PeterDonis said:
I believe a billion light years of separation is sufficient for that (and I'll assume it is for the rest of this post). If the separation is not large enough, the electrons will start falling towards each other because of the gravity of the matter in the universe between them. The effect of dark energy, which is what you are describing, only overcomes that if the separation is large enough.
Thank you for your answer.
PeterDonis said:
First, it's important to point out a key factor in the scenario as you've specified it: neither electron is comoving. That is, neither electron sees the universe as homogeneous and isotropic. If they did, they would not start out at rest relative to each other; they would start out moving apart.
Second, since the electrons are a billion light years apart, it will take at least a billion years (actually more, as we'll see in a moment) for a light signal to travel from one to the other. And in that time, the universe will have expanded. Even if the expansion is not accelerating (i.e., even if there were no dark energy), that expansion itself would tend to pull the electrons apart (because the matter in the universe is expanding). So even without dark energy, the electrons would move apart over a billion years and the light travel time between them would increase, which would cause the spacing of the pulses as received by the second electron to increase.
All that dark energy really does is make the spacing between the pulses increase faster than it otherwise would.
So in your view dark energy causes the durations between received pulses at the second craft to increase over time, by a greater amount than can be explained through gravity alone.
I'd like to clarify a few points of the thought experiment. I define Time = 0 as the same time a light pulse is received by the second craft which is measured by the second craft to be the same wavelength as a pre-agreed transmission wavelength. We've also pre-agreed the first craft will cease transmissions if it detects fictitious forces or acceleration and the second craft will cease observations if it detects acceleration or fictitious forces.
Suppose I'm on the second spacecraft and I don't have enough information about the universe to know in advance or deduce what the outcome of the measurements on red shift and interval between pulses will be. In my craft I consider what possible outcomes might be measured. Since Time = 0 is the time that I first measure a pulse which from my spacecraft appears not to be red or blue shifted from the pre-agreed transmission frequency and I know the first spacecraft is sending pulses every second and I know the wavelength, over time I can observe both whether these pulses appear red or blue shifted and whether the interval between arrival times changes.
Since I've stated I don't have enough information on the second craft to know what the results will be in advance, I consider the possible measurements and what implications they have.
I consider a subset of possibilities-- I am now only considering the range of possibilities in which measurements show that over time the pulses become more and more redshifted from the pre-agreed frequency.
From this subset of red-shifting possibilities, I consider the implications of what it means if the following occurs:
-Pulses become more and more red shifted and interval between received pulses increases to more than one second
-Pulses become more and more red shifted and interval between received pulses remains exactly one second
-Pulses become more and more red shifted and interval between received pulses decreases to less than one second
Now from this list of possibilities I consider the implications of only one:
-Pulses become more and more red shifted and interval between received pulses increases to more than one second
I can list possible meanings of this particular result without being entirely certain if any of the meanings I've listed are true:
Possibility A: Subtracting the effects of gravity, since light is taking a longer and longer time to reach me from the first craft and the light is redshifted, the second craft must be increasing its distance, because light always takes the same amount of time to cover a given distance between 2 co-moving points in spacetime
Possibility B: Subtracting the effects of gravity, Since neither ship measured acceleration or rotation, the two ships are in fact the same distance according to some metric, but the geometry of spacetime is contracting, causing light to take a greater and greater time to cover the same distance
From the results of the experiment plus any other information I could gather from the second ship, how do I correctly interpret the meaning of the results of the described a measurement showing the pulses become more and more red shifted and interval between received pulses increases to more than one second as measured on the second craft?