Transcript/Why Solutions to the Twin Paradox are WRONG

Transcript

Two objects sit in the empty reaches of space at rest relative to one another. Suddenly, they blast apart. How do their notions of space and time alter with respect to one another? And what happens when we try to bring them back together again? This is dialect.

And this is why solutions to the twin paradox aren't really solutions at all. Okay? So from my perspective, every second that passes, I stay in place. That's not possible.

The distance between his clock and my perspective. There are a lot of videos on YouTube claiming to have solutions to the twin paradox. Unfortunately, almost all of these videos, or at least the more popular ones, are just kind of wrong.

Okay, that's not entirely the case. It's not that their solutions are wrong. It's that their solutions aren't solutions to the right problem.

It's that these videos don't even realize what the problem is that they are trying to solve. It's not even just YouTube videos. Textbooks, internet pages, popular books they often have the same issue.

As they struggle to explain away the paradox, often obfuscating their answer with complex jargon diagrams or math. They each overlook one crucial point. To understand what that point is, let's return to our setup.

Consider a universe consisting of two objects. We'll name these objects alice and Bob? Now, these objects suddenly accelerate apart. According to relativity, there are now two distinct perspectives to consider.

First, Alice's perspective. She can claim she's at rest, in which case, Bob's clocks will slow down as he speeds away, and he will appear to age more slowly than her. Secondly, there's Bob's perspective.

He can claim he's at rest as well, and in which case, Alice's clocks will be the one slowing down as she speeds away, and she will appear to age more slowly than he does. Now. As long as everyone travels at constant velocity away from each other, this will be a happy universe with no logical inconsistencies.

These objects will merely agree to disagree on each other's respective time intervals and then go their separate ways. But what if one or both of the objects suddenly turns around, and then Alice and Bob are brought back together again? If we remain in Alice's perspective, bob will have aged less. If we remain in Bob's perspective, alice will be the one who has aged less.

So, of course, the paradox asks, who is truly older, alice or Bob? There are two equally valid, symmetrical perspectives here, but we can only have one reality note here that we don't discuss why time dilation occurs. There's plenty of other videos out there that do a great job of this. The main thing that's important to understand before going forward is that Alice and Bob won't agree on who is older, and it's very unclear how they'd be able to reconcile this difference.

So how do other videos solve this paradox, then? Let's take a look. First, it is important to note that these other videos formulate the problem in a different way. They start with the premise that one twin is located on Earth, while the other accelerates away in a rocket ship.

Why is this difference important? Well, let's start by noting that the addition of Earth is arbitrary. It doesn't enter into the math or the equations in any way. So in fact, it's fair to get rid of the Earth altogether and just have the two twins in an empty region of space.

Additionally, the whole rocket ship context is pretty superfluous. We can just consider two nondescript objects that break apart and come back together again. This will still be, after all, the twin paradox.

Keep this difference in formulation in mind. We'll come back to it. Okay, so now we're going to take a look at three different videos.

Obviously, we don't have time to watch them in full length, though I recommend that you do. Instead, I'm going to skip straight to snippets of the videos where they identify exactly what their so called solution to the twin paradox really is. Seconds.

And this is the resolution to the twins paradox. Because you changed velocity, your notion of simultaneous times rotates. So your accounting of how time passes in parts of the universe far away from you will have gaps in it.

Well, so how do we solve this paradox? Well, the answer lies in the details. When your twin turns around, she has to accelerate, which means she's no longer in an inertial reference frame while she accelerates. And so special relativity no longer applies to her.

When Adam fires his rockets to turn around, he is extremely far away from the Earth. Therefore, Adam will believe that the gravitational field is causing time on Earth to flow much faster than time on his ship. But what about Sarah's point of view? From Sarah's point of view, this external gravitational field never existed.

All right, let's review. Each of these videos posits a cause for the breaking of the symmetry of the twin paradox. That is, they give a reason why one twin is older than the other.

The reason itself is pretty easy to pinpoint. Let's review video by video. First, we have minute physics, which is by far the most popular of the videos.

His answer is word for word that you, meaning the space traveling twin, changed velocity, meaning accelerated, will have gaps in it. Physics girl's answer is basically the same. She says when your twin turns around, she has to accelerate no longer in an inertial reference frame while she accelerates.

Last, we have the video by Eugene, and I'm not even going to attempt to butcher that name. His videos are very, very smart, some of the best videos you'll find about physics on YouTube. So I was actually pretty disappointed when I watched this video.

He basically gives the same answer. However, he cloaks it in a discussion of general relativity and how that is formulated differently than special relativity. But the basic answer is the same.

It comes at the point when he says, when Adam fires his rockets. This is essentially indicating that it is Adam, the space going twin, who is the one who accelerates. And that's the cause for him seeing a time dilating gravitational field while the Earthbound twin sees nothing.

So here we have three different videos, all with the same answer. They all say that it is the space traveling twin who accelerates, and this is what causes the breaking of the symmetry. But there's an incredible assumption here, and that assumption is acceleration is absolute.

That is, each of these videos posits that all observers will agree that it is the space traveling twin who's the one who really accelerates, while the Earthbound twin does not. This assumption is profoundly unrelativistic. It boggles my mind.

The whole point of relativity is that there are no preferred frames of motion. Each twin has an equal right to say that it is the other twin who accelerated or turned around or fired his rockets. In general relativity, it is not just the apple that falls to the Earth.

It is also the Earth that falls to the apple. Both points of view are equally valid. That is why it is so important to consider our initial setup in which we have a universe with only two objects that break apart and come back together again.

There is nothing else in this universe for these objects to move relative to. So what's to decide whether one object's acceleration was really more real than the others? The answer is there isn't. In this scenario, there is no objective way to determine which object will be older when the two are recombined.

Now, when you have this setup with Earth and rocket ships, it seems much more obvious who's the one who's accelerating, right? This is because you no longer have the same symmetry that you did in the two object universe. But the symmetry of this situation is not broken by acceleration. It is broken by the addition of the Earth and the fixed stars.

This is the crucial point that the other videos overlook. We can't say that the space traveling twin is absolutely the one who accelerates, but we can say that the space traveling twin accelerates relative to the Earth and the rest of the fixed stars. That is why these other videos don't get it right.

They go ahead and assign one of the twins's accelerations as being absolute without offering any justification for doing so. They don't understand what the twin paradox is about. The twin paradox isn't about, hey, who's going to be older, alice or Bob? If we've already decided that it's Bob who's really accelerating, it's pretty easy to show that answer is Alice.

The actual paradox is about why the space going twin's acceleration is more real than his counterparts. And that's the kind of question that doesn't have an easy answer. It involves exploring ideas of mass and inertia.

But that's why, at the end of the day, these so called solutions to the twin paradox are highly misleading. They are right only in the most superficial sense. This is why most people who are new to the subject after hearing so called solutions still come away with an intuitive sense of skepticism.

Because the twin paradox is actually still a paradox. Well, that's all for now. This has been dialect.

Thanks for watching.

Summarization

- There are a lot of videos on YouTube claiming to have solutions to the twin paradox. But they often overlook one crucial point. How do their notions of space and time alter with respect to one another? And what happens when we try to bring them back together again?

- Three different videos on YouTube offer solutions to the twin paradox. Each of the videos posits a cause for the breaking of the symmetry of the paradox. The answer lies in the details. There is no objective way to determine which object will be older when the two are recombined.