# Time dilation due to the expansion of the universe

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This is not a homework question. I want some help in being able to clearly perceive the expansion of the universe and the consequences thereof.

We know that the universe is expanding in an accelerated manner. It is my understanding that space alone cannot expand without affecting the local time. Thus as per GTR, depending on the curvature of space-time and the energy density, time too shall suffer a change due to the changing space.

Assuming that there is no curvature of space-time and no mass or energy contained in a chunk of space (assuming the zero point energy of empty space as zero) between two galaxies A and B, let us say that the local time at a point P in this space goes as $$t_0$$. If we on Earth could somehow observe this point and measure the time at P as $$t$$,

1. When we talk about the rate of expansion for example as in Hubble's Law, do we follow the comoving coordinates or the proper coordinates?

2. How would $$t$$ and $$t_0$$ relate to each other if the rate of expansion is uniform and accelerating respectively?

3. How much is 1s for the comoving observer at the inflation period in terms of the usual 1s now on Earth?

1. Hubble's law $$v=H_0 d,$$ relates the recession velocity $$v$$ of a distant object to it's physical distance $$d$$. Today, the physical distance coincides, by definiton, to the comoving distance $$chi equiv d/(1+z)$$, but if you want to know how fast two galaxies at a redshift of, say, $$z=1$$, you must plug in their physical distance at that time (and use $$H(z)$$, the Hubble parameter at that time, rather than $$H_0$$). Depending on how you measure their mutual distance, there are various ways to calculate this.

2. When we observe a galaxy at redshift $$z$$, general relativity predicts that we see its time dilated by a factor $$1+z$$. That is, some physical process which takes a proper time $$t_0$$, will be observed to take a time $$oxed{t = t_0(1+z),}$$ which is the formula you're after.
A good example of this is the time it takes for the brightness of a supernova to decline; a supernova at $$z=1$$ declines half as fast as a local (i.e. $$z=0$$) supernova (see e.g. Goldhaber et al. 2001).
Calculating the distance to that supernova, or the age of the Universe at the time it's observed, is a bit more complicated, involving a model of the expansion rate of the Universe (see e.g. this question about the Friedmann model).

3. Taking inflation to end when the Universe was $$tsim10^{-32},mathrm{s}$$ old, the corresponding redshift was of the order$$^dagger$$ $$zsim4 imes10^{25}$$, so if we could observe physical processes there, they'd be dilated by a factor $$sim4 imes10^{25}$$, so 1 second would, at this dilation, take a 3 billion years. However, already 1 second after inflation, the expansion rate of the Universe had already slowed down so much that the corresponding redshift, and hence dilation factor, was "just" $$sim4 imes10^9$$. So the next second would only, from our point of view, seem to take $$sim140$$ years.

Note that these considerations don't really have anything to do with the accelerated expansion, but is just a consequence of the expansion.

Note also that special relativity predicts the same time dilation; that is, if galaxies were flying through space rather than just being carried along with expanding space, we would observe the same relation between redshift and time dilation. However, the special relativistic interpretation of redshifts is incompatible with the relation between redshifts and magnitudes of supernova, and can be ruled out at $$23sigma$$ (Davis & Lineweaver 2004).

$$^dagger$$This can be calculated as follows: Until the Universe was $$t_mathrm{eq}sim50,000,mathrm{yr}$$ old, corresponding to a redshift of $$z_mathrm{eq}simeq3400$$ (Planck Collaboration et al. 2018) its dynamics was dominated by the energy density of radiation, causing the size (scale factor $$a=1/(1+z)$$) to evolve with time as $$apropto t^{1/2}$$. Calculating backward from $$t_mathrm{eq}$$ yields $$asim10^{-26}$$ at $$tsim10^{-32},mathrm{s}$$, corresponding to $$zsim10^{26}$$.

## Time dilation due to the expansion of the universe - Astronomy

Could we say that the Big Bang is still happening? I mean, isn't the observed expansion of the Universe the Big Bang in action? In other words, if we draw planets, stars, galaxies, star systems on a piece of paper and then crush the sheet into a ball and leave it, it will slowly begin to unfold and this will happen for a while. If we are patient enough we can see the sheet of paper unfolded again, as it was in the first moment.

Ever since the big bang happened our universe has been expanding. As a matter of fact, the continued large-scale expansion of the universe is one of our best arguments for why we know that our universe started from a very small dense state.

But while we continue to see other galaxies flying away from us faster and faster our own milky way galaxy and all the stars, planets, humans and paper balls inside of it are bound by local forces that are far stronger. Our stars and planets hold together by gravity, so while the universe at large will continue to grow on large scales our solar system will stay at the same size. Similarly, humans and paper are held together by electromagnetic forces. So to answer your question: a piece of paper on earth does not expand over time, to see the effects of the big bang we need to observe faraway galaxies.

Thanks for your great question, the expansion of the universe is a fascinating thing to think about since it is so different from our everyday life.

## What is Time Dilation?

One of the most interesting topics in the field of science is the concept of General Relativity. You know, this idea that strange things happen as you near the speed of light. There are strange changes to the length of things, bizarre shifting of wavelengths. And most puzzling of all, there’s the concept of dilation: how you can literally experience more or less time based on how fast you’re traveling compared to someone else.

And even stranger than that? As we saw in the movie Interstellar, just spending time near a very massive object, like a black hole, can cause these same relativistic effects. Because mass and acceleration are sort of the same thing?

Honestly, it’s enough to give you a massive headache.

But just because I find the concept baffling, I’m still going to keep chipping away, trying to understand more about it and help you wrap your brain around it too. For my own benefit, for your benefit, but mostly for my benefit.

There’s a great anecdote in the history of physics – it’s probably not what actually happened, but I still love it.

One of the most famous astronomers of the 20th century was Sir Arthur Eddington, played by a dashing David Tennant in the 2008 movie, Einstein and Eddington. Which, you should really see, if you haven’t already.

So anyway, Doctor Who, I mean Eddington, had worked out how stars generate energy (through fusion) and personally confirmed that Einstein’s predictions of General Relativity were correct when he observed a total Solar Eclipse in 1919.

Arthur Eddington

Apparently during a lecture by Sir Arthur Eddington, someone asked, “Professor Eddington, you must be one of the three people in the world who understands General Relativity.” He paused for a moment, and then said, “yes, but I’m trying to think of who the third person is.”

It’s definitely not me, but I know someone who does have a handle on General Relativity, and that’s Dr. Brian Koberlein, an astrophysics professor at the Rochester Institute of Technology. He covers this topic all the time on his blog, One Universe At A Time, which you should totally visit and read at briankoberlein.com.

In fact, just to demonstrate how this works, Brian has conveniently pushed his RIT office to nearly light speed, and is hurtling towards us right now.

Dr. Brian Koberlein:
Hi Fraser, thanks for having me. If you can hang on one second, I just have to slow down.

