Time-reverse symmetry of the principle of relativity

[JesseM]

Not to belabor this, but if a mass loses velocity (decelerates, without changing direction) in a frictionless environment due to gravity alone, in which direction must the source of gravitational force be with respect to the mass' velocity vector - and is that direction the same for both the forward and reverse time scenarios?

One simple example would be a ball tossed upwards on the moon's surface--as its height increases, its velocity decreases, at least until it turns around (if the ball's velocity is greater than or equal to the escape velocity it'll never turn around, of course). What would be the time-reverse of this? Well, it would just be a ball moving downwards towards the moon's surface, its velocity increasing as it falls. Both imply that the gravitational force is pointing in the same downward direction.

 

[Chrisc]

Kev, that is not my point.
I have offered no proof of the mechanics. They follow from the time forward mechanics.
When a small mass is brought to rest by a larger, the time-reverse is a large mass brought
to rest by a smaller, even when the conservation of kinetic energy is considered.
I have not mentioned the kinetic energy as it does not change the principle of the mechanics.
Go ahead and conserver the kinetic energy of the collision forward in time so as to reduce
the velocity of the larger mass after collision from what I've shown.
It's total kinetic energy is still such that it is too great to be assumed by the smaller mass
when the collision is reversed.
But as such a collision occurs forward in time, it's reverse must follow the same(inverse)
kinematics. If not the second law would predict increased entropy backward in time.

Let me make it clear I am not disputing the time-reverse symmetry of the laws of dynamics,
the time-reverse asymmetry of the second law of thermodynamics,
the time-reverse symmetry of SR or the conservation of energy.

I am pointing out and questioning the conflict or discrepancy that arises
when one attempts to hold each true under the time-reverse mechanics
of a particular event observed from both inertial frames of the bodies in question.

You can't have your cake and eat it too.

You must in principle hold to one of the following:
One can claim the second law does not statistically forbid
such dynamics but qualifies them as so astronomically improbable
that they have never (and probably never will) been observed.
But in taking this position, one must then explain how and why
the time reverse version of the same event when observed
at rest with respect to the smaller mass, is not ALSO as astronomically
improbable but it is in fact the ONLY probable dynamics.
This is not a trivial exception to the law, but the necessary norm of the law
under time-reverse symmetry of the dynamical laws.
This fails the principle of the second law.
-OR-
One can take the position that time-reversal requires time defines a
continuous symmetry of dynamics whereby time is not a simple
reversal of the order of kinematics but a physical dynamic that
will produce, indeed demand the astronomically improbable events
of decreasing entropy.
This fails the principle of time-reverse symmetry of the laws.

In taking either position, one realizes that the observed(considered)
mechanics present, in principle, a discrepancy between frames.
A discrepancy that implies, depending on which laws one chooses
to uphold and which one chooses to question, a unique or
privileged inertial frame of reference in that it distinguishes
relative motion from absolute motion with respect to these laws of dynamics.

DaleSpam, as I mentioned above I am not disputing the time-reverse symmetry
of the laws of dynamics in what they express as you've written them above.
When in previous posts I've said, the laws are violated
I am simply pointing out that they must be, or the second law must be.
If you prefer to hold the laws symmetric through time-reversal, I won't argue
that choice, but I will ask you to explain how you rationalize that choice against
its contradiction of the second law.
As for the time-reverse symmetry you offer in the orbital example, it is not
an example in which the principle of time-reverse symmetry of dynamics is tested.
You've given an example of the quantitative symmetry of kinematics through
time reversal. Until your example includes a change in dynamics
in the forward time scenario, the time-reverse symmetry of the "dynamical" laws
governing that change are not tested.

JesseM, a ball tossed upwards on the moon is under the force you impart by throwing
(momentum, kinetic energy)and the gravitational forces of the moon and the ball.
Let the ball free fall from infinity and then reverse the film. Why is the ball being
"pushed" away with less force as the distance increases?
Is the ball's decelerating frame an inertial frame?

I am out of town for the next few days, but I look forward to your answer
to the ball toss question JesseM.


GeorgeJones, this is a struggle, but it is still primarily a question of relativity.

 

[JesseM]

Kev, that is not my point.
I have offered no proof of the mechanics. They follow from the time forward mechanics.
When a small mass is brought to rest by a larger, the time-reverse is a large mass brought
to rest by a smaller, even when the conservation of kinetic energy is considered.
I have not mentioned the kinetic energy as it does not change the principle of the mechanics.

Do you disagree that the example I provided in my last response to you, an elastic collision where a large mass is brought to rest by a smaller one which has a smaller initial velocity, makes perfect sense in the time-forward version? The point, again, is that your description is far too vague, the only situation where a collision would seem strange in reverse is if there is a change in the linear kinetic energy after the collision (an inelastic collision), and in this case all inertial frames will agree on whether the linear kinetic energy increased or decreased when they analyze the same collision.

JesseM, a ball tossed upwards on the moon is under the force you impart by throwing
(momentum, kinetic energy)and the gravitational forces of the moon and the ball.
Let the ball free fall from infinity and then reverse the film. Why is the ball being
"pushed" away with less force as the distance increases?

