| Davini994
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| 221571. Thu Oct 18, 2007 10:52 am |
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| gruff5 wrote: | | Are you saying that the time dilation only happens during the acceleration/deceleration phases? Would this mean that the spaceship that cruised at (very) high speed for 5 years would have the same amount of time dilation as one that cruised for only 1 day? |
The ‘paradox’ is due to a comment which is often somewhat buried in discussions regarding special relativity, probably because it’s mind bending enough without. The comment being these formulas assume that measurements are made at the same point in space; there is no spatial separation of clocks. When there is spatial separation, then this factor also has to be considered.
The easiest way to get a handle on it is If you think of the measured time in terms of wavefronts, i.e. assume that each twin emits a beam of light with period 1s, i.e. a wavefront every second. Then, when the twins are receding, the time between each wavefront is greater than a second, so each twin measures the other to be aging slower. This is due to time dilation, and doppler shift.
When the travelling twin round, and the twins are approaching, the wavefronts are received quicker than when receding due to the changed direction of the doppler shift.
***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. Minkowski diagrams describe this quite nicely once you’ve managed to get your head round them, which isn’t hugely easy.
The further the travelling twin goes, for a given distance, the greater the time that this occurs for, and therefore the greater the difference.
This is something that causes awful confusion about special relativity, note the conversation that went on not so long ago about approaching a clock at the speed of light. I didn’t contribute, as once I’d read through what had been posted I needed a good lie down.
I’m not sure I’ve explained that very well; if true let me know, as there’s an excelent section in my y1 degree text book, which I’ll dig out and paraphrase if required, and I’m sure much better than what I’ve written.
***
The question about high energy particles is a good one, I haven’t considered it before. It again is related to this spatial separation. i.e. time dilation can occur one way round in one frame, and the other in the other, because the spatial separation has changed, and the way this is measured in the ‘simple’ equations does not take this into account.
You’d have thought the astronauts clocks would run faster would they not? |
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| gruff5
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| 221673. Thu Oct 18, 2007 3:59 pm |
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| Quote: | | ***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. Minkowski diagrams describe this quite nicely once you’ve managed to get your head round them, which isn’t hugely easy. |
Yes, yes, YES! Brilliant Dr Bob! I've read quite a bit of pop. sci. on the time dilation twin paradox and never got this aspect sorted until now. So, the travelling twin sees the home twin ageing rapidly just on his return trip, yes? So, it's more about the reverse in direction of travel, than acceleration per se. The maths would show that of course, but I feel a lot better being able to understand it in an intuitive way. Still spooky that the light information received determines reality, but I'll slowly let that seep into my understanding.
I'm still unsure about the meson question. Is this a symmetrical case, where both earth and meson age at the same rate? The rapid closing speed means that although they'll both see wavefronts at an 'approaching rate', a reduced number of wavefronts in total will be received (less perceived ageing altogether)? Is that right?
I assume the astronauts (or more likely their boffin advisors) must have thought their clocks had run faster to be claiming overtime. From the lowered gravitation field having trumps over any high speeds time dilation? |
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| dr.bob
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| 221727. Fri Oct 19, 2007 3:33 am |
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| gruff5 wrote: | | Yes, yes, YES! Brilliant Dr Bob! I've read quite a bit of pop. sci. on the time dilation twin paradox and never got this aspect sorted until now. So, the travelling twin sees the home twin ageing rapidly just on his return trip, yes? So, it's more about the reverse in direction of travel, than acceleration per se. |
No.
Firstly, I didn't say that bit. Davini did.
Secondly, that's almost certainly not how it works. For two reasons:
1) time dilation is governed by the relative speed that something is moving relative to yourself. That's speed, not velocity. Direction is unimportant. Someone moving away from you will age just as slowly as someone moving towards you at the same speed.
2) all motion is relative. Remember that, it's one of the cornerstones of the entire theory of relativity. Thus, if you see the person on earth moving towards you, they will see you moving towards them. So if the direction of movement was responsible for an increase in aging, you'd both see it in each other, and you'd both end up the same age.
Trust me, acceleration is the key. |
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| gruff5
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| 221780. Fri Oct 19, 2007 5:45 am |
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Sorry Dr Bob and Divini for getting my attributions mixed up! :-(
I'll take the acceleration aspect on trust then. I suppose the short burst of acceleration puts the travelling twin into a different inertial frame of reference for the next five years (say) of high speed cruising? And this inertial frame of reference stays there until another burst of acceleration/deceleration? I can see I'm not truly going to get this until I've studied the Minkowski diagrams and the relevant maths.
