Let me try to word this another way.
I'm trying to see how, when viewing a process (transition between energy levels) from a relatively moving frame, the process appears to occur slower. I know you could answer "because time dilates," but I'm looking for a slightly deeper explanation. Again...
My question boils down to seeing how time dilation manifests in spontaneous transitions between energy levels (i.e. why looking at spontaneous transitions in a moving frame would appear to slow). Some good surrounding info in above posts, the link below might give the answer I'm looking for...
For the 4-force in SR you need a 1/gamma in the spring constant, the result is gamma^2 under the sqrt, hence the gamma overall, matching the time dilation equation.
Thanks all. Some of you mentioned a spring mass system and I can see how time dilation for that would naturally follow from relativistic mass increase, analogous to the light clock using constant c.
There are many posts about time itself changes and therefore everything changes, understood...
I know SR says experimental results are = in all frames and hence the transitions (and everything) must slow like the "light clock", but what I'm looking for is something analogous to the light clock argument, you might call it a more "direct" explanation (if it exists). Edit: might also call...
A common way to introduce time dilation is to show the example of a "light clock" which bounces photons back/forth and ticks each time a photon passes a certain point. Wikipedia does it this way, for example. From such a clock, it's easy to see why the constancy of the speed of light would...
Copy, thanks. I am thinking in our proper time, so in our proper time the BH never forms, right.
Understand your point with some time coordinates it does form.
Looking at Kruskal diagrams, it seems to me we should not be able to see evidence of black holes. Assuming our frame is a hyperbola of roughly constant ##r## in such a diagram, as the black hole's constituent mass comes together time slows (from our POV) to the extent that it never crosses the...
The book I'm reading (General Relativity: The Theoretical Minimum by Susskind) says the metric is approximately ##d\tau^2 = (1+2gy)dt^2 - dy^2## where the grav potential is ##gy## but yes I see this doesn't jive with stuff I see on Wikipedia. I must have misunderstood what this metric was...
Using an example of 1 space dimension and 1 time dimension, consider the metric ##d\tau^2 = a dt^2 - dx^2## near a heavy mass (##a>1##).
From what I've read a clock ticks slower near a heavy mass, as viewed from an observer far away. A clock tick would be representative of ##d\tau## right...
The Lorentz transformation ensures different inertial observers measure the same speed of light. Are there other transformations, or other ways to setup a "space-time" that also have this property of invariance? Is the Lorentz transformation the unique solution?
Thanks for the response. It seems like that argument, applied to a weighted die, would say that each side is equally probable. If I know the system (die), but not the state it is in (side faced up after rolling), then the condition of max uncertainty is a function of the weighting, not...
I'm reading "Statistical Mechanics: A Set of Lectures" by Feynman.
On page 1 it says that, for a system in thermal equilibrium, the probabilities of being in two states of the same energy are equal. I'm wondering if this is an empirical observation or if it can be derived from QM?
I think I understand. I realize that calling the entangled pair local to one another (because the wave function overlaps) is a bit satisfying at first, but of course there's still something "nonlocal" in a sense to "spread the information around the wavefunction's spatial extent."
Since the...