I was reading something yesterday about a star cluster some scientists were recently looking at with Hubble, and I got to wondering how gravity effects time. I know the example of the Sun on a rubber sheet called spacetime and how it causes a dip, but how does that specifically effect time?
So I present the following question to the brilliant minds of the SDMB: if I were standing on the Sun’s surface, how would my watch behave? Would it move quickly, slowly, the same, or not at all? Why?
It would quickly resemble the clocks in Persistence of Memory, and then it would wander lonely as a cloud.
I think it would appear to tick at one second per second - that is, it would appear to behave completely normally (if you, the local observer, had taken sufficient steps to prevent it and yourself from being melted, crushed, etc). Reason being that you, the local observer are affected similarly by any distortion of time.
“What would a clock on the sun look like from Earth?” might have a different answer.
Yes, I think for this thought experiment, you might need to assume:
(1) that the temperature is one at which human bodies and watches remain intact and in working order – say in the range 0 C to +60 C.
(2) that the surface of sun is solid rather than plasma.
(3) the the watch is stationary relative to the surface of the sun.
And although a clock runs slow in high gravity or under high acceleration, the Sun’s surface gravity isn’t humungous. 28 times that of Earth, to be sure, but not clock-stoppingly high.
Well, unless your watch (not to mention you) can withstand ~10,000[sup]o[/sup] F, I’m going to have to go with “not at all”.
If we move to PhysicsLand (where pullies are frictionless, ropes don’t stretch, and measuring devices are indestructible) the answer was covered by Einstein. Based on my (totally non-expert) memory of the theory of relativity, a frame of reference under acceleration appears to experiences time slower when observed from a frame not under acceleration (or under lesser acceleration). Acceleration from gravity counts, so the higher the gravity, the slower time progresses as observed from outside that gravity field.
Wikipedia has the surface gravity of the sun at ~30 times that of Earth. So if you were on the sun holding up your watch, and I was here on Earth looking at your watch’s second hand, I’d see it taking more than one second (by my measurement) to tick forward. However, you (being in the same frame of reference as your watch) would see your watch performing normally at one tick per second, and when you looked at my watch, mine would appear to be ticking faster than once per second.
The difference isn’t going to be much, though. I tried chugging through the third equation at this page, and using M & r values for the Sun (and disregarding the Earth’s separate gravitation dilation on me), your watch would be running about 0.7 millionths of a second slow compared to mine.
The fractional time loss of a clock in a gravitational well relative to one “out of the well” is, to a very good approximation, the gravitational potential divided by c[sup]2[/sup]. For a star the mass of the sun, this works out to about two parts in a million.
Of course, as was pointed out Mangetout, if you were watching the clock while sitting next to it (and assuming that you & the clock were stationary, just above the Sun, and encased in heat-proof unobtainium), you wouldn’t see it behave any differently than normal. However, if you decided to send pulses of light out from your clock at a rate of one per second, they would be received at a rate of one every 1.000002 seconds by an observer “far away” from the Sun; this is what’s usually meant by “gravitational time dilation.” The answer would also be slightly different if you were orbiting the Sun rather than sitting stationary above it; this can basically be understood via the well-known time dilation from Special Relativity (i.e. the clocks of moving objects are observed to run slow.)
Upon preview, it appears that sciguy’s answer is different from mine; it’s not clear to me, however, whether the Wikipedia article he linked to gives the result for the time dilation between stationary observers or between freely falling observers (another factor which can make a difference.)
Well you could do the experiment at night.