One twin stays on Earth while the other takes off on a rocket sheep (i meant to say ship, but accidentally typed sheep… and now I like it!) near the speed of light.
Through a telescope, the Earth twin sees that his rocket twin appears younger than himself. (makes sense… just like we can only see stars as they were years ago, but not as they are now because of the speed of light.)
RESOLUTION: The rocket twin, not the Earth twin, reversed directions during his journey. Since the rocket twin (riding the rocket sheep) didn’t travel with constant velocity, the two viewpoints are not the same. Hence, you can tell who is younger: the rocket twin.
I need help understanding that part.
If the Earth was revolving at twice the speed it is now, would everyone live to be 160 or so due to aging slower?
I recently moved to East Washington. There is a LIGO near me in Hanford. For those of you who don’t know, LIGO is one of 3 novel observatories costing hundreds of millions of dollars each, with arms extending several miles in perpendicular directions made to detect a kind of radiation that has never been observed but that general relativity tells physicists must exist: gravitational waves. Does anyone know any results from these projects? Are they open to the public? Is there anything there worth seeing?
Thanks,
Art
BTW, I got most of this info from a special issue of Discover devoted to Einstein.
Well, I don’t understand (1), and don’t have enough info for (3), but (2) is easy enough:
No.
Time dilation (the slowing that occurs as the speed of light is approached) is not a simple “go twice as fast, time’s twice as slow” linear relationship. It’s a geometric curve, with the following formula:
The average orbital speed of Earth is a hair under 3 * 10[sup]4[/sup] m/s, or about one-thousandth the speed of light (3 * 10[sup]8[/sup] m/s). Plugging this into the above formula:
t’ = t * sqrt (1 - 1[sup]2[/sup] / 1000[sup]2[/sup])
= t *sqrt (0.999999)
= t * 0.9999995
As you can see, the total time imparted by Earth’s orbital speed is pretty slight. Were one million years to pass on Earth, a stationary observer would experience one million years, six months. Big deal.
Doubling Earth’s orbital speed to one five-hundredth the speed of light results in (aside from changing its orbit and making it unhabitable):
t’ = t * sqrt (1 - 1[sup]2[/sup] / 500[sup]2[/sup])
= t * sqrt (0.999996)
= t * (0.999998)
So for one million years on Earth, an observer experiences one million and two years. More, but hardly significant.
In any case, we wouldn’t notice (aside from going into extinction when the planet started moving twice as fast). Even if time were moving at half-speed relative to a fixed observer, 80 years would still feel like 80 years, even if the observer thought it was 160.
I don’t know about #3 but here is my (limited) understanding of #2.
The key word here is Relativity. The twin example works because one twin is moving at a different rate relative to the other twin. For the twin that is moving it appears that the other twins time is going slow. Since everyone on earth is going the same speed the age of everyone would stay the same. Time slows for the person moving. If everyone is moving at the same velocity then everyones time is going at the same rate. Now, if a an observer got off the earth and the earth somehow accelerated to near the speed of light then according to the observer everyone would be living longer. To the people on earth nothing changed so everyone appears to age at the same rate.
According to relativity, there’s no privileged reference frame. You should be able to consider either twin as being at rest, and the numbers will all work out. However, when the twin on the rocket sheep gets back to Earth, he really will be younger than the twin who stayed home. If they compare watches, the rocket twin’s watch will be behind.
But why is it that twin who’s younger? Since there’s no privileged reference frame, shouldn’t we be able to consider the rocket sheep as being at rest, and the Earth as having zoomed around and changed direction? The resolution, as you say, is that the rocket sheep twin is the one who felt the acceleration, so he’s the one who has his time slowed down.
IANAPhysicist, but I did read a bunch of those Feynman books
As sleestak said, the slowing is relative. While the sheep-twin is moving away, they will both see the other as slowed down. It makes no sense to ask “which one is really slowed down?” But we can ask, “If the sheep-twin stops, turns around, returns to Earth, and stops on Earth, whose clock will be ahead of whose?”
Now, to properly answer this question, we need to take account of the sheep-twiin’s acceleration: slowing down, turning around, stopping on Earth. That means we need General Relativity. I won’t go into the details, but it’s the acceleration that makes the sheep’s reference frame different from the Earth’s.
slee got the right answer, but it’s not because "Time slows for the person moving. " As I said already, any two observers moving relative to each other will BOTH see the other one slowed down. Brian was right on both counts: the effect would be very small, and even with a much larger velocity, the time by your watch would still be about 80 years.
