Quadruplet Paradox Question: Acceleration vs. Velocity

[Seminole Boy]

Four boys: Alfredo, Bucky, Declan, and Franklin.

They're on an island (with lots of beautiful girls!).

Alfredo likes looking at beautiful bikini-clad girls. He settles on the beach.

Bucky hops in a spaceship.

Declan hops in another spaceship.

Franklin hops in a machine attached to the earth.

Bucky goes .9c through space in S-like (talking about the letter) motion for ten days.

Declan goes .9c through space in a straight line, loops (doesn't stop) at the 5-day mark, and heads back to Earth in straight line.

Franklin is spun around in this machine at .9c for the same amount of time.

They all start their journeys at the same exact moment and go .9c for "ten days." And they all return to the starting point at the exact same moment.

Who is oldest? Who is the youngest?

 

[PeterDonis]

Bucky goes .9c through space in S-like (talking about the letter) motion for ten days.

Ten days relative to whom? I'm going to assume you really mean ten days according to Alfredo, here and in the other cases. I'm also going to assume that the time spend in acceleration for everybody is negligible--i.e., that when people change speeds (from zero to 0.9c or vice versa, whether it's in a straight line or rotating), the time it takes them to do so is negligible according to any of the observers.

(We're also assuming that the Earth's gravity is negligible in this entire problem. Really, to set the scenario up properly, everyone should start and end floating at rest in a space station somewhere far away from all gravitating masses.)

Who is oldest? Who is the youngest?

Alfredo is the oldest. Everyone else is the youngest; they have all aged exactly the same amount, given the above assumptions.

 

[ghwellsjr]

Yes, and the amount that the three others have aged is easily calculated as the inverse of gamma or 4.359 [STRIKE]years[/STRIKE] days.

 

[PeterDonis]

Yes, and the amount that the three others have aged is easily calculated as the inverse of gamma or 4.359 years.

Days, not years, correct? The OP gives all times as days.

 

[Seminole Boy]

Peter Donis! Yes, ten days according to Alfredo. Also, I didn't mean to call them "twins" but I'm sure you understood this to be immaterial.

Okay, are all four boys moving through space or spacetime? I cannot seem to distinguish one from the other in the correct way. It seems like the time in spacetime is just the added dimension to three-dimensional space, so moving through space is the same as moving through spacetime. In other words, the rest of the animal kingdom simply moves through space, as they don't understand time as we do. We are going through spacetime--and they are too, but they don't know it.

 

[PeterDonis]

Okay, are all four boys moving through space or spacetime?

All four are "moving" through spacetime ("moving" is not really the best term for it--see further comments below). Which ones are moving through space depends on which reference frame you adopt. The most natural reference frame for analyzing the problem is the frame in which Alfredo stays at rest the whole time; in that frame, Alfredo is not moving through space and the others are.

It seems like the time in spacetime is just the added dimension to three-dimensional space, so moving through space is the same as moving through spacetime.

It isn't. What I said above about Alfredo illustrates the difference; Alfredo is not moving through space (in the frame I described), but he *is* moving through spacetime.

However, as I said above, "moving" through spacetime isn't the best way to describe what Alfredo is doing while he sits still. Spacetime is usually conceived as a single 4-dimensional geometric object; and objects within spacetime are just curves in that geometry. The curves are usually called "worldlines". Alfredo has a worldline that just looks like a vertical straight line in a standard spacetime diagram drawn in his rest frame (time on the vertical axis, space on the horizontal axis--or axes, if we need more than one spatial dimension).

It is possible to think of Alfredo as "moving" along his worldline, in the sense that different points on his worldline correspond to different readings on his clock; he experiences his clock to be "moving", so he himself must be "moving" as well. But this interpretation breaks down for photons and other objects that move at the speed of light; a photon does not have a "clock" moving with it in the usual sense, and can't be said to "experience time", but it can still be said to "move" through spacetime.

The upshot of all this is that viewing objects as "moving through spacetime" has limits, conceptually, and breaks down when you try to push it beyond those limits. But all objects, even photons, have worldlines, and different points on those worldlines correspond to different events that those objects can potentially participate in; so if that's all you mean by "moving through spacetime", then every object moves through spacetime in that sense.

In other words, the rest of the animal kingdom simply moves through space, as they don't understand time as we do. We are going through spacetime--and they are too, but they don't know it.

"Moving" through spacetime has nothing to do with whether or not the object knows that it is doing so. Rocks move through spacetime in the sense that matters here (see above).

