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Author Topic:   The Twins Paradox and the speed of light
Iblis
Member (Idle past 3895 days)
Posts: 663
Joined: 11-17-2005


Message 100 of 230 (534624)
11-09-2009 9:24 PM
Reply to: Message 99 by lyx2no
11-09-2009 8:20 PM


Re: Back to the basics
However, in a galaxy far, far away enough your aliens would be travailing away from us fast enough to make any time dilation you care to name.
Would they? I don't believe that's correct.
To begin with, the standard argument might be that it is the acceleration that creates the time-dilation we expect in bodies moving at speeds relative to one another. But expansion isn't acceleration in a classical sense, there isn't a force pushing on either of the planets making them move faster and faster. What is happening is that the space between them is expanding at a constant rate. This causes bodies at greater distances from one another to recede faster and faster.
The usual prop is to take a yardstick and double it in size so its now 6 feet long. Marks that were at 1 inch and 2 feet 11 inches (2 feet 10 inches apart) are now at 2 inches and 5 feet 10 inches (5 feet 8 inches apart). But marks that were at 1 foot 5 inches and 1 foot 7 inches are now only 2 inches further apart. Thus, the outer marks are "moving much faster" than the inner ones.
Do it again a couple times, and now the outer marks are "moving faster and faster and faster" at inordinate rates, while the inner marks, though also "increasing in speed", are being more reasonable about it. Do it every second, get the length up past 30,000 km or so and the outer marks are going "faster than light". Yes? But they aren't really, as far as they are concerned, they are just sitting there right where they always have. Hard to see where real time-dilation, as opposed to red-shifting, would come from in this case.
But, let's skip that for now. Let's say expansion of space does accelerate them somehow. Fine. If so, it accelerates both planets equally. This would be similar to a twins problem where the guys both get into spaceships, rocket off on identical trips in opposite directions, stop "at the same time" and turn around and zoom back, to meet on earth again; and are very surprised after hearing all this jargon about warp-drive messing up your family chronology, to discover that they are actually still the same age!
What you are looking for is something more like maybe, a galaxy or star or whatever traveling at real speeds relative to us. Say some yellow sun was shootng past us at 0.7 the speed of light, yeah? Due to some sort of big explosion a few billion years back. And it had a planet orbiting it that was pretty much identical to earth. But because it had really accelerated to attain its speed, it would experience real time-dilation. So then when you "teleport" there everything will be happening much slower than it would here on earth, and be much more massive. This would probably kill you, imagine a bunch of very slow but massive air molecules sort of perforating you.
See the difference?

This message is a reply to:
 Message 99 by lyx2no, posted 11-09-2009 8:20 PM lyx2no has replied

Replies to this message:
 Message 101 by lyx2no, posted 11-09-2009 11:09 PM Iblis has replied

  
Iblis
Member (Idle past 3895 days)
Posts: 663
Joined: 11-17-2005


Message 102 of 230 (534638)
11-10-2009 12:20 AM
Reply to: Message 101 by lyx2no
11-09-2009 11:09 PM


Re: Back to the basics
This is the bit where cavediver wondered if he'd end up in a westward listing head-stand if he tele-ported to Fremont.
Yep I was thinking of that a lot while I wrote the post.
or you'll be splattered against that other world at 0.7c.
Sure, absolutely. Perforated by unusually massive air molecules moving at a low speed relative to one another, but 0.7c relative to you. And noticeably foreshortened along the lines of acceleration. And probably a couple other things I am neglecting to remember now too.
Or sure, if we compound our magic with even more magic and "change our frame of reference too" then I suppose the only difference one would note related to time-dilation would be when one traveled back and forth? Very similar to the way it would work when actually traveling, without the magic nonsense at all, except discarding the extra acceleration and consequent dilation involved in moving.
only to get back in his ship with his sister world friend
You realize you are answering the main version of the twins problem from this thread rather than my variation that you are quoting, right? My twins undergo the same amount of acceleration and deceleration and consequent Lorentz time-dilation. They both travel, in opposite directions, and when they get back, they are the same age again after all.
Yes, when they observed each other during the voyage apart each would see the other as slowed down. This is Doppler time-dilation. An observer on the planet of origin would observe both of them as even more slowed down. This is a combination of Doppler and Lorentz. The trip back would be even more interesting. Even though both would be slowed down relative to the planet by Lorentz time-dilation, they would observe each other as being incredibly sped up! This is Doppler again, blue-shift this time. An observer on the planet would observe them as sped up also, but not as much, because he would also be observing the Lorentz dilation. Then when they meet, all that stuff will have canceled out altogether, and they will be the same age. Their children may have had kids who had kids already on the point of origin already, sure. That's the basic twins problem again, only with two travelers. But our two travelers undergo identical time-dilation, both the part that cancels out on return and is effectively an optical illusion, Doppler; and also the part that doesn't undo itself on the return trip, acceleration relative to the frame of reference regardless of direction, Lorentz.
See the difference now?
see the expansion as motion
Seeing something doesn't make it "real".
Percy and I baited cavediver for hours in one of Jar's threads to get me this understanding, I'm pretty attached to it.
Message 142
cavediver writes:
It's not really a coincidence. There is a real part - the length of the space-time path, known as the Proper Time of the asttronaut - and there are distorted observations of the path. As the astronaut and observer come back to rest wrt each other back on Earth, there are no more distortions.
...
The observer really has no clue what is going on until the astronaut stops accelerating (at Centauri or back on Earth) The combination of Doppler and Lorentz severely screws up observations.

