Time dilation due to gravitation forces and velocity

[ronald_hinh]

TL;DR Summary

I'm trying to understand what the time dilation looks like when moving through space and then approaching a planet's gravity field.

I'm trying to understand what the time dilation looks like when moving through space and then approaching a planet's gravity field. So I have the broad understanding that if you are moving near the speed of light in a spaceship, your clock ticks normal but the clocks on other stationary objects that you observe in space appear to tick faster. As you get closer to a planet, the gravitational forces also slow down time. If you continue to move through the gravity of the planet at the same speed as you were before, then from an outside observer's reference, your clock will be even slower than before. This is correct? If the ship has velocity inside the gravity of the planet, from an outside observer, the ship's clock will still ticker slower than the planet's.

So for example, object A is you moving in the spaceship moving at some velocity. Object B is some planet like Mars. Object C is a planet caught in the pull of a black hole (like in Interstellar).

Lets say we set a marker for the time for all 3 objects to start at 9:00AM from the frame of reference of Object A:

Object A's (ship) clock initially: 9:00 AM
Object B's (Mars) clock initially: 9:00 AM
Object C's (blackhole planet) clock initially: 9:00 AM

How would each clock look assuming Object A remains near the speed of light and if 1 minute passes?
These are just arbitrary time scales but I just really need to understand if something is faster or slower from the ship's frame of reference:

Object A after 1 minute: 9:01 AM
Object B after 1 minute: 9:08 AM (from Object A's frame of reference)
Object C after 1 minute: ? (would this be greater than 8 minutes or less than 1 minute?)

And then how will this change if the ship is inside the gravity field of either B or C to make a notable difference?

I can't wrap my head around this. Also if anyone has any good article references that would help me understand that would be great.

Thanks

 

[PeroK]

It might be better to focus on a simple scenario. There is an object $A$ at rest relative to a planet or star at some radial distance $R$. And, a second object $B$ in a circular orbit at the same radial distance.

According to a distant observer, also at rest relative to the planet or star, $A$'s time will be dilated due to gravitational time dilation and $B$'s time will be further dilated due to the orbital velocity.

 

[Orodruin]

Summary:: I'm trying to understand what the time dilation looks like when moving through space and then approaching a planet's gravity field.

So I have the broad understanding that if you are moving near the speed of light in a spaceship, your clock ticks normal but the clocks on other stationary objects that you observe in space appear to tick faster.

This is incorrect. You will find clocks moving relative to you to tick slower, not faster. However, this is also symmetric. In an inertial frame frame where you are moving, your clock will appear to run slow. This is not a contradiction but a consequence of simultaneity depending on the frame.

 

[ronald_hinh]

It might be better to focus on a simple scenario. There is an object $A$ at rest relative to a planet or star at some radial distance $R$. And, a second object $B$ in a circular orbit at the same radial distance.

According to a distant observer, also at rest relative to the planet or star, $A$'s time will be dilated due to gravitational time dilation and $B$'s time will be further dilated due to the orbital velocity.

Thanks I think that helps me understand it a lot more.

This is incorrect. You will find clocks moving relative to you to tick slower, not faster. However, this is also symmetric. In an inertial frame frame where you are moving, your clock will appear to run slow. This is not a contradiction but a consequence of simultaneity depending on the frame.

Hm ok I am just a little confused then. If a ship leaves Earth traveling at the speed of light, time on ship will tick slower than on the earth. So when the ship returns, more time would have passed on earth. Isnt this still true from the ships frame of reference? If the clock on Earth actually ticks slower from the ships reference, how can more time pass when it returns to earth?

 

[anuttarasammyak]

Isnt this still true from the ships frame of reference? If the clock on Earth actually ticks slower from the ships reference, how can more time pass when it returns to earth?

In SR Earth remains at rest in a IFR. Ship going and coming back are at rest in two different IFRs. Symmetry breaks here.

 

[Halc]

If a ship leaves Earth traveling at the speed of light, time on ship will tick slower than on the earth. So when the ship returns, more time would have passed on earth. Isnt this still true from the ships frame of reference? If the clock on Earth actually ticks slower from the ships reference, how can more time pass when it returns to earth?

A ship cannot travel at light speed relative to anything. So say it just goes real fast.
Yes, more time will have elapsed on Earth due to the trip out and back.
The ship has no single inertial frame of reference, so 'the ship's frame of reference' is an accelerated one, and yes, this is true of an accelerated frame. Clocks in the direction of acceleration tick faster, and those behind tick slower, all in proportion to the separation between them.
Relative to anyone inertial frame (such as the outbound frame, just to pick one), the out-and back traveler is moving faster than Earth on average, so his clock accumulates less time.

 

[phinds]

If a ship leaves Earth traveling at the speed of light, time on ship will tick slower than on the earth.

Absolutely not. The clocks on both places will tick at one second per second. You are confusing time dilation with differential aging. Yes, there is a time difference when they meet up again but that is NOT because their clocks tick at different rates, it's because they have taken different paths through space-time and so their clocks have ticked a different number of seconds. Exactly like if two cars leave NY and travel to Boston, both going 60 mph but taking different routes their odometers will show a difference when they meet up, but not because they were traveling at different speeds.

 

[Orodruin]

Hm ok I am just a little confused then. If a ship leaves Earth traveling at the speed of light, time on ship will tick slower than on the earth. So when the ship returns, more time would have passed on earth. Isnt this still true from the ships frame of reference? If the clock on Earth actually ticks slower from the ships reference, how can more time pass when it returns to earth?

I wrote a PF Insight on this quite some time ago https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/

 

[PeterDonis]

Moderator's note: An off topic subthread has been deleted.