 

[Seminole Boy]

Peter:

Here is where we seem to be missing. Alfredo is moving through space. Being attached to the Earth is the exact same as being in outer-space. Everything is in "space." Bucky and Declan needn't even be in "outer-space" for my question to make sense (and it's partly where Franklin comes in). Put them in spaceships that simply fly around in the Earth's atmosphere at .9c. That atmosphere, in terms of its space, is the exact same as the space next to Jupiter, gravitational time dilation effects aside. (I liked your post before about putting the triplets on a ISS far removed from appreciable mass.)

So, yes, Alfredo is attached to earth, which is in relative motion. It's a slow motion through spacetime, but he's not at rest. This is kind of why I keep saying that acceleration seems not to make sense in the traditional sense. Change in direction should be unimportant, as direction has no meaning (in an absolute sense). All that matters is relative speed. I look at the spacetime continuum as this elastic (in that it adjusts for different relative speeds) fabric into which we keep colliding. It gives us this idea of motion (motion relative to the non-motion of space) and the relative speeds at which we collide into it (go through it, encounter it, whatever) give us relative notions of time.

 

[PeterDonis]

Here is where we seem to be missing. Alfredo is moving through space. Being attached to the Earth is the exact same as being in outer-space.

Being "in" space is not the same as moving through space. Moving through space is frame-dependent, as I said before. There is a valid reference frame in which Alfredo, attached to the Earth, is at rest. Such a frame is non-inertial, true, but it can still be constructed.

Alfredo is attached to earth, which is in relative motion. It's a slow motion through spacetime, but he's not at rest.

You do realize that you just contradicted yourself, right? "Relative motion" only makes sense *relative* to something; it is not an absolute thing (that's why it's called "relative" motion). The Earth is *not* in relative motion to itself. So the Earth *is* at rest, relative to itself. It is not at rest relative to, say, the Sun.

Change in direction should be unimportant, as direction has no meaning (in an absolute sense). All that matters is relative speed.

Once again, you're contradicting yourself. Speed has no meaning in an absolute sense, any more than direction has. You recognize this by calling it "relative" speed, but then you talk as if it were absolute. It's not.

I look at the spacetime continuum as this elastic (in that it adjusts for different relative speeds) fabric into which we keep colliding.

Why do you think spacetime "adjusts for different relative speeds"? It doesn't; as far as objects in relative motion are concerned, spacetime is a fixed geometric object and doesn't adjust at all. It does "adjust" to the presence of matter, but that's something different from what you appear to be talking about.

 

[Seminole Boy]

Speed may be relative, but it is what affects time dilation. Direction doesn't.

I have to watch my language with you. You think very technically. Spacetime doesn't really adjust. It just allows for different interpretations of time--that's what I meant by adjusting.

You keep talking about the Earth and its not being in relative motion (or at rest). I'm talking about Alfredo. He's at the beach and a seagull flies by. He doesn't need the sun to see that he's in relative motion through space. He can just see that he's in motion relative to the birds and waves and bikinis.

I do not see how there van be a valid reference frame in which Alfredo is at rest, if there is no state of absolute rest. Are you talking about relative rest, something I've never heard of? I'm not trying to complicate this, but you seem to be hijacking reference frames and manipulating them. What am I missing?

 

[PeterDonis]

Speed may be relative, but it is what affects time dilation.

Which is also relative. I think I've said in previous threads on similar topics that the key thing that makes the difference in aging between observers like Alfredo and the others "absolute" is that they all meet up at the end and come to rest relative to each other, so they can all compare clocks. "Speed" alone is not enough; there also has to be a change in direction for at least some of them. (In your scenario, everybody except Alfredo changes direction at least once.) So it's not correct to say that direction has nothing to do with it whatsoever; "absolute direction" has nothing to do with it (since there's no such thing), but *changes* in direction certainly do.

I have to watch my language with you. You think very technically. Spacetime doesn't really adjust. It just allows for different interpretations of time--that's what I meant by adjusting.

The reason I keep trying to pin you down is that I don't think the concepts you are reasoning with are well-defined. You think that phrases like "different interpretations of time" or "relative motion through space" (see below) mean something well-defined, but actually they don't.

You keep talking about the Earth and its not being in relative motion (or at rest). I'm talking about Alfredo. He's at the beach and a seagull flies by. He doesn't need the sun to see that he's in relative motion through space. He can just see that he's in motion relative to the birds and waves and bikinis.

Yes, he's in relative motion to all those things, but how does that show that he is "in relative motion through space"?

I do not see how there van be a valid reference frame in which Alfredo is at rest, if there is no state of absolute rest. Are you talking about relative rest, something I've never heard of?

Relative rest is just the flip side of relative motion. A "reference frame" as I'm using the term here (a better term would be "coordinate chart") is just a way of describing spacetime by assigning 4-tuples of numbers (4 because spacetime has 4 dimensions) in a continuous way. If you assign numbers so that every event on Alfredo's worldline has a different value of the time coordinate but the same values of all 3 space coordinates, then Alfredo is at rest in that frame. There's nothing problematic about this; it's an integral part of the mathematical machinery of relativity.

