Undergrad Is Time Reversal Symmetry Truly Fundamental?

[Alfredo Tifi]

It is often told that fundamental laws are insensitive to +t/-t change. Let's try this one: a little mass m1 object is accelerating towards a big object M2, in -x direction in space and +t in time, due to gravity or following space-time free fall line (along a geodetic). Now, revert the video and look at the -t history. What happens is absolutely innatural. Am I not speaking of some fundamental law?

 

[jbriggs444]

It is often told that fundamental laws are insensitive to +t/-t change. Let's try this one: a little mass m1 object is accelerating towards a big object M2, in -x direction in space and +t in time, due to gravity or following space-time free fall line (along a geodetic). Now, revert the video and look at the -t history. What happens is absolutely innatural. Am I not speaking of some fundamental law?

A small object flying away from a big object and decelerating as it goes is natural and in complete accordance with the laws of classical mechanics. Any object launched with a velocity greater than or equal to escape velocity will follow such a free-fall geodesic trajectory. [If the incoming object fails to intersect with the surface of the big object, it will continue on just such an outbound path]

Edit: trajectories with less than escape velocity are reversible as well.

 

[Dale]

Now, revert the video and look at the -t history. What happens is absolutely innatural.

Why do you say it is unnatural?

In the simplest case we have $x(t)=0.5 g t^2+v_0 t+ x_0$. What do you get when you make the transformation $t \rightarrow -T$

 

[Alfredo Tifi]

... Any object launched with a velocity less than or equal to escape velocity will follow such a free-fall geodesic trajectory...

Thank you Jbriggs to help me recognizing a misconcept of mine :-)

 

[Alfredo Tifi]

Why do you say it is unnatural?

In the simplest case we have $x(t)=0.5 g t^2+v_0 t+ x_0$. What do you get when you make the transformation $t \rightarrow -T$

Sorry Dale. I just mistaken a spatial mirrored motion for a time inversion (repulsion instead of attraction).

 

[Dale]

No problem, I am glad we could help!

 

[Ralph Dratman]

It is often told that fundamental laws are insensitive to +t/-t change. Let's try this one: a little mass m1 object is accelerating towards a big object M2, in -x direction in space and +t in time, due to gravity or following space-time free fall line (along a geodetic). Now, revert the video and look at the -t history. What happens is absolutely innatural. Am I not speaking of some fundamental law?

To see the effects of time reversal in classical mechanics you just have to change the sign of all velocities -- that is, reverse their direction. In a gravity field the original, un-reversed falling object would be speeding up, falling faster and faster. Imagine you reverse the velocity. Now the object is moving upward, presumably because someone on the ground threw it up into the air. The object retraces its path, but this time its speed will be decreasing as gravity gradually slows it down. Then the graph of height versus time will be exactly the same.