I recently learned about the Andromeda paradox, a real effect in Einstein's relativity. I didn't understand it and that really annoyed me. Let me play you the clip that confused me so much. It's from a recent Star Talk episode with astrophysicist Hakeim Olusi. What is the Andromeda paradox? Oh, the Andromeda paradox is the fact that if you and I are looking at Andromeda 2 and a half million lighty years away, then what happens is suppose you're sitting in your chair and I'm running by and at the second I run by you, we both look up at Andromeda because I'm moving and you're stationary, we're going to see events that are days apart even though we're in the same location at the same time. And you think that relativity and you think that the light say relativity and keep talking. How far in this scenario, how far away from me are you when you're running by? We're in the same place. We're in the same place essentially. So you're like literally running. I've never heard of this paradox. It's a little known paradox. And the thing that you see and I see are days apart. Days apart because of our physical perspective. Well, here's what you would think. You would think the light is arriving right now. We should all be receiving this light. But that's not how it works. Motion changes the perception of time. Did you see how confused Neil looks? That was exactly my reaction, too. like this can't possibly be true, right? This doesn't make any sense. Then again, relativity has this way of messing with your brain. And when I looked up the Andromeda paradox, it turned out that it originally came from Roger Penrose, who I think understands Einstein's theories better than Einstein himself. So now I wasn't just annoyed at myself for not understanding this paradox, but also embarrassed because I thought I'd read Penrose's books. But let's look at exactly what Penrose said, or rather wrote. This is from his 1989 book, The Emperor's New Mind. Two people pass each other on the street and according to one of the two people, an Andromedan space fleet has already set off on its journey, while the other, the decision as to whether or not the journey will actually take place has not yet been made. That sounds very similar to what Hakee says on the podcast, but note that Penrose didn't say that the people who pass each other actually see the event. Penrose goes on, "How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact, neither of the people can yet know of the launching of the space fleet. They can know only later when telescopic observations from Earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter and come to the conclusion that at that time according to one of them the decision lay in the uncertain future while to the other it lay in the certain past. Was there then any uncertainty about that future or was the future of both people already fixed? What Penrose is going on here is that in Einstein's theory the notion of now becomes subjective. Neil and Hakee go on to talk about this in the podcast, but I think they've messed up the relation to the Andromeda paradox. Let me draw this in a space-time diagram because I think this will clarify it. In a space-time diagram, we have space on the horizontal and time on the vertical axis. You have to imagine that this one-dimensional space is actually threedimensional. And well, good luck with that. If you just stand still, then you move on a vertical line in this diagram like this. If your friend walks by at a slow pace and meets you just when the clock strikes zero, then that'll look like this. Let's say that Andromeda's over here. It doesn't matter exactly at what velocity it moves relative to the two people. So, let's just say it doesn't move relative to you. In these diagrams, light travels by definition at a 45 degree angle. You can see immediately that there is exactly one light signal arriving from Andromeda at the place and time the two people meet. So they must agree on what they see. This is why I was so confused by what Hakee said. It just can't be correct. And indeed, what Penrose talks about in his Andromeda paradox is something else. What these people see is something that happened in the distant past. Andromeda is 2 and a half million light years away. So we can only see what happened 2 and a half million years ago. Penrose is instead talking about what happens in Andromeda at the moment these people meet. And for this you have to introduce a notion of now or of simultaneity. You can do this for example by saying well suppose I place a flashlight left of me at a distance of 100 m and one right of me at a distance of 100 m. At which moments do they have to flash so that I see them flashing at the same time? The answer is the flash events both have to be on the same horizontal line. And since I know how far away the flashes took place and how long they traveled, I can figure out which event in my path coincides with these two flashes. So these three events happened at the same moment. And this tells me that generally everything that happens on this horizontal line happens at the same moment. In each moment, everything on a horizontal line is now for me. But here's the thing. Your friend who walks by doesn't agree because between the moment these lights flash and he sees them flash, he's moved. So he sees the flash he's moving towards earlier. But your friend could find out what happens at the same time, the same way as you by putting two flashlights at the same distance from him. And if the flashes arrive at the same time, he'd know they happened simultaneously. The issue is though that his idea of simultaneity doesn't agree with yours. His simultaneous surfaces are tilted relative to yours and so his now doesn't agree with yours. But let's come back to Penrose and the fleet of Andromedans. Suppose the Andromedans want to invade the Milky Way. Here they discuss the idea and here the fleet takes off. The issue is that as you meet your friend, they are still discussing it in that moment according to you. But according to your friend, they've already left. Now, neither you nor your friend can possibly know anything about this because the information from Andromeda can't yet have reached you. But this brings up the question of whether the decision was already made. As Penrose writes, was there then any uncertainty about that future or was the future of both people already fixed? So the Andromeda paradox brings up this question of whether the future still open or already fixed. The usual conclusion from the relativistic discussion of now is that the future is as fixed as the past. This is what's called the block universe. The only other way to consistently make sense of a now in Einstein's theories is to refuse to talk about what happens now elsewhere. That's logically possible, but it's just not how we use the word now. We talk about things that happen now elsewhere all the time. So I find this an unsatisfactory solution and I believe that the block universe is correct. I explain the consequences of this in more detail in my book existential physics but to come back to the star talk in the podcast. The two go on to discuss the question of now in Einstein's theories and that's all well and good but I think that they didn't correctly explain just what the paradox is. It's not just you. Relativity really is confusing. Even physicists get it sometimes wrong. I find it endlessly fascinating how much physics tells us about the fundamental structure of reality. It's not just relativity, but also quantum physics and generally differential equations and all the maths that we use. If you want to learn more about all of this, I recommend you have a look at the courses on Brilliant. Brilliant offers courses on a large variety of topics in science, computer science, and mathematics. All their courses have interactive visualizations and come with follow-up questions. Whether you want to know more about large language models or algebra, want to learn coding in Python, or know how computer memory works, Brilliant has you covered. It's a fast and easy way to learn, and you can do it whenever and wherever you have the time. And they're adding new courses each month. I even have my own course on Brilliant. It's an introduction to quantum mechanics. It'll help you understand what a wave function is and what the difference is between superpositions and entanglement. It also covers interference, the uncertainty principle and Bell's theorem. And after that, you can continue maybe with the course on quantum computing or differential equations. And of course, I have a special offer for viewers of this channel if you use my link brilliant.org/sabina org/sabina or scan the QR code. You'll get to try out everything Brilliant has to offer for a full 30 days and you'll get 20% off the annual premium subscription. So, go and check this out. Thanks for watching. See you tomorrow.