h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Twins Paradox & Absolute Space - A826346
Author: Russell - U190219

Twins Paradox



Quote, Gottfried Leibniz:

"Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it."

End quote.


The Twins Paradox

A solution:

(r1)<-----(origin)----->(r2)

Imagine not just twins, but triplets.

One sibling (s1) travels velocity (v1) in rocket one...(r1).

Another sibling (s2) travels velocity (v2) in rocket two...(r2).

The third sibling (s3) remains at the origin.

The rockets travel at exactly the same speed even during the inevitable "acceleration phase".

(r1)<-----(origin)----->(r2)
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------v-------------

Initially r1,r2, and the origin were "at rest with respect to each other, or it could be said that they were all within the same inertial reference frame. The downward pointing arrow represents the time axis and as you can clearly see, time is perpendicular to space. The rockets launch.


Since both rockets are moving at exactly the same speed but in opposite directions, the reference point at the origin effectively cannot be in relative motion with respect to both (r1) and (r2) simultaneously. Because if we say the the origin is moving to the left with respect to (r2), that would contradict with the origin's motion to the right with respect to (r1). In effect, the point of origin must be at rest with respect to both (r1) and (r2). So the point of origin can be explained as being "at rest" with respect to the two rockets. The origin cannot be in motion to the left or the right. When the two siblings return from their adventure. They will find their twin at the origin much older than themselves according to the relativistic time dilation formula...

t = (t')/[1-(v^2)/(c^2)]^(1/2)


Some theories postulate space as a "surface" or manifold. Tangent vectors are also on the surface of space(intrinsically speaking of course). With a little imagination these tangent vectors can be visualized as two putative "bugs" crawling on the surface of a 2D coordinate plane.

............(B1)<---(origin)--->(B2).....(1)

.........(B1)<------(origin)------>(B2)..(2)

.......(B1)<--------(origin)-------->(B2).(3)

....(B1)<-----------(origin)----------->(B2).(4)

The smallest measurement of time that has any meaning is a unit of "Planck time".

(hG/c^5)^(1/2) A quantum of time.

The time axis is perpandicular to the space axis.

The origin is at rest with respect to B1 and B2.

B1 and B2 are moving at exactly the same speed because they have "inertia measurement devices" to adjust their rates of velocity accordingly, i.e. a "constant acceleration".

There seems to be an aspect to space that is "absolute", otherwise, why should our reference frame be the prefered rest frame?


Space is a conductor, more specifically, space is a conductor of electricity and magnetism, with permittivity "epsilon" and permeability "mu". The velocity of electromagnetism through the vacuum of space is "c" , approximately 3 x 10^8 meters per second. Using the letters "e" for permittivity and "u" for permeability the speed of light in the vacuum is:

c = 1/e*u

Let Dx be an interval of displacement along a spatial axis.

Let Dt be an interval of "time".

Dx/Dt = c = 1/eu

Dx/Dt = 1/eu

(Dx)*(eu) = Dt

Since c is a constant, i.e. 1/eu , then Dx and Dt change in tandem, depending on the relative velocity of the observer.

Space is orthogonal to time.











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Hi Russel,

see my post on your other current PR entry for my thoughts on this.

cya
spiff

Hello, new one...

First thing: You don't have to post the Entry to the conversation thread (That happens quite commonly to newbies... )

As with your other entry on the Heisenberg Uncertainty, this one too requires a lot of background from the lay reader. As I suggested in the other thread: Try expanding your thoughts a little bit.

Cheers,

HELL

BTW - I noted that you have already published this article elsewhere. I don't know what the legal section of h2g2 will say about this - It's probably OK.

Anyhow, I think that you will have to re-write this anyways, to increase readability and to straighten things out for the layperson... So, I don't see that this would matter. (It's just that I noted a footnote with Copyright and all rights reserved stuff on that other page of yours. After inclusion to the Edited Guide, the Copyright (IIRC) goes to BBC...)

HELL

Thank you Hell.

I forgot to delete that copyright stuff, from the drag-drop copy of my webpage.

Thanks.

Hello again Hell

I have updated the "Twins Paradox" and will be happy to clarify and explain things in a more layman-esque fashion if you so desire.

Just tell me the specific paragraphs that need further simplification.

If I can't explain it to my grandmother, then I don't really understand it.



Russ

I'll be short and to the point Russ. Don't confuse that with unpoliteness, please.

1. The beginning is definetly a lot better (just remove that smiley... It's not Edited Standard and will be removed anyways.)