It isn't being pushed in the reverse movie, it's still being pulled. That's what time-symmetry means, that the laws are exactly the same whether you play the movie forward or backward, meaning there's no way to tell whether a given film is actually being played forward or backwards.

In your example of a ball free falling from infinity, the reverse version just looks like a ball shot away from the planet with an initial velocity greater than or equal to the planet's escape velocity. In this case it will continually be moving away from the planet, but its velocity away from the planet is constantly decreasing because the planet is constantly exerting force back in the direction of the planet (though as the distance increases the force decreases because gravitational force follows an inverse-square law). Do you understand that if we toss a ball upwards and its velocity decreases as it rises, this is because the planet is pulling on the ball, not pushing?

Is the ball's decelerating frame an inertial frame?

What do you mean by "the ball's decelerating frame"? Do you mean a coordinate system where the ball is at rest while the planet moves away from it, or do you mean a frame where the ball is decelerating as it moves away from the planet? If the former, no, it's not inertial, at least not in Newtonian mechanics which is what we're discussing (in general relativity any freefalling object will be at rest in a local inertial frame which only covers an infinitesimally small region of spacetime). If the latter, that wouldn't be the "ball's frame", because when you talk about an object's frame in physics that's always shorthand for the object's rest frame, if an object is decelerating in a given frame, that isn't the object's own rest frame obviously. You can certainly use an inertial frame to analyze the behavior of an accelerating object though, and that's what's normally done in Newtonian mechanics when we look at the motion of a projectile fired away from a planet, using a frame where the center of mass of the planet/object system is defined to be at rest (if the object's mass is negligible compared to the planet's, then this is just the rest frame of the planet's center).

 

[Dale]

When a small mass is brought to rest by a larger, the time-reverse is a large mass brought to rest by a smaller.

No, the time-reverse of "a small mass being brought to rest by a larger" is "a small mass being accelerated from rest by a larger". From this comment and from previous comments about time-reversed gravity being repulsive it is clear that you don't even understand the concept of time-reversal.

DaleSpam, as I mentioned above I am not disputing the time-reverse symmetry
of the laws of dynamics in what they express as you've written them above.
When in previous posts I've said, the laws are violated
I am simply pointing out that they must be, or the second law must be.
If you prefer to hold the laws symmetric through time-reversal, I won't argue
that choice, but I will ask you to explain how you rationalize that choice against
its contradiction of the second law. As for the time-reverse symmetry you offer in the orbital example, it is not
an example in which the principle of time-reverse symmetry of dynamics is tested.
You've given an example of the quantitative symmetry of kinematics through
time reversal. Until your example includes a change in dynamics
in the forward time scenario, the time-reverse symmetry of the "dynamical" laws
governing that change are not tested.

Is English a second language for you? Frankly, I am beginning to think that either there must be some severe language barrier or you are being deliberately obtuse. Between kev, JesseM, and myself all of your points have been correctly explained multiple times. Your responses often border on word-salad, and your useage of physics terminology is generally nonsensical and illogical.

I cannot tell if by "second law" you mean "the second law of thermodynamics" or if you mean "Newton's second law". So here is my last try, and I will address both the second law of thermo and Newton's second law.

When we say that a law is symmetric under time reversal we mean that it has the same form wether expressed in terms of t or tau = -t.

Newton's second law:
(1) f = m \frac{d^2x}{dt^2} making the substitution t = -tau we obtain the time-reversed law
(2) f = m \frac{d^2x}{d(-\tau)^2} = m \frac{d^2x}{d\tau^2} which is the same form as (1) so Newton's 2nd law is time-reverse symmetric.

Newton's law of gravitation:
(3) \frac{d^2x}{dt^2} = -\frac{G m x}{|x|^3} making the substitution t = -tau we obtain the time-reversed law
(4) \frac{d^2x}{d(-\tau)^2} = \frac{d^2x}{d\tau^2} = -\frac{G m x}{|x|^3} which is the same form as (3) so Newton's law of gravity is time-reverse symmetric.

Second law of thermodynamics:
(5) \frac{dS}{dt} \geq 0 making the substitution t = - tau we obtain the time-reversed law
(6) \frac{dS}{d(-\tau)} = -\frac{dS}{d\tau} \geq 0 which is not the same form as (5) so the second law of thermodynamics is not time-reverse symmetric.

You can use the same approach for any law. It is really not any more difficult or complicated than this, and there is no need to conjure up example after example when you can see the symmetry (or asymmetry) in general from the laws themselves.

 

[Chrisc]

Do you disagree that the example I provided in my last response to you, an elastic collision where a large mass is brought to rest by a smaller one which has a smaller initial velocity, makes perfect sense in the time-forward version? The point, again, is that your description is far too vague,

I don't disagree. Yes it makes perfect sense.
My description seems vague because you are trying to read too much into it.
I am talking about the principles of the laws not the time-reverse symmetry of the equations.
Perhaps it will be more obvious to you if I use your example.