 

[Seminole Boy]

Yes, he's in relative motion to all those things, but how does that show that he is "in relative motion through space"?

Because space is right in front of his eyes. The rascals up on the ISS are moving through space just as your fingers are when you type.

Thanks for trying to explain all this to me. I'm merely an armchair physicist (nonscientist) who recently began studying physics.

 

[Dale]

This is absurd. There is nothing to be gained from four "twins" that cannot be handled with two. All the extras do is add needless complexity and distractions.

 

[Dale]

Yes, he's in relative motion to all those things, but how does that show that he is "in relative motion through space"?

All you do is pick any inertial reference frame. It doesn't have to be one where anyone is at rest, but it does have to be inertial. Then you simply apply the time dilation formula and you get:

Alfredo is the oldest. Everyone else is the youngest; they have all aged exactly the same amount, given the above assumptions.

 

[1977ub]

This is absurd. There is nothing to be gained from four "twins" that cannot be handled with two. All the extras do is add needless complexity and distractions.

... as long as OP knows that different paths don't matter, only velocity / gamma ... clock postulate and all that ... people don't necessarily know that if all they've heard about is the "out and back" Twin Paradox ...

 

[Vanadium 50]

Seminole Boy, if you are really interested in understanding, you want to pare down the number of siblings, not increase it.

 

[PeterDonis]

Because space is right in front of his eyes. The rascals up on the ISS are moving through space just as your fingers are when you type.

No, the ISS is right in front of his eyes. "Space" as you're trying to use the term (and as it's used in relativity) isn't just the emptiness you look at when you look up into the sky. It's a mathematical concept that is used in the theory in a certain way, as part of a reference frame. There is no absolute meaning to "space" in this sense; you can't see if you're "moving through space" just by looking at what's in front of your eyes.

 

[pervect]

This is absurd. There is nothing to be gained from four "twins" that cannot be handled with two. All the extras do is add needless complexity and distractions.

I've seen the phenomenon where people make up their own examples a lot, and it usually doesn't end well. Though there are exceptions.

The underlying issue is that the "standard" examples have generally been chosen to make the point as simply and painlessly and with as little distraction as possible.

Making the problem more complex generally doesn't aid in understanding. Typically the "answer" to complex problems made up by people who aren't familiar with relativity is "the problem wasn't completely specified" :(

Typically this happens because the person specifying the problem assumed "universal now", and thus assumed that 'at the same time" means something specific rather than something that depends on the observer.

(I haven't closely studied this example to see if it follows these general observations or not.)

I'm not sure what to do about it, except to try to encourage people to understand the standard pedagogical examples before they make up their own. I also have to agree with the observation that 2 twins is enough - you don't need 3. Or 4. Or 5. Or six, or more. You only need 2.

There aren't any new issues that arise if you use a whole lot of twins, you have the same basic issues that you have when you use two.

That said, different people have different ways of learning, but I'd like to encourage people to try to learn relativity by studying the standard textbooks and simple problems, rather than making up their own, complex examples.

 

[Vanadium 50]

Usually when people are trying to learn something, they know that they want to simplify. Look at most of the sections here - when was the last time you saw someone say "Help! I want a really complicated example!".

 

[Alain2.7183]

This is absurd. There is nothing to be gained from four "twins" that cannot be handled with two. All the extras do is add needless complexity and distractions.

I don't agree. I think some of the issues that are troubling the OP CAN be highlighted via his multiple siblings example. He is struggling to understand how and if direction of motion plays any role in "traveling-twin-type" scenarios. His example focuses on that issue. The one (correct) answer that he has been given is that, in determining the FINAL ages of all the siblings (when they are reunited), the directions of motion of the three other siblings (relative to the inertial sibling) are unimportant. The directions are also unimportant for determining the inertial sibling's "viewpoint" of the other siblings' ages during the entire trip. But the directions of motion of the other siblings IS quite important in determining the "viewpoint" of each of those other (accelerating) siblings about the ages the various siblings.

 

[HallsofIvy]

Yes, he's in relative motion to all those things, but how does that show that he is "in relative motion through space"?

This indicates that you are not quite clear on what "relative" means. It makes no sense to say "in relative motion" with specifying relative to what. Alfredo is in motion relative to each of the other boys. He is NOT in motion relative to himself. And, as I said, "in relative motion through space" is meaningless.

Because space is right in front of his eyes. The rascals up on the ISS are moving through space just as your fingers are when you type.

Relative to me, yes. Relative to themselves, no.

Thanks for trying to explain all this to me. I'm merely an armchair physicist (nonscientist) who recently began studying physics.