However, since the day would only be 12 hours long, you’d live twice as many days.
Thanks for all the responses, I’m getting a clearer picture in my head now.
Does anyone know anything about Ligo? As far as I know… they’re building one in Hanford, WA, one in LA, and one in Italy. They won’t trust the results from just one place, so they have to verify with all 3 I think. It sounds interesting, if anyone knows more info please share.
No, you are misunderstanding. I’m not sure exactly how to explain this, but normally, when people talk about relativity, measurements are already corrected for these kinds of effects. The following is the standard preliminary to discussing relativity in physics books.
Imagine that each observer has an infinite three-dimensional Cartesian grid in space. At each point in space, the observer has a little helper with a clock. At the origin, the observer burst of light is released; this burst marks the t=0 point. Each little helper observes the burst, and uses the speed of light (known constant) and his distance from the origin (computed from his coordinates in space) to compute the time that has passed since the burst was released. He then sets his clock to this time. Thus, the burst is used to synchronize all the clocks in the observer’s grid. Suppose the observer observes two events: one takes place at (t1, x1, y1, z1); another at (t2, x2, y2, z2). The times t1 and t2 are measured by the little helpers at (x1, y1, z1) and (x2, y2, z2) respectively. They are not the times as measured by the observer, sitting at the origin, when he observes the events.
Now, each observer has his own grid with little helpers. In general, these grids are moving with respect to each other.
Suppose two observers are moving with respect to each other at a constant velocity. Both observers carry a clock. Each will observe the other’s clock to be moving slower than his own. (Note that these observations are in the context of the discussion about the grids above.) The situation is entirely symmetric.
In the twin paradox, this symmetry is broken, because one twin has to accelerate to come back.
I have not studied general relativity, so I am not sure exactly what will happen.
(Special relativity deals with the special case where observers are moving at constant velocity with respect to each other. General relativity deals with more general scenarios where there is acceleration.) People on the Earth should appear to age normally to each other. However, an outside observer would probably detect a difference if the Earth started to rotated faster. I am not exactly sure how to account for the fact that people on Earth should experience less gravity.
I am not a gravitational wave astronomer, but we do have a few in the department, including people who are analysing LIGO data. As far as I know, there are no results from this yet – the main problem is still seperating a real event from the noise, which can be rather difficult. We may have better luck with the space based interferometer, LISA, but the problem there is stability of the phase of the lasers – we appear to be getting there, but its hard work. The problem there is that if the phase of the laser changes in time, then fluctuations in phase may be mistaken for a real event, or a real event overlooked, which would seriously undermine the credibility of the project.
Another physicist who doesn’t actually work on gravitational waves chiming in… Depending on who you ask, once LIGO is doing “science runs” it’ll observe somewhere between 0.1 and 10 “gravitational wave events” per year. Which (since it’s only supposed to run for 5-10 years before being upgraded, raises the possibility that it won’t see anything at all before then.) Right now, however, I believe they’re doing “engineering runs”, which basically involve running the device and trying to track down & eliminate the sources of noise that they see.
LIGO is a phenomenal feat of engineering, BTW. I think this was really hammered home to me when I attended a talk this summer on it. The speaker mentioned that they’re monitoring changes in the length of the arms that are less than the Compton wavelength of the mirrors used to reflect the light. The mind boggles.
You don’t actually need GR. The reason that you can’t use the sheep-twin’s reference frame is that he doesn’t have “a” reference frame. He has two different reference frames, one on the way out and one on the way back. If you use the “sheep on the way out” reference frame, for instance, he’s stationary for half the trip, but then he’s moving very fast on the return, so that’s where the age difference comes from. You can use any reference frame you like, but once you choose your reference frame you have to stick with it.
As for LIGO, they are collecting data, and there are a few hypothetical sources which they could see right now. They haven’t actually seen anything definite yet, but that’s not too surprising, since the sort of sources they could see right now are expected to be fairly rare. Of course, even the lack of a detection is a result of a sort, since it tells us that there aren’t any gravitational wave sources that “bright” or close to us, but it’s a somewhat boring result. Once LISA is launched, we do fully expect to see some definite detections within minutes of it being turned on, and if we don’t see any, we’re going to have to radically refine our ideas about either General Relativity or stellar evolution. But it’s going to be several years before LISA gets off the ground, even in the best case.
As it happens, I am working on this, to some degree.