Fraser Cain:
What just happened there? Why were you all slowed down?

Brian:
It’s actually an interesting effect known as time dilation. One of the things about light is that no matter what frame of reference you’re in, no matter how you’re moving through the Universe, you’ll always measure the speed of light in a vacuum to be the same. About 300,000 kilometres per second.

And in order to do that, if you are moving relative to me, or if I’m moving relative to you, our references for time and space have to shift to keep the speed of light constant. As I move faster away from you, my time according to you has to appear to slow down. On the same hand, your time will appear to slow down relative to me.

And that time dilation effect is necessary to keep the speed of light constant.

Fraser:
Does this only happen when you’re moving?

A representation of the coordinate system of the warped space around Earth. Credit: NASA

Brian:
Time dilation doesn’t just occur because of relative motion, it can also occur because of gravity. Einstein’s theory of relativity says that gravity is a property of the warping of space and time. So when you have a mass like Earth, it actually warps space and time.

If you’re standing on the Earth, your time appears to move a little bit more slowly than someone up in space, because of the difference in gravity.

Now, for Earth, that doesn’t really matter that much, but for something like a black hole, it could matter a great deal. As you get closer and closer to a black hole, your time will appear to slow down more and more and more.

Fraser:
What would this mean for space travel?

Brian:
In many times in science fiction, you’ll see the idea of a rocket moving very close to the speed of light, and using time dilation to travel to distant stars.

But you could actually do the same thing with gravity. If you had a black hole that was going out to another star or another galaxy, you could actually take your spaceship and orbit it very close to the black hole. And your time would seem to slow down. While you’re orbiting the black hole, the black hole would take its time to get to another star or another galaxy, and for you it would seem really quick.

Orbiting near a moving black hole doesn’t seem like the safest mode of transportation, but time dilation might make it worth the risk. Credit: NAOJ

So that’s another way that you could use time dilation to travel to the stars, at least in science fiction.

Fraser:
All right Brian, I’ve got one final question for you. If you get more massive as you get closer to the speed of light, could you get so much mass that you turn into a black hole? I’d like you to answer this question in the form of a blog post on briankoberlein.com and on the Google+ post we’re going to link right here.

Brian:
Thanks Fraser, I’ll have that answer up on my website.

Once again, we visited the baffling realm of time dilation, and returned relatively unscathed. It doesn’t mean that I understand it any better, but I hope you do, anyway. Once again, a big thanks to Dr. Koberlein for taking a few minutes out of his relativistic travel to answer our questions. Make sure you visit his blog and read his answer to my question.

## Gravitational Time Dilation

If two clocks are now situated in two locations separated by a difference in gravitational potential, the same phenomenon will occur. The difference of elapsed time is due to two observers or systems located next to gravitating bodies of different masses or simply non-equal distances from a single gravitating mass. As such, a clock located closer to a massive body (lower gravitational potential) will run slower than one situated further away (larger gravitational potential).

#### Experimental Confirmation of Velocity Time Dilation

The speculations of gravitational time dilation have been confirmed by establishing a simple difference in altitude and thus gravitational potential, between two atomic clocks (an extremely precise timekeeping device based on electron transition frequency). The result of this procedure was, as expected, a slight difference in elapsed time. The results do however remain negligible when experiments are Earth-bound, as much larger distances would be required to observe greater discrepancies.

This, combined with the postulate of special relativity explains the concept of time in black holes. As stated, as an object approaches the black hole, of theoretically infinite mass at the singularity, gravity becomes stronger and stronger. As such, the breakdown of time at the singularity is explained by the fact that the gravitational potential at the singularity would be of virtually zero. However, as phenomena occurring beyond the event horizon are imperceptible by any outside observers, these predictions remain theoretical.

## Ep. 606: Time Dilation – Skipping Through Time

Have you ever wanted to be a time traveler? Good news! You’re time traveling right now. Into the future at one second per second. Too long? Don’t want to wait? Good news, Einstein’s got you covered. Today, let’s talk about the weird world of time dilation.

### Transcript

Fraser Cain: Astronomy Cast Episode 606: Time Dilation. Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos. Where we help you understand not only what we know, but how we know what we know.

I’m Fraser Cain, publisher of Universe Today. And with me as always is Dr. Pamela Gay. A senior scientist for the Planetary Science Institute and the director of CosmoQuest. Hey, Pamela, how you doing?

Dr. Pamela Gay: I’m doing well. It is a glorious spring day. And while the stars don’t shine as many hours each night, it is great to have Mercery over on the horizon. Have you gotten out to go look at it yet?

Fraser Cain: I thought we went through this. I can’t see Mercury. I have no view to the East and I have no view to the West. Mercury is – I’m just gonna have to take it on faith that Mercery even exists.

Dr. Pamela Gay: Okay. I understand. I am going to have to go to a field somewhere.

Dr. Pamela Gay: Because I, too, have no horizon. But I have access to cornfields that don’t yet have much corn in them.

Fraser Cain: The only time I’ve ever seen Mercery I was in Australia. That’s it. And you have the benefit that the ecliptic sort of rise is straight overhead in Australia. So, you know, as opposed to things here being very low down to the horizon.

Fraser Cain: But yeah. And so, someone was like, “Oh, yeah. And there’s Mercery.” And I was just like, “This is the first time I’ve ever seen Mercery.” Too great.

Dr. Pamela Gay: I think I have seen it from the roof of a building at Harvard. The Science Center in Harvard Yard – or just outside Harvard Yard – has a small telescope on its roof that I used to work with. And light pollution always makes it questionable if you know what you’re actually looking at. Because there just aren’t enough stars. But I think I’ve seen it, but now that I live someplace darker, I’m gonna try again.

Fraser Cain: All right. So, if people wanna see Mercery and they do have, oh, I dunno, a horizon …where and when should they look?

Dr. Pamela Gay: So, if you go out right now it is located between the very, very bright Venus and the super-thin crescent moon. The moon’s getting higher and higher, and thicker and thicker each day. But it remains above Venus in the West/Northwest. So, go out –

Fraser Cain: Just after sunset.

Dr. Pamela Gay: Venus will pop out brightest and then look up.

Fraser Cain: Have you ever wanted to be a time traveler? Well, good news. You’re time traveling right now into the future at one second per second. Taking too long? Don’t wanna wait? Good news. Einstein’s got you covered. Today, let’s talk about the weird world of time dilation. All right, Pamela. Time dilation. What?

Dr. Pamela Gay: So, one of my favorite things that was like this breakthrough understanding for me with relativity. Was the understanding that no matter who you are and what you’re doing the speed of light will appear exactly the same. And in order for that to happen, how you perceive time has to change.

So, the way to think about this is what we’re used to in day-to-day life is …if I’m standing on side of the road in front of my house. And a car zips by, it appears to zip by at 30 miles per hour if they’re following the law. Now, if I’m going down the road at 30 miles per hour, the car in front of me – in theory, if they’re following the law – should appear to be moving zero miles per hour relative to me.

