# Light from MACS 1149-JD implausible

I constantly hear about seeing the light from a galaxy, now in the 13B-year-old realm. Specifically, galaxy MACS 1149-JD was recently found to be 13.2B light years away, meaning that it is at least 13.2B years old. What I can't comprehend, is that the galaxy itself would have to be moving away from us (or us apart from one another) at at least the speed of light in order for that light to not have reached us until now. That's simply not possible, as the Hubble constant is around 70km/s, so the rate of expansion of the universe is a tiny fraction of the speed of light. In addition, when it is said the the universe is just over 13B years old, and we observe light from 13B light years away, the same problem persists. In theory we should have seen the light already. Could someone please explain?

Drakkith
Staff Emeritus
The rate of expansion causes galaxies to recede from us at an increasing velocity of about 70 km/s per megaparsec in distance. That means that every megaparsec adds another 70 km/s to their recession velocity. Add it up over billions of light years and you have a recession velocity greater than c. The galaxy is around 40+ billion light years in distance now, thanks to expansion pushing it away all this time, and is moving around three times the speed of light away from us if my quick calculations are correct.

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cepheid
Staff Emeritus
Gold Member
I constantly hear about seeing the light from a galaxy, now in the 13B-year-old realm. Specifically, galaxy MACS 1149-JD was recently found to be 13.2B light years away, meaning that it is at least 13.2B years old. What I can't comprehend, is that the galaxy itself would have to be moving away from us (or us apart from one another) at at least the speed of light in order for that light to not have reached us until now.
The *present* distance of such a galaxy is actually much greater than 13.2 billion light years, and it is *presently* receding away from us at a rate greater than the speed of light, but this was not always true at all times in the past, when it would have been receding more slowly.

That's simply not possible, as the Hubble constant is around 70km/s, so the rate of expansion of the universe is a tiny fraction of the speed of light.
NO. The Hubble constant is equal to 70 km/s/Mpc (Seventy kilometres per second PER MEGAPARSEC). The speed of recession is not the same for every object. The speed of recession v is given by Hubble's law:

v = H0d

Where d is the present distance to that object. So Hubble's law says that the farther an object is away from us, the faster it is receding away from us. 1 parsec = 3.26 light years. And so a megaparsec = 1,000,000 parsecs. If the light from that object left 13.2 billion years ago and is just reaching Earth now, then that object is at about redshift 10, and in the standard cosmological model, it's distance would actually be 31.5 billion light years or 9660 Mpc, which I figured out using this calculator: http://www.astro.ucla.edu/~wright/CosmoCalc.html. See the last paragraph of my post for an explanation why its distance is greater than the light travel time from it. So, plugging that distance into the Hubble's law, we get v = 70 km/s/Mpc * 9660 Mpc = 676,200 km/s, which is much greater than c = 300,000 km/s.

First of all, why is Hubble's law true? Why would more distant objects be moving away from you faster than more nearby objects? Well, if you think about it, this is actually perfectly consistent with a uniform expansion of space. To understand uniform expansion, let's consider a simpler universe with 1 spatial dimension instead of 3 (just as a thought experiment). Suppose in our infinite 1D universe, galaxies are evenly spaced apart from each other, just like the tick marks on a ruler. Suppose at some initial time, every tick mark is 1 "unit" of distance apart:

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The tick with the dot above it represents us (the observer in question). Now, the way a uniform expansion works, is that the distance between tick marks increases by the same amount everywhere. Suppose that after 1 "unit" of time, the 1D universe has expanded such that the distance between adjacent tick marks (galaxies) is now twice what it was before:

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At t = 0:

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At t = 1:

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At t = 0, the tick mark adjacent to ours was 1 unit away, and the tick mark next to that one was 2 units away, etc. The one at the end of the row was 8 units away.. But at t = 1, the adjacent tick mark was now 2 units away, the next one over is now *4* units away, and the one at the end of the row is 16 distance units away. So the one next to us receded away from us at a speed of 1 (in whatever unit system we're using), whereas the one next to that was moving at a speed of 2, and the one at the end was actually moving at a speed of 8. So, the farther tick marks are moving away faster than the more nearby ones, because of the uniform expansion of space. (There is more space in between the tick marks than there was before). This is how the expansion of the universe works, and it is the reason why it obeys Hubble's law. (Note: in my convenient example, I chose distance and time units such that H0 = 1).

The next question you're probably asking is, how can an object be receding away from us at or faster than the speed of light (as the really distant objects are)? The answer is that this doesn't violate the rule from Special Relativity that nothing can travel faster than c, because nothing is travelling through space faster than c. No information is being transmitted faster than c, and nothing is "outrunning" a light ray. The recession is due to the expansion of space itself (meaning that distances between objects are getting larger). And General Relativity says that space itself can and does expand faster than c (or, to put it another way, distances can increase at a rate that is greater than c).

In addition, when it is said the the universe is just over 13B years old, and we observe light from 13B light years away, the same problem persists. In theory we should have seen the light already. Could someone please explain?
The universe is 13.7 billion years old. So, IF the universe were static, then the most distant object whose light has had time to reach us would be 13.7 billion light years away. However, the universe is not static: it is expanding. Therefore, an object whose light left 13.7 billion years ago has actually since expanded away from us, and is now presently at a distance much greater than 13.7 billion light years. In fact, in the standard cosmological model, such an object would be (presently) about 46 billion light years away.

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Thank you for the answers! Awesome! So in a sense, the space itself is expanding more quickly, not the absolute distance of the objects themselves through some fixed-sized absolute space. And the reason that we can be traveling apart at a rate greater than c is because the relativity in terms of velocity is to objects that we are closer to, not necessarily the objects billions of light year away, correct?

Drakkith
Staff Emeritus