A small question

[uncool]

A small question I thought of recently:

If the universe is the surface of a hypersphere, then what happens if an item goes 'around' the hypersphere and meets back up with the earth? Who will have aged more and why? (Assuming constant velocity and all that) Both will think that the other was moving and therefore slowed down, and each one would be equally correct.

-Uncool-

[Johnny5]

A small question I thought of recently:

If the universe is the surface of a hypersphere' date=' then what happens if an item goes 'around' the hypersphere and meets back up with the earth? Who will have aged more and why? (Assuming constant velocity and all that) Both will think that the other was moving and therefore slowed down, and each one would be equally correct.

-Uncool-[/quote']

 

I think this is something i thought of long ago, but maybe not, because I'm not sure what you mean.

 

You make reference to "aging more"

 

Right?

 

So the argument operates under the assumption that SRT time dilation is a real phenomenon right?

 

And then you add to that argument the concept of a "hypersphere."

 

You mix the two together, to see if the ideas are consistent with one another. Either they are logically compatible, or not.

 

So, please correct me if I am wrong, but you mean something like this:

 

Suppose the time dilation formula is a true statement in frame S.

 

Let Gonzo and Bonzo, identical twins, be currently at rest in inertial reference frame S.

 

Gonzo and Bonzo both own a 24th century digital Timex, which can measure time to one part in ten to the fiftieth.

 

For all practical intent and purpose, their watches, given to them by their father as a birthday present, are identical.

 

Currently, their watches are synchronous.

 

If you put the two watches next to each other, you see the same number on the display. That is the meaning of synchronicity.

 

Ok so Bonzo gets in a spaceship in reference frame S, which accelerates off to the right with magnitude A.

 

Rather than ever decelerating, Bonzo travels all the way around a Hypersphere, until he passes Gonzo.

 

On the flyby, which took time t in Bonzo's spaceship frame, Bonzo sticks his arm out the spaceship window and Gonzo takes a polaroid of his brother's wrist as Bonzo passes by.

 

Gonzo then compares his wrist watch's reading with the snapshot, and notes what?????

 

Or as a variation, to illucidate the problem,

 

Suppose that both Gonzo and Bonzo get in identical spaceships, and accelerate identically, perfect symmetrical accelerations, and they both travel until they meet each other again.

 

Relativity implies that each brothers watch must be less than the other's.

 

Yet they are in a common reality.

 

Therefore, SRT and the universe being a hypersphere are not compatible ideas.

 

Is that what you were thinking, something along these lines or no?

[uncool]

That is almost what I had been thinking.

However, I want to do away with the acceleration, just leave the velocity. For example: he accelerates from earth, goes around once, and then once he sees the earth again, he synchronizes the watches. He then passes the earth, and goes in another orbit.

However, I just thought of something else. Since they would be the surface of a hypersphere, the two would automatically be accelerating when compared to the other - in another dimension.

-Uncool-

[Tom Mattson]

Gonzo then compares his wrist watch's reading with the snapshot' date=' and notes what?????

[/quote']

 

He notes that Bonzo's clock has not ticked off as much time as his own. Rather than complicate matters with circular travel, you can work it out with one straight line path outwards and another inwards.

 

Suppose that both Gonzo and Bonzo get in identical spaceships, and accelerate identically, perfect symmetrical accelerations, and they both travel until they meet each other again.

 

Relativity implies that each brothers watch must be less than the other's.

 

No, relativity does not imply that. Work it out explicitly (without the handwaving this time). For simplicity, take the paths to be linear, antiparallel over-and-back paths.

 

Therefore, SRT and the universe being a hypersphere are not compatible ideas.

 

That's an amazing conclusion since at no point did you:

 

1. explicitly solve the problem or,

2. ever make use of the definition of a hypersphere.

 

I'll echo what Janus said to you: You should stop trying to explain relativity to anyone until you understand it yourself. Someone will let you know when that is.

[Johnny5]

That is almost what I had been thinking.

