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Deviation in Path between 2 particles due to Non-Uniform Gravitational Field

Physics Asked by Neev Shah on April 24, 2021

I came across this question while doing the exercises in the book Spacetime Physics by Taylor and Wheeler.

You are launched upward inside a railway coach in a horizontal position with respect to the surface of Earth, as shown in the figure. After the launch, but
while the coach is still rising, you release two ball bearings at opposite ends of the train and at rest with respect to the train. Riding inside the coach, will you observe the distance between the ball bearings to increase or decrease with time?

So, I understand that 2 particles close together in free fall are in an inertial frame and would stay at rest with respect to each other. But since they are falling towards the center of the earth, over time their separation would decrease if we consider the non local effects of the earth’s gravitational field.

What I am not able to understand intuitively is when the particles are going up (under no influence, hence still a local inertial frame), would their separation increase or decrease with time if we consider the non local effects of gravity? I would have guessed it would increase since it would be like the opposite of the first case, but that seems to be wrong. How do I intuitively visualize this?

One Answer

So, I understand that 2 particles close together in free fall are in an inertial frame and would stay at rest with respect to each other.

To make them stay at rest relative to each other, you need the tidal forces to vanish, which you can't do just by putting them in free fall.

But since they are falling towards the center of the earth, over time their separation would decrease if we consider the non local effects of the earth's gravitational field.

It would increase, not decrease.

What I am not able to understand intuitively is when the particles are going up (under no influence, hence still a local inertial frame), would their separation increase or decrease with time if we consider the non local effects of gravity?

It would decrease. Since it increases when they're falling down, it has to increase when you reverse the direction of time. The problem has time-reversal symmetry, so playing the movie of the motion backward is a valid motion.

Answered by user282979 on April 24, 2021

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