A ball in free fall from infinity to the moon.
The gravitational potential of the ball at infinity is theoretically infinite.
The gravitational potential of the same ball upon "approaching" the surface of the moon is
by comparison infinitesimal.
Between infinite and infinitesimal there exists a substantial difference in potential energy.
When your film runs backwards this difference must be reasoned.
How?
There is no one throwing the ball. There is no way to reason the motion of the ball
"decelerating" (negative acceleration) away from the moon except via the
gravitational energy of each.
The gravitational potential must be inverted to account for the motion of the ball.
Do not think to include the collision of the ball as the energy that launches
it back into space. The event is the free-fall of the ball, not the collision.
The free-fall can be explained without the collision, so the inverse of this free-fall must
also be explained without the collision.

When the ball is in free fall to the moon, the ball's frame is an inertial frame.
When the ball is in the reverse of free fall away from the moon under no more
influence than inverted gravitational potential, is it also an inertial frame?

 

[Chrisc]

No, the time-reverse of "a small mass being brought to rest by a larger" is "a small mass being accelerated from rest by a larger". From this comment and from previous comments about time-reversed gravity being repulsive it is clear that you don't even understand the concept of time-reversal.

According to your distinction between the kinematics of time-reversal above,
you must then admit the time-reversal of "a small mass accelerating a larger mass"
is "a larger mass being brought to rest by a smaller".
You have simply chosen a preferred frame as did I. In either case the energy
transfered between the masses when the larger is brought to rest or as you prefer
to state it, the smaller is accelerated, contradicts the second law of thermodynamics.

English is my first language.
I think the language barrier is a matter of preconceptions.
You assume I don't know the meaning of the time-reverse symmetry of the laws.
Instead of trying to understand what I'm saying you keep restating what you
think I don't understand.
There are three considerations to the symmetry of the dynamical laws under time-reversal.
The symmetry of the equations:
the quantitative equality of the statements when time is + or -.

The symmetry of the principle of the law:
the principle is unchanged when time is + or -.

The symmetry of the mechanics governed by the law:
the kinematics "AND" dynamics are unchanged when time is + or -.

You have pointed out the symmetry of the quantitative statements of the equations.
I assume you would then agree that the principle of causality remains unchanged
during time-reversal, even though what we identify as cause and effect in the
forward time event become reversed to uphold the law in the time-reverse event.
Effect becomes cause and cause becomes effect.
If you agree, what is the answer to the question I asked of JesseM regarding the
motion of the ball moving away from the moon in time-reversal?
What is the "cause" of the balls motion with respect to the moon?

 

[Dale]

Oh well Chrisc, I really tried to help you understand here. Enjoy your ignorance, it appears deliberate to me.

If you agree, what is the answer to the question I asked of JesseM regarding the motion of the ball moving away from the moon in time-reversal? What is the "cause" of the balls motion with respect to the moon?

I'm sure JesseM will point out all of the incredibly obvious and basic mistakes you made, starting with the second sentence of your moon example.

 

[Antenna Guy]

...all of the incredibly obvious and basic mistakes you made, starting with the second sentence of your moon example.

Upon reading of the fourth sentence of the referenced example, it seems obvious that the word "energy" should be understood to follow the word "potential" in the second and third sentences. If this clarified wording is still an "obvious and basic mistake", I'm curious to hear why you think so.

Regards,

Bill

 

[yuiop]

There is no one throwing the ball. There is no way to reason the motion of the ball
"decelerating" (negative acceleration) away from the moon except via the
gravitational energy of each.
The gravitational potential must be inverted to account for the motion of the ball.
Do not think to include the collision of the ball as the energy that launches
it back into space. The event is the free-fall of the ball, not the collision.
The free-fall can be explained without the collision, so the inverse of this free-fall must
also be explained without the collision.

Here is an experiment you can actually do in your back garden. Film a ball released from a fixed height onto a trampoline and film the rebound (almost) back to its starting point. When the film is played backward it will be hard to tell the difference from the film playing forward. Sure the final height is not as high as the starting height but that is due to friction from the air and the trampoline. If there was no air and the trampoline was frictionless it would not be possible to tell which way the film was playing. The ball is being accelerated downwards as it falls AND as it rebounds. With no energy losses the situation is perfectly symmetrical. With energy losses the second law of thermodynamics comes into play and gives an arrow of time that removes the symmetry.

When the ball is in free fall to the moon, the ball's frame is an inertial frame.
When the ball is in the reverse of free fall away from the moon under no more
influence than inverted gravitational potential, is it also an inertial frame?

Yes.

 

[JesseM]

I don't disagree. Yes it makes perfect sense.
My description seems vague because you are trying to read too much into it.
I am talking about the principles of the laws not the time-reverse symmetry of the equations.
Perhaps it will be more obvious to you if I use your example.

Do you agree that for any system governed by time-reversible equations, if you film a situation where there is no change in entropy, there will be absolutely nothing to tell a physicist whether the film is being played backwards or forwards? If you disagree with this, it's apparent that you don't understand what "time-reverse symmetry" actually means, this is logically implied by time-reversible equations.

A ball in free fall from infinity to the moon.
The gravitational potential of the ball at infinity is theoretically infinite.

Actually, by convention the gravitational potential is usually treated as being zero at infinity, and being negative at finite distances, the absolute value of the negative potential being greater the closer you approach the object's surface.