However' date=' I want to do away with the acceleration, just leave the velocity. For example: he accelerates from earth, goes around once, and then once he sees the earth again, he synchronizes the watches. He then passes the earth, and goes in another orbit.[/quote']

 

Ok so regardless of how this happened, at the moment he passes his brother, he is not accelerating, the relative speed is v.

 

Then, he travels in a huge circle spanning the whole universe, at a constant relative speed v.

 

When he passes by his brother for the second time, and compares his watch to his brother's, will they still be synchronous.

 

That is your question.

 

According to SR theory, the laws of physics are the same in all inertial frames.

 

Each brother is in an inertial reference frame, at the moment the second orbit begins, and throughout the second orbit, each is still in an inertial frame.

 

According to SR, each brothers clock will read less than the other's.

 

The only flaw that I can see in that conclusion, is that since the orbit is curved, they really aren't in an inertial frame, since an object must move in a straight line at a constant speed in an inertial frame.

 

The logical conclusion is this.

 

The universe is not hyperspherical.

[Johnny5]

Rather than complicate matters with circular travel' date=' you can work it out with one straight line path outwards and another inwards.

[/quote']

 

What do you mean one straight line path outwards and another inwards?

 

I thought the person wanted Bonzo to travel in some great big giant circle, even though really he is moving in a straight line.

 

[Tom Mattson]

I thought the person wanted Bonzo to travel in some great big giant circle' date=' even though really he is moving in a straight line.

[/quote']

 

I know the original poster wanted to know about motion on a hypersphere, but you flubbed that up, so I thought you might benefit from looking at a more simplified model.

[Tom Mattson]

According to SR' date=' each brothers clock will read less than the other's.

[/quote']

 

Still waitin' for you to derive this.

[swansont]

According to SR' date=' each brothers clock will read less than the other's.

[/quote']

 

 

No, that's not true. In the standard twin paradox setup, the acceleration is not part of the initial problem. The clocks are synchronized after that. One of the reasons you keep running into logical conundra with relativity is that you don't apply SR properly.

 

Rate and phase are not the same thing. "Reading less" does not mean the same as "ticking slower"

 

If you do the analysis, you will find that under conditions in which SR applies, both observers see the other clocks run slow. Once you have an acceleration you can no longer meet that condition Here is a treatment that shows that to be true for the outbound leg of the journey (i.e. before the turnaround acceleration).

[Spyman]

Well, if the universe is a hypersphere, then how do we know which clock will tick slowest ?

 

If 2 spaceships with constant velocity synchronizes their clocks when they pass and then moves on without acceleration in a straight line and then check their clocks again when they pass each other the second time.

 

Will they still be synchronized ? Or which will lag behind ?

 

In a hypersphere they won't need to turn around to meet again, right ?

(At least not in the 3D we know about and can measure.)

 

Finally they will arrive at the synchronization point again, but at different times which will show a different speed and which was the fastest one.

 

But did they know that already from the second pass or not ?

[uncool]

What I mean is that one stays right here, while the other one goes off in a spaceship. At some time when the two are together (for example, let's say the first goes around once), they synchronize their watches. The one in the spaceship zooms off into the distance, and eventually comes right back around. Therefore, there will have been no acceleration, and the standard objection cannot be used. As the spaceship twin's time is slower (to me), his time should read less when he comes back around. However, it would appear the same way to him, and therefore it would seem to him as if mine should read less. As no acceleration occurred between the synchronization and the re-reading, each view seems to be correct. How is this possible?

-Uncool-

[Johnny5]

I know the original poster wanted to know about motion on a hypersphere, but you flubbed that up, so I thought you might benefit from looking at a more simplified model.

 

Well unless i introduce coordinate systems, it's hard to know exactly what I did. Then after having done that, we can get very mathematical. I felt the more relaxed Gonzo Bonzo error was sufficient to elucidate the point, rather than introducing coordinate transformations from one frame to the other.

 

Is that what you want to see?

[Johnny5]

Still waitin' for you to derive this.

 

I am trying to stay on topic, so it will have to be in another thread. It's not hard at all.

 

Kind regards Dr Mattson ?

