As the universe expand, do we expand too?

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The first piece of evidence that showed our universe is expanding came in the light from distant galaxies. If you look at the spectrum of the sun you see these dark lines. And we see those lines in the spectra from galaxies except they are shifted to longer wavelengths, towards the red end of the spectrum. So we say their light is red-shifted.

Now the usual explanation for this red shift is that: as the light is traveling through expanding space, the photons themselves become “stretched.” So short wavelengths get longer. This is known as cosmological redshift. The explanation is fairly intuitively satisfying and most people go on without giving it a second though.

But the problem is if you do give it a second thought, you think, well, If expanding space can stretch something like a photon, Something that’s so incredibly tiny, does it also stretch atoms and molecules? Is expanding space stretching stars and galaxies? And what about you – are you expanding with the universe?

To answer these questions we’ve got to take a closer look at what it really means to redshift. Physicists actually talk about three different types of redshift: Doppler Redshift, where observers moving relative to one another measure photons to have different wavelengths.

Gravitational Redshift, where observers at different locations in a gravitational field measure different wavelengths and Cosmological Redshift, where observers exchanging photons over vast cosmological distances in an expanding universe measure different wavelengths.

These three cases appear very different and they’re governed by different equations, so how does each redshift actually occur? Let’s start with a photon in a gravitational field. There is this famous experiment conducted in 1959 by Pound and Rebka sending photons up and down a 22m tower at Harvard. Now, they used gamma rays but I’ll represent them with visible light.

They found that photons detected at the top of the tower were red-shifted relative to the source by the exact amount predicted by General Relativity(which is a tiny amount – I’m dramatically exaggerating the effect so you can see it). Now where along the photon’s path does this red shift take place? Well it seems to happen continuously.

The photon loses a little bit of energy, each millimeter it climbs up that tower. Meaning that the photon in the middle of the tower would appear green. Now according to Einstein’s equivalence principle, being at rest on Earth’s surface is indistinguishable from being in a rocket in deep space accelerating up at 1g.

So we could do the same experiment in a rocket ship and we should get the same result. If we send blue photons from the back of the rocket they should be red when they reach the front. And in the middle of the ship they would be green.

This is exactly what we saw at rest in a gravitational field so the equivalence principle holds. Now imagine there are a line of external observers just hanging out in space at rest relative to each other and they can all see into the rocket. Let’s also say the rocket is initially at rest and the thrusters are switched on the instant the photon is released.

Now since both observers are at rest at this moment, they will both measure the photon as having the exact same wavelength – it’s blue. But what about when the photon reaches the middle of the rocket? Well we know someone inside will see it as green. But what about a stationary observer outside? Well to them the photon has just been moving through ordinary flat spacetime, so it must look blue – just as blue as it was when it was emitted.

So what’s the deal? How can the same photon look green and blue at the same time? Has the equivalence principle been violated? The answer is no.

It matters a lot to this measurement, who is doing the observation. Consider this: after the photon is emitted the rocket accelerates, it’s speeding up so by the time the photon reaches the middle of the rocket, everyone inside is moving at high velocity relative to the source when the light was emitted and relative to the observers outside the rocket.

So it makes sense that the photon as measured inside will look different – it’ll be redshifted – this is the Doppler redshift because the observer in the middle of the ship is moving very quickly away from the source. By the time the photon makes it to the top of the rocket, the rocket will be going even faster and this is why it appears red, but to a stationary observer outside, well it still looks blue. This thought experiment shows us that wavelength and energy are not intrinsic properties of photons.

They are properties of the photon-observer system. Now let’s recreate the Harvard tower experiment. Observers in the building see the photon red shifted as it climbs. But here’s a question for you: what woulda free-falling observer see? Well they would be just like the stationary observers in space, watching the rocket accelerate up.

The physics of these two situations are identical! So they would measure no redshift – to them the photon would look blue the whole time. What I want to show is that there aren’t actually three different types of redshifts – there is only one. We’ve seen that gravitational redshift, can equivalently be seen as a doppler redshift when we do the same analysis in an accelerating rocket ship. So what about cosmological redshift? Well, for this we have to zoom waaaay out- past our solar system, the milky way galaxy, our local cluster of galaxies.

We want to zoom so far out that the galaxies in the observable universe are like molecules in a fluid: The cosmic fluid. At this scale, we can treat the whole universe as being smooth and uniform – cosmologists say it is homogeneous. And just as you don’t notice the individual molecules in a cup of water, at this scale we don’t notice individual galaxies in the cosmic fluid. And the cosmic fluid looks the same in every direction, there is no preferred orientation – it’s said to be isotropic.

Now what you’ll notice is that the cosmic fluid is spreading out. It doesn’t matter where you look, you seethe same thing – things moving apart. The density of the cosmic fluid is decreasing over time. And this is the basic property of an expanding universe. We can draw some coordinates on the universe. We could pick any different coordinate system we like, but one way it’s often done is to make a coordinate system that expands with the cosmic fluid.

So there will be certain observers whose coordinates don’t change over time. And these are known as co-moving observers- they are at rest with respect to the cosmic fluid. By the way on Earth we are not a co-moving observer. Our galaxy is moving at 600 km/s relative to the cosmic microwave background radiation.

Now let’s pick two co-moving observers a large distance apart and have them exchange a photon. Its wavelength will be stretched by the amount the universe has expanded during the photon’s journey. This is the standard picture of cosmological redshift. But now consider a bunch of other co-moving observers along the path of this photon.

Each one absorbs the photon and instant a neouslyem its another, identical to the one they measured. Now, each successive observer will measure a slightly longer wavelength than the observer before them, the photon stretching out just as you’d expect in an expanding universe.

But the reason they would give for this redshift would be different. To each observer, their neighbouring co-moving observers would appear to be moving away from them in locally flat space-time. So they would attribute the increase in wavelength to the Doppler shift, just due to the relative motion between them.

The entirety of the cosmological redshift then can equivalently be thought of as the result of a long series of Doppler shifts. What we’ve seen is red shifting is not something that happens to a photon itself. Instead it depends on what’s happening to observers at the point of emission and absorption of that photon.

Because of this, there are actually not three different types of redshift, there’s only one, described by a single underlying mathematical framework. They only look different depending on your frame of reference. Now, it can be convenient to talk about expanding space when you have two comoving observers exchanging a photon over vast distances in an expanding universe –

then the photon’s wavelength is stretched by the amount the universe expanded during its journey – that’s nice and simple. But you can equally well describe this redshift by a long chain of Doppler shifts, no expanding space required.

The misconception is to think that because photons are redshifted as they travel across the universe, that means ‘expanding space’ is pulling on things and stretching things apart. That’s not how it works. Space is not like that. So let’s come back to the central question of this video: which is do you expand with the universe?

The answer is no. Because: On the scale of people, the universe is not homogeneous, I mean matter is condensed down into objects and the Earth. And the universe is not isotropic, looking up looks decidedly different from looking down down.

The basic assumptions we made about our expanding universe just don’t apply here. I mean the local spacetime curvature is dominated by the Earth. So what if we took you out into deep space ,the middle of nowhere. Then would you expand? Still no. because your body is held together by electromagnetic forces.

But what if we could turn off the electromagnetic force, so your body is just a jumble of particles that don’t interact. Well in that case… over time you would expand. But only because our universe is now dominated by dark energy. So the take home message of this video is that red shifting photons don’t mean space is expanding and pulling on everything, stretching things apart.

So molecules are not expanding, and neither are stars and neither are galaxies, and neither are you… except under extraordinary circumstances. -Why’s it red? -That tells you it’s recording. Here we go.

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