The gravitational potential of the same ball upon "approaching" the surface of the moon is
by comparison infinitesimal.

No, it'd be some finite negative number.

Between infinite and infinitesimal there exists a substantial difference in potential energy.

The difference in potential energy would be finite; zero at infinity, some finite negative number at the surface. Of course where you set the zero is somewhat arbitrary, you could define the potential function to be zero at the surface, but in this case it would have some finite positive value at infinity (the difference between the potential at the surface and the potential at infinity would have to be the same regardless of where you set the zero--the potential is always larger at greater distances from the surface).

When your film runs backwards this difference must be reasoned.
How?
There is no one throwing the ball. There is no way to reason the motion of the ball
"decelerating" (negative acceleration) away from the moon except via the
gravitational energy of each.
The gravitational potential must be inverted to account for the motion of the ball.

You're totally confused about basic vector analysis here. If a ball is thrown away from the moon, and the gravitational force vector is pointing back at the center of the moon, then naturally the ball's speed in the "upward" direction will be decreasing. This does not require any change in the potential function (the potential must be greater at bigger distances, since increasing potential energy balances out decreasing kinetic energy as the ball's speed decreases while it's moving away from the moon--the sum of kinetic plus potential energy must always be conserved!) Perhaps you should study some basic Newtonian mechanics before pontificating about how everything physicists believe about time-reversal symmetry is wrong.

When the ball is in free fall to the moon, the ball's frame is an inertial frame.

Not in Newtonian mechanics it isn't. In Newtonian mechanics, the ball is being acted on by a force (gravity), so it is not moving inertially. In general relativity a freely-falling object does have a local inertial rest frame, but I think you need to review basic Newtonian physics before trying to tackle general relativity.

 

[Chrisc]

Oh well Chrisc, I really tried to help you understand here. Enjoy your ignorance, it appears deliberate to me.I'm sure JesseM will point out all of the incredibly obvious and basic mistakes you made, starting with the second sentence of your moon example.

DaleSpam, I am grateful for the time and energy you put into this thread.
I am sorry you think it was wasted.
As poorly as I may be communicating my point, I am most definitely
not being deliberately argumentative. My point has not been addressed
as it has been bogged down in the manner I presented it.
You may have noticed JesseM did not answer the question but turned it
once again into a ball being tossed not a ball in free-fall.

 

[Chrisc]

Here is an experiment you can actually do in your back garden. Film a ball released from a fixed height onto a trampoline and film the rebound (almost) back to its starting point. When the film is played backward it will be hard to tell the difference from the film playing forward. Sure the final height is not as high as the starting height but that is due to friction from the air and the trampoline. If there was no air and the trampoline was frictionless it would not be possible to tell which way the film was playing. The ball is being accelerated downwards as it falls AND as it rebounds. With no energy losses the situation is perfectly symmetrical. With energy losses the second law of thermodynamics comes into play and gives an arrow of time that removes the symmetry.

Kev, in other words...
If it weren't for the second law of thermodynamics, we would
observe the time-symmetric mechanics of the laws.
The second law of thermodynamics is a law of observation, a law
based on empirical evidence not principle.
It can be statistically derived from the mechanics of closed systems, but
this too is evidence not principle.
That the dynamical laws do NOT display mechanics of time-reverse symmetry
is still one of the greatest mysteries in physics.
This means either the dynamic laws are wrong, or the second law of thermodynamics
is evidence of a yet undiscovered dynamical law.
If we observe the principles at work in the dynamic laws in the simplest form possible
so as to remove the second law of thermodynamics from our considerations,
we should be able to reason from the principles of the laws alone, the dynamics
of the time-reverse mechanics they present.
As we cannot agree on the mechanics of my example, we will use JesseM's.
The film of a ball in free fall from any height above the major mass for any
duration of time up to but NOT including the collision.
You will agree this forward time event includes the dynamical law
of gravitation and excludes the second law of thermodynamics?
Watching this film in reverse, the ball begins at some small height above the major
mass and moves away with constantly decreasing velocity.

How do the dynamics of gravitation account for the time-reverse mechanics
of the ball?
Upon careful consideration, I think you will find the answer is frame dependent.
Which is the point of my original post.

 

[Chrisc]

You're totally confused about basic vector analysis here. If a ball is thrown away from the moon, and the gravitational force vector is pointing back at the center of the moon, then naturally the ball's speed in the "upward" direction will be decreasing. This does not require any change in the potential function (the potential must be greater at bigger distances, since increasing potential energy balances out decreasing kinetic energy as the ball's speed decreases while it's moving away from the moon--the sum of kinetic plus potential energy must always be conserved!) Perhaps you should study some basic Newtonian mechanics before pontificating about how everything physicists believe about time-reversal symmetry is wrong.

JesseM, the event is isolated to the free-fall of the ball, not the throwing and free-fall of the ball.
Is there a way to interpret the dynamics of gravitation when it is still as you say, an "attractive"
force under time-reversal, that explains the ball moving "away" from the moon?

 

[JesseM]

JesseM, the event is isolated to the free-fall of the ball, not the throwing and free-fall of the ball.
Is there a way to interpret the dynamics of gravitation when it is still as you say, an "attractive"
force under time-reversal, that explains the ball moving "away" from the moon?

