Time Dilation: Direction of Motion's Effect

[Lars1408]

Earth moves through space in a certain direction at a certain speed. Moving faster slows down your clock while moving slower increases your clock.

Does this mean that the direction your moving in has an effect on time dilation? In other words, if you move along with the earth’s initial speed (Vearth+Vspeed) will your clock go slower than if you were to go against its initial speed (Vearth-Vspeed)?

 

[Ibix]

Moving faster slows down your clock while moving slower increases your clock.

This phrasing implies that there is an absolute sense in which some things are moving faster than others. This not correct. A correct statement is that clocks moving relative to you tick slowly as measured by you.

Does this mean that the direction your moving in has an effect on time dilation?

No. Space is homogeneous and isotropic as far as we are aware. Attempts to detect the motion of the Earth relative to a notional ether provided null results, which eventually led us to relativity theory.

 

[PeroK]

Moving faster slows down your clock while moving slower increases your clock.

This is not really true. There is no such thing as absolute speed or absolutely moving faster or slower. All motion is relative. You may be increasing your speed in one reference frame and descreasing your speed in another.

Does this mean that the direction your moving in has an effect on time dilation? In other words, if you move along with the earth’s initial speed (Vearth+Vspeed) will your clock go slower than if you were to go against its initial speed (Vearth-Vspeed)?

In the reference frame of the Sun, say, then an object on the surface of the Earth is moving due to both the Earth's orbit and its rotation. If you add further motion relative to the surface of the Earth, then the speed relative to the Sun may increase or decrease and hence the velocity-based time dilation in the Sun's frame may increase or descrease

This sitiuation is complicated by the presence of gravity, hence there is also a factor based on gravitational time dilation to take into account. Technically, that takes you into the realm of General Relativity.

 

[etotheipi]

No because $\gamma$ is a function of $\vec{v}^2$. But in your example time dilation calculated by someone in an inertial frame would sort of depend on the orientation of the velocity $\vec{v}'$ w.r.t. the Earth (itself with velocity $\vec{v}_E$ w.r.t. the inertial frame) literally just because it would factor into the measured velocity $\vec{v}$ in the inertial frame when you do the velocity addition. But nothing deeper than that

 

[Lars1408]

This is not really true. There is no such thing as absolute speed or absolutely moving faster or slower. All motion is relative. You may be increasing your speed in one reference frame and descreasing your speed in another.
In the reference frame of the Sun, say, then an object on the surface of the Earth is moving due to both the Earth's orbit and its rotation. If you add further motion relative to the surface of the Earth, then the speed relative to the Sun may increase or decrease and hence the velocity-based time dilation in the Sun's frame may increase or descrease

This sitiuation is complicated by the presence of gravity, hence there is also a factor based on gravitational time dilation to take into account. Technically, that takes you into the realm of General Relativity.

So if person A moves along Earth's orbit around to sun in the same direction as Earth at 100.000km/s and person B moves at the same speed along the orbit but in opposite direction (against Earth's initial orbital direction) than the time dilation of both person A and person B will be the same compared to someone on earth. But the clock of person A will move slower when compared to the sun's clock than the clock of person B compared to the sun's clock? Is this a correct interpretation?

 

[Lars1408]

No because $\gamma$ is a function of $\vec{v}^2$. But in your example time dilation calculated by someone in an inertial frame would sort of depend on the orientation of the velocity $\vec{v}'$ w.r.t. the Earth (itself with velocity $\vec{v}_E$ w.r.t. the inertial frame) literally just because it would factor into the measured velocity $\vec{v}$ in the inertial frame when you do the velocity addition. But nothing deeper than that

I don't really understand this, but thanks anyways

 

[PeroK]

So if person A moves along Earth's orbit around to sun in the same direction as Earth at 100.000km/s and person B moves at the same speed along the orbit but in opposite direction (against Earth's initial orbital direction) than the time dilation of both person A and person B will be the same compared to someone on earth. But the clock of person A will move slower when compared to the sun's clock than the clock of person B compared to the sun's clock? Is this a correct interpretation?

If we ignore gravitational time dilation and the rotation of the Earth, then yes. A simpler scenario is to take gravity and orbits out of the equation:

1) Clocks A, B and C are at rest relative to each other, and moving to the right at constant speed in some inertial reference frame. Call this frame S.

2) Clock A moves to the left and relative to B and clock C moves to the right relative to B. Both A and C have the same time dilation in B's reference frame.

3) All three clocks now have different time dilation in frame S. C has the greatest time dilation.

In general time dilation depends only on the speed of a clock relative to the inertial reference frame in which the time dilation is measured.

 

[Lars1408]

If we ignore gravitational time dilation and the rotation of the Earth, then yes. A simpler scenario is to take gravity and orbits out of the equation:

1) Clocks A, B and C are at rest relative to each other, and moving to the right at constant speed in some inertial reference frame. Call this frame S.

2) Clock A moves to the left and relative to B and clock C moves to the right relative to B. Both A and C have the same time dilation in B's reference frame.

3) All three clocks now have different time dilation in frame S. C has the greatest time dilation.

In general time dilation depends only on the speed of a clock relative to the inertial reference frame in which the time dilation is measured.

Thanks, good explenation

 

[Nugatory]

@Lars1408 your original question, "Does the direction of motion influence time dilation?" has been answered: It does not, all that matters is the relative speed.

There is one implication that you may not have fully appreciated.

Suppose that A and B are moving relative to one another. We can describe this situation by saying that A is at rest while B is moving in one direction, or that B is at rest while A is moving in the opposite direction (or we could say that they are both moving at different speeds, but that just complicates the analysis and brings in some unnecessary digressions, so we won't go there now).

This situation is symmetrical. If we choose the description in which A is at rest we will find that B's clock is running slow relative to A's clock, and if we choose the description in which B is at rest we will find that A's clock is running slow relative to B's clock - there is no frame-independent answer to the question "which one is time dilated?".