# Space expansion and speed of light

I recently saw a video on gravitational waves that says that expansion of space can only be measured due to changes in speed of light as everything else that could have been used to measure the expansion has expanded too and hence the relative expansion has become zero. I feel that had space been the one to expand, we should have observed an increased speed of light. To illustrate further, say there are two points in space A and B which are $d$ distance apart. Light takes time T to get from A to B. Now A and B are stretched apart, i.e. we as observers now see an increased distance between A and B, say D but space still thinks that the distance between them is $d$ (I feel this is the part where I might have gone wrong). Since speed of light in space is constant, it still travels between A and B in time $T$, whereas we as observers will see it travelling a distance $D$ ($D>d$), in time T. Hence implying that speed of light increasd due to expansion in space. But the video on gravitational waves suggests that expansion in space slows light down. If that is the case then wouldnt it be much more intuitive to say that the distance between particles has increased due to some reason and that space has remained the same?

Heres a link to the video: https://youtu.be/4GbWfNHtHRg

When an EM wave starts its way to us from a far away galaxy that is receding from us, light will eventually travel through regions of space that are really empty, meaning regions of space between galaxy clusters.

In those regions, there is really no matter that would have any gravitational effects that could withstand the expansion of space, so space itself is expanding.

When the EM wave travels through regions like that, it travels in expanding space. There, space is stretching out, so the EM wave that is traveling in it will be stretched out too. The EM wave will have a longer wavelength, and so smaller frequency. The EM wave will be redshifted. It will have smaller energy.

Now in your case the distance for a distant observer goes from d to D. For a distant observer, the distance will be D now, and the time for the EM wave to travel through that region will increase from T to T2. Because light will still travels with speed c. So d/T=D/T2. So the speed of light will be still c.

The only case when an observer would see light travel with speed less then c is when light travels near a mass that has strong gravitational effects. That is the Shapiro effect.

In your case the speed of light is still c.

I think there is physics and epistemology here. Maybe I am misunderstanding fundamental concepts but I see speed of light and accelerating expansion of space like this:

1. We deduce that space is expanding at an accelerated rate because we have certain measures of light travel from supernova and pulsars and taken together with a constant speed of light, the conclusion is that space is expanding and at a increasingly faster rate.

2. The expansion is not of stuff into a void, but an expansion of the metric of the space part of spacetime itself

3. The speed of light is measured in time taken to travel a certain distance; but this distance is an arbitrary one that is or was uncoupled from expanding space. In terms of speed as km/h, the reference was the meter in Paris.

But

If we think of the speed of light as time taken to travel a certain distance, where the distance is not the line in Paris but some small increment of the total length of the dimension, then as the dimension stretches, the length of the interval changes. Usually this is how we measure along a dimension; a set increment of all that there is.

And so we have a choice: We can say lightspeed in km/h is constant and space is expanding or Space isn't expanding and lightspeed in space-unit-increments/h is getting slower

• I believe your understanding of the speed of light is incorrect. First of all remember the defintion of metre (which can be found in Wikipedia): The metre is defined as the length of the path travelled by light in a vacuum in $1/299 792 458 of a second. So the speed of light is always, always equal to$299 792 458 m/s* in a vacuum. The meter doesn't change either, as it is defined in terms of a fundamental constant (the speed of light). – João Vítor G. Lima Dec 1 '18 at 16:37
• If there are two points A and B, 1 meter apart, light takes $1/299 792 458$ of a second to travel between them. Suppose that the distance between them becomes 2 meters due to expansion. Then light will take double the time to travel between A and B ($2/299 792 458$ of a second). The speed of light didn't change. – João Vítor G. Lima Dec 1 '18 at 16:39
• Thank you for the clarification. I appreciate it. Would you oblige me a follow up. If a meter is defined in terms of the speed of light how is the speed of light defined in terms of meters traveled per second. Isn’t that a tautology ? – James Z Dec 2 '18 at 19:28
• Not really. Since we have a clear definition of second, all we have to do is set the lenght light travels in a second as equal to "m". Now have a definition of meter based on the speed of light. – João Vítor G. Lima Dec 2 '18 at 22:23