- 4231 -
SPACETIME - galaxies leaving exceed that. How can the universe expand faster than
light travels? The supreme law of the
universe is nothing can go faster than the speed of light. Yet,
some galaxies are moving away from us faster than the speed of light.
What gives?
-
--------------------- 4231 - SPACETIME - galaxies leaving exceed that.
- We live in an
expanding universe. Every day the galaxies we can see get farther apart from
each other, on average. There are slight motions on top of that general
expansion, leading to instances such as the Andromeda Galaxy heading on a
collision course for the Milky Way. But in general, in the biggest of pictures,
the galaxies are getting farther away from each other.
-
- A key feature of
this expansion is how uniform it is. Imagine a bunch of folks standing around
the edges of a stretchy piece of fabric, tugging at it. Let us assume they're
choreographed well and are able to walk backward and pull at the same rate.
You, standing in the middle, would correctly observe that your
"universe" is expanding: any objects placed on that fabric would
slowly move away from you.
-
- Because stretchy
stuff is stretchy, the objects on the fabric close to you would appear to move
away with some speed, but the farther objects would appear to move faster. Even
though the folks doing the pulling are moving at a constant speed, the apparent
stretch changes with distance!
-
- Now, let's jump to
the universe. Edwin Hubble was the first
to measure the expansion rate. The more modern value is 68 kilometers per
second per megaparsec.
One megaparsec is 1
million parsec, which is 3.26 million light-years.
-
- It means that if
you look at a galaxy 1 megaparsec away, it will appear to be receding away from
us at 68 km/s. If you look at a galaxy 2 megaparsec away, it recedes at 136
km/s. Three megaparsec away? 204 km/s. And on and on: for every megaparsec, you
can add 68 km/s to the velocity of the far-away galaxy.
-
- So it's easy enough
to compute: At some point, at some obscene distance, the speed tips over the
scales and exceeds the speed of light, all from the natural, regular expansion
of space.
-
- Yes, the movement
of that galaxy can be interpreted as a "speed": you can measure the
distance to it, wait awhile and measure it again. Distance moved divided by
time equals speed, and the speed you measure can be faster than light.
-
- It's true that in
special relativity, nothing can move faster than light. But special relativity
is a local law of physics. That means
that you will never, ever watch a rocket ship blast by your face faster than
the speed of light. Local motion, local laws.
-
- But a galaxy on
the far side of the universe? That's the domain of general relativity, and
general relativity says that galaxy can have any speed it wants, as long as it
stays way far away.
-
- It goes deeper
than this. Concepts like a well-defined "velocity" make sense only in
local regions of space. You can only measure something's velocity and actually
call it a "velocity" when it's nearby and when the rules of special
relativity apply.
-
- Stuff far away,
like the galaxies we're talking about it? If it's not close, it doesn't count
as a “velocity” in the way that special relativity cares about. Special relativity doesn't care about the
speed.
-
-
November 20, 2023
SPACETIME - galaxies leaving exceed that 4231
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Tuesday, November 21, 2023 ---------------------------------
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