[Enzos]

Hi naked scientists,

Haven't ever seen this podcast I keep reading about here, but I've been reading through your forums for quite some time now and have found answers to many of my questions. There is just this little thing about C I don't get.

If C is always about 300000m/s relative to you, no matter how fast you go relative to earth. Then why isn't it possible for a spaceship/meteorite/rock/whatever to speed say 600000m/s faster then earth through space? C will still be C relative to that spaceship/meteorite/rock/whatever.

Is it possible that momentum is some sort of dimension with C as it's horizon? If something has a momentum >C relative to earth could it be dark matter and vice versa?


You guys are probably pacepalming right now, :P
but anyway, what am I not getting?
sincerely,

Enzo from Italy

[damocles]

The simple and perhaps most illuminating answer is that when you add velocities, a simple sum does not give the right answer.

If you add two velocities (along one direction), v(total) = v(1) + v(2) – ^v(1)*v(2)/_c

If v is much smaller than c, you can see that velocities will add up as you expect, but when you get close to c, then they do not.

Examples:
v(1) = v(2) = 0.01 c; v(total) = 0.0199 c -- not 0.02 c
v(1) = v(2) = 0.5 c; v(total) = 0.75 c -- not c
v(1) = v(2) = 0.9 c; v(total) = 0.99 c -- not 1.8 c
 

Screwy formula -- see Imatfaal post below

[MikeS]

c remains constant because time compensates in just the right manner to keep it so.

Imagine yourself in an accelerating spaceship.  The faster you go the more time dilates or slows down from the perspective of a distant observer.  This is a real effect but you are not aware of it as everything in your local time frame has slowed by the same amount.  Time to you appears to pass as normal. 

As you approach the speed of light time almost stops.  If you could reach the speed of light time, for you, would stop but you would be unaware of it.  Also as time slows down so it requires more and more energy to accelerate.  Eventually the energy required heads towards infinity.  By the energy/mass equivalence principle mass also increases towards infinity.  Infinite mass implies infinite gravity and zero passage of time.

I hope that shows you why mass can never accelerate up to the speed of light.  In brief, for mass to accelerate up to the speed of light would require infinite energy and it's mass would become infinite also the passage of local time for it would infinitely decrease (stop).

[simplified]

Energy can not make motion without time.High energy has less ability to recieve time.

[imatfaal]

The simple and perhaps most illuminating answer is that when you add velocities, a simple sum does not give the right answer.

If you add two velocities (along one direction), v(total) = v(1) + v(2) – ^v(1)*v(2)/_c

If v is much smaller than c, you can see that velocities will add up as you expect, but when you get close to c, then they do not.

Examples:
v(1) = v(2) = 0.01 c; v(total) = 0.0199 c -- not 0.02 c
v(1) = v(2) = 0.5 c; v(total) = 0.75 c -- not c
v(1) = v(2) = 0.9 c; v(total) = 0.99 c -- not 1.8 c
 

Not sure if Damo's answer was screwy because of the formatting or otherwise.  If you are adding two collinear velocities the formula is as follows


if then you get


if then you get

c remains constant because time compensates in just the right manner to keep it so.

  Remember that distance is also changed thru a lorentz transform - its not just time that changes

[MikeS]

c remains constant because time compensates in just the right manner to keep it so.

  Remember that distance is also changed thru a lorentz transform - its not just time that changes

True, and that affects the length of the spaceship but I believe not the surrounding space which is not moving (apart from any small frame dragging effect).  So, just time adjusting in just the right manner is sufficient to keep c constant without taking into account length contraction.  Also I think I am correct in saying that you either take into account time contraction or length contraction, not both at the same time.

[wolfekeeper]

Atoms are held together by electromagnetic forces; so if an spaceship/meteorite/rock/whatever containing atoms by some miraculous means went faster than light, it would fall apart.

[yor_on]

The thing is, how do you define a speed?

You do it by measuring out a distance. Then you need a clock, in your absolute vicinity. Then you need to decide what is 'still', which is easiest to do relative something big that you might be standing on, as our Earth :)

Then you 'clock' something that moves the distance you measured up, and so becomes able to define a speed to it, relative yourself on your uniformly moving, and therefore in most respects able to be defined as 'standing still', Earth.

So now you have a speed.

But the weirdest thing is that you can have different uniform motions on that thing you define as being 'still'. There is nothing stating that all uniform motions in the universe must be the same, as measured from Earth. There are all sorts of uniform motion in the universe, some faster that Earths, others slower. And the idea behind 'c' being a constant is that no matter what uniformly moving 'frame of reference' (as our Earth) you stand on, that speed must come out the exact same, when you measure lights speed in a vacuum locally.

So what is the speed of light?
Well, it's a constant firstly, a 'speed' secondary as I see it.

That one is the most important thing to realize about radiation. That is is a constant, 'speeds' doesn't make sense for it. Except as defined locally from a uniform motion, in which case it has the same 'speed' everywhere. Eh, and yes, that one has been tested to smithereens, over a hundred years or more.. And I agree, it's weird..

All speeds we have are arbitrarily defined relative what we find to be 'still'. What Einstein did was to define what type of frames of reference you could call 'still', and those are all uniformly moving. So the whole question of 'speeds' becomes slightly twisted as we don't have a 'absolute frame of reference' that we can measure all other 'speeds' from.

But if you accept that all uniform motion express itself the same, then you have one sort of 'frame' you can use, but then a 'speed' also becomes relative you measuring. And that makes sense, because when you measure you do it relative your wristwatch and your ruler. You don't call Andromeda and ask them, if you did, it would be their measurement, not yours.
=

And one more thing that may not be so obvious at first.

If light always must be the 'fastest' thing you can measure, giving you a same 'constant speed', no matter what 'speed' you find your uniformly moving (earth) you stand on to have, relative some other object.

Do you think that anything other, as some rocket, that you measure can outdo that lights 'speed'?
==

And if you find it impossible, do you think your friend being at another (uniformly moving) 'frame of reference', having a different 'speed' relative your earth, can find the rocket to move FTL?

Just imagine yourself teleported to him and wonder what you will see.

That's 'locality'.
==

You might also ask yourself, if now light/radiation always have one 'speed'? And if all I measure is a result from interactions, relative the 'information carriers' that light/radiation becomes for my measurements, and senses. What would happen if something really could go FTL?

Would I even see it?

=

cleaned up the spelling etc, a little :)

[yor_on]

Here is a very good description, by a very nice guy, of how Einstein might have though as according to what historical evidence we have. And if one get stuck on something Google might be a friend.

http://www.aip.org/history/einstein/essay-einstein-relativity.htm