I believe only the eigen states of energy are the stationary states and do not depend on time, so if we are measuring spin eigen states, they could be time dependent. Isn't the time independent Schrodinger equation a energy eigen value equation?
When we are measuring the spin of the electron in the experiment, we choose the spin property as its eigen state for the measurement. The eigen vectors corresponding to these states could be time dependent. Can we still break the problem into solving time independent Schrodinger Equation and...
Hi Vanadium,
Actually I was reading about the Penrose interpretation of Quantum Mechanics, where he assumes that the state vector reduction occurs only if the difference between the alternatives is equal or greater than a graviton level. He then says that matter having mass near the Planck Mass...
Hi all,
According to quantum mechanics, the graviton is the measure of the smallest amount of curvature possible in space-time. I read that the mass which would be required to create this curvature is Planck Mass which is close to the value 10^-5g.
But the elementary particles, like electrons...
I know all this and I in my original question I did not ask for reason as to why clocks in gravity run at different speeds. I was trying to ask about its implications.
This is not true. The difference in gravitational potential between any two points inside hollow sphere is zero, so time is not...
If you are considering dilation w.r.t to clock outside the spherical shell, then I think you are wrong in saying that time does not have extrinsic curvature, now using the correct terminology according to you. This is because as we cross the boundary of the shell we would see the curved...
As I have already said I am not talking about curvature but curvilinear time coordinate:
Also I do not understand what do you mean by time dilation inside a hollow sphere. Since it has no gravitational field, time would flow at same rate at any position inside hollow sphere. So when you are...
Einstein's idea of Equivalence Principle was that freely falling reference frames can be "locally" considered inertial, which he knew how to deal with using SR. Based on this idea, Einstein argued what would happen in a gravitational field. And then found that accelerated frames could also be...
Hi Smattering, as I said earlier, I am not trying to define curvature in one dimension. I am only talking about the curvilinear time coordinate which is used to explain the falling of the object "near" Earth's surface as is shown in the video, so I am neglecting the tidal effect. I understand...
In Minkowskian space distance is measured by:
In Rindler coordinates it changes to:
What I am saying is we cannot use the Minkowskian formula to calculate the distances in an accelerated frame. Special relativity holds only for the frames in which the above Minkowskian distance is invariant.
The curvature of time axis is what I am calling time warping.
This is true, what I am saying is we can consider this time "warping" or the curvature of the time axis as can be seen in the video to be the gravitational time dilation. In other words, the difference in the clock rates at different...
I think special relativity is valid where Minkowskian distance in spacetime is invariant between various frames of reference. This is not the case with the accelerated frames where, as you said, distance is measured with different metric.
Could you please explain the reason behind this. I see no flaw in saying that gravitational time dilation is time warping. I think the constant speed of light in the inertial frames is the cause of this time dilation which is manifested as a curved time (locally) in a gravitational field.