# Expansion of the universe and the speed of light

## Main Question or Discussion Point

Our current understanding of the universe is that nothing can travel faster then the speed of light. so far science in general has been unable to prove otherwise.

However:

As far as we know the age of the universe is 14.6 Billion years (give or take an eon or two) and our measurment of the size of the universe puts it at around 93 Billion light years in diameter. Doesn't this prove that the speed of light can indeed and has been breached? all matter in the universe was at one point traveling much faster then the speed of light, if it was a physical impossibility then the universe should only be 29.2 billion light years in diameter.

yes this is the random thought that passes through my brain as the work day comes to a close. any input is greatly appreciated.

Don

phinds
Gold Member
2019 Award

Our current understanding of the universe is that nothing can travel faster then the speed of light. so far science in general has been unable to prove otherwise.

However:

As far as we know the age of the universe is 14.6 Billion years (give or take an eon or two) and our measurment of the size of the universe puts it at around 93 Billion light years in diameter. Doesn't this prove that the speed of light can indeed and has been breached? all matter in the universe was at one point traveling much faster then the speed of light, if it was a physical impossibility then the universe should only be 29.2 billion light years in diameter.

yes this is the random thought that passes through my brain as the work day comes to a close. any input is greatly appreciated.

Don
This is a VERY common misconception. Google "metric expansion"

And by the way, it is NOT true that the "universe" is ~93billion LY across, that's the OBSERVABLE UNIVERSE. There is a big difference.

marcus
Gold Member
Dearly Missed
...Our current understanding of the universe is that nothing can travel faster then the speed of light...
That is correct. Universal distance expansion is not travel. Nobody gets anywhere by it, or changes their neighbors or surroundings. Just the distances to everybody increase. It is a type of geometry change that is not governed by the Special Relativity speed limit.

But I'll just throw in this suggestion, this will get you hands-on experience (using online calculator) with superluminal rates of distance expansion. Go here:
http://www.einsteins-theory-of-relativity-4engineers.com/CosmoLean_A17.html
Press "calculate".

This gives data for galaxies whose light has been wave-stretched by a factor S. The oldest galaxies we have seen so far have S=10 or possibly protogalaxy blob-like things at S=11.
So this takes you from the earliest galaxies down to the present at S=1

If you take any galaxy's NOW distance and divide by 13.9 billion years (13.9 Gy) you will get the speed the present distance to it is now growing, as a multiple of the speed of light.

You can see that for most of the galaxies which we can observe the present distance to the galaxy is increasing faster than c.

If you take any galaxy's THEN distance (shown in the 6th column of the table) which is the distance it was at when it emitted the light we are now receiving, and divide that by what the Hubble time was then at that point in history (shown in the 4th column of the table) you will get the speed at which that distance was increasing at that time. That was when the galaxy emitted the light.

Try it. This is a good new online cosmology calculator and it should be worth your while getting familiar with it if you are at all interested in cosmology.

Here's what you get just pressing calculate with the default settings:

10.000 0.100000 0.558636 0.839354 30.904385 3.090438
9.000 0.111111 0.654419 0.982718 29.996628 3.332959
8.000 0.125000 0.780996 1.171895 28.923902 3.615488
7.000 0.142857 0.954192 1.430183 27.629840 3.947120
6.000 0.166667 1.201987 1.798431 26.027218 4.337870
5.000 0.200000 1.578299 2.354007 23.971768 4.794354
4.000 0.250000 2.199330 3.258063 21.205546 5.301386
3.000 0.333333 3.356888 4.884824 17.220763 5.740254
2.000 0.500000 5.964010 8.147992 10.901000 5.450500
1.000 1.000000 13.754797 13.899959 0.000000 0.000000

It has a nice feature that if you don't like or can't use the 6 decimal precision then at the top of each column you can type in a 3 in the box instead of the 6 that is there and then press calculate again and it says:

