# Is 2.5x speed of light possible between two objects?

The main excerpt is: "Distant galaxy moves away from us as much as 2.5 times the speed of light"

I'm not a physicist, I can somehow comprehend the idea that 2x speed of light can be reached, like in the case of 2 light beams shot to opposite directions. But 2.5x? Would 1000000x speed of light possible in theory between 2 objects?

• Nope, speed of light is an universal costant and is the maximum speed at which all energy, matter, and information in the universe can travel. Thus, the excerpt you cited does not make sense.
– Carlo_R.
Nov 16, 2012 at 21:58
• Alexander Vilenkin, in his pop-sci book titled "Many Worlds in One", has claimed that, because expansion differs from relative motion, the most rapid rates of expansion are not limited to the speed of light. As space is neither a substance nor an energy, what's expanding might perhaps, in Vilenkin's view, be the vacuum energy (sometimes described as "dark energy" or "repulsive gravity") that space has often been presumed to contain since the supernovae 1a experiments of the late 1990's showed its expansion to be accelerating (and, consequently, not caused only by a cosmological constant). Jun 19, 2021 at 1:39

While it is often good to read mainstream press regarding science with a critical eye, in this case there is an explanation.

First, though, there is a misconception that needs to be cleared up. If you fire two objects in opposite directions, say with speeds $v_1$ and $v_2$, their relative speed (the speed of either one as seen by the other) is not $v_{1+2} = v_1 + v_2$ as far as special relativity is concerned. It is actually $$v_{1+2} = \frac{v_1+v_2}{1+v_1v_2/c^2},$$ where $c$ is the speed of light. (See Wikipedia for a derivation.) When $v_1,v_2 \ll c$, the more intuitive formula is a very good approximation. However, as speeds approach $c$, you find things can never move apart faster than $c$. The limit is not $2c$. That's special relativity for you.

The catch is in general relativity, which is absolutely needed for cosmological distances. It turns out the very universe itself is growing larger, the space between "stationary" objects growing larger all the time. (In fact this expansion is accelerating, the discovery of which earned the 2011 Nobel Prize in physics.) The space between two distance objects can expand at any rate; it is not an actual motion of an object through space. There are more details due to lookback time, what your precise definition of "distance" is, etc., but the end result is there is some meaning to saying a galaxy is receding faster than light, or faster than $2c$ even.

Edit: The answer to the question of what is the maximum velocity requires some modeling of the constituents of the universe, and a solid understanding of horizons (I cited a beautiful but technical diagram that comes in handy for this sort of thing in an answer to another question). Long story short: the furthest objects within our past light cone have a comoving distance of about 46 billion light years. Hubble's Law tells us the proper distance to those objects is increasing at a rate of about $10^6\ \mathrm{km}/\mathrm{s}$, which is a little more than $3c$. The answer is not much different if you take into account the fact that pre-recombination light is scattered, so we can't quite see $46\ \mathrm{Gly}$ away.

• I think the formula you gave only assumes observable speed between those 2 objects fired in opposite direction looked from object A to object B. But if there is an observer in the middle, he can conclude that the total length traveled is 2 times the speed of light, correct? Nov 16, 2012 at 23:40
• With what yardstick do you measure distance when space itself gets larger, along with your yardstick? If the distance between two objects is one meter, but then space expands, but so does the one meter ruler between then, so that they stil look one meter apart, what has changed?
– Kaz
Nov 16, 2012 at 23:44
• @user14742 Yes, that is correct.
– user10851
Nov 16, 2012 at 23:53
• Even if I have a road where 2 cars are stationary, but the road itself is enlarging and therefore making cars get further from my standpoint, I would still contrive the speed between cars to be relative to me, not based on the odometer that shows 0 in a car. Nov 16, 2012 at 23:53
• @Kaz Empty space expands, but solid objects tend not to, nor do gravitationally bound systems. In fact, a loose definition of "proper distance" is "the distance we would measure if we simultaneously placed a bunch of metersticks end-to-end from A to B."
– user10851
Nov 16, 2012 at 23:58

I guess it's talking about the candidate galaxy MACS0647-JD [arXiv:1211.3663], which has a redshift of $10.3 \lesssim z \lesssim 11.3$, which means it's around $D \sim 32\,\text{Gly}$ away in terms of proper distance. By Hubble's law, its recessional velocity is about $H_0D \sim 2.3c$.

This recessional velocity represents the rate of distance increase in a frame field formed by observers at rest with the large-scale bulk of the matter of the universe (on average). In that frame, the galaxies are not even moving with respect to one other; they're at rest while the space between them is expanding. It does not cause anything to actually outrun a light-signal locally.

• Wikipedia: "Recessional velocity is the rate at which an object is moving away" <- For me this counts as a speed, atleast in layman terms. I don't mind whether there have to be "observers" in the middle to get the calculation. Nov 16, 2012 at 23:30
• If you want to consider it speed, then the answer to your question is "obviously it's possible". On the other hand, Hubble's law takes the cosmological time of the comoving frame, in which by definition the galaxies are at rest on average. Thus, there is we can make a distinction between motion through space and expansion of space, which are not equivalent. Nov 16, 2012 at 23:49