Cecil, I enjoyed your recent column on EP, but I suspect your spacesuit might have a vacuum leak.
In example #1 what you’re citing is s difference in perspective, nothing more. From the perspective of the accelerating floor (which presumably “knows” it is accelerating) you are not falling towards it, you’re about to become the “bug on the windshield”.
In #2, yes, it takes longer for that photon from the floor to reach the receptor, but the reason is that it simply has to travel further. The speed of light is a constant, and the time it takes to reach the receptor gives you the distance traveled. This is the same principal as used in the LASER based based speed guns employed by your friendly highway patrol. Time doesn’t change, the speed of light doesn’t change, only the distance traveled changes.
You might perceive that time is running slower or faster, depending on your position, but the reality is that the only thing which changes is distance.
I believe (Chronos and Stranger will no doubt shortly correct any error ) that what you have said is true to an extent, but misses the point. Once you have accepted 1 is true (the equivalence principle), and that 2 is true (the doppler effect), then 3 becomes true (time is a function of how fast things happen, such as the frequency of waves; relatively speaking, something happening at the same speed can nevertheless be happening faster or slower than it is elsewhere), and this leads to the conclusion of 4 (gravity being accelleration, different gravity potentials will result in the speed of things being relatively different).
What causes the mind to go <boing> at all this is having to think of being constantly accellerated as a result of gravity. Obviously true, but you don’t think of things that way, usually (he says as he sits firmly in his chair thanks to the accelleration of gravity :smack: ).
I’m having one difficulty with Cecil’s step #2. During the time that the photon was en route to the front receptor, how did the force that caused the front receptor to accellerate get there faster than light?
I’m assuming that the engines are in the back of the ship, but the general question remains regardless of where they’re placed. The example seems to assume that the whole ship accellerates as a unit.
if the time difference changes what frequency is measured on the ceiling … and color is based on frequency … does that mean that with enough change in speed, the color of the light could change also?
Of course it could It could even become something other than visible light. This happens all the time with the red shift caused by the ever-expanding universe.
So is there some place in intergalatic space, as far from any sources of gravity as you can go, where time runs faster? Has anyone calculated by how much?
When discussing the frequency shift of the light, Cecil has described “gravitational red shift”, which is a different phenomenon (also predicted by the general theory of relativity).
To clarify my previous post:
The main reason this explanation breaks is that both the observed (floor) and the observer (ceiling) are part of the same (accelerating) frame of reference. So time moves at the same speed at the ceiling and the floor.
And I am back to argue with myself. My above posts are wrong. Time is indeed slower on the ceiling relative the floor.
My misunderstanding was that I though that gravitational time dilation should depend the strength of the gravitational field/acceleration. However, it seems it is instead just dependent on gravitational potential energy. This makes it consistent with Cecil’s explanation.
) that what you have said is true to an extent, but misses the point. Once you have accepted 1 is true (the equivalence principle), and that 2 is true (the doppler effect), then 3 becomes true (time is a function of how fast things happen, such as the frequency of waves; relatively speaking, something happening at the same speed can nevertheless be happening faster or slower than it is elsewhere), and this leads to the conclusion of 4 (gravity being accelleration, different gravity potentials will result in the speed of things being relatively different).
