What is the speed of light relative to (in space)?

From what I understand the universe is expanding faster than the speed of light and accelerating so that it's possible that a given galaxy: $A$ will no longer be visible to another given galaxy: $B$.

So, if a light wave is emitted from galaxy $A$ toward galaxy $B$ after it has passed the point where neither galaxy is visible to each other, how can the speed of the light wave be measured if there is no fixed point in space for it to be measure against (as the light wave will never be visible to either galaxy again)?

5 Answers

To any observer between 'A' and 'B' where the light wave passes, it passes with the speed of light. Adding a velocity $v$ below the speed of light $c$ to the speed of light results in the speed of light, simplified $c+v=c$, where the '$+$' means relativistic addition of velocities, not the '$+$' of arithmetics.

Depending on the relative velocity of two observers at the (almost) same point they will observe different Doppler shifts of the light, more precisely of spectral properties of the light. By analysing the spectrum of the light the observers may be able to determine the Doppler shift, meaning relative velocity, to the object which caused the emission or absorption line in the spectrum.

The light will eventually reach galaxy B even though the space between them is expanding. It is important to remember that it is the space that is expanding not galaxy B moving away from galaxy A. Imagine putting two dots on a balloon and blowing it up. It is the rubber between the dots that is stretching, not one dot moving about the balloon's surface away from the other dot.

Imagine a photon of light leaving galaxy A. After a period of time it will have travelled some distance towards galaxy B. Let's say it has travelled 1% of the distance so it has 99% to go. Space is expanding equally in front of and behind the photon, so even if it were to stop moving it would stay at 1% of the total distance. But it doesn't stop, it moves nearer. It will eventually get half way and again the space is expanding both behind and in front of the photon. Now there is the same amount of space in between the photon and galaxy A as there is between the photon and galaxy B. No matter how much expansion there is the photon is still in the middle. Eventually the photon will get all the way to galaxy B.

No matter how fast the universe is expanding and how slow the photon is moving it will eventually reach galaxy B although it may take a very very long time.

As the space the photon is in is expanding the wavelength of the photon will slowly change. This is red shift.

Now for the problem with this answer. I believe this answer is only valid if the speed of the expansion and the speed of the photon is constant, but the expansion of the universe appears to be accelerating.

• Does this mean a galaxy that leaves our view will come back into view when light that left the galaxy finally reaches us? I was under the impression that there was a point where we could never see anything beyond that point (even if this point is changing). – taintedromance Mar 5 '14 at 23:21
• Once we can see a galaxy we will always see it. We can only see the observable universe. The observable universe is smaller than the whole universe. – RedPython Mar 6 '14 at 17:54
• @taintedromance, RedPython - It takes light about a nanosecond to travel 1 foot. If the space between galaxy B and the photon expands at a rate of more than 1 foot every nanosecond, then the distance between galaxy B and the photon will always be increasing, so the photon will never reach Galaxy B. (See my answer here.) – Kevin Fegan Oct 8 '16 at 2:15
• "Once we can see a galaxy we will always see it." - For a galaxy that we can see (now), once the space between us and that galaxy begins to expand at a rate faster than the speed of light, we will never see any light that leaves that galaxy in the future. Of course, we will continue to see light that previously left that galaxy, so we will continue to "see" it for a very long time. – Kevin Fegan Oct 8 '16 at 2:22

Consider 2 distant galaxies "moving" apart due to the expansion of space. A photon of light is leaving galaxy A towards galaxy B. The space between galaxy B and galaxy A is expanding. This includes the space between galaxy B and the photon.

It takes light about a nanosecond to travel 1 foot. If the space between galaxy B and the photon expands at a rate of more than 1 foot every nanosecond, then the distance between galaxy B and the photon will always be increasing, so the photon will never reach Galaxy B.

As I understand it, the speed of light is constant. The speed is not relative to where the light originated from or to an observer at any arbitrary location. It is measured relative to the light itself. At one moment in time the light is at some location, and a given amount of time later it has moved a distance given by the speed of light.

• You are on a spacecraft traveling in a straight line, very fast, lets say (arbitrarily) at 25,000 kilometers per hour. The particular speed of the spacecraft, or even that it is moving very fast is irrelevant and is mentioned only as an example.
• You pass by another spacecraft traveling in a straight line, in the exact opposite direction as your spacecraft, also traveling at 25,000 kilometers per hour.
• The 2 spacecraft are traveling parallel to each other.
• At the moment you pass the other spacecraft, you project a light out of the front of your spacecraft.
• At that same moment, a light is projected out of the rear of the other spacecraft.
• The light from both spacecraft is traveling parallel to each other in the same direction, and at the same speed ("the speed of light").
• The light from both spacecraft will reach a distant object at the same time.

There is nothing special about the point in space where the galaxies move out of view of each other. This is just the point where their respective Hubble spheres (the sphere at which the expansion speed is equal to the speed of light for the given observer) overlap. The speed of the light will still be c from the perspective of an observer between the Hubble spheres of A and B

To answer your question:

The speed of light is relative to the metric of the space itself.

That is, if you imagine that there is a network of rules and clocks at rest with respect to each other floating in space, the speed of light is relative to that group of rules and clocks if the group is inertial.