10.000 0.100 0.559 0.839 30.904 3.090
9.000 0.111 0.654 0.983 29.997 3.333
8.000 0.125 0.781 1.172 28.924 3.615
7.000 0.143 0.954 1.430 27.630 3.947
6.000 0.167 1.202 1.798 26.027 4.338
5.000 0.200 1.578 2.354 23.972 4.794
4.000 0.250 2.199 3.258 21.206 5.301
3.000 0.333 3.357 4.885 17.221 5.740
2.000 0.500 5.964 8.148 10.901 5.451
1.000 1.000 13.755 13.900 0.000 0.000

anyway this should really make you start wondering how the light got here. Because for every galaxy with S = 3 or bigger (and this is MOST of the galaxies which we can see with a telescope) the distance WAS increasing faster than c when it emitted the light (6th col divided by 4th col) and the distance IS increasing faster than c today as we are receiving the light (5th col divided by 13.9 Gly). That is for the OVERWHELMING majority of galaxies in the sky. So maybe you will ask some questions.

However it has nothing to do with Star Trek and actual superluminal *travel* which is more in the fantasy department.

Last edited:
Thank you both for the information. and thank you for the calculator, it should prove very interesting to try out.

Chalnoth
By the way, the correct statement is that nothing can outrun a light ray. Relative speed is only well-defined locally, so trying to extrapolate to the speeds of far-away objects in curved space-time frequently leads to very weird results. But nothing ever can outrun a light ray. And nothing in our expanding universe has.

bcrowell
Staff Emeritus
Gold Member

Last edited by a moderator:
But the universal expansion itself can outrun the light within it.

Chalnoth
But the universal expansion itself can outrun the light within it.
That statement doesn't even make sense.

marcus
Gold Member
Dearly Missed
About "sense" I think no one person is the authority about what does or does not make it. People do sometimes differ as to what does or doesn't make sense to them.
The verb outrun has several senses. Personally I like what the Collins Thesaurus gives as its first.
outrun
verb
1. outdistance, beat, escape, leave behind, get away from, shake off, outstrip, lose, ...
Collins Thesaurus of the English Language – Complete and Unabridged 2nd Edition. 2002 © HarperCollins Publishers 1995, 2002
=========
out·run (out-rn)
tr.v. out·ran (-rn), out·run, out·run·ning, out·runs
1.
...
b. To escape from: outrun one's creditors.
The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company.
=========
outrun [ˌaʊtˈrʌn]
vb -runs, -running, -ran, -run (tr)
1. ...
2. to escape from by or as if by running
3. ...
Collins English Dictionary – Complete and Unabridged © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003
================

Brainiac please have a look at this calculator.
The S=1 row describes the present. It says at present the cosmic event horizon is 15.622 billion ly. That means that if today a galaxy is 15.7 billion ly from us, a flash of light we send towards it cannot reach it.
the distance to such a galaxy is expanding too fast for light to bridge. In a sense the expansion "outruns" the light. The galaxy outdistances and gets away from the light.
But it is really the expansion process itself that does this, in a curious way, not the galaxy. The galaxy is not going anywhere---the distances between things are just expanding.

I'll think about what you said, it might make sense and be an apt way of expressing what happens.

==================

I would rephrase what Chalnoth said and not use the word "outrun". I would probably say nothing ever overtakes and passes light. that would make clear that the things were in the same local reference frame, where speeds are well defined, and racing "neck and neck" so to speak.

Translating math into English words is often a bit tricky, different meanings and so on. Semantic disagreement is not real disagreement, we just hear words differently.

Last edited:
marcus
Gold Member
Dearly Missed
But the universal expansion itself can outrun the light within it.
I thought about this--it's epigrammatic. Maybe it is an apt way to refer to the existence of a cosmic event horizon. Some distances are expanding too rapidly for light to ever bridge.
Maybe you would say it again in more words. No harm in restating something, or saying the obvious. I'd be interested to hear more about what you had in mind.

Do you happen to know what REDSHIFT is the threshhold of unreachability? If we look at a galaxy today and see that its redshift z is above a certain zhorizon then we know that today's signals from us can never reach them no matter how long they wait and vice versa. That would not be the case were the cosmological constant zero. the whole thing depends on having a positive Lambda. You may know all about that.

