The only way to fly! 
Posted on 03/22/2006 5:34:03 PM PST by KevinDavis
March 22, 2006: Consider a pair of brothers, identical twins. One gets a job as an astronaut and rockets into deep space. The other stays on Earth. When the traveling twin returns home, he discovers he's younger than his brother.
This is Einstein's Twin Paradox, and although it sounds strange, it is absolutely true. The theory of relativity tells us that the faster you travel through space, the slower you travel through time. Rocketing to Alpha Centauri—warp 9, please—is a good way to stay young.
(Excerpt) Read more at science.nasa.gov ...
I seem to recall that they were traveling faster than Warp 10 in the very last episode of TNG. That was the one where Picard was simultaneously experiencing three different time periods, and in the most futuristic time (where everyone was old and gray) the new, improved Enterprise was traveling at Warp 13 under Admiral Riker's command, I think. They were trying to figure out what created the huge anti-time disturbance that wiped out all of mankind, and eventually realized it started in the future and moved backwards through time, growing larger as it went earlier and earlier into history.
Uh, or something like that. Not that I ever watched that show or anything...
The only way to fly!
Actually a double episode, #177 and #178, broadcast originally during May of 1994 and entitled "All Good Things..." Picard eventually discovers, as he travels back and forth through time, that paradoxically HE has created the temporal anomaly which threatens to annihilate all life in the universe.
The best you could hope to achieve would be some "large fraction" of the speed of light, so that your trip time would be comparable to the light travel time, so we're talking generation ships, or suspended animation here.
I saw a paper once years ago ( like forty years ago ) that outlined the payload for an acceleration and deceleration to and from .9c . It was ridiculous. Assuming conversion of fuel mass into pure light-speed propulsion, the payload was something like 1/100,000 or whatever. Very discouraging!
Interstellar ramjets? At "gamma = 2" or .86c, it costs as much kinetic energy to scoop up a particle as can be gained by ejecting its rest energy as photons, the theoretically best propulsion efficiency.
... Corrections cheerfully acknowledged !
Actually a double episode, #177 and #178, broadcast originally during May of 1994, once again featuring the relationship between the Captain of the Enterprise and the entity known as Q, and entitled "All Good Things..." Picard eventually discovers, as he travels back and forth through time, that, paradoxically, HE has created the temporal anomaly which threatens to annihilate all life in the universe.
Sorry for the double - er, triple, now - post. For a moment there, my computer seems to have entered the aforementioned temporal anomaly. Or maybe it just went nuts. Picard, indeed, expressed the same concern about himself.
I just want my flying car!!!
Mine's got eleven.
In my graduate education, the idea of mass dilation was deprecated. It is after all predicated on the imperative to preserve F = ma. It was pointed out that mass became a directional quantity, since the particle's resistance to perpendicular acceleration was not increased at all, so it was better to identify the concept of mass with the "rest mass", and simply adopt the relativistic momentum, presevering the Newtonian F = dP/dt.
I arrived at the idea that "hitting power" was the measure of speed to be adopted, instead of travel time, much as in ballistics. A bullet going at 0.99c is going to dump 7.1 times its rest energy into a target, compared with 2.3 for a .9c bullet, so it has about 3 times the kinetic energy even if it's only going 10% faster by elapsed time.
It's interesting. I've seen both tennis and hockey commentators speak of "heavy" shots, as though there were some mystical ability to impart momentum to a ball or puck, independently of making it go faster. Pffffffthathinatin'
I'm not going to, uh, with a ten foot, uh...
This is logically correct, but possibly misleading. The twin paradox pertains even when the "clock hypothesis", that there are no physical effects on a clock due to acceleration, is adopted.
The simplest model I know of for the twin paradox is to assume an instantaneous transfer of the twin from an outbound to an inbound spaceship, at the same relative speed. In this case the outbound and inbound legs are both "time dilated" by the same amount and the twin arrives younger by a factor of 1/gamma.
Alternatively, one can simply accept, according to the clock hypothesis, that the "proper time" experienced by an object is the "integral of d_Tau", measured in any inertial frame. Thus was the twin paradox dispensed with forthwith in one pithy exposition I read once. Note that the twin can travel along any path of a given length at constant speed, arriving back at earth, and experience the same aging deficit. All hail pithiness.
"You just blew my mind!"
Welcome, where have you been?
Lurking... lol. I'm the dumb geek.
The episodes with Seven of Nine were rather memorable, I thought :-)
I thought the cube of the warp number was the light-speed-multiple - Warp 2 is eight times the speed of light, Warp 3 is 27 times, etc.
I'm not much of a trekkie, so this could be totally off-base
iirc, in the original series, the warp factors worked like so:
1=C, 2=2C, 3=4C, 4=16C, 5=256C etc... a square progression
and, in the movies and TNG, worked like so:
1=C, 2=2C, 3=8C, 4=64C, 5=4096C etc... a cube progression
like I say, I'm not a Trekkie, so I could be totally wrong on this
In the original series Warp was a square progression (btw, that means W1=1C, W2=4C, W3=9C, W4=16C, W5=25C)
In TNG, it's an exponential curve with Warp 10 equaling infinty.
IIRC, YMMV.
And then everything you think is common sense turns out to be false, so you either begin drinking heavily or just huddle in a corner and shake.
Or you start watching South Park to make some meaning of life."
I especially enjoyed last night's episode of South Park.
It gave new meaning to my life.
Relatively speaking, of course.
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