[Johnny5]

No' date=' that's not true. In the standard twin paradox setup, the acceleration is not part of the initial problem.

[/quote']

 

Well it must enter somewhere, in order to be realistic.

 

Actually, my analysis of SR, and I mean my personal one, is extrodinarily complex. Far more than anything I've shown here.

 

And in the analysis, i have to define the "rest rate" of the clocks. Though I've never heard anyone discuss rest rate of clocks, at least not in those words. I hear talk of proper time, but such talk is not more clear than what is done in my analysis.

 

And to finally make the point, in that analysis when two clocks with the same rest rate, are initially in sync, and one of them is accelerated, the formulas of SR lead to a clear contradiction.

 

I can elaborate, but it gets highly mathematical, and I would prefer to do it in latex. But I have learned that once I get that mathematical, I lose everyone.

 

So...

 

so...

 

so there you go.

 

Regards

 

PS: the analysis i am speaking of, was for submission to the AJOP, but I'm not gonna bother. In that analysis, I do discuss clock readings. And I pay very careful attention to frame transformations.

[Johnny5]

Rate and phase are not the same thing. "Reading less" does not mean the same as "ticking slower

 

 

 

Would you please elaborate, because under certain conditions, they (reading less, ticking slower) would correspond, under others they would not.

 

Regards

 

PS: Perhaps this should be moved to another thread, since the original poster wanted to talk about hypersphere. You know, sometimes it is difficult to stay precisely on topic.

[Johnny5]

What I mean is that one stays right here' date=' while the other one goes off in a spaceship. At some time when the two are together (for example, let's say the first goes around once), they synchronize their watches. The one in the spaceship zooms off into the distance, and eventually comes right back around. Therefore, there will have been no acceleration, and the standard objection cannot be used. As the spaceship twin's time is slower (to me), his time should read less when he comes back around. However, it would appear the same way to him, and therefore it would seem to him as if mine should read less. As no acceleration occurred between the synchronization and the re-reading, each view seems to be correct. How is this possible?

-Uncool-[/quote']

 

Let me really focus here.

 

Ok I followed. You are going to do an analysis, over a period in which their is no linear acceleration. But, if the guy goes around in a circle, was their not change in direction? Which implies acceleration? Yes or no?

 

 

In other words, if there is no acceleration, there is no change in the velocity vector, in which case the universe isn't hyperspherical. On the other hand, if the universe is hyperspherical, then there had to be change in direction, in which case there was acceleration.

 

Or what?

 

You tell me.

[Tom Mattson]

I felt the more relaxed Gonzo Bonzo error was sufficient to elucidate the point' date=' rather than introducing coordinate transformations from one frame to the other.

[/quote']

 

It doesn't elucidate the point. All you did was handwave your answer and state what you believe relativity predicts.

[Johnny5]

It doesn't elucidate the point. All you did was handwave your answer and state what you believe relativity predicts.

 

Well then, if you think you can do a better job, then by all means have at it.

 

You have SR formulas, and the concept of a Hypershperical universe. Mix them together and what do you have?

 

PS: As an aside, I take it you have a PhD, but just to be sure, do you? If you do, then I can refer to you as Dr. Mattson; which seems appropriate.

 

Don't think I've forgotton about the topic of vector division, and the elegant mathematical analysis which you gave. And we still have your question in quantum mechanics, about observables. I remember you showing me the basics of bra/ket notation, and analysis.

 

I don't forget anything which makes sense... Dr. Mattson.

 

Kind regards, as always.

[Tom Mattson]

Well then' date=' if you think you can do a better job, then by all means have at it.

[/quote']

 

What I am saying is that this problem is not as simple as you are making it out to be. I am not sure I have the solution right now, I'd have to work it out.

 

What I am saying is that you don't have the solution either, and that you should not be prattling on like this as though you do have it. I'll say it again: You have no business explaining relativity to anyone, because you don't have the foggiest idea of what it says yourself.

 

You have SR formulas, and the concept of a Hypershperical universe. Mix them together and what do you have?

