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Re: Gravitic antitelephone? | |
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by Belial666 » Sat Feb 28, 2015 1:36 pm | |
Belial666
Posts: 972
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Sure, length contraction. But that doesn't affect the light frequency of an external source measured by either clock, or nor enough to measure anyway.
For example, a Honorverse dreadnought that's a kilometer long "shrinks" only 286 meters by the time it acheives 0.7 c over the course of 9+ hours. A speed difference of 1 cm/second isn't going to measurably affect the redshifting due to a speed ten orders of magnitude greater than it. The ship uses the measured redshift to stop accelerating and the clocks use it to synchronize when acceleration stops. Both clocks are going to measure the same redshift for ten significant digits so they are going to be showing the same time, to the limits of measuring accuracy. On the contrary, 0,7 c is going to impose a very measurable difference between the two frames of reference. |
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Re: Gravitic antitelephone? | |
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by phillies » Sat Feb 28, 2015 2:07 pm | |
phillies
Posts: 2077
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Your niece has written a 22 volume book? I suppose it keeps her busy and out of trouble.
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Re: Gravitic antitelephone? | |
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by SWM » Sat Feb 28, 2015 2:49 pm | |
SWM
Posts: 5928
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It makes enough of a difference. If the two clocks are only 1 km apart, it doesn't have to be very big. Try calculating how much difference in time the stationary observer would see between when the rear clock gets hit and when the front clock gets hit. If the front and rear clocks are 1 km apart (e.g. at opposite ends of your dreadnought example) and the final velocity is 0.7 c, I calculate the rear clock appears to be hit 9.8e-10 seconds before the front clock gets hit. If you work through the General Relativity equations, you will find that the differential acceleration adds up to that same very small difference between the two clocks. To get up to 0.7 c, you will either need a very high acceleration (where even a tiny difference in acceleration makes a noticable difference in the time dilation factor) or a lower acceleration over a longer period of time (where the minute differences in dilation eventually add up). Either way, it adds up to 9.8e-10 seconds. --------------------------------------------
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Re: Gravitic antitelephone? | |
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by SWM » Sat Feb 28, 2015 3:47 pm | |
SWM
Posts: 5928
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I just did a quick calculation. The ratio of time dilations experienced by the front and rear of the contracting dreadnought turns out to be approximately the ratio of the accelerations.
Using the numbers provided by Belial666, if the dreadnought accelerates at 600 gees for 9 hours, the ship appears to shrink (to a stationary observer) at an average rate of 0.88 centimeters per second. That means that the ratio of acceleration of the rear clock to the acceleration of the front clock is 1.0000015. In other words, the rear clock is (on average) accelerating 1.0000015 times faster than the front clock. If that ratio of acceleration were constant, it would lead (over the course of 9 hours) to a difference of 0.048 seconds between the front and rear clocks! That is far larger than the actual 9.8e-10 seconds I calculate for the actual case. The reason this simplistic calculation overestimates it by so much is that the Lorentz contraction of the accelerating ship starts out incredibly slowly. For almost the entire duration of the acceleration, the gamma factor is near zero. It is only as the relative velocity approaches 0.7 c that we start getting noticeable length contraction. Since it is the length contraction which results in the (apparent) differential acceleration of the front and rear of the dreadnought, it is only the last portion of the acceleration that actually has any effect on the apparent discrepancy between the front and rear clock. --------------------------------------------
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Re: Gravitic antitelephone? | |
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by kzt » Sat Feb 28, 2015 3:56 pm | |
kzt
Posts: 11360
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So simple. I can't see why David doesn't include this in his model of how the Honorverse works.
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Re: Gravitic antitelephone? | |
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by SWM » Sat Feb 28, 2015 4:08 pm | |
SWM
Posts: 5928
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Re: Gravitic antitelephone? | |
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by cthia » Sat Feb 28, 2015 4:21 pm | |
cthia
Posts: 14951
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Not exactly. She keeps a journal of all of her projects, notes, musings, equations, epiphanies, and on and on. She used to write on everyting from a very young age, much to the chagrin of my sister, as often she would have a misplaced bill or something that my niece would have in her room - having written on that days mail. I suggested to my sister that she give her a leather bound journal for her eighth birthday present. 192 page journals. I wish I could share with you the look on her face at that first journal. It was as if she received a pony. She slept with it. Often do now. Here is a related post from some time ago.
She is actually visiting me this weekend. A reprieve for her and sis from all of the snow. Volume 22 is all Tolman's Paradox. At the suggestion of her professor. Then she reworked it with many more goodies, and related subject matter. Professionals visit my sister just to complete a particular journal from a previous visit. Tierney doesn't allow anyone to take them. Though many often beg. Very interesting they are. And thought provoking. And frightening at times. She would rather write than type because she can draw. Her illustrations are very detailed. She's a very accomplished artist. That runs in my family, drawing. Yet it skipped me. My sister often finds her guests off reading one of my niece's journals. You can get lost in them. She says she's working on number 32 now, and she has it with her. Always. Note: EFE abbreviates Einstein Field Equations. GTR abbreviates General Theory of Relativity. Son, your mother says I have to hang you. Personally I don't think this is a capital offense. But if I don't hang you, she's gonna hang me and frankly, I'm not the one in trouble. —cthia's father. Incident in ? Axiom of Common Sense |
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Re: Gravitic antitelephone? | |
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by cthia » Sat Feb 28, 2015 4:35 pm | |
cthia
Posts: 14951
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A nice site. http://galileoandeinstein.physics.virgi ... e_dil.html Son, your mother says I have to hang you. Personally I don't think this is a capital offense. But if I don't hang you, she's gonna hang me and frankly, I'm not the one in trouble. —cthia's father. Incident in ? Axiom of Common Sense |
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