So, if my explanation of the aberration concentrated beam, 3 posts back, is right, what makes it is still valid for a hypothetically single source element, say one atom radiating light?
I think I might have explanation of "why moving atoms preferentially emit forwards" without the help of quantum theory.
This is because if we suppose the filament is formed of multiple small elements, then firing the light by the rear element should be seen first before the near element by the...
Nice explanation but still there are 2 points;
1) Are those two opposing effects, aberration and the inverse square law, exactly compensated? I am not familiar with the first.
2) Coming to the source, if the ground watcher draws a line between the filament of the lamp and the point where the...
Does it mean the density of the light on the wall of the lamp in the direction of the motion is apparently larger than the other side relative to the ground observer?
Just a question; if we have a very precise protractor, we can still be able to measure the sum of the angles of a small triangle on the surface of a sphere and confirm it is more than ##\pi##. Similarly, can a free faller be able to confirm his frame is not inertial when he has very precise...
When he mentioned " they will all continue to move with respect to one another in the same way as they would if they were not acted on by those forces., this means they move inertially.
Newton had already noticed this, and indeed he stated it, more or less, in Corollary VI to the laws of motion:
If bodies are moving in any way whatsoever with respect to one another and are urged by equal accelerative forces along parallel lines, they will all continue to move with respect to...
I agree with FactChecker. To see this in a simple way, imagine we are dealing with 1-D force acting on an object moving along x-axis back and forth around the center. If the force is instantenous, the object will continue moving to the right side of the axis to some point and then back in the...
How if instead of the sun, there is a magical structure pulls the earth with a long rope and rotates it. Still the pulling force has to propagate with some propagation speed due to the electromagnetic force at the rope's mollecular level. Will be any instability in the rotating earth orbit? In...
But this confuses me again because this would mean the proper time is not invariant. I mean in accelerating frame with no gravity, will the metric in front of ##dt## be a function of the acceleration? if yes, then how the proper time attached to the clock at rest in this frame is invariant?
But I think their metric are different in their respective accelerating frames. And the metric is a function of the acceleration not as simple as in Minkowski metric.
What I learnt is that the inertial space is locally flat like a flat tangent surface to the curved surface of a sphere for example. So if the bigger sphere is the galaxy, the free falling Sun is then a locally flat space. But again the sun is another curved spacetime surface. Does it mean there...
Also one more conflicting point for me. If the sun is also considered to be a free faller relative to the centre of galaxy, then the coordinates of it should be linear and the space-time is flat but we know that the coordinate of the solar system is curvilinear and the space-time is curved. So...
I got it, thank you. But again, why the absolute simultaneity does not hold in general relativity where the sun bends the space around it far away from the center?
So the free faller will not notice the gravitational wave. Why? the wave is a physical wave propagates outward from the center of the sun and the faller moves inward to the center of the sun, so logically they should meet!
This mean that not only the change in the sun mass, but also the information about the change in its position still needs to propagate in the form of gravitation wave. If, so can we detect this wave knowing that the sun is moving inside the galaxy?
I don`t understand why there should be an instantaneous propagation speed in a solar system where the mass of the sun is stable over the time. I do not feel this is the correct answer, what I missed here?. Even from the history, Einstein looked at it from different view point. He thought that...
I am trying to understand why the special relativity is not suitable for describing the gravity.
Consider a counterexample assuming it is the suitable and the space-time containing a gravitational mass is flat. Then one could describe the acceleration of a test particle from his inertial frame...
Just a bit of calculus, the equation of classical potential at a distance ##r## from the source is given by,
$$\Phi=\frac{-1}{r}$$
Taking the second derivatives with the respect of ##r## will give ##\frac{-2}{r^3}##, why should it be zero?
If the field is measured at distance ##r## from the center of the mass, then it should satisfy or be approximated to Poisson equation.
$$\bigtriangledown ^2 \Phi=4 \pi G \rho$$
Now $$\Phi=\frac{1}{2}g_{00}$$
So, given that ##T_{ij}## is a representative of ##\rho##, ##g_{00}## not Ricci tensor...
I start to understand the point but still more to go!
Consider a test particle in the spacetime region outside a massive body, such as a planet around the Sun, should the space at a distance ##r## from the center of the Sun but outside the surface of the Sun have a vanishing SET and Ricci...
I will try to be more clear. Einstein field equation equates the left hand side which is represented by Einstein tensor, or Ricci tensor, with the right hand side which is represented by energy momentum tensor.
When Einstein in his famous paper, spoke about vanishing Ricci tensor in a...
I am still confused about one thing, having said that Ricci tensor is nill does not help in calculating the equation of motion or geodescics, right? I mean to calculate the trajectory of particle in graph C which represents the gravity, Ricci must not be zero because the motion of the particle...
Nice trick, so the lesson is; wherever the space is flat, Ricci tensor will be always zero no matter how the metric is a function of coordinates because we can always find a new coordinates-system in the same space where the metric is constant.
But this is an indirect proof right? the complete...