Sure, you can imagine the ball falling in from outer space, experiencing an elastic collision with the surface of the moon (so there's no change in entropy), and bouncing away. And if you're willing to have a spontaneous decrease in entropy, you could have a ball initially at rest on the surface, then random molecular movements happen to converge to give the ball a major "kick" away from the surface (the time-reverse of a ball falling in from space and landing splat on the surface, its kinetic energy dispersed as heat into the ground).

Either way, the question of how the ball got going in the first place is logically separate from the question of whether we need attractive or repulsive gravity to explain the motion of the ball as it moves away from the moon, specifically the fact that the ball's speed away from the moon is continually decreasing as it moves further away. There can be only one correct answer to this question: gravity must be attractive and constantly pulling the escaping ball back in the direction of the center, decreasing its outward velocity, if gravity were repulsive the ball's outward velocity would be continually increasing as it moved away from the moon. Again, just basic vector analysis.

 

[Chrisc]

Sure, you can imagine the ball falling in from outer space, experiencing an elastic collision with the surface of the moon (so there's no change in entropy), and bouncing away. And if you're willing to have a spontaneous decrease in entropy, you could have a ball initially at rest on the surface, then random molecular movements happen to converge to give the ball a major "kick" away from the surface (the time-reverse of a ball falling in from space and landing splat on the surface, its kinetic energy dispersed as heat into the ground).

Again you have inserted a collision to explain the attractive force of gravity during time-reversal.
Are you saying there is no way to explain the time-reverse mechanics of gravitation?

Either way, the question of how the ball got going in the first place is logically separate from the question of whether we need attractive or repulsive gravity to explain the motion of the ball as it moves away from the moon,

Gravitation is "how the ball got going in the first place" in the time forward version of the event.
Gravitation is all that comes into play in the time-reverse version as well since the event
begins and ends with the free-fall of the ball. (i.e. without any collision taking place)
So the motion of the ball away from moon in the time-reverse version has everything to do
with the force of gravity.

... specifically the fact that the ball's speed away from the moon is continually decreasing as it moves further away. There can be only one correct answer to this question: gravity must be attractive and constantly pulling the escaping ball back in the direction of the center, decreasing its outward velocity, if gravity were repulsive the ball's outward velocity would be continually increasing as it moved away from the moon. Again, just basic vector analysis.

It would seem the only answer when gravity is a force, but not when it's the geometry of space-time.

 

[JesseM]

Again you have inserted a collision to explain the attractive force of gravity during time-reversal.
Are you saying there is no way to explain the time-reverse mechanics of gravitation?

If you take the time-forward version and play it backwards, everything that happens can still be explained with exactly the same laws. Not sure what part of this is confusing you.

Gravitation is "how the ball got going in the first place" in the time forward version of the event.

Uh, have you forgotten that "first" and "last" are naturally reversed in the time-reversed version? In the time-forward version, the "beginning" is the ball in deep space, being pulled towards moon by gravity, and the "end" is it colliding the moon. So naturally, in the time-reversed version the beginning is the time-reversed version of the collision which propels the ball outward. Do you disagree that everything in the time-reversed version can be explained using the same laws? It's easiest to see if we just imagine a ball that repeatedly collides elastically with the moon so it falls from some height, bounces upward to exactly the same height, falls back down and bounces again, forever. The time-reversed version of this movie will look identical to the time-forward movie.

Gravitation is all that comes into play in the time-reverse version as well since the event
begins and ends with the free-fall of the ball. (i.e. without any collision taking place)

I thought your scenario involved a collision, but fine, whatever time you define as the endpoint of the time-forward version (a time before the ball actually hits the moon), take the instantaneous velocity at that final moment in the time-forward version and reverse it in the time-reversed version, and set that as the beginning point of the time-reversed version. Starting with that initial velocity, and using exactly the same laws of physics, the ball will now move in a perfect backwards version of the time-forward version.

So the motion of the ball away from moon in the time-reverse version has everything to do
with the force of gravity.

Yes, and given the right choice of initial velocity (just a velocity with the opposite direction as the final velocity in the time-forward version), the motion will be just like a backwards version of the time-forward version if you have the law of gravitation operate the same way on this initial condition as it did on the initial condition of the time-forward version.

It would seem the only answer when gravity is a force, but not when it's the geometry of space-time.

GR displays time-reversal symmetry too, which automatically means that a backwards movie of any GR scenario will be obeying the same laws.

 

[Chrisc]

Yes, and given the right choice of initial velocity (just a velocity with the opposite direction as the final velocity in the time-forward version), the motion will be just like a backwards version of the time-forward version if you have the law of gravitation operate the same way on this initial condition as it did on the initial condition of the time-forward version.

There is a flaw in your reasoning here.
You presume a collision occurs prior to observation in order to impart an initial velocity
on the ball that sustains your expectation of the mechanics of gravitation in the time-reverse version.

