| Joe2141
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| 224418. Sat Oct 27, 2007 10:26 pm |
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| Davini994 wrote: | | Joe2141 wrote: | | Davini994 wrote: | | The travelling twin receives them at the approaching rate immediately. |
And why is that? because the traveling twin is truly in motion, that is moving upstream through the ether which is the universal cosmic medium for light signal transmissions?? No, that explanation isn't relativistic, isn't right. |
er... no-one claimed that. I certainly didn't; in my earlier explanation it's clear I believe it is due to spatial separation and the concept of simultaneity. |
If by "earlier" you mean "found in a different thread" then I haven't seen it. If it means your post at the top of page 5 of this thread, you made nothing clear therein. But relax! I'm not on your case. Like you yourself confessed a short while back, perhaps jokingly,
| Davini994 wrote: |
I spent 4 years working on the subject, but I haven't got a clue about half of it. |
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| Davini994
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| 224436. Sun Oct 28, 2007 4:38 am |
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Apologies then Joe, it looks like I'm being a bit touchy then. I had a very silly argument earlier in the week, and it looked a little like the same might be happening again.
I shall calm myself;)
| Davini994 wrote: | | 2) I *am* saying it is the acceleration that matters. Or more specifically, the change from one inertial reference frame to another. When you measure the wavefront this difference drops out explainably in the received wavefronts after the turn around until c*distance.* |
I'll be clear now though, if this isn't: I wasn't trying to say that GR is required, or aether.
GR isn't needed to explain the twin paradox, just the change of reference frame of one of the clocks.
And the difference does not depend on any aether or anything non-SR, only that there is a change of inertial reference frame for one clock, and not for the other. |
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| Davini994
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| 224451. Sun Oct 28, 2007 6:20 am |
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| Welcome to QI.com by the way Joe! |
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| gruff5
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| 224503. Sun Oct 28, 2007 12:56 pm |
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So, a rainy, dreary Sunday afternoon - good time to cast the imagination QI-ward...
The twin paradox is about illustrating the time dilation effects of SR specifically. So, you really do have to remove the accelerations of clocks and/or astronauts in your model, otherwise you will need to include the GR effects from those (gets v. hairy, as Joe said) |
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| gruff5
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| 224504. Sun Oct 28, 2007 1:01 pm |
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Davini wrote:
| Quote: | | I'll be clear now though, if this isn't: I wasn't trying to say that GR is required, or aether. |
Not sure that anyone other than me is interested in the possibility of aether, but FWIW...
You might ask "wasn't the aether thing ruled out a century ago with SR theory?" Well, no, as I've been finding out by digging around on wikipedia. There's a comprehensive (long) and interesting article on Lorentz ether theory (LET) at:-
http://en.wikipedia.org/wiki/Lorentz_ether_theory
Right near the end it summarises "Because both LET and SR are based on the Lorentz transformation, they are fully equivalent and it is not possible to distinguish between the theories by experiment." |
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| Davini994
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| 224510. Sun Oct 28, 2007 1:17 pm |
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| gruff5 wrote: | So, a rainy, dreary Sunday afternoon - good time to cast the imagination QI-ward...
The twin paradox is about illustrating the time dilation effects of SR specifically. So, you really do have to remove the accelerations of clocks and/or astronauts in your model, otherwise you will need to include the GR effects from those (gets v. hairy, as Joe said) |
Picky as I am...
As it's a thought experiment, you have the clock jump from one inertial frame of reference to the other. I didn't discuss GR, only SR; GR effects don't need to be considered.
The description in Joe's link is an excellent and usefuly way of describing it if acceleration is brought up as a concern. But isn't fundamentally any different to the original.
Although the clock doesn't change reference frame, the frame in which the time is measured does, and does so instantaniously in the same way as before.
Nothing is invalidated by this. |
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| gruff5
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| 224548. Sun Oct 28, 2007 5:37 pm |
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| Quote: | Picky as I am...
As it's a thought experiment, you have the clock jump from one inertial frame of reference to the other. I didn't discuss GR, only SR; GR effects don't need to be considered. |
No problem, being picky is being scientific ;-) To continue the pickiness...