Dr. Pamela Gay: And so, we’re used to seeing everything with relative speeds. The faster I’m going, I’ll see people on the side of the road appearing to go in reverse. People around me, I see their motions relative to my own. So, it seems like using that human experience that the faster I go, I should eventually be able to catch up to those photons and perceive them as moving side by side with me.

But the reality is that while some outside observer might somehow perceive me and those light particles going at almost the same speed. I will never go as fast as the light. I will never see that. I will always see light. At the exact same speed relative to me.

Fraser Cain: And that is such – I mean, when you think about Einstein’s ability to perceive the world in a fascinating way. To have this thought experiment that you’re traveling almost at the speed of light. And then you shine a flashlight, and you watch the flashlight. And in your mind, you be like, “Well, do I see the photons speeding away –

Fraser Cain: – just a little faster than me or do I see the photons speeding away at the speed of light?” And the only way – if you see them at the speed of light – is if time itself is changing.

Dr. Pamela Gay: And so, this brings up that bizarre reality that Buck Rogers in the 21 st century is actually a possible outcome of someone orbiting at a high enough velocity. Now, the fact that orbital mechanics doesn’t allow you to zip around the planet that fast. Let’s say instead they put themselves in this massive orbit at super high speeds.

Dr. Pamela Gay: That’s more realistic. Orbit around the sun instead. But …well, good ole Buck Rogers perception of time will slow.

Fraser Cain: Okay. So, then you talk about this idea of speed. So, let’s break down time dilation. And I mean, I wanna ask why is time dilation? But I know the answer. And the answer is because. Right? Relativity. Because that’s how the universe works. So, let’s proceed right past ‘why’ and go straight to ‘how.’ How time dilation? And there’s sort of two factors. Two ways that you can get time dilation. And the one is the speed.

So, let’s break this down in some examples. And now you’re providing this example. The twin paradox is the classic one, right?

Fraser Cain: We’ve got two people. One here on earth. One gets in the spacecraft. What happens next?

Dr. Pamela Gay: Well, so we actually got to see this with the Kelly twins. And the reality is that the astronauts on the International Space Station are experiencing time ever so much slower. And the way you figure out who experiences the change in time is you look to see who experienced the force. And who experienced that acceleration that got them to that faster velocity.

So, in this case, you accelerate yourself up to the International Space Station and to a velocity that keeps you circling the planet instead of falling back. And time slows.

Fraser Cain: Right. And in that sort of very slightly –

Fraser Cain: And it’s more complicated because of course the International Space Station and the twin who’s on the ground are in a gravity well. But let’s say you have the one who accelerates up to close to the speed of light. Flies for 10 years, and then returns. And then the twins meet up. So, what you’re saying is that it’s not the speed.

Fraser Cain: It’s the acceleration that you experience to get yourself up to that speed.

Dr. Pamela Gay: That determines who is the one who is experiencing the time change.

Dr. Pamela Gay: It’s the velocity that you accelerate to that determines how much time slows down.

Fraser Cain: Right. And so, twin No. 1 is sitting on earth. Twin No. 2 gets in a spacecraft. They accelerate – and that’s the key – to close to the speed of light. Compared to the twin who’s just sitting on the planet.

Fraser Cain: They then return – it’d take them 10 years. Or I guess the person traveling experiences 10 years and returns home to earth to see that the twin who was on earth has experienced –

Fraser Cain: – vastly more time.

Dr. Pamela Gay: Humans only live so long. The human on earth –

Dr. Pamela Gay: – experienced death.

Fraser Cain: Right. And so, the twin – so, I just want to be sure I got this clear. So, the twin who flies on the spacecraft experiences 10 years. The twin who stayed on earth experiences hundreds, maybe thousands, maybe millions of years.

Dr. Pamela Gay: Essentially, the closer you get to the speed of light. The closer you get to stopping time for yourself while time passes for those on earth.

Fraser Cain: Right. Because you’re experiencing the acceleration.

Dr. Pamela Gay: Well, and so the key is who is the one whose time stops for?

Dr. Pamela Gay: We always see things in our frame of reference. And this is where that car idea is important to think about. So, relative to me standing on the sidewalk and the Uber driver zipping down the street. The Uber driver, if they perceive themselves as not moving. Will see me moving at 30 –

Dr. Pamela Gay: – miles per hour. So, if you have two spaceships in space it’s harder to sort out who’s the one moving and not than it is on earth.

Dr. Pamela Gay: And clearly, compared to the trees, the ground, and everything else, I’m not moving. But in the vastness of space, you stick two spacecrafts down and throw the rockets on one and don’t tell the people on board who is having the rockets thrown. You might feel it. But you can also say, “Hey, we just spun your spacecraft so you felt gravity.” So, the two could experience the same thing.

Fraser Cain: All right. So, we talked about speed/velocity as one. And I gotta be careful, right? Because I’m using speed/velocity interchangeably. And that is bad physics, Fraser. Bad. So, velocity. Right? Velocity is speed and direction.

Dr. Pamela Gay: So, in the equations to figure it out, they use the scalar velocity. Which is the speed.

Dr. Pamela Gay: And so, for figuring out how much time has changed you can just say speed.

Fraser Cain: Okay. Okay. All right. So, we talked about speed.

Fraser Cain: And the other way is to be in the presence of a gravity well.

Dr. Pamela Gay: It’s true. It’s true.

Fraser Cain: And I think we’re all really fortunate because Interstellar came out a couple of years ago. And they had this happen. And so, we got to see what it did. So, what’s going on with that.

Dr. Pamela Gay: So, the closer you get to a massive object. The way to think about it here is in a normal situation down on the planet earth, if I throw a ball slightly, I see it moving at one speed. If I throw it really hard I see it moving at another speed. And then, if I go to Jupiter and I use the exact same amount of force to throw the exact same amount of balls. They’re gonna move much slower. Because more –

Dr. Pamela Gay: – gravity. Now, for a poor innocent little light particle trying to escape from the super high-mass object, that light particle is experiencing all that gravity. And in order for that light particle to continue always moving at the same speed of light, time is gonna have to change as it escapes from different gravity wells.

Fraser Cain: Right. Okay. And like we saw – you know I was talking about this idea of watching the movie Interstellar. And we saw how in Interstellar he goes down to the surface of this planet that’s orbiting around this supermassive black hole. He’s there for a day. Comes back out and the rest of the universe – the rest of his family – has experienced 80 years. Or some ridiculous amount of time.

Fraser Cain: And so, it was not because of the speed they were doing to go through the wormhole and blah blah blah. It was because they spent this time close to the black hole in the gravity well. And so, I think, going back to that conversation that we had about the acceleration is the key.

Fraser Cain: When you’re in a gravity well, you’re experiencing acceleration.