It seems you are not distinguishing the kinematics of the event from the dynamics.
When the "separation" of two bodies in free space is a "diminishing" value attributed to gravitation,
the "separation" of the same bodies in the time-reverse is an "increasing" value attributed to gravitation.
Thus in accordance with the second law of thermodynamics, the time-reverse version will never bring the two bodies back together,
they will return to a lower entropic state exactly opposite to the mechanics of the time-forward version.
In your explanation, the two bodies will eventually succumb to gravitational force in the time-reverse version and begin to move together again.
That would be truly unique physics as it would require the time-reverse version "creates" new events.

 

[Antenna Guy]

Uh, have you forgotten that "first" and "last" are naturally reversed in the time-reversed version? In the time-forward version, the "beginning" is the ball in deep space, being pulled towards moon by gravity, and the "end" is it colliding the moon. So naturally, in the time-reversed version the beginning is the time-reversed version of the collision which propels the ball outward. Do you disagree that everything in the time-reversed version can be explained using the same laws? It's easiest to see if we just imagine a ball that repeatedly collides elastically with the moon so it falls from some height, bounces upward to exactly the same height, falls back down and bounces again, forever. The time-reversed version of this movie will look identical to the time-forward movie.

This begs an interesting question..

Let's say that some observer stationary with respect to the moon is watching this ball bounce to-and-fro from a distance of, say, 1 light minute. When the proverbial switch is thrown to reverse time, does the ball "back-up" before continuing on its' way, or does the observer determine that the ball must be one minute behind where he sees it?

Regards,

Bill

 

[JesseM]

There is a flaw in your reasoning here.
You presume a collision occurs prior to observation in order to impart an initial velocity
on the ball that sustains your expectation of the mechanics of gravitation in the time-reverse version.

Basically all physics problems involve taking some set of initial conditions and evolving them forward according to the dynamical laws; you are free to pick any initial conditions you want, although you can also use the same dynamical laws to "retrodict" what must have been happening before that initial state.

You are free to choose the endpoint of the timeframe you're looking at anywhere you want in the time-forward version, and of course if you take the endpoint and reverse the velocities that will be the initial condition for the time-reversed version. You say "you presume a collision prior to observation" in the time-reverse version, but you are free to make the endpoint of the time-forward version be after a collision occurs, in which case the beginning point of the time-reversed version will be before the collision, so your observation period will include the collision, it won't be "prior to observation". No matter what initial conditions and end conditions you pick for the time-forward version, if you play it in reverse the system will still be obeying exactly the same dynamical laws in the time-reversed version. Do you disagree with this or not?

It seems you are not distinguishing the kinematics of the event from the dynamics.

The time-reversed kinematics are obeying exactly the same dynamical laws as the time-forward kinematics. This follows logically from the fact that the dynamical laws exhibit time-symmetry (the equations are unchanged when you substitute -t for +t), if you don't understand this then you're still missing the most basic idea of what time-reversal symmetry means.

When the "separation" of two bodies in free space is a "diminishing" value attributed to gravitation,
the "separation" of the same bodies in the time-reverse is an "increasing" value attributed to gravitation.

What's attributed to gravity is not whether the separation is increasing or decreasing (which depends on the initial velocity of the object); rather, gravity determines whether the velocity in the outward direction is increasing or decreasing. If you observe an object which has been given a kick upward, and another object which is falling to the ground, the first object's separation is increasing while the second object's separation is decreasing, but in both cases the velocity in the upward direction is decreasing, and that's because gravity is attractive rather than repulsive. If you take a movie of a falling object and reverse it, in the reversed movie the object's velocity in the upward direction will still appear to be decreasing.

Thus in accordance with the second law of thermodynamics, the time-reverse version will never bring the two bodies back together

In the case of an object which falls, experiences an elastic collision with the moon, and bounces back upward, there is no change in entropy (only inelastic collisions involve entropy changes), so the second law is totally irrelevant here. In the case of an inelastic collision where entropy does increase, the time-reversed version would be a massive violation of the second law, but that's OK because the second law is actually not a fundamental dynamical law, but rather a statistical consequence of the fact that most low-entropy initial conditions tend to rise in entropy as you evolve them forward according to the dynamical laws; but there are a small minority of low-entropy initial conditions which do actually decrease in entropy as you evolve them forward according to the same dynamical laws, so decreases in entropy are permitted by these dynamical laws, although for cosmological reasons we expect them to be extremely rare in the real world.

they will return to a lower entropic state exactly opposite to the mechanics of the time-forward version.

Again, the dynamical laws are perfectly compatible with decreases in entropy, the laws of thermodynamics are understood to be statistical only.

In your explanation, the two bodies will eventually succumb to gravitational force in the time-reverse version and begin to move together again.

Not necessarily, if the time-forward version featured an object falling in from infinity, then the time-reverse version will feature an object that can escape to infinity because its velocity is greater than or equal to the escape velocity for the moon (and that's all 'escape velocity' means, that the object's outward speed is great enough so that even though gravity will cause the outward speed to continuously decrease, the rate of decrease will get smaller and smaller as the object moves further out since the gravitational pull is weaker at greater distances, and if the object's speed was greater than or equal to the escape velocity its outward speed will never reach zero at any finite distance, so it'll just keep moving out forever).

That would be truly unique physics as it would require the time-reverse version "creates" new events.