2. Towards the end it gets a bit sparse. Fill in with some more explanative paragraphs and draw intermediate conclusions. Be a bit redundant - the formulas are there, I know, but some people prefer to have them explained with words and examples.

3. Important: I miss a conclusion paragraph.

4. I still don't like the formalism. Maybe you should try GuideML - it's very similar to HTML. With GuideML you can use super- and subscripts, italics and bolface characters - It might help. You can also add greek characters (although I wouldn't encourage that - as a Netscape user, they woun't appear right on my monitor). Checkout the Quantum Mechanics Entry ( A781823 ) There are some Formulas in there. You can checkout how it was done by looking at this:

http://www.bbc.co.uk/dna/h2g2/alabaster/test781823

BTW: You can analyze all pages by replacing the 'A' with 'test' in the URL.

There are help-Entries to guide you through that - But, again, this is just a suggestion, and it will require some work.

I'll be around, if you need help just bark.

HELL

This theory could be a bit controversial, since relativity basically says that there are no "absolutes". Yet the equations agree with the invariance of Gaussian curvature on the 3 dimensional manifold.

We approach the absolute as a limit, Dx--->0. The cobordism of the differential manifold sequences do agree with the quantum gravity perterbations.

Taking the duality hyothesis at face value or as a self evident truth, the mathematical formalism crystalizes into a set of perfectly juxtaposed eigenfunctions, consequently, the equations of Maxwell, Kaluza Klein, and Einstein can be formalised, and simplified, because Tensor algebra and Heisenberg matrices present themselves as a single differential equation.

Russ

... Nice... but....

*My* grandmother wouldn't understand this.

Keep going Russ...

HELL

Hi there!

Well, I can safely say that this goes over my head completely

This may sound incredibly patronising, but perhaps you could use easier words that the layperson might understand? For example, what is 'orthagonal'? I understand the need to be detailed... but this has flown over my head completely... maybe twiddle with some of the words?

Caper Plip

I have grave reservations about this one. I am not an expert on relativity, but I think this entry is making a mountain out of a molehill. Here's what Encyclopaedia Britannica says about the Twin Paradox:

'The "paradox" supposedly consists of a violation of the principle of relativity, according to which no asymmetric distinctions exist between different inertial frames of reference. The fallacy of this argument lies in the fact that no inertial frame of reference is associated with the second clock, as it cannot have moved free of acceleration throughout its journey: at least once its velocity (i.e., the direction of its motion) must have been changed drastically, so as to enable it ever to return to its mate. Hence no violation of the principle of relativity; no paradox is involved.'

This entry does not seem to agree with this. Or if it does, then it is not explained at all well. So I think that Russell has misunderstood the paradox and developed his own personal theory to explain it, when no explanation is necessary.

That was my reaction as well, but then Russell uses big words like "cobordism", so clearly has some scientific background.

I have not the slightest idea about what cobordism is supposed to be. (And, after some internet/textbook research, I don't feel very guilty about that.) Be that as it may.

I agree with Gnomon. It would be nice to have an entry about the twin paradox, but this one is pretty interesting to discuss with fellow student in the refectory, not to be included into the Edited Guide.

(If I were one of those fellow students, I would disagree, for several reasons.)

However, I think it should be a thankful task for Russel to explain the conventional approach to the twin paradox. He's surely able to do that, and I'm sure we'd be keen to see it.

Umm.

It starts off vaguelly OK, right up to the point marked 'a solution'. Then it rapidly devolves into equations and physics speak, at which I lost all interest. Which is a shame, because I'd like to see a decent entry on the Twins Paradox.
Even the start bit is dodgy, as it assumes the reader understands time dilation and relativity. But it is at least equation-free.

Nice try, but try again, eh?
-Martin

I think the general consensus is that this Entry needs some thorogh skim-over to make it more understandable for a more generally interested reader, like my grandmother. It's a nice topic and some bits are already quite well-written.

See you around,

HELL

The problem is that the author's primary intention is to use h2g2 as a platform for his own semi-professional resaerch (which may be interesting). He doesn't seem to be willing to think down on normal level and to explain just the historical twin paradox in a simple fashion.

Therefore, he seems to have lost interest.

Just my impression, though.

I think you're right. Mind you, I'm also not entirely convinced he knew what he was talking about - see Gnomon's objection.

The author hasn't posted since mid-september, so I think this and his Heisenburg entry should be moved to the Flea Market, he clearly isn't going to revise them. Agreed?

Tango

Hi there new Scout!


I'd say, off they go.

Thanks! Now I have to work out how to suggest they are moved, I email the list right?

Tango