Dr. Pamela Gay: Yes. It’s the – what is doing the fundamental altering of your movement through space and time. And that gravity well is doing its darndest to keep you attached to it.

Dr. Pamela Gay: And to keep that light attached to it.

Dr. Pamela Gay: And the more the gravity pulls on you and light, the more time has to slow down so that light is always perceived as going at the same tick.

Fraser Cain: Right. Right. Okay. So, now let’s put this all together. What if you are in a gravity well. Say you’re orbiting a black hole. And you’re also going very quickly compared to somebody who is going – I guess a black hole is a bad idea because you’ll be standing – but let’s say you’re on the earth. Right? I mean, but this is a practical example that we can actually do.

Fraser Cain: Where you are on the surface of the earth.

Fraser Cain: And so you’re in the presence of a gravity well.

Fraser Cain: Or you’ve got your twin who’s flying in space on the International Space Station. They are in less of a gravity well because they’re at a higher orbit. But they’re moving faster.

Dr. Pamela Gay: Yes. And to be fair, I haven’t redone these calculations in ages.

Fraser Cain: Yeah, I haven’t either, and I apologize. Because it’s not in my head.

Dr. Pamela Gay: So, last time I did these calculations, assuming I did them correctly – and I really hope I did. What I figured out was time goes more slowly for the astronaut, because the time dilation effect compared to being on the ground is greater for them. Because of the amount of acceleration that went into getting them where they are. Whereas, if you stopped them in space, this would cause them to fall to the earth. So, don’t do this.

Dr. Pamela Gay: And compared the time dilation due to their lesser pull from the center of the earth. But they’re still being pulled on, just less.

Dr. Pamela Gay: But the dilation caused by the lesser pull at altitude compared to the surface of the planet – that time dilation due to gravity is a smaller effect than the time dilation due to accelerating so they don’t fall.

Fraser Cain: And there’s gotta be like a perfect balance.

Fraser Cain: Where you essentially experience no difference in time compared to the person who’s on the surface of the planet. Because your speed of movement balances perfectly out. The fact that they’re in a greater gravity well. And so you –

Dr. Pamela Gay: And this would be a great homework problem.

Fraser Cain: Yeah, there you go.

Dr. Pamela Gay: And right now everyone is very glad I am not still teaching physics for engineers who get calculus.

Fraser Cain: You would assign it.

Dr. Pamela Gay: Because yeah…

Dr. Pamela Gay: You should be able to totally calculate out what density planet do you need? So, that someone on the surface and someone safely in orbit have the exact same ticking of the clock. Although, you can never sync those clocks. Because it takes time for light to get between the two points. But the ticks are the same duration tick.

Fraser Cain: All right, so now I wanna blow peoples’ minds. And –

Dr. Pamela Gay: I love time dilation. I just wanna say that –

Fraser Cain: Yeah. Yeah. Yeah.

Dr. Pamela Gay: – I absolutely love this concept.

Fraser Cain: Yeah. Absolutely. And so, one very popular science fiction show that’s come out in the last little while is The Expanse. And they have these really powerful fusion rocket – Epstein rockets – that are able to take your spacecraft really, really fast. And so, if you could just jam on the engine and you had an unlimited fuel supply somehow. And you just kept accelerating, accelerating, accelerating …what would happen to time for you and the rest of the universe?

Dr. Pamela Gay: Your time, by your perception, your heart would continue to beat the exact same way. But –

Fraser Cain: You’d continue to be pressed into the seat at 1g.

Dr. Pamela Gay: Yeah. But the more your velocity increases …and here it’s the absolute value of it, that speed, the nonvector, scalar portion that matters. With each moment of acceleration, the moments that an outside observer sees you experience become fewer and fewer.

Dr. Pamela Gay: You will stop aging over time. You will stop breathing to the person watching because everything is slowed down so absolutely much. And in other science fiction series – I’m thinking of Hyperion here. There’s this wonderful example of in the future when high-speed travel between solar systems becomes practical. People of means can deposit their money and invest it in good things. And then skip through time become wealthier and wealthier. And experiencing less and less.

And I mean, imagine just how hard it would be on one hand to pop out of space travel and see all the amazing technological changes that have occurred. But at the same time be like, “And I’m rich now.”

Fraser Cain: But the part that’s kinda crazy is that you could keep on accelerating and from your perspective you would never reach the speed of light. Because it’s impossible. But you would still be experiencing 1g of acceleration for days, months, years, decades.

Fraser Cain: And even though, if you did the math, and you’re like, “I should have gotten faster than the speed of light.” You won’t and yet the distances that you’ll be traveling and the time that the rest of the universe will be experiencing just continue to grow.

Fraser Cain: For as long as you can keep this going.

Dr. Pamela Gay: And crazy things start to happen that we’ve discussed in other episodes many years ago. So, go digging through the archives. The way the equations for relativity work out is your momentum increases in ways that aren’t entirely linearly related to your mass. And the impact of this increase momentum, the faster and faster you go, is that it’s like you were gaining more and more mass.

Now, the reality is the number of atoms in your body will not change unless biological things occur. But your ability to destroy things if you hit them increases because of this apparent change in mass that is due to the relativistic effects on your momentum.

And this led to a question with which I broke a physicist and never really got a good answer. They sort of ended up walking away mumbling. And the question was if a body of mass goes fast enough so that its equivalent mass via momentum is such that it would be a black hole is it actually a black hole?

Dr. Pamela Gay: And the answer I’ve gotten from other theorists was no –

Dr. Pamela Gay: – that’s crazy talk.

Dr. Pamela Gay: But I did break one physicist –

Dr. Pamela Gay: – this way. I was proud of myself.

Fraser Cain: So, the part that’s crazy is that if you could keep this acceleration up, you could be going to the point that in like a decade you would cross the Milky Way. In two decades you would go to Andromeda. In three decades you would be billions of lightyears away. And in about less than a human lifetime you would travel more than the distance to the edge of the observable universe.

Dr. Pamela Gay: But the problem is the amount of energy that it takes –

Dr. Pamela Gay: – to keep accelerating your –

Dr. Pamela Gay: – increasing effective mass. Not your actual mass increasing.

Dr. Pamela Gay: Your effective mass increasing.

Dr. Pamela Gay: You would exceed the mass-energy of the universe before you exceeded the speed of light. Which is part of how we never actually go faster than the speed of light.

Fraser Cain: Yeah. And so for someone watching you. You would just be very close to the speed of light. And you’d be doing that for billions of years.

Fraser Cain: From your experience because you’re continuing to accelerate you would be like .999999% the speed of light. And so, it would take you two and a half million years to get to Andromeda. It would take you –

Fraser Cain: – 46 billion years to get to the edge of the –

Dr. Pamela Gay: But you wouldn’t experience it.

