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[Starver]

Just saying, I'm not someone you need to explain the twin paradox or whatnot for, especially when you are just agreeing with me in a roundabout fashion.

http://www.xkcd.com/1716/ or GTFO...

[Max™]

Do you think I would be here if I had a timelike oracle, instead of using it to avoid fps death?

More seriously though, the end of that Baez article is what I was talking about, drawing the spacetime diagrams lets you see why different observers in arbitrarily chosen frames will see what they see, and clarify what only seems like a paradox if you say, arbitrarily choose a frame which makes it look paradoxical.

Code: [Select]

b (xb, yb, zb, tb) <- twin and twin' reunite
|\
| \
|  \ 
|  /  <- twin' turns around to head back
| /
|/
a (xa, ya, za, ta) <- twin remains on earth while twin' leaves
One twin follows the left path and doesn't move spatially (ignoring acceleration due to gravity/the motion of the earth/solar system/galaxy and whatnot), so the interval along their path: s² = x² - c²t² is all temporal, their Δx = 0, and we'll just say their Δt = 1.

While twin' follows the other path with a spatial component, which means their s² = x'² - c²t'² has a spatial component, but s² is invariant, so if this twin has Δx' > 0, then they must have Δt' < 1 for them to arrive at the same coordinate tuple (xb, yb, zb, tb) as their stationary twin.

If you draw segments from the path of twin' back to the stationary twin and choose them so their elapsed t' is the same as the other elapsed t, i.e. twin observes it has been five minutes in their frame, and twin' does the same, the segments wind up tilted at an angle due to the velocity of twin', and any slicing you choose in this fashion will wind up with twin' unable to cover every point along the path of twin. There simply aren't enough available moments in the path of twin' to pair them up with those in the path of twin, i.e. twin' actually experiences less time, doesn't move as far through time, ages less, however you wish to say it, it's all just the geometry of spacetime in the end, and less confusing than trying to wrap yourself around all the different effects and constraints and implications of "let there be a light clock consisting of blah blah blah blah on the ship of twin' and blahblah blahblah" and so forth.

[Il Palazzo]

A solution which, as is readily seen, doesn't invoke GR at any time.

[Max™]

ಠ_ಠ

...General Relativity is about the geometry of spacetime, Special Relativity is now known to be a special case in which the curvature of said geometry can be ignored, but the actual formulation as a geometric theory came about with GR, and any acceleration of frames moves us back to working within GR again. Changing directions involves acceleration, and breaks symmetries which are critical for the depiction of any sort of apparently paradoxical effects in SR.

[Il Palazzo]

This will end up being a rolling eyes contest, as you stubbornly refuse to acknowledge that there's no GR needed to explain the twin paradox, or keep insisting that SR can't deal with acceleration.

[Max™]

Ah, I see what was being missed here, I didn't mean it was required to explain it, just that it is better at explaining it, especially where things that may seem paradoxical in SR but are more easily understood in GR are concerned. As for SR handling acceleration, yes, it can be done, but it is a kludge, and inelegant compared to doing it in GR.

[origamiscienceguy]

SR works well for straight lines,but GR is better for everything else.

[mainiac]

So do we need GR for this discussion?

[Il Palazzo]

Only if you want to look like you understand it when you don't.

[Max™]

Listen sugar, it's literally been 30 years since I started studying and learning about relativity and black holes and spacetime and all sorts of other stuff, we don't need to go into a full derivation of the EFE's here, but there's no need to be condescending because I don't see the point in ignoring that looking at the geometries involved from a GR perspective makes it easier to understand what is going on behind the weirdness in SR.

Look at the link you provided: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html

The Equivalence Principle analysis of the twin paradox does not use any real gravity, and so does not use any General Relativity.  (General Relativity is the study of real gravitational fields, not pseudo ones, so it has nothing to say about the twin paradox.)  Nevertheless, what General Relativity does say about real gravitational fields does hold in a restricted sense for pseudo gravitational fields.  The one thing we need here is that time runs slower as you descend into the potential well of a pseudo force field.  We can use that fact to our advantage when analysing the twin paradox.  But it needs to be emphasised that we are not using any actual General Relativity here, and no one ever needs to, to analyse the paradox.  We are simply grabbing a result about real gravitational fields from General Relativity, because we know (from other work) that it does apply to a pseudo gravitational field.

We begin with a couple of assertions that belong in the realm of General Relativity.  (We postpone asking what SR has to say about these assertions.)

    Free choice of reference frames: You can describe the physics of a situation in pretty much any reference frame you like, but some frames demand the introduction of force fields that don't show up in other frames.  You can call these "pseudo-force fields", or even "pseudo-gravitational fields".
    Uniform "gravitational" time dilation: Say you have two identically constructed clocks.  One is deep down in a uniform "gravitational" potential well (or "pseudo-potential", if you prefer); the other is higher up.  If the two clocks compare rates by sending light signals back and forth, then both will agree that the lower clock runs slower than the higher clock.  This can be rephrased as "Time runs slower as you descend into the potential well of a uniform pseudo-force field."

The effects involved there are one way to look at it, but as he notes here:

The Spacetime Diagram Analysis is closer to the spirit of GR (vintage 1916) than the Equivalence Principle analysis.  Spacetime, geodesics, and the invariant interval: that's the core of General Relativity.

Also here:

Most physicists feel that the Spacetime Diagram Analysis is the most fundamental.  It does amount to a sort of "Universal Interlingua", enabling one to see how superficially different analyses are really at heart the same.

Perhaps now you can see why I said what I did, rather than assuming I'm just talking out of my ass about a field I happen to enjoy studying?

So do we need GR for this discussion?

For a simplified explanation of why weirdness in SR happens? Yes. Relativity of Simultaneity and such are weirder than the swept area of a line.

[Il Palazzo]

It's fine, man. I'm just not buying your expertise. I'm sure you can live with that.

[Max™]

It's a bit snarky for my taste, as I've already shown I know what I'm talking about and that you apparently didn't read your offered reference, but I don't know who you are so maybe you've got some reason for being snippy or some context I'm missing here, so you do you.

[mainiac]

It's fine, man. I'm just not buying your expertise. I'm sure you can live with that.

You tell him to live with it but then you bait him again...

[WillowLuman]

Now don't get your hopes up, but here's a possible 11 ghz signal from a star 95 light-years away

[Egan_BW]

ALEINS CONFIORMS HYPE HYPE HYPE