Davina, I'm fine with your explanation of SR with the wavefronts picture, I found that incredibly useful. :-) It's the original twin paradox expt itself that I'm being picky about.
A thought experiment like that has to be careful about stating the conditions for the expt. By virtue of an astronaut twin (or physical clock) changing direction, it will undergo acceleration -> GR effects. Those GR effects might invalidate the thought expt and then can't be ignored.
I did a google on 'twin paradox' and the top reference (wiki) says:-
"In physics, the twin paradox refers to a thought experiment in Special Relativity, in which a person who makes a journey into space in a high-speed rocket will return home to find they have aged less than an identical twin who stayed on Earth."
Paul Langevin came up with this embellished version of Einstein's prediction in 1911 and unsurprisingly didn't consider GR coz it was still four years off beng discovered by Einstein. He talked about acceleration causing the asymmetry, but that's inaccurate - it's the change of direction that does it.
Now note that the Apollo astronauts put in a claim to NASA for 1 millisecond's overtime , ie the boffins who advised them calculated they had aged more as a result of their high-speed rocketry. Because of GR, under the Apollo conditions the twins paradox went badly wrong in practice!
It's the GR effects from reduced gravity trumping the GR effects of the rocket accelerations and SR time dilation that have caused the Apollo effect.
So, in fact that Stella/Terra/Alf version is not GR free either. Through gravity of the earth, GR will be having a time dilating effect on earthbound Stella. So, to be pure SR, this version should really have Stella floating in space, well away from any planets.
Time for a lie down, I think.... ;-) |
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| samivel
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| 224571. Sun Oct 28, 2007 6:40 pm |
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lol
I'm sure that'll catch on around here. |
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| Davini994
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| 224580. Sun Oct 28, 2007 7:08 pm |
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| Samivel wrote: |
lol
I'm sure that'll catch on around here. |
Oooh, that caught on ages ago. I tend to ignore it, as it's like trying to stamp out hetrosexuality;)
Last edited by Davini994 on Mon Oct 29, 2007 3:29 pm; edited 2 times in total
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| Davini994
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| 224618. Mon Oct 29, 2007 5:38 am |
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That could well be the gayest post I've ever made, but no matter.
Regarding the GR issue, you make good points, and I'm outnumbered (!) so I either haven't been clear or I am wrong.
Thinking about it, I'm probably wrong, I've given out an assumption, which I know to be valid, having gone through it before, but it needed clearing up.
And that assumption, which I've glossed over is: the validity of flipping from one IRF to another, in a thought experiment, without considering the acceleration bit inbetween.
And especially this line:
| Davina McCall wrote: | | The travelling twin receives them at the approaching rate immediately. |
Which I know to be true, because I know it's valid to flip from one inertial reference frame to another, and from that moment receive info as if you'd always been in that frame.
But we hadn't covered that had we, and what's in Joe's link does this very nicely. |
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| gruff5
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| 224655. Mon Oct 29, 2007 7:00 am |
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I wanna see the gayest post, but it's gone!! Sorry, Davini994, but at least I didn't call you Bob this time or it could have been worse - Davini449 (eek!)
I don't think you're wrong. It's entirely reasonable to say 'let's ignore the minor effects of GR for this illustration of SR at relativistic speeds'.
I think there's a difference between thought expts used to illustrate things (time dilation, gravity & acceleration equivalence) and people making statements like "we know that if you do this, then you'll get this result". Thought expts are allowed to be loose, they're an exploration of ideas. I'd win pedant of the year award if I were to quibble that a tram couldn't possibly travel at the speed of light down the streets of Vienna!
But if someone says that a rocketing twin will arrive home younger than a home twin, then I can quibble. The Apollo scenario shows that this isn't enough (it depends on the speeds, gravity strength of the home planet etc). Joe's link had calcs with numbers in it, so it would be fair enough to point out the numbers were v.slightly out because of GR from gravity.
So, on a thought expt basis, I've no probs with how you used flipping IRFs! Though at one point I think you said that the travelling twin saw the home twin ageing instanteously at the return point and I wasn't sure about that one, I assumed it would be just faster ageing? |
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| Joe2141
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| 224679. Mon Oct 29, 2007 8:17 am |
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gruff5:
Earth's gravity contributes precisely zero to the scenario, since its strength/influence is so many orders of magnitude smaller than the huge/significant influence of the gamma factor (1.5) distortions attributed to frames moving at .75c.