Fraser Cain: But you wouldn’t experience it. And yet the rest of the universe would. And so you would be – you would have to wait. You know, we’d have to wait 50 billion years for you to reach what was the edge of the observable universe. It’s absolutely mind-bending.

Fraser Cain: And awesome. And it’s like this one hope that we can travel vast distances in a single human lifetime. Although, you have to say goodbye to everyone and everything you know.

Dr. Pamela Gay: Well, just travel with your friends. Travel with your friends.

Fraser Cain: That’s a good way to do it. All right. Thanks, Pamela.

Fraser Cain: Do you have some names for us this week?

Dr. Pamela Gay: I do. I need to find the right window. I have so many monitors. I love my monitor fort.

Dr. Pamela Gay: I have a monitor fort.

Fraser Cain: Yeah. That’s awesome.

Dr. Pamela Gay: This is what one should build – monitor forts.

Fraser Cain: Yeah. Yeah. I love it. I’ve never heard it said that way, and I think it’s great.

Dr. Pamela Gay: So, as always, we are here thanks to you. You out there, thank you. Thank you for supporting us and making everything we do possible. For allowing us to pay Rich, Allie, Beth, Nancy. All the people that keep Fraser and I on the straight and narrow. Because Lord knows we need herded. So, thank you for making this possible. Thank you for paying our server bills …our everything else. Thank you.

And this week in particular I would like to thank Kevin Parker, David Truog, Bill Nash, Helge Bjørkhaug, Richard Hendricks, Janelle Duncan. And it turns out that because it’s the end of the month, those are the only names I’ve got.

Dr. Pamela Gay: So, thank you.

Fraser Cain: Thanks, everybody. And thank you, Pamela. And we’ll see you next week.

## Does the expansion of the universe cause time dilation?

If space and time are part of the same thing, does the expansion of the universe make time expand to? If so, does it make time slow down, similar to the time dilation around a black hole?

See the sidebar of r/math to render equations.

Does the expansion of the universe cause time dilation?

Time dilation is really just difference in elapsed times according to different observers. It should be understood as ultimately arising from the different coordinate systems of the two observers. Time, just like space, is really just a coordinate. In this earlier post I give much more detail about how to find time dilation factors for general metrics. In the case of cosmological expansion (say, for a flat universe), the metric has the form

To understand how time is measured by different observers, we should first understand what the coordinates in this metric even mean. The coordinates [ (t,x,y,z) ] are so-called co-moving coordinates, or cosmological coordinates. This graph shows what's going on. There is a fixed spatial grid which simply expands along with the universe as time increases. If an observer remains at a fixed grid point for all time, then that observer is a so-called co-moving observer or isotropic observer. According to this type of observer, the universe looks spatially homogeneous and isotropic. That is, no matter what direction he looks and no matter which grid point he is at, the universe looks the same (on large scales). Cosmological time is, in fact, defined by those two properties. All co-moving observers, no matter their location in the universe, have synchronized clocks.

Okay, what if you are not a co-moving observer? Then you have coordinates that are not the same as the co-moving coordinates. In particular, you have a different time coordinate. A fortiori, some elapsed time acoording to a co-moving observer is not the same elapsed time for you. In that sense, cosmic expansion of space does cause time dilation (but that's nothing special really).

Let's look at the time dilation factor now. Suppose we are a co-moving observer and, in our coordinates, another observer moves along the path in spacetime given by

So the time dilation factor is

where [ v(t) ] is the speed of the second observer. Note very carefully that we are describing the second observer in terms of our co-moving coordinates. For instance, a speed of [ v(t) = 0 ] does not mean that the second observer does not appear to move. What that means is that the second observer's spatial coordinates (in our cosmological coordinates) do not change. In other words, [ v(t) = 0 ] means that the second observer is also a co-moving observer. Also note that the local speed of light is not [ v_ = 1 ] , but rather [ v_ = 1/a(t) ] , which can be greater than or less than 1.

To describe the apparent change of distance between co-moving observers, we use a different spatial coordinate system based on proper distance. The co-moving distance [ chi ] and the proper distance [ d ] are related by

The time derivative of the proper distance is

The first summand on the right-side is sometimes called the recessional velocity (as described by Hubble's law) and the second summand is sometimes called the peculiar velocity. The peculiar velocity is the apparent velocity of an object as measured by a local co-moving observer. That is, if we want to measure the peculiar velocity of some object, the co-moving observer who happens to be right next to that object has to measure its speed. (We cannot measure the velocity of distant objects.)

Note that [ chi'(t) ] , being the time derivative of the co-moving coordinate, is bounded above by [ v_(t) = 1/a(t) ] , the local speed of light in co-moving coordinates. Hence the peculiar velocity [ V_(t) = a(t)chi'(t) ] is bounded above by 1. That is, a local observer always measures objects right next to him to move at less than 1 (or c in dimensional units). (This is what is meant when we say that in GR we have to modify the rule that light always has the same speed. It is only true that objects right next to us cannot travel faster than light and that light rays right next to us have speed 1.)

Anyway. back to time dilation. The time dilation factor is written above in terms of [ v(t) = chi'(t) ] , which is the time derivative of the co-moving coordinate. It is more natural to write the time dilation in terms of the peculiar velocity since that is what we can measure directly. We then have that

which looks an awfully lot like the usual time dilation formula from SR. As an example, suppose we are a co-moving observer that sees some other observer with a constant peculiar velocity [ V ] . Then if we measure a time interval of t between two events, that other observer will measure the time interval

The second observer measures a smaller time interval. So whereas all co-moving observers agree that the universe is about 13.8 billion years old, a non-co-moving observer measures the age of the universe to be younger, how young depending on how fast he moves with respect to the co-moving observers.

Let's consider a fun example. We operationally define the co-moving observers to consist of the frame in which the CMB is homogeneous and isotropic. We see the CMB with a prominent dipole anisotropy, which occurs because we are not co-moving observers. Our peculiar velocity through the CMB causes some of the CMB to appear redshifted and some of the CMB to appear blueshifted. The peculiar velocity of Earth through the CMB is about 600 km/sec. A time period of t for the co-moving observers is, for us, a time period of

[ au = tsqrt<1-V^2>approx tleft(1- frac<1><2>V^2 ight) approx tleft(1-2 imes 10^<-6> ight) ]

So if the age of the universe is about 13.8 billion years for co-moving observers, then the age of the universe for us is about the same, minus 28,000 years.

If space and time are part of the same thing, does the expansion of the universe make time expand to?