 

I'll try to get back to the thread with that.

 

PS: As an aside, I take it you have a PhD, but just to be sure, do you? If you do, then I can refer to you as Dr. Mattson; which seems appropriate.

 

You can see my username, and you can safely assume that that is what I would like to be known as.

[Johnny5]

You can see my username' date=' and you can safely assume that that is what I would like to be known as.[/quote']

 

Everyone wants to be a physics expert these days. Even Bonzo and Gonzo.

[Spyman]

What I mean is that one stays right here, while the other one goes off in a spaceship.

Sorry, I just wanted to remove the uncertainty of the movement of the person on Earth...

 

The Earth is moving in a complicated pattern, it rotates, it revolves the Sun, it revolves the Milky Way, problably revolves around our group of galaxies to and even more.

 

When the spaceship returns to the starting point, (where the clocks was set), the Earth will not be there.

[Spyman]

Let me really focus here.

 

Ok I followed. You are going to do an analysis' date=' over a period in which their is no linear acceleration. But, if the guy goes around in a circle, was their not change in direction? Which implies acceleration? Yes or no?

 

 

In other words, if there is no acceleration, there is no change in the velocity vector, in which case the universe isn't hyperspherical. On the other hand, if the universe is hyperspherical, then there had to be change in direction, in which case there was acceleration.

 

Or what?

 

You tell me.[/quote']In which direction is the change ?

 

If the spaceship goes around in an hypersphere there is no measurable change in direction in our 3D.

 

Would the guy in the spaceship feel this acceleration or does it even count as acceleration ?

 

Would this "acceleration" perfectly match up with the time dilation caused by relativistic speed ?

 

Would it be possible to measure the radius of the hypersphere this way ?

(Not all the way around but a long part.)

 

 

(I missed this post last time a went to this thread and for some reason I can't edit my last post any more.)

(Strange this post I can edit ?)

[Johnny5]

(I missed this post last time a went to this thread and for some reason I can't edit my last post any more.)

(Strange this post I can edit ?)

 

The edit time has been changed to six hours. After you make your post' date=' it is editable for only six hours.

 

As for your last posts, the main thing I see is that the idea of a hypersphere goes against so much classical physics, as to be the source of endless problems in the conceptualization of relative motion.

 

The sheer number of problems caused, suffices to indicate that the universe is not hyperspherical. The motion of the ship has to take place in some frame. If there is no frame of reference that this can happen in, its over for the idea. If an object travels in a straight line, then the direction of its motion cannot change, and if its speed is constant, it will not return to where it was, [i']intuitively[/i]. If it does manage to return to its starting point, the rational conclusion is that its direction changed, hence it was accelerating.

 

So therefore, the one who defines a hyperspherical universe, needs to state whether or not the direction of motion changes, in this example problem. That is, they must explain the frame in which the motion is to be analyzed in. They will undoubtedly find that their definition is riddled with contradictions.

[Spyman]

As for your last posts' date=' the main thing I see is that the idea of a hypersphere goes against so much classical physics, as to be the source of endless problems in the conceptualization of relative motion.

 

The sheer number of problems caused, suffices to indicate that the universe is not hyperspherical.[/quote']All models of the Universe on a grand scale has this cind or bigger problems and even though I have problems visualising a hypersphere with expanding space and personally don't like the idea of new dimensions, it is the model thats, (at least for me), have the highest probability for the moment.

(Even though my model has changed and improved a lot since I joined this forum and it's still developing.)

 

How else can one explain that the redshifts is uniform in all directions ?

 

To remain on the topic, I agree with You that this problem must have a solution or else the idea of a hypersphere is false or relativity needs to be corrected.

 

I really would like to see an explanation of the experts, (Tom Mattson or swansont) ...

(Instead of just telling us how bad Your answer was.)

[Johnny5]

I didn't know that the concept of hypersphere is used to explain redshift. I certaintly don't believe that is necessary.

 

At this point, i would focus upon the definition of 'hypersphere' most importantly, does the idea have direction of motion constant, yet you return to where you were.