Gravitational vs geodesic proper time

westwood
Messages
3
Reaction score
0
I've been trying to learn GR and I've been back and forth through Schutz's first course book. I think I understand the basic principals, but one thing still eludes me: a traveler in free fall travels along the geodesic, the path of longest proper time. If the path between two points passes through a strong gravitational field, it should take longer (more ticks on the traveler's clock) than it would have if the field had not been in the path. But as the traveler passes through the field, gravitational time dilation makes their clock show down (fewer ticks on the traveler's clock). Do these two effects compete against each other or am I missing something? Somehow I got it in my head that gravitational time dilation would somehow _cause_ the geodesic to have the longest proper time, but that doesn't seem to work. Please help straighten me out.
 
Physics news on Phys.org
IMO this is a good question, and shows that you're thinking about the right things and engaging actively with the material. Pat yourself on the back :-)

There's a good discussion of this kind of thing here: http://www.astro.ucla.edu/~wright/deflection-delay.html They analyze deflection of light by the sun. Newtonian physics predicts that the light will speed up (assuming light can be treated as a material particle that is initially moving at c), so it gets to its destination sooner. GR predicts that it will arrive late. There is a classic experiment by Shapiro that tested this. The slowing is directly related to the deflection according to the wave theory of light. I guess this isn't perfectly on target for your question, since you were asking about a material particle (for which proper time is meaningful), whereas this is all about light.

One thing that I think you may be messing up is that it sounds like you're interpreting least action as a comparison of field and no field, for a fixed path. Actually it's a comparison of different paths, for a fixed field.
 
This solution is wrong (I don't think gravitational time dilation is fundamental, and it's better to define it with some experiment in mind, and usually you need to be able to define an equivalent Newtonian potential, which is not always possible in general relativity), but I cannot resist.

Two clocks start at some height above the ground. The one that drops will follow the geodesic and fall deeper and deeper into the potential well, running slower and slower compared to the one that stays in the air.
 
Last edited:
Thanks for all your responses. I think my problem is that I was trying to compare a trajectory in the cases where it does and does not pass through a gravitational field, when in fact there must be two different trajectories.
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
Back
Top