The FLRW metric in cosmological coordinates (and for a flat universe) has the form

In these coordinates, the timelike coordinate is left undistorted. Only space is affected by the expansion factor. However, we can easily change to a different coordinate system in which the timelike components of the metric are not trivial. If we use so-called conformal time, then the metric has the form

So it appears in these coordinates that time does get distorted, but that the entire metric is really just a scaled version of the Minkowski metric from SR. But be careful! The coordinate [ eta ] is not the same as cosmological t or Minkowski t. So to say that [ eta ] is distorted by the metric doesn't really say much. Indeed, [ eta ] has the interpretation of the time as measured by a clock whose ticking rate decelerates along with the expansion of the universe. So [ eta ] is, in a sense, already measuring a time coordinate that gets "distorted". The lesson here is that in GR, the coordinates are rather arbitrary, and in the absence of preferred coordinates, there really is no definitive way to answer the question of whether cosmological expansion also affects time. It depends on your coordinates.

If so, does it make time slow down, similar to the time dilation around a black hole?

Again, it's important to be precise about what we mean by "time slowing down". As I explained above, all co-moving observers have synchronized clocks that tick at the same rate. An observer that has a non-zero peculiar velocity with respect to the co-moving observers does, in fact, measure a smaller time interval, given a fixed time interval as measured by the co-moving observers. In this sense, the time dilation should remind you more of time dilation in SR, where it arises only as a result of relative motion. The co-moving observers are somewhat analogous to a set of inertial observers of SR. A set of observers that are moving at some constant peculiar velocity with respect to the co-moving observers are somewhat analogous to a second set of inertial observers of SR. (The analogy breaks down, however, for several reasons. For one, time dilation, length contraction, and all that is not symmetric between different sets of observers. The co-moving observers, for instance, really have experienced the most proper time since the big bang.)

## Cosmological time dilation using type Ia supernovae as clocks **

Alhough there is little doubt at present that the redshift of distant galaxies is due to an expansion of the universe, we present in this paper a direct confirmation for the cosmological expansion. This work is based on the first results from a systematic search for high redshift Type Ia supernovae. We discovered over twenty seven SNe, before or at maximum light. In this paper we report on the first seven of these, with redshift z = 0.35 – 0.46. Type Ia SNe are known to be a homogeneous group of SNe, to first order, with very similar light curves, spectra and peak luminosities. In this paper we report that the light curves we observe are all broadened (time dilated) as expected from the expanding universe hypothesis. Small variations from the expected 1 + z broadening of the light curve widths can be attributed to a width-brightness correlation that has been observed for nearby SNe (z < 0.1). We show in this paper the first clear observation of the cosmological time dilation for macroscopic objects.

## A "Whodunit" of Cosmic Proportions

By: J. Kelly Beatty November 14, 2011 11

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In a few months I'll be teaching my high-school students about cosmology and, in particular, how Edwin Hubble discovered that the universe is expanding. That's how most of us learned it, anyway, but it's not the whole story. In fact, it's not even correct.

During the 1920s, astronomers Edwin Hubble (left) and Georges LemaÃ®tre both came o the realization that the universe is expanding.

Carnegie Inst. of Washington / Catholic Univ. Louvain

Two takes on the expansion-rate of distant galaxies, plotted as their distance versus their recession velocity, as deduced independently by Edwin Hubble and Georges LemaÃ®tre. Click on the image for a larger view.

E. Hubble / D. Block / H. Duerbeck

November 14, 2011 at 2:53 pm

I read years ago in New Scientist about the Big Rip theory to explain a quickening red shift. If the speed of light slows with time since the Big Bang in proportion to the mass of the electron increasing this would stabilize increasingly heavy metals with time as an obvious red shift is produced. Sound waves are conducted by whole atoms and cannot be conducted in a vacuum, is like light 22 billion years from now.

November 15, 2011 at 6:30 am

Thanks for promoting this historical wrong. However, it clearly states in both the Physics Today and the arXiv articles that Michael Way and Harry Nussbaumer are in once case a "research scientist" and the other an "Astronomer" -- Dr. Nussbaumer has also published an entire book on this subject. Best Wishes.

November 15, 2011 at 1:48 pm

Lemaître deserves to be mentioned, but Hubble made a better job of it and deserves most of the credit. Kind of like Leif Ericson and Christopher Columbus. Sure, Ericson was first to North America, but what did he do about it, who did he tell? Columbus was 500 years late, but he followed up.

November 18, 2011 at 5:57 pm

In Cosmos 30 years ago, Carl Sagan had a whole section devoted to red shift and Milton Humason's contribution. Neither Hubble nor Lemaitre got a mention.

November 18, 2011 at 6:22 pm

While Hubble did observe a relation between the distance of a star and its redshift, he never claimed that the redshift was due to the expansion of the universe.

November 20, 2011 at 4:32 pm

Neither Hubble nor Lemaitre were the first to discover that the universe is expanding. The Bible talks about the expansion of the universe 9 times in Job 9:8, Psalm 104:2, Isaiah 40:22, 42:5, 44:24, 45:12, 51:13, Jeremiah 10:12, and Zechariah 12:1.
I also recently read a book (The Grand Tour: A Traveler's Guide to the Solar System, page 199) that claims that the earth was not discovered until 500 (yes, FIVE HUNDRED) BC! Yet, Job talked about the earth floating in space in 2000 BC (Job 26:7).
The Bible is a very unique book it records the true account of origins (which is not the big bang), many scientific facts which have all been confirmed, and has no contradictions (even though it was written by 40 different authors over 1,600 years) but most of all, it tells us how we can be reconciled to the very Creator and upholder of the universe.

I hope that this will be a call to other astronomers to study what the Bible says for themselves I know that this is greatly needed!

November 21, 2011 at 2:09 pm

There is allways a christian fanatic from the USA to comment off topic.

We still have a long way to go for undesrtanding the Universe, the "who is who wars" are slowing Science down. If scholars are so ego prone, real investigation is delayed.

My opinion only, not puting down any one in particular. YanLu

November 22, 2011 at 8:38 pm

Since the article's topic is who first reported the expansion of the universe, Janessa's comment is not "off topic" at all. Moses wrote the Bible book of Job around 1473 B.C.E. Job 9:8 and the other verses Janessa references even fit with the remarkable finding that the rate of universal expansion is accelerating. The Grand Designer is even now "stretching out the heavens," as the more humble than Hubble priest Lemaitre would no doubt agree.

November 22, 2011 at 8:41 pm

Janessa, interesting comments. The expanding universe is not 100% solid ground despite what S&T posts. Reports like
'Quasars again defy a big bang explanation' JOC 24(2):8-9, 2010 don't make the press releases. Marcus Chown in New Scientist reported that QSOs closer to earth (6 billion LY distant) should have light variation effects that may take a month to change and the more distant QSOs (10 billion LY distant or more) should show about a two month time dilation effect due to big bang expansion of the universe. None of this time dilation effect has been observed. This raises the question that the QSOs observed are much closer to earth so their redshift numbers or z numbers cannot be related to cosmological expansion of the universe. As John Hartnett reports in JOC, QSOs offer no support to the big bang model because of the time dilation effect that is missing in their light records. This is just one of many problems with the expanding universe interpretation.

