« on: 26/06/2018 21:40:51 »
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Suppose there is an atom clock in alpha centauri, syncronized to the earth. An observer there could detect now, signals sent from here in jan 2014, considering 4 light years of distance.OK
No. The light or signals arriving at AC are the same for both the Clock at AC and the ship. They both, at the moment of passing, detect signals that left Earth in Jan 2014.
A spaceship coming from earth at 0.5c, crosses alpha centauri when the clock at the star shows jan 2018. The corresponding time at earth for the ship is t' = t - vx = t - 0,5 * 4 = jan 2016. An observer in the ship could detect signals sent from here in jan 2012.
Again, this ship would be receiving the same signals from Earth at that moment as AC and the Other ship; those that left Earth in Jan 2014. All events( such as light carrying a certain bit of information to an observer) must be consistent across all frames of reference.
A spaceship with the opposite velocity, flying to earth at 0.5c, crosses alpha centauri also when the clock at the star shows jan 2018. The corresponding time at earth for the ship is t' = t + vx = t + 0,5 * 4 = jan 2020. An observer in the ship could detect signals sent from here in jan 2016.
Just remember, that in any frame, light will travel at c relative to that frame (this is illustrated by the fact that in all three diagrams above light is drawn at a 45 degree angle).
If it is right, there is any intuitive way to realize how that gap of 4 years between the available signals for the ships should happen? I am always unconsciouly dealing with light speed as a normal material speed, instead of a constant, when I try an intuitive explanation.
But when deriving the Schwarzschild solution, after calculating the Ricci tensor (Rμν) and the Ricci scalar (R), from the spherical symmetries of the problem, both are non zero.If so then that's news to me. Can you find a source on the internet which shows that to be true? Clearly from Einstein's equations in vacuo R = 0 so I can't see how it can not be zero.
How is it possible that the field equation are zero while Rμν and R are non zero?They can't be. It seems to me that there has to be problem with your assertion above where you state that the Ricci scalar and tensor as zero.
Wouldn't be a big coincidence if the spinning velocities were just the necessary to hold the system in equilibrium, not expanding or colapsing?It would be even a greater coincidence that we would be seeing all these expanding galaxies at the same point of their expansion. As we look further and further out into the universe we are seeing it as it was during earlier and earlier ages. If the galaxies were expanding over time, we should be seeing more and more "compact" galaxies as we look deeper into space. Also, given the magnitude of these measured star velocities, If they weren't stable, they would dissipate in a few hundred million to a billion years. Since stars need relatively dense regions in which to form, Stars would only form while the galaxy was in its compact form. But out own Sun is some 4+ billion years old already. Ergo, if our galaxy were expanding as you suggest, our galaxy would dissipated by now and we would not see ourselves as being in the midst of a relatively compact structure like we presently do. Put another way, the lifetime of a galaxy as a fairly compact object would be much, much, shorter than the lifetime of the stars it is made of.
a (huge) artificial satellite... a beam of light reaches the satellite surface (and) bounces back from a mirror at its centerFrom this description I am imagining something like a huge partially reflective balloon in a circular orbit around Earth, inflated by a low-pressure gas, with something like a retroreflector at its center?
For someone in the earth, the time would be bigger than 2r/c due to the satellite orbital speed.I don't expect so. There is no clock on board the satellite, so we are really just talking about the speed of light in an (almost) vacuum.
The beam should be travelling a curved path from the surface to the center and back to the surface from earth perspective.I don't expect so. The photons in the laser beam travel in a straight line. Some will be reflected from the metallic surface of the balloon; others will bounce off the mirror. Because they are traveling radially out from the Earth and returning radially to the Earth, any curve will be negligible. (When Eddington was trying to test the General theory of Relativity, he used light traveling tangentially to the Sun's surface, close to the Sun's much larger mass, and was able to demonstrate a small bend in direction.)
For someone in the earth, the time would be bigger than 2r/cSince the Earth is in a gravitational well, time will pass more slowly on Earth. So I expect that the measured time will be smaller than 2r/c.