?I'm kindof getting stuck in a loop when I think about this. If you start off moving towards the star at .5c, due to length contraction you are moving faster towards the star than .5c? And when you then factor that in, the distance again contracts? Ad infinitum.Basically, whose reference frame are you moving in V and whose in V effective?

Thanks, got it.

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Be careful here. A photon's 4-velocity certainly has a time component, but it also has an "equal" space component. It's the magnitude of the vector that is zero.

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Can you explain this a little further. From your vector "analogy", it seems that if something is travelling through space at c, it won't be traveling through time.Thanks for answering these questions, and feel free to stop anytime. I can go asking questions ad infinitum.Even better than this, do you recommend any books on general and special relativity?

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It's time for you to start answering your own questons
clue: which frame are you talking about? Do you see light rays travelling through time... or not?

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Sorry for the delay. This is how I analyze the situation with light.From my perspective (and I guess all reference frames besides light's), light is travelling at c. This would mean that a photon would have infinite length contraction and infinite time dilation.From the photon's reference frame, I am moving at c. Therefore, my reference frame has infinite length contraction and infinite time dilation. So for a photon, it travels a distance of zero when going from the sun to my eyes.Do I see light rays travelling through time? I think so. I kindof get caught up when trying to think of light as an electromagnetic disturbance or as a particle (photon). But if it takes light 8 minutes to get from the sun to the earth, I guess it would have to be travelling through time.This message has been edited by JustinC, 07-18-2005 04:32 PM