This message is a reply to:
 Message 101 by lyx2no, posted 11-09-2009 11:09 PM lyx2no has replied

Replies to this message:
 Message 104 by lyx2no, posted 11-11-2009 6:58 AM Iblis has not replied

  
Iblis
Member (Idle past 3895 days)
Posts: 663
Joined: 11-17-2005


Message 115 of 230 (534957)
11-12-2009 2:15 AM
Reply to: Message 106 by cavediver
11-11-2009 7:54 AM


direction Re: Back to the basics
the two clocks' time directions are different
What do you mean when you say that?
I'm not begging the question, I'm trying to understand what statements like that one are describing. Maybe I need another picture? Don't get me wrong, T+S=C, Pythagoras is right even when one of your legs is drawn in time, that's a wonderful picture!
But I persist in thinking of time as one-dimensional, and therefore having only two directions, forward and backward. Space is 3-dimensional, and therefore it's obvious that which dimensions we pick are totally arbitrary, as long as they are at right angles to one another. If spacetime is 4-dimensional, then it seems to follow that all 4 dimensions would be arbitrary? So just as I can swap length from North to West just by rotating, I ought to able to swap South for Past somehow. No?
But in that case, what would a different "direction" in time actually mean? A different speed? a different route? Feel free to whack me about the ears, I'm trying but I'm pretty sure I'm still missing important stuff.

This message is a reply to:
 Message 106 by cavediver, posted 11-11-2009 7:54 AM cavediver has not replied

  
Iblis
Member (Idle past 3895 days)
Posts: 663
Joined: 11-17-2005


Message 124 of 230 (535258)
11-14-2009 5:03 AM
Reply to: Message 123 by Bolder-dash
11-14-2009 4:23 AM


yes and no, with a side of maybe
When one object is accelerating it will experience time slower relative to an object not accelerating
Not "accelerating", accelerated. Accelerating an object dilates its proper time; that proper time remains dilated (in respect to objects that have undergone less acceleration) even after it stops accelerating; the only way to "un-dilate" it is to decelerate the object a corresponding amount.
what if the object (one of the twins in this case) is simply going in circles around the other twin
Three parts:
a) Traveling in a circle around something at a steady rate constitutes circular acceleration, the source of "centrifugal force"
b) Because it's circular, though, it's progressively equal acceleration in all directions, so there's as much deceleration to it as there is acceleration
c) It becomes somewhat more complex when bound in the circle by gravity, but doesn't affect the basic equalization, the extremely tiny time-warp associated with being in orbit has to do with gravitation rather than classical acceleration
What if ... spinning ... around an axis ... just part ... vibrating
It's all the same question from there on in. Spinning, circling, orbiting, and vibrating all involve equal amounts of acceleration and deceleration by direction.
You are kind of spooking yourself by using phrases like "at the speed of light" though. The forces necessary to create circular or vibratory acceleration-deceleration such as to create relativistic speeds will reduce your twin to plasma and then energy.
Imagine how much force is necessary to speed something up to the speed of light in say a minute, or a second. Then imagine having to subject it to that much force to decelerate it back to "0". Then imagine having to continue to subject it to that much force to get it back up near C in the opposite direction. Then do it again, and again, and again, and again, every minute or second.
* I'm seriously wrong here somewhere, btw. For example, in the vibrating version, the acceleration forward will dilate the proper time, a tiny bit, and then the deceleration will un-dilate it, and the acceleration backward will dilate it some more (not reverse it!) and then that deceleration will un-dilate it, ad nauseam.
After a bit that ought to add up to a chunk of time lost wouldn't it? Why wouldn't the same thing happen in an orbit situation? Does it get just drowned out by the significantly larger differential the other way due to distance from the gravity source?
Edited by Iblis, : jot and tittle
Edited by Iblis, : more Big Dope

This message is a reply to:
 Message 123 by Bolder-dash, posted 11-14-2009 4:23 AM Bolder-dash has not replied

Replies to this message:
 Message 125 by lyx2no, posted 11-14-2009 8:29 AM Iblis has not replied

  
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