Thanks both,
Gruff |
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| Davini994
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| 221826. Fri Oct 19, 2007 8:01 am |
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| dr.bob wrote: | ...
Secondly, that's almost certainly not how it works. For two reasons:
... |
Well, yes it is. For 2 reasons!!!
1) I wrote it from memory, which came directly from my Y1 physics text book, Tipler. I checked it through last night, and what I wrote is pretty much word for word. It's very much a standard thought experiment, so you are disagreeing with pretty much everyone if you disagree with what I have written.
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.*
Dilation to and from being the same isn't relevant, the thought experiment is in terms of observed time for the whole trip.
*there is another way of doing this sort of thing, which is adjusting the time measured based on c times measured distance. If you think it through in these terms, then the travelling twin measures the home twin to age instantly at the turn around point. |
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| Davini994
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| 221829. Fri Oct 19, 2007 8:04 am |
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| Gruff5 wrote: | | Still spooky that the light information received determines reality, but I'll slowly let that seep into my understanding. |
Good point. It's about how you measure time at a distance. You use information which travels at c. As mentioned above briefly, you can correct this factor out, and indeed that would be more usual. But you still get the same 'light determining reality' as your corrections are based on the relative speed.
For the twin paradox it can be explained without this and still works. |
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| Davini994
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| 221848. Fri Oct 19, 2007 9:01 am |
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| Gruff5 wrote: | | I'm still unsure about the meson question. Is this a symmetrical case, where both earth and meson age at the same rate? The rapid closing speed means that although they'll both see wavefronts at an 'approaching rate', a reduced number of wavefronts in total will be received (less perceived ageing altogether)? Is that right? |
You have an excellent turn of phrase Gruff5. Yes, that’s what I was stumbling towards, rightly or wrongly. So what I think is:
The increased rate is due to the non-relativistic Doppler shift, which is blue. But this can be taken out, leaving only the ‘time dilation’ (ha!) Doppler component, which is red whether approaching, receding, or going anywhere. (but overall always blue on approach).
The reason that both can measure time faster in their rest frame relates to the concept of simultaneity, which is very important. i.e. event A being measured as before B in frame C, and B before A in frame D. I’ve had a go at getting an example down in a readable form, but I’m struggling slightly, it’s not too clear in my head.
If you use the unadjusted time measure, then you are talking about the time light takes to to get between the events. This difference is proportional to the separation, which it has to be as we are talking about rate that time passes.
…
No, not sure how to get there on this one. There’s another section in Tipler, explaining it in terms of trains and platforms. I shall see if I can push it back in my ear on Sunday, in which case I’ll paraphrase again. Assuming no one can fill me in. Or tell my why I'm wrong on the mesons.
p.s. feel free to confuse me with Dr Bob anytime you like, not sure how he feels about it though;) |
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| gruff5
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| 222350. Sun Oct 21, 2007 2:29 pm |
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| Quote: | | *there is another way of doing this sort of thing, which is adjusting the time measured based on c times measured distance. If you think it through in these terms, then the travelling twin measures the home twin to age instantly at the turn around point. |
Thanks, Davini, your explanation is really helping. I guess this is where the 'simoultaneity' thing comes in? The twins can't ask "Yes, but what's happening right *now* over there with my twin?", the twins can only measure the other's situation from observation.
The wavefronts thing is making sense to me; I find 'inertial frames of reference' a bit abstract for me to get to grips with. And I'd be interested to see any further clarifications that you come up with, from Tipler or wherever. One can also use the Img button to add images (for diagrams) to posts I notice, which could be useful.
I saw a nice diagram in the book "Introducing Einstein" that illustrated the way perception of the order of events (A & B in your example) can be altered in these conditions. Made sense at the time, but I'd like to get these concepts into my psyche so that they come 'naturally' without starting from scratch each time! GR tensor calculus looks way beyond me currently/forever, but looking at SR maths, it could be manageable, so I would like to get to grips with that sometime - do you find it hard?
Don't forget the real QI is on tonight (9pm) there's been a whole weekend of it on the TV I just found out! |
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| npower1
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| 222372. Sun Oct 21, 2007 3:51 pm |
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Gruff5 said
| Quote: | | GR tensor calculus looks way beyond me currently/forever, but looking at SR maths, it could be manageable, so I would like to get to grips with that sometime - do you find it hard? |
I would expect anyone, whatever their age, specialty, or current knowledge, posting on this site could understand the maths of SR with relative ease.
