In the book "The Elegant Universe" Brian Green says Einstein once said everything in the universe is moving at the speed of light. How can this be? I thought bodies with mass couldn't reach c.
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Greene isn't talking about ordinary speed, he's using a sort of idiosyncratic definition of "speed through spacetime" which personally I think is more misleading than helpfulsee this thread for more details.
I assume this is a misunderstanding about Greene's talking about "speed through time". Greene says you can think of everything moving at the speed of light, but things that don't really move at the speed of light are experiencing most of their "motion" through time rather than space. This can be confusing terminology because the idea of "motion" usually means the amount of space covered in a certain amount of time, but Greene is appealing to the fact that time flows in a direction as well.
edit: I've never read anything from Einstein that stated anything close to "everything moves at c", and I would be surprised if someone dug up an example of Einstein using that terminology. If Greene says "Einstein said everything moves at c," he most likely meant Einstein's theories can be interpreted in such a way.
Several authors have used this metaphore  it gives you a simple derivation of the transforms. But like Ellipse  I cannot find any reference to it in Einstein's original writings
The velocity 4vector, i.e. the "velocity" in 4D Minkowski spacetime has an invariant magnitude [itex]c[/itex] for all objects. The point is however that this 4vector cannot be interpreted as a normal velocity like velocities in space. The vector is defined as [tex]\frac{dx_\mu}{d\tau}[/tex] whereas normal spatial velocities are [tex]\frac{dx}{dt}[/tex]. ([itex]\tau[/itex] is proper time, defined as [itex]\tau=t/\gamma[/itex]).
What Greene does is rewriting the components of this 4vector from the usual Minkowski form (+) into Euclidean form (++++) which also changes the spatial velocity components in normal velocity components [tex]\frac{dx}{dt}[/tex]. You then end up with a temporal velocity component [tex]c\frac{d\tau}{dt}[/tex] which is supposed to be the velocity through the time dimension. Greene's approach is common for what is called "Euclidean relativity", a not very well known alternative mathematical framework for the usual Minkowski framework.
By "everything is moving at c," a 4D spacetime is referred to rather than a 3D traditional space. Basically, if we are not moving in the first three dimensions relative to an outside observer, then we are moving completely in the 4th dimension. As we move closer to a total of c in the first 3 dimensions, though, less of our "4Dvelocity" is directed in the "t" direction and therefore we appear to experience less time to an outside observer.
Basically, this is just a simple way to try to explain the effects of relativity; that is, if we move at a velocity closer to c in space, we move at a slower "velocity" through time.
If my guess is correct, i believe that it was an example about the limit of going to close to the speed of light and its effect on the dilation of time.
With an analogy of a fast moving vehicle trying to calculate its maximum speed by going through a series of test runs.
The first direction taken from point A to B taken to be parrallel to an axis, and the rest of the runs be slightly deviated from the original axis (cause by human error) causing a slight slower time achieved than the rest of the runs.
Eg
yaxis 


_______ xaxis
With either of the Axis being Space and Time
With the above analogy being given then more speed less time and less speed more time
I hope i am understandable. Cause i have the above book though. Kinda slow to digest if you are a bit of a beginner(me) and you try to understand everythig in the book =P