Let two observers B and T be at the base and top of a building respectively. Given gravitational time dilation, both observers measure T’s clock running faster than B’s clock. Questions: 1. Does B measure the Moon orbiting the Earth faster than T measures? 2. Does B measure the Earth-Moon distance as less than T measures? I think: 1. Yes, just like T’s clock runs faster. 2. Yes, in concordance with Kepler’s third law, which implies that objects orbiting faster orbit closer. What do you think?
Correct. Each observer will measure his own clock running normally. B will measure T's clock as running fast. T will measure B's clock as running slow. Yes, he will. Yes, time dilation and length contraction go hand-in-hand. - Warren
Thanks. Does B measure the building’s height as less than T measures? Assume the measurement is done with laser ranging. I think yes. If B measures the Earth-Moon distance as less than T measures, then B also measures the Earth-Top distance as less.
I'm not so sure. Kepler's law is derived from Newton's gravitational law, which does not hold in general relativity.
Been thinking about this. The implication of Kepler’s law that objects orbiting faster orbit closer must be true in GR as well, otherwise Kepler’s law would be useless even in slightly curved spacetime. The site linked to above graphically confirms that GR matches Kepler in this respect.
zanket Keplers law does not hold if the gravitational fields are strong, as in the case of a black hole or neutron star, or in the case of our Sun and Mercury. It cannot explain precession. From the site:
True. To avoid confusion, I change #2 at the top of this thread to: 2. Yes, in concordance with GR, which implies that objects orbiting faster orbit closer.
I think I can tidy my logic a bit on #2 at the top of this thread. In GR, circular orbits for a given orbital velocity have a specific radius. The radius decreases as the orbital velocity increases. B measures a faster orbital velocity for the Moon than T measures, so B calculates the Moon’s orbital radius as less than T calculates. The proper Earth-Moon distance lessens as altitude lessens.
I would like to find out the question about time dilation in General Relativity. Let’s assume that we have got two identical clocks. Such clock is a box with two parts, one part is filled with one kind of gas (for example Oxygen) and the second with other kind (let it be Hydrogen). These two gases cannot mix until the wall in this box is not removed. So, the time motion is defined with pure physical phenomena-Diffusion. Please Register or Log in to view the hidden image! So, we have got two such identical clocks and one of them is located on the Earth motionlessly and the second one starts flight in space and immediately the wall between these two parts is opened and these two gases begin to mix. The flying clock reaches subluminal speed (let’s assume 0.9 c), then keeps this velocity for a while, and then decelerates to zero. Then it returns to the Earth in the same manner. So, will these two clock show the same time? In other words, will the parameter of the mixture (or amount of mixing, I am not sure how this can be expressed in a correct way) of these two gases will be the same for these two clocks? I want to know if the time dilation in General Relativity (which deals with accelerating, right?) deals with REAL time dilation, or maybe this is an illusion? Please Register or Log in to view the hidden image!
The clocks will not show the same time. Yes, it is real, not an illusion. The time passes at different rates for the different reference frames that is why the clocks will read differently
As the name implies, time dilation is the dilation of time -- so it affects all time dependent physical processes.
origin Russ_Watters Ok, thanks Please Register or Log in to view the hidden image! now please tell me: will the same effect (time dilation) occur if the moving clock flies in space with some constant speed on the round orbit? The motion is always acceleration because the direction constantly changes, right? And as I am aware exactly the acceleration (increasing/decreasing the speed or changing the direction of motion) cause the time dilation. OnlyMe Russ_Watters It would be very interesting to discover such phenomena that is time INdependent
That is the precisely what is occurring with GPS satelites. The acceleration (due to gravity) is lower at the satellites orbit than on earth so the time passes at a faster rate. The speed of the satellites results in the time passing at a slower rate. Both of these effects are taken into account to allow your GPS to give you an accurate position.
Yes, but I have a probably minor quibble with at wording: acceleration causes you to "move", but it is the different motion through spacetime that causes (is) the time dilation.
origin So, one effect causes time dilation, the second one-acceleration. Which one would prevail? The time passes faster or slower on the geostationary satellites compare to the terrestrial clocks?
The GPS satellites are not in geostationary orbits. The GR effect, is greater than the SR effect. So overall a GPS satellite clock runs faster than one on the surface of the earth. SR - the satellite's velocity slows the clocks. The GR effect, on the satellite causes the clock to run faster.
