Re: expansion of the universe

From: Eliezer S. Yudkowsky (
Date: Sat Apr 19 2003 - 08:38:48 MDT

Perry E. Metzger wrote:
> No, I know that part already. What I don't understand is why it isn't
> a violation of special or general relativity for that to happen -- so
> far as I knew your relative speed to another object in space could
> never exceed c. (Or perhaps it is okay because of physics I don't
> know. I was sort of reaching for more detail on this.)

It would be better to say that the local measured relative speed of an
object never exceeds the local measured relative speed of light in a
vacuum. Under Special Relativity alone, with spacetime universally flat,
the measured speed of light is the same everywhere you look - 186,000
miles per second; it's not just a good idea, it's the law. Under General
Relativity spacetime is not flat; it can be curved and, in fact, can be
expanding. Imagine a balloon covered in raisins. As you blow up the
balloon, the raisins get farther apart; this is inflation. The local
speed of any raisin can never exceed c, but it's also possible that if two
raisins start out 186,000 miles apart and motionless relative to each
other, a ray of light starting from one raisin to the other will not have
reached the second raisin one second later because of the expansion of
space in the meanwhile. If you pick two sufficiently distant points on
the balloon, it may be that even if the two raisins are motionless
relative to each other, a ray of light from one can never reach the other
because the balloon is inflating too fast.

Or that's the simple explanation. I think the real explanation would have
to be phrased in terms of spacetime intervals rather than space and time,
since as we all know, "space" and "time" are not basic physical quantities
but only things that we attempt to measure using rulers and clocks, which
are themselves complete physical objects that change according to the real
Einsteinian rules. The invariants are the relativistic quantities, which
are prior to any separate space and time; our interpretation of "length"
as "shrinking" in a fast spaceship is really a statement about what
happens to the relativistic physical objects called rulers under various
circumstances. So rather than talking about an "expanding distance"
between two raisins, or claiming that they are "186,000 miles apart", or
that they are "motionless" relative to each other, or that a photon has
not reached a location "one second" later, we should really talk about
physical rulers laid between two physical clocks and photons traveling
between them. I don't know how to write that description because I don't
know the math, just the qualitative explanation given to nonphysicists. I
don't even know how to define the relative motionlessness of two objects
in an expanding universe because I don't know how "motion" is being
measured. Special relativity and general relativity are being obeyed,
obviously, but I don't know what it looks like in clocks and rulers. Any
physicists hanging around?

Leonardo Wild has been asked not to post to SL4 for one month due to
failing to meet SL4 standards of scientific literacy.

Eliezer S. Yudkowsky                
Research Fellow, Singularity Institute for Artificial Intelligence

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