November 24, 2011 at 9:47 am

Attributing scientific merit to an English translation of a Hebrew adaptation of a creation myth passed on orally from generation to generation seems shaky ground to say the least. There are many interpretations of the &ldquooriginal&rdquo Hebrew text, but a scientifically accurate description of the universe (let alone the suggestion that it prophesies the big bang theory) is not one proposed by many scholars. May I therefore suggest that in future we concentrate on the science and leave the interpretation of creation myths for different fora. Do the &ldquotheologians&rdquo not understand how offensive this evangelising is to followers of other faiths?

## As The Universe Expands, Does Space Actually Stretch?

The fabric of expanding space as illustrated over cosmic time. One of the consequences of the . [+] expansion is that the farther away a galaxy is, the faster it appears to recede from us, and that the farther away a light source is, the greater the redshift of the light's wavelength by the time we receive it.

NASA, Goddard Space Flight Center

It’s been almost 100 years since humanity first reached a revolutionary conclusion about our Universe: space itself doesn’t remain static, but rather evolves with time. One of the most unsettling predictions of Einstein’s General Relativity is that any Universe — so long as it’s evenly filled with one or more type of energy — cannot remain unchanging over time. Instead, it must either expand or contract, something initially derived independently by three separate people: Alexander Friedmann (1922), Georges Lemaitre (1927), Howard Robertson (1929), and then generalized by Arthur Walker (1936).

Concurrently, observations began to show that the spirals and ellipticals in our sky were galaxies. With these new, more powerful measurements, we could determine that the farther away a galaxy was from us, the greater the amounts its light arrived at our eyes redshifted, or at longer wavelengths, compared to when that light was emitted.

But what, exactly, is happening to the fabric of space itself while this process occurs? Is the space itself stretching, as though it’s getting thinner and thinner? Is more space constantly being created, as though it were “filling in the gaps” that the expansion creates? This is one of the toughest things to understand in modern astrophysics, but if we think hard about it, we can wrap our heads around it. Let’s explore what’s going on.

An animated look at how spacetime responds as a mass moves through it helps showcase exactly how, . [+] qualitatively, it isn't merely a sheet of fabric. Instead all of 3D space itself gets curved by the presence and properties of the matter and energy within the Universe. Multiple masses in orbit around one another will cause the emission of gravitational waves.

The first thing you have to understand is what General Relativity does, and doesn’t, tell us about the Universe. General Relativity, at its core, is a framework that relates two things that might not obviously be related:

### Explained: Why This Week’s ‘Strawberry Moon’ Will Be So Low, So Late And So Luminous

• the amount, distribution, and types of energy — including matter, antimatter, dark matter, radiation, neutrinos, and anything else you can imagine — that are present all throughout the Universe,
• and the geometry of the underlying spacetime, including whether and how it’s curved and whether and how it will evolve.

If your Universe has nothing in it at all, no matter or energy of any form, you get the flat, unchanging, Newtonian space you’re intuitively used to: static, uncurved, and unchanging.

If instead you put down a point mass in the Universe, you get space that’s curved: Schwarzschild space. Any “test particle” you put into your Universe will be compelled to flow towards that mass along a particular trajectory.

And if you make it a little more complicated, by putting down a point mass that also rotates, you’ll get space that’s curved in a more complex way: according to the rules of the Kerr metric. It will have an event horizon, but instead of a point-like singularity, the singularity will get stretched out into a circular, one-dimensional ring. Again, any “test particle” you put down will follow the trajectory laid out by the underlying curvature of space.

In the vicinity of a black hole, space flows like either a moving walkway or a waterfall, depending . [+] on how you want to visualize it. At the event horizon, even if you ran (or swam) at the speed of light, there would be no overcoming the flow of spacetime, which drags you into the singularity at the center. Outside the event horizon, though, other forces (like electromagnetism) can frequently overcome the pull of gravity, causing even infalling matter to escape.

Andrew Hamilton / JILA / University of Colorado

These spacetimes, however, are static in the sense that any distance scales you might include — like the size of the event horizon — don’t change over time. If you stepped out of a Universe with this spacetime and came back later, whether a second, an hour, or a billion years later, its structure would be identical irrespective of time. In spacetimes like these, however, there’s no expansion. There’s no change in the distance or the light-travel-time between any points within this spacetime. With just one (or fewer) sources inside, and no other forms of energy, these “model Universes” really are static.

But it’s a very different game when you don’t put down isolated sources of mass or energy, but rather when your Universe is filled with “stuff” everywhere. In fact, the two criteria we normally assume, and which is strongly validated by large-scale observations, are called isotropy and homogeneity. Isotropy tells us that the Universe is the same in all directions: everywhere we look on cosmic scales, no “direction” looks particularly different or preferred from any other. Homogeneity, on the other hand, tells us that the Universe is the same in all locations: the same density, temperature, and expansion rate exist to better than 99.99% precision on the largest scales.

Our view of a small region of the Universe near the northern galactic cap, where each pixel in the . [+] image represents a mapped galaxy. On the largest scales, the Universe is the same in all directions and at all measurable locations, with the major difference being that distant galaxies appear smaller, younger, denser, and less evolved than the ones we find nearby: evidence for cosmic evolution with time, but no changes in isotropy or homogeneity.

In this case, where your Universe is uniformly filled with some sort of energy (or multiple different types of energy), the rules of General Relativity tell us how that Universe will evolve. In fact, the equations that govern it are known as the Friedmann equations: derived by Alexander Friedmann all the way back in 1922, a year before we discovered that those spirals in the sky are actually galaxies outside of and beyond the Milky Way!

Your Universe must expand or contract according to these equations, and that’s what the mathematics tells us must occur.

But what, exactly, does that mean?

You see, space itself is not something that’s directly measurable. It’s not like you can go out and take some space and just perform an experiment on it. Instead, what we can do is observe the effects of space on observable things — like matter, antimatter, and light — and then use that information to figure out what the underlying space itself is doing.

When a star passes close to a supermassive black hole, it enters a region where space is more . [+] severely curved, and hence the light emitted from it has a greater potential well to climb out of. The loss of energy results in a gravitational redshift, independent of and superimposed atop any doppler (velocity) redshifts we'd observe.

For example, if we go back to the black hole example (although it applies to any mass), we can calculate how severely space is curved in the vicinity of a black hole. If the black hole is spinning, we can can calculate how significantly space is “dragged” along with the black hole due to the effects of angular momentum. If we then measure what happens to objects in the vicinity of those objects, we can compare what we see with the predictions of General Relativity. In other words, we can see if space curves the way Einstein’s theory tells us it ought to.

And oh, does it do so to an incredible level of precision. Light blueshifts when it enters an area of extreme curvature and redshifts when it leaves. This gravitational redshift has been measured for stars orbiting black holes, for light traveling vertically in Earth’s gravitational field, from the light coming from the Sun, and even for light passing through growing galaxy clusters.