And technically, one can figure in distortions incurred due to a ship's acceleration, without calling upon GR per se. Such distortions are derived, through calculus tricks, from the basic SR Lorentz transform. I have those formulas and they are not complicated. But the Terra/Stella/Alf scenario is certainly the simplest of them all.
Davini994:
You could be right about the wavefront arrivals, not sure; but that whole explanation begs for some missing link, some crucial connector, or at the least a quantitative example illustrating. You made it sound too much like the astronaut twin is the one truly in motion and we all know that's misleading. |
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| gruff5
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| 224786. Mon Oct 29, 2007 1:17 pm |
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Thanks, Joe, that's really QI. Though:
| Quote: | | Earth's gravity contributes precisely zero to the scenario, since its strength/influence is so many orders of magnitude smaller |
OK, it's pretty irrelevant, but perhaps more accurate to say 'almost nothing' than 'precisely zero'?
I'm also not sure how much we can deduce from the wavefronts model. Might need to actually calculate the effect of time dilations on the rate of wavefront emission? What it definitely does show for me is how flipping inertial frames of reference brings in an asymmetry for the astronaut twin. |
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| Davini994
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| 224805. Mon Oct 29, 2007 1:42 pm |
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As before, 'truly in motion' certainly wasn't the intented implication. This is a misunderstanding due to failed communication between the two of us.
The key connector is this:
| Davini994 wrote: | | ***This is the key bit***: The home twin receives wavefronts at the ‘receding’ regularity for the period of time that it takes for the light to reach him from the turnaround point. The travelling twin recieves them at the approaching rate immediately. That’s where the difference is. |
And as the example came straight out of my y1 ThPh book I'm happy it's right, although simplified; I just need to convince you of this;)
Personally I'm much happier with principles than numbers, but to copy straight out of Tipler, word for word (don't tell the publishers!):
Taking v/c = 0.8
buoy is 8ly away from earth
1 signal sent per year
receding f = 1/3 restframe f
approaching = 3 restframe f
Ulysses travels, Homer stays at home; in Ulysses frame, it takes 6y to reach the buoy , so he receives 2 signals (1/3 per year).
It takes 6y to get back again so he recieves 18 signals (3 per year), so he thinks Homer will have aged 20 years.
In Homers frame:
He receives signals at the rate of 1/3 per year for the 10y it takes for Ulysses to reach the buoy... AND!!! another 8 years, as Ulysses is 8 ly away when he flips inertial frames, so the light takes another 8 years to reach him. = 18 years and 6 signals.
As Ulysses is travelling at 0.8c: he takes 10y to get back, where the light from the inertial frame takes 8. So there is only 10-8=2 years of receiving at the approaching rate. 2 times 3 =6, so Homer thinks Ulysses will age a total of 12 years.
So you've got the count; and as you are only counting the period for the round trip, i.e. starting and ending with the twins in the same physical space, you don't need to worry about adjustments for spatial separation, or synchronisation.
It doesn't mean that the aging rate is different on the 2 legs of the jounrney though; this thought experiment can be used in the same way to explain a one way trip. Although you need to be a little careful about synconicity there of course. |
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| Joe2141
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| 224813. Mon Oct 29, 2007 2:41 pm |
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It seems to check out -- presumably. But I find it unsatisfactory for this reason. In Ulysses' frame the outbound trip takes 6y instead of 10y due to the Earth-to-buoy frame being length-contracted. Your explanation there employs the Lorentz transform in its ciphering. But this whole entire thing about the signal arrivals totally ignores relativity and the transforms! You can't say that regular signal arrivals can be expected from a sender who is laboring under time dilation, can you!? So that explanation of your's is maybe doing the mathematical equivalent of what in diction is called "mixing metaphors".
Whereas the Terra/Stella/Alf scenario employs the LT consistently throughout, and thereby demonstrates that the transforms embody no inherent self-contradiction as regards the Twins Paradox. |
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