Sean Carroll

Even though there is not absolutely a reference frame in physics, there is approximately a rest frame in the universe where stars and galaxies typically move at about one one-thousandth the speed of light with respect to each other. So the Doppler effect is actually just not very big. There are circumstances in which it matters. In fact, there's a phenomenon called the finger of God.

Even though there is not absolutely a reference frame in physics, there is approximately a rest frame in the universe where stars and galaxies typically move at about one one-thousandth the speed of light with respect to each other. So the Doppler effect is actually just not very big. There are circumstances in which it matters. In fact, there's a phenomenon called the finger of God.

And the finger of God is this. If you have a cluster of galaxies, okay? So you have a cluster of galaxies and... That means you have a bunch of galaxies, and they're orbiting the common center, which means that some of them will be in the—you're measuring two things. You know, this is back in the day. You aren't measuring the distances directly.

And the finger of God is this. If you have a cluster of galaxies, okay? So you have a cluster of galaxies and... That means you have a bunch of galaxies, and they're orbiting the common center, which means that some of them will be in the—you're measuring two things. You know, this is back in the day. You aren't measuring the distances directly.

You're measuring the redshift and using that to infer a distance to the galaxy. And then you can accurately measure its position on the sky, right? You know, its angular position on the sky. So your inferred distance measure to the galaxies is contaminated by the fact that the galaxies are moving.

You're measuring the redshift and using that to infer a distance to the galaxy. And then you can accurately measure its position on the sky, right? You know, its angular position on the sky. So your inferred distance measure to the galaxies is contaminated by the fact that the galaxies are moving.

You're measuring the redshift and some of that, not most of it, just a small amount, but some of it is from the Doppler effect. And that Doppler effect that affects the redshift and therefore your inferred distance only is added to the distance measure radially, that is to say in the direction of your line of sight.

You're measuring the redshift and some of that, not most of it, just a small amount, but some of it is from the Doppler effect. And that Doppler effect that affects the redshift and therefore your inferred distance only is added to the distance measure radially, that is to say in the direction of your line of sight.

The angular distance you just measure by taking a picture of the galaxies on the sky. So you have accurate measure of where the galaxies are in the sky and a distorted measure of where they are along your line of sight. So you take what should be a relatively spherical blob of galaxies in a cluster, and when you plot it in what you think is position in space, it is elongated in the direction of u.

The angular distance you just measure by taking a picture of the galaxies on the sky. So you have accurate measure of where the galaxies are in the sky and a distorted measure of where they are along your line of sight. So you take what should be a relatively spherical blob of galaxies in a cluster, and when you plot it in what you think is position in space, it is elongated in the direction of u.

It's the finger of God that the joke was, this is a finger of God pointing at you saying, you are wrong, because you have small errors in your measure of distance.

It's the finger of God that the joke was, this is a finger of God pointing at you saying, you are wrong, because you have small errors in your measure of distance.

Now, this was a thing back in my day, in the early days of my cosmological career, because measuring galaxies and their redshifts and their distances was a painstaking process, and we didn't have a lot of them, and therefore the ones we had were relatively nearby.

Now, this was a thing back in my day, in the early days of my cosmological career, because measuring galaxies and their redshifts and their distances was a painstaking process, and we didn't have a lot of them, and therefore the ones we had were relatively nearby.

as you go to further and further clusters of galaxies, et cetera, the relative importance of this Doppler effect becomes less and less because the overall recession velocity becomes more and more dominant.

as you go to further and further clusters of galaxies, et cetera, the relative importance of this Doppler effect becomes less and less because the overall recession velocity becomes more and more dominant.

So these days, this kind of thing is not that important in terms of making maps of galaxies, and even its existence is perfectly well understood, and there are statistical techniques for compensating for that mistake. So yes, these differences exist. No, they're not very big. Yes, even the small differences are things that we know about and are able to compensate for.

So these days, this kind of thing is not that important in terms of making maps of galaxies, and even its existence is perfectly well understood, and there are statistical techniques for compensating for that mistake. So yes, these differences exist. No, they're not very big. Yes, even the small differences are things that we know about and are able to compensate for.

Alex Reinhart says, why do you think that complexity science concepts have caught on in a popular way, especially chaos theory, but also things like economic examples and flocking, but aren't captured in most STEM university educations? This is just my perception. Yeah, I think your perception is kind of right. And I think that there's a couple of things going on.

Alex Reinhart says, why do you think that complexity science concepts have caught on in a popular way, especially chaos theory, but also things like economic examples and flocking, but aren't captured in most STEM university educations? This is just my perception. Yeah, I think your perception is kind of right. And I think that there's a couple of things going on.