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We all know that stuff can't go faster than the speed of light - it's length becomes negative and all kinds of weird stuff happens.

However, this is in relation to what? If two objects, each moving at 0.51 times the speed of light in relation to some point pass each other, do they disappear?

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    $\begingroup$ in relation to anything. as the speed of light is universal, nothing can see any other nothing moving at the speed of light (which is reserved for massless fields) $\endgroup$
    – lurscher
    Commented Apr 29, 2013 at 4:11
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    $\begingroup$ Dear @Undo, lengths don't become negative in relativity. On the other hand, relativity does change something you probably take for granted - namely that the relative velocities simply add up. They don't. Relativity changes the properties of space and time and mixes them so that the right way to combine velocity in relativity is not addition but $(U+V) / (1+UV/c^2)$. For $U=c$, this simply gives $c$ back, confirming one of the basic postulates/assumptions of special relativity, namely that the speed of light in the vacuum is $c$ regardless of the motion of the source as well as the observer. $\endgroup$
    – Luboš Motl
    Commented Apr 29, 2013 at 6:41
  • $\begingroup$ See this related question. physics.stackexchange.com/questions/60091/… $\endgroup$
    – ABC
    Commented Apr 29, 2013 at 6:41
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/11398/2451 , physics.stackexchange.com/q/32140/2451 , physics.stackexchange.com/q/32140/2451 , and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Apr 29, 2013 at 7:28

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in relation to anything else that can make such measurements.

As the speed of light is universal, nothing can see any other massive field moving at the speed of light (which is reserved for massless fields)

your 0.51 number suggests that you expect that naive addition of velocities holds when velocities approach the speed of light. This is wrong. Here is an article explaining the relativistic velocity addition expression:

http://en.wikipedia.org/wiki/Velocity-addition_formula

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  • $\begingroup$ 'Relativistic velocity addition expression' shudders $\endgroup$
    – user20703
    Commented Apr 29, 2013 at 4:21
  • $\begingroup$ @Undo Stick to the easy 1D case: $v_1$ "$+$" $v_2$ is simply $(v_1+v_2)/(1+v_1v_2/c^2)$, which you can check never exceeds $c$ in magnitude if $\lvert v_1 \rvert, \lvert v_2 \rvert < c$. $\endgroup$
    – user10851
    Commented Apr 29, 2013 at 6:09
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This is essentially the same as lurscher's answer, but from a different perspective.

Special Relativity is often thought of as some kind of mystical force that acts on objects and stops them moving faster than light. This misconception is the reason for questions like this one. Special Relativity is actually just a prescription for telling us what events in another inertial frame look like in our inertial frame.

So if your object moving at 0.51$c$ fires a bullet at 0.51$c$ SR tells us that as measured in our inertial frame the velocity of the bullet is given by the relativistic addition law and cannot exceed the speed of light. SR doesn't mean objects can't move faster than light, and indeed galaxies farther away than about 50 billion light years are moving faster than light relative to us. Indeed, if the universe is infinite (and the FLRW metric applies to all of it) infinitely distant galaxies would be moving infinitely fast relative to us. However SR tells us we will never measure the velocity of a distant galaxy to be faster than light.

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  • $\begingroup$ I do not understand. The galaxis moving faster than light from us should be any distance, their light would be reach the Earth one time. If it will, we can measure their red shift, and so their velocities. I am wrong? $\endgroup$
    – Arpad Horvath
    Commented Apr 29, 2013 at 8:11
  • $\begingroup$ If something is receding from us faster than light it is causally disconnected from us. We and it will never interact. $\endgroup$
    – John Rennie
    Commented Apr 29, 2013 at 10:32
  • $\begingroup$ Do you mean, that we can not calculate the time, the light arrive to us with time = original_distance / c because the Universe is expanding? $\endgroup$
    – Arpad Horvath
    Commented Apr 29, 2013 at 11:30
  • $\begingroup$ There is so much space created (by expansion) between the object and you, that the speed of light is too slow to ever make that distance. Just like it is not possible to pay off dept, if its interest becomes higher than your salary. $\endgroup$
    – Martin Ueding
    Commented Mar 21, 2014 at 10:46
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The speed of light seems to be the undisputed speed limit of the universe, in relation to the fact that to travel faster than a massless photon is able to travel would not only be physically impossible because no object containing mass would be able to stand the blinding speed, even in the vacuum of space without atmosphere to create drag.

Also, there is the time aspect. If you are on a spaceship going 99% the speed of light, and your twin brother is on another spaceship going 9% the speed of light, traveling to the same location, by the time your twin were to arrive, he would have experienced 90% more time than you have, even though you have both travelled the same distance.

Also, traversing the universe at the speed of light, for a human, would require technologies that we could only dream of.
First, you would need to somehow find a way to shield the inhabitants of the ship from the deadly effect of inertia and g-forces inside of the ship. For a human, 186,000 miles/second would kill in a fraction of a millisecond, the force would flatten all of your internal organs, your brain, your eyes, everything, against the back of your body. Bones would literally liquify, the heart wouldn't be able to beat against the immense force of inertia.

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    $\begingroup$ there is a misunderstanding in your last paragraph. The effects you describe would happen if the accelerations were higher than a few g . A constant acceleration could take to .99999999.... of the speed of light if it mere g and lower. The people in the spaceship would feel nothing unusual to an earth environment. If the acceleration stopped and they were coasting they would a feel free fall situation. $\endgroup$
    – anna v
    Commented Apr 29, 2013 at 4:42