Expansion Greater Than Light
Name: Al R.
I was watching television when some journalists were discussing advances
in science. One of them mentioned expanding universe. The phrase that
really got my attention was something to the effect that the expanding
universe might someday accelerate beyond the speed of light. I started
looking around for information regarding faster-than-light experiments.
The best I could ascertain was that under certain conditions it was
possible to have the tails of wave impulses pass their respective
heads--thus only energy surpassed the speed of light. No particles and no
meaningful information were known to exceed the speed of light in a
Is there a viable theory of the expansion of the universe that proposes
that it might expand faster than the speed of light?
This is a bit of a technical question, but here goes to the best of my
The speed you refer to when you say that the "tail" of a
wave packet overtakes the "head" refers to the 'phase velocity'. This term
appears in the wave function of the photon in the exponential term and can
exceed 'c'. The 'phase' cannot carry any information, so the apparent
paradox is not real. The velocity of the wave packet (photon) itself cannot
exceed 'c'. It is that velocity that is usually referred to when talking
about the speed of light. You can follow-up on this distinction in Richard
Feynman' Lectures on Physics Vol. 1, 48-5 to 48-7.
Theoretical physicist Joao Magueijo wrote a speculative book "Faster
than the Speed of Light" in which he discusses the "what if" consequences of
somehow overcoming the restriction of light (or any other things) traveling
at "supra-luminal" speeds. He is a "hard core" theoretical physicist, so he
isn't just spinning a tale, but he admits up front that the book is
speculation. There is nothing wrong with speculation as a scientific tool
(although you will not find it in traditional listings of the "scientific
There are three conceivable conditions where the limit of the speed of
light is not experimentally determined. The first is the very first
fractions of a second after the Big Bang when the physical laws of the state
of energy (there was no "matter" yet) are not known. That is, we do not know
if our current laws applied to that fraction of a second. Nobody has any
evidence to the contrary, but nonetheless it is an open question. The second
is the newly discovered observation that the Universe is actually expanding
at an increasing rate, rather than "slowing down" due to the attractive
force of gravity. Related to this is so called "dark energy" and "dark
matter". That is, all the observable matter in the Universe is not nearly
large enough to account for its experimentally observed behavior. No one
knows what this "dark energy" and "dark matter" is. It is not just cold
inter-galactic "stuff", it must be obeying a different set of physical laws
than regular matter. So until these physical laws are elucidated, the
question of the speed of light remains an open issue. The third is extremely
small dimensions, for example time intervals less than < ~10^-43 seconds.
Here the so-called "Standard Model" breaks down.
For all dimensions and spaces in between, however, the speed of light
has been constant for the entire age of the Universe. At the small scale
particle accelerators have experimentally verified this and on the large
scale, observations of distance stars and galaxies have experimentally
verified this. It is interesting to point out that the constant speed of
light, and the fact that nothing travels faster is equivalent to the
statement that energy is conserved. Another "fact" that has been verified
millions of times.
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Update: June 2012