GR is another kettle of fish. The mathematics and its implications are still being worked on (Stephen Hawkings work comes to mind).
Hopefully Dr bob and davini994 won't disagree with me. |
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| Davini994
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| 222439. Mon Oct 22, 2007 4:37 am |
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I agree npower.
The difficulty with Special Relativity comes with rationalising the situation, rather than the maths. As I think will be proved if you search for special relativity on here! We're all confused at some point. The maths all drops out fairly nicely once you've got the situ.
Inertial reference frame just means that they aren't accelerating.
GR is even more head bending, but the maths is also *preposterously* complicated on top. Don't let anyone tell you that Einstein was not a good mathematician.
Incidentally, resolving the difference in measured time, by counting wavefronts, also works for a one way trip, i.e. stationary; travel; stop at receiver.
I'll see if there's anything on the net about simultaneity. As I say I'll need to relearn it as it's fallen out of my head at some point. |
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| Joe2141
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| 223991. Fri Oct 26, 2007 6:42 am |
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| 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. |
That's undeniable.
| 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.
You can say that acceleration is the decider of the paradox and you'd be correct. But even without accelerations, the home twin is older at the reunion because of the direction change of the astronaut twin. Same difference you say but no, since hairy or GR formulations aren't required in order to plumb it -- only an understanding of the relativity of simultaneity under Special Relativity.
| Davini994 wrote: | | I'll see if there's anything on the net about simultaneity. As I say I'll need to relearn it as it's fallen out of my head at some point. |
Something on the net about simultaneity: http://www.sysmatrix.net/~kavs/kjs/addend4.html |
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| gruff5
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| 224136. Fri Oct 26, 2007 11:09 am |
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Joe wrote:
That's a neat reference. It gets a bit bogged down in the numbers, but I like the way it shows that the SR twin paradox is *not* dependent on accelerations (sorry, Dr Bob!), but that changes of direction are the important bit.
| Quote: | | 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. |
As you might have seen from the "Does absolute space exist?" topic, I'm suggesting that it might exist. And I'm not even sure that aether has been ruled out as a light medium by the Michelson-Morley expts - though I stand to be corrected on that.
Einstein didn't see a need in SR calculations for absolute space, but that doesn't mean it doesn't exist. Let's (for one moment) say that it does exist and even that light is propagated thru the aether at the speed c. Well then, we measure the velocity of the travelling twin relative to the aether and do the maths for her time dilation against cosmic time.
http://en.wikipedia.org/wiki/Cosmic_time
Then we do the same thing for the home twin relative to the aether - Earth is, after all, moving through space. To find out how the twins age w/r/t each other, we find the difference between their two time dilations. This is still relativistic - relativity relayed thru the 'stepping stone' of the aether.
But it would be a bit pointless to attempt this approach. Firstly, the aether (if it exists) is ethereal and currently ungraspable (tho' possibly you could do a guesstimate by referring to the hubble flow). Secondly, in this twin scenario you're only interested in the *relative* ageing of one twin to the other. So, there are fewer steps in the calculations if you ignore the stepping stone (absolute space or the aether) and just compare their velocities directly to each other. |
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| ali
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| 224152. Fri Oct 26, 2007 11:32 am |
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| gruff5 wrote: | | I like the way it shows that the SR twin paradox is *not* dependent on accelerations (sorry, Dr Bob!), but that changes of direction are the important bit. |
A change of direction *is* an acceleration. |
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| gruff5
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| 224167. Fri Oct 26, 2007 11:51 am |
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Ali wrote:
| Quote: | | A change of direction *is* an acceleration. |
Ah, but did you look at the reference from Joe2141?
It set up the twins paraxdox in such a way that no accelerations are involved. Very neat! |
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| Davini994
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| 224406. Sat Oct 27, 2007 7:17 pm |
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| 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 simulanaeity.
| Joe2141 wrote: | You can say...
Same difference you say... |
???
Again, no-one suggested these things... the description I wrote requires only to consider a change in inertial reference frame of one of the clocks. Which is no different from the passing over version in the link, although it is worded very nicely I must say.
Although no clock changes inertial reference frame, the path on which you are measuring the period of time still does, for Stella/Alf. |
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