Not sure what you mean here--all the events in the time-reverse version are just mirror images of events in the time-forward version.

 

[JesseM]

This begs an interesting question..

Let's say that some observer stationary with respect to the moon is watching this ball bounce to-and-fro from a distance of, say, 1 light minute. When the proverbial switch is thrown to reverse time, does the ball "back-up" before continuing on its' way, or does the observer determine that the ball must be one minute behind where he sees it?

Regards,

Bill

Time-reversal symmetry doesn't actually involve a system suddenly reversing direction at some time, which would be a violation of the dynamical laws. Rather, it means that if you take a film of some system and play it backwards, the dynamical laws are such that it would be possible in principle to create a different system whose behavior in the forward direction would look exactly like the backwards film of the first system.

 

[Chrisc]

Basically all physics problems involve taking some set of initial conditions and evolving them forward according to the dynamical laws; you are free to pick any initial conditions you want, although you can also use the same dynamical laws to "retrodict" what must have been happening before that initial state.

You are free to choose the endpoint of the timeframe you're looking at anywhere you want in the time-forward version, and of course if you take the endpoint and reverse the velocities that will be the initial condition for the time-reversed version. You say "you presume a collision prior to observation" in the time-reverse version, but you are free to make the endpoint of the time-forward version be after a collision occurs, in which case the beginning point of the time-reversed version will be before the collision, so your observation period will include the collision, it won't be "prior to observation". No matter what initial conditions and end conditions you pick for the time-forward version, if you play it in reverse the system will still be obeying exactly the same dynamical laws in the time-reversed version. Do you disagree with this or not?

I agree that is what is meant by the time-reverse symmetry of mechanics. I disagree that it has been reasoned beyond the kinematics of gravitation.
If gravitation is the dynamic responsible for the motion of bodies forward in time, then gravitation and "only" gravitation is responsible for the motion of those same bodies backward in time.

The time-reversed kinematics are obeying exactly the same dynamical laws as the time-forward kinematics. This follows logically from the fact that the dynamical laws exhibit time-symmetry (the equations are unchanged when you substitute -t for +t), if you don't understand this then you're still missing the most basic idea of what time-reversal symmetry means.

It does not follow logically at all. You are assuming the time-reverse symmetry of the kinematics proves the time-reverse dynamics remain unchanged. In physics today, time IS kinematics and nothing more, so to state the inversion of kinematics(Time) is proof of unchanged dynamics is not logical but self-referencial.
You have simply stated: kinematics - our measure of time - is symmetric under the inversion of time - because the inversion of time is the inversion of kinematics.

What's attributed to gravity is not whether the separation is increasing or decreasing (which depends on the initial velocity of the object); rather, gravity determines whether the velocity in the outward direction is increasing or decreasing. If you observe an object which has been given a kick upward, and another object which is falling to the ground, the first object's separation is increasing while the second object's separation is decreasing, but in both cases the velocity in the upward direction is decreasing, and that's because gravity is attractive rather than repulsive. If you take a movie of a falling object and reverse it, in the reversed movie the object's velocity in the upward direction will still appear to be decreasing.

You are suggesting gravity is not responsible for the motion of bodies, but only responsible for the change
of some pre-existing, initial motion and therefore gravity remains an attractive force under time-reversal.
If two bodies are held at rest by a force acting on one or both that counters the "attractive" force of gravity,
the two bodies "will" move together when the force holding them at rest is removed.
While the force remains, there is no motion between the two bodies. Gravity is not changing the motion as there is no motion.
In the time-reverse version of this example, the force holding the two bodies at rest must continue to hold them
at rest as the kinematics remain unchanged. According to your claim of time symmetric dynamics, that force must
be a vector of opposite sign which will now act to push the two bodies together.
As the two bodies must remain at rest, how do you explain gravitation as an attractive force now holds the
two bodies against the force that is now also acting in the same direction in the time-reverse?

In the case of an object which falls, experiences an elastic collision with the moon, and bounces back upward, there is no change in entropy (only inelastic collisions involve entropy changes), so the second law is totally irrelevant here. In the case of an inelastic collision where entropy does increase, the time-reversed version would be a massive violation of the second law, but that's OK because the second law is actually not a fundamental dynamical law, but rather a statistical consequence of the fact that most low-entropy initial conditions tend to rise in entropy as you evolve them forward according to the dynamical laws; but there are a small minority of low-entropy initial conditions which do actually decrease in entropy as you evolve them forward according to the same dynamical laws, so decreases in entropy are permitted by these dynamical laws, although for cosmological reasons we expect them to be extremely rare in the real world.

You are implying the second law of thermodynamics is irrelevant in the dynamics of any event that does not involve inelastic collisions.
That is not exactly true, the second law is recognized today as a very fundamental statement about dynamics in general.
A two body system that never experiences a collision of any kind, will under gravitation exhibit the increased
entropy predicted by the second law. Consider any satelite body that experiences changing kinetic energy
as it imparts motion on the body it orbits until the two settle to a stable binary system where the total kinetic
energy has moved toward equilibrium.
That it is not a fundamental law is a result of nobody being able to reason its existence.
As you mentioned, it is "fact" and it is one of the most overwhelming facts in the history of physics.
If you do not recognize the overwhelming evidence of the second law of thermodynamics must arise from
some as yet unrecognized dynamic, you must then attribute the overwhelming evidence as nothing more than
coincidence or curiosity. I can't imagine you would relegate the most universal fact of mechanics to curiosity
simply because it is not yet formalized from dynamical laws.