Similarly, gravitational time dilation, the bending of light by large masses, and the precession of everything from planetary orbits to rotating spheres sent up to space has demonstrated spectacular agreement with Einstein’s predictions.

A photon source, like a radioactive atom, will have a chance of being absorbed by the same material . [+] if the wavelength of the photon doesn't change from its source to its destination. If you cause the photon to travel up or down in a gravitational field, you have to change the relative speeds of the source and receiver (such as driving it with a speaker cone) in order to compensate. This was the setup of the Pound-Rebka experiment from 1959.

E. Siegel / Beyond the Galaxy

But what about the Universe’s expansion? When you think about an expanding Universe, the question you should be asking is: “what, observably, changes about the measurable things in the Universe?” After all, that’s what we can predict, that’s what’s physically observable, and that’s what will inform us as to what’s going on.

Well, the simplest thing we can look at is density. If our Universe is filled with “stuff,” then as the Universe expands, its volume increases.

We normally think about matter as the “stuff” we’re thinking about. Matter is, at its simplest level, a fixed amount of massive “stuff” that lives within space. As the Universe expands, the total amount of stuff remains the same, but the total amount of space for the “stuff” to live within increases. For matter, density is just mass divided by volume, and so if your mass stays the same (or, for things like atoms, the number of particles stays the same) while your volume grows, your density should go down. When we do the General Relativity calculation, that’s exactly what we find for matter.

While matter and radiation become less dense as the Universe expands owing to its increasing volume, . [+] dark energy is a form of energy inherent to space itself. As new space gets created in the expanding Universe, the dark energy density remains constant.

E. SIEGEL / BEYOND THE GALAXY

But even though we have multiple types of matter in the Universe — normal matter, black holes, dark matter, neutrinos, etc. — not everything in the Universe is matter.

For example, we also have radiation: quantized into individual particles, like matter, but massless, and with its energy defined by its wavelength. As the Universe expands, and as light travels through the expanding Universe, not only does the volume increase while the number of particles remains the same, but each quantum of radiation experiences a shift in its wavelength towards the redder end of the spectrum: longer wavelengths.

Meanwhile, our Universe also possesses dark energy, which is a form of energy that isn’t in the form of particles at all, but rather appears to be inherent to the fabric of space itself. While we cannot measure dark energy directly the same way we can measure the wavelength and/or energy of photons, there is a way to infer its value and properties: by looking at precisely how the light from distant objects redshifts. Remember that there’s a relationship between the different forms of energy in the Universe and the expansion rate. When we measure the distance and redshift of various objects throughout cosmic time, they can inform us as to how much dark energy there is, as well as what its properties are. What we find is that the Universe is about ⅔ dark energy today, and that the energy density of dark energy doesn’t change: as the Universe expands, the energy density remains constant.

When we plot out all the different objects we've measured at large distances versus their redshifts, . [+] we find that the Universe cannot be made of matter-and-radiation only, but must include a form of dark energy: consistent with a cosmological constant, or an energy inherent to the fabric of space itself.

NED WRIGHT'S COSMOLOGY TUTORIAL

When we put the full picture together from all the different sources of data that we have, a single, consistent picture emerges. Our Universe today is expanding at somewhere around 70 km/s/Mpc, which means that for every megaparsec (about 3.26 million light-years) of distance an object is separated from another object, the expanding Universe contributes a redshift that’s equivalent to a recessional motion of 70 km/s.

That’s what it’s doing today, mind you. But by looking to greater and greater distances and measuring the redshifts there, we can learn how the expansion rate differed in the past, and hence, what the Universe is made of: not just today, but at any point in history. Today, our Universe is made of the following forms of energy:

• about 0.1% neutrinos, which now behave like matter but behaved like radiation early on, when their mass was very small compared to the amount of (kinetic) energy they possessed,
• about 4.9% normal matter, which includes atoms, plasmas, black holes, and everything that was once made of protons, neutrons, or electrons,
• about 27% dark matter, whose nature is still unknown but which must be massive and clumps, clusters, and gravitates like matter,
• and about 68% dark energy, which behaves as though it’s energy inherent to space itself.

If we extrapolate backwards, based on what we infer about today, we can learn what type of energy dominated the expanding Universe at various epochs in cosmic history.

The relative importance of dark matter, dark energy, normal matter, and neutrinos and radiation in . [+] the expanding Universe are illustrated here. While dark energy dominates today, it was negligible early on. Dark matter has been largely important for extremely long cosmic times, and we can see its signatures in even the Universe's earliest signals. Meanwhile, radiation was dominant for the first

10,000 years of the Universe after the Big Bang.

Notice, very importantly, that the Universe responds in a fundamentally different way to these differing forms of energy. When we ask, “what is space doing while it’s expanding?” we’re actually asking which description of space makes sense for the phenomenon we’re considering. If you consider a Universe filled with radiation, because the wavelength lengthens as the Universe expands, the “space stretches” analogy works very well. If the Universe were to contract instead, “space compresses” would explain how the wavelength shortens (and energy increases) equally well.

On the other hand, when something stretches, it thins out, just like when something compresses, it thickens up. This is a reasonable thought for radiation, but not for dark energy, or any form of energy intrinsic to the fabric of space itself. When we consider dark energy, the energy density always remains constant. As the Universe expands, its volume is increasing while the energy density doesn’t change, and therefore the total energy increases. It’s as though new space is getting created due to the Universe’s expansion.

Neither explanation works universally well: it’s that one works to explain what happens to radiation (and other energetic particles) and one works to explain what happens to dark energy (and anything else that’s an intrinsic property of space, or a quantum field coupled directly to space).

An illustration of how spacetime expands when it’s dominated by Matter, Radiation or energy inherent . [+] to space itself, such as dark energy. All three of these solutions are derivable from the Friedmann equations. Note that visualizing the expansion as either 'stretching' or 'creating new space' won't suffice in all instances.

Space, contrary to what you might think, isn’t some physical substance that you can treat the same way you’d treat particles or some other form of energy. Instead, space is simply the backdrop — a stage, if you will — against or upon which the Universe itself unfolds. We can measure what the properties of space are, and under the rules of General Relativity, if we can know what’s present within that space, we can predict how space will curve and evolve. That curvature and that evolution will then determine the future trajectory of every quantum of energy that exists.

The radiation within our Universe behaves as though space is stretching, although space itself isn’t getting any thinner. The dark energy within our Universe behaves as though new space is getting created, although there’s nothing we can measure to detect this creation. In reality, General Relativity can only tell us how space behaves, evolves, and affects the energy within it it cannot fundamentally tell us what space actually is. In our attempts to make sense of the Universe, we cannot justify adding extraneous structures atop what is measurable. Space neither stretches nor gets created, but simply is. At least, with General Relativity, we can accurately learn “how” it is, even if we can’t know precisely “what” it is.
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