Last edited:
Chalnoth
About "sense" I think no one person is the authority about what does or does not make it. People do sometimes differ as to what does or doesn't make sense to them.
But in this case, expansion and speed have different units. Saying that space can expand faster than light is like saying that a car can travel faster than 3000rpm's. Now, a car's engine might easily go faster than 3000 rpm's, but it makes no sense to say that it can't go down the road faster than this (or that it can go down the road faster), because 3000rpm is not a speed.

But yes, saying that nothing can overtake and pass a light ray is a more accurate way of putting it.

About "sense" I think no one person is the authority about what does or does not make it. People do sometimes differ as to what does or doesn't make sense to them.
The verb outrun has several senses. Personally I like what the Collins Thesaurus gives as its first.
outrun
verb
1. outdistance, beat, escape, leave behind, get away from, shake off, outstrip, lose, ...
Collins Thesaurus of the English Language – Complete and Unabridged 2nd Edition. 2002 © HarperCollins Publishers 1995, 2002
=========
out·run (out-rn)
tr.v. out·ran (-rn), out·run, out·run·ning, out·runs
1.
...
b. To escape from: outrun one's creditors.
The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company.
=========
outrun [ˌaʊtˈrʌn]
vb -runs, -running, -ran, -run (tr)
1. ...
2. to escape from by or as if by running
3. ...
Collins English Dictionary – Complete and Unabridged © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003
================

Brainiac please have a look at this calculator.
The S=1 row describes the present. It says at present the cosmic event horizon is 15.622 billion ly. That means that if today a galaxy is 15.7 billion ly from us, a flash of light we send towards it cannot reach it.
the distance to such a galaxy is expanding too fast for light to bridge. In a sense the expansion "outruns" the light. The galaxy outdistances and gets away from the light.
But it is really the expansion process itself that does this, in a curious way, not the galaxy. The galaxy is not going anywhere---the distances between things are just expanding.

I'll think about what you said, it might make sense and be an apt way of expressing what happens.

==================

I would rephrase what Chalnoth said and not use the word "outrun". I would probably say nothing ever overtakes and passes light. that would make clear that the things were in the same local reference frame, where speeds are well defined, and racing "neck and neck" so to speak.

Translating math into English words is often a bit tricky, different meanings and so on. Semantic disagreement is not real disagreement, we just hear words differently.

That's exactly what I meant. That space expands so fast in certain regions that light can't traverse them completely as it otherwise would if space were not expanding. That's why the present detectable universe is expected to become eventually undetectable. The light will be "attempting" to reach us but will never do so because of the additional space that is being added at a pace faster than light can keep up with. Hopefully I didn't fumble something this time. But if I semantically did it again, please feel free to correct me.

I have been having the same thought? I assume that if the universe is expanding this has been taken into account ie added to the speed of light calculation?

phinds
Gold Member
2019 Award
That's exactly what I meant. That space expands so fast in certain regions that light can't traverse them completely as it otherwise would if space were not expanding. That's why the present detectable universe is expected to become eventually undetectable. The light will be "attempting" to reach us but will never do so because of the additional space that is being added at a pace faster than light can keep up with. Hopefully I didn't fumble something this time. But if I semantically did it again, please feel free to correct me.
The bolded part is kind of an awkward way to say it, but I get what you mean. What is more reasonable to say is that there will ALWAYS be an "observable universe", it's just that after enough time of expansion, there won't be anything in it to observe, other than the local cluster.

phinds
Gold Member
2019 Award
I have been having the same thought? I assume that if the universe is expanding this has been taken into account ie added to the speed of light calculation?
It is not clear what you are asking. The expansion of the universe and calculations of the speed of light have NOTHING to do with each other.

The bolded part is kind of an awkward way to say it, but I get what you mean. What is more reasonable to say is that there will ALWAYS be an "observable universe", it's just that after enough time of expansion, there won't be anything in it to observe, other than the local cluster.
Thanks. The way you express it is definitely the right way.