 

[yuiop]

... but there are a small minority of low-entropy initial conditions which do actually decrease in entropy as you evolve them forward according to the same dynamical laws, so decreases in entropy are permitted by these dynamical laws, although for cosmological reasons we expect them to be extremely rare in the real world.

Hi jesse, I am interested inthis sort of stuff. Can you give an example of the rare cases where decreases of entropy are permited in the forward time direction? (In an isolated system.)

If you do not recognize the overwhelming evidence of the second law of thermodynamics must arise from
some as yet unrecognized dynamic, you must then attribute the overwhelming evidence as nothing more than
coincidence or curiosity. I can't imagine you would relegate the most universal fact of mechanics to curiosity
simply because it is not yet formalized from dynamical laws.

Not sure if I agree or disagree here. If you do a computer simulation of a group of particles in one corner of a box and assign initial random velocities to the particles and thereafter constrain the particles to move in a deterministic fashion, only changing velocity when they collide with each other or the walls, they seem to obey the laws of thermodynamics and disperse even though there is clearly no physical dynamic controlling the motion of the particles so that they conform with the 2nd law. On the other hand the computer itself is constrained to move forward in time... In the computer program the location and velocity of the individual particles are stored in arrays and if the simulation is halted and reversed without randomising the the particle variables the particles disobey the second law. So in a deterministic universe reversing time creates a universe that violates the 2nd law. However, if we program the particles to have small random uncertainties as per Heisenberg, the simulation would look a lot like our universe in the forward direction and when the simulation is reversed the 2nd law would be maintained even in the reverse time direction, although it might appear that entropy is decreasing for a short period when the simulation is reversed, over longer time periods it will increase or stay the same.

 

[DrGreg]

Hi jesse, I am interested inthis sort of stuff. Can you give an example of the rare cases where decreases of entropy are permited in the forward time direction? (In an isolated system.)

Decreases in entropy are always permitted, just extremely unlikely. And all the less likely if you look over a larger area over a longer period of time.

The Second Law of Thermodynamics isn't really a "law", it's a statistical rule-of-thumb. Or, if you like, a "law of averages".

In the UK where I live we have a National Lottery; the chances of winning the jackpot are 14 million to one against. So I could say there is a "Law of Lotteries": "You will not win the jackpot". That's extremely likely to be true, but occasionally false, and on those rare occasions no theorems of probability have been broken.

Not sure if I agree or disagree here. If you do a computer simulation of a group of particles in one corner of a box and assign initial random velocities to the particles and thereafter constrain the particles to move in a deterministic fashion, only changing velocity when they collide with each other or the walls, they seem to obey the laws of thermodynamics and disperse even though there is clearly no physical dynamic controlling the motion of the particles so that they conform with the 2nd law. On the other hand the computer itself is constrained to move forward in time... In the computer program the location and velocity of the individual particles are stored in arrays and if the simulation is halted and reversed without randomising the the particle variables the particles disobey the second law. So in a deterministic universe reversing time creates a universe that violates the 2nd law. However, if we program the particles to have small random uncertainties as per Heisenberg, the simulation would look a lot like our universe in the forward direction and when the simulation is reversed the 2nd law would be maintained even in the reverse time direction, although it might appear that entropy is decreasing for a short period when the simulation is reversed, over longer time periods it will increase or stay the same.

In your example, the particles begin in one corner, but within that corner they are randomly distributed (in position and momentum). When you reverse time, the particles begin in an apparently random configuration, but it's not really random at all, it's what results from running your original simulation forward. And if that configuration were to occur by chance (extremely unlikely but not actually impossible), then the particles really would all collect in one corner, in a short-term local violation of the 2nd law, not only in your simulation but in real life too.

All motions depend on initial conditions, and if you choose the initial conditions carefully enough you can get a highly unlikely but permissible outcome.

 

[Chrisc]

...
The Second Law of Thermodynamics isn't really a "law", it's a statistical rule-of-thumb. Or, if you like, a "law of averages".

In the UK where I live we have a National Lottery; the chances of winning the jackpot are 14 million to one against. So I could say there is a "Law of Lotteries": "You will not win the jackpot". That's extremely likely to be true, but occasionally false, and on those rare occasions no theorems of probability have been broken.

There are billions of apples grown every year around the world. The chances of them not falling to the ground if left untouched are billions to one against. So I could say there is a "Law of Apples". I would not be wrong in my prediction of what that law states, I would be wrong in assuming its statistical nature defines the fundamental physical principles involved in the motion of apples from trees to the ground.
Likewise the statistical nature of mechanics toward increased entropy is not wrong (statistics never are) in its prediction of a tendency to equilibrium, but it does not define the fundamental physical principles responsible for the entropy.
Nor do the dynamical laws predict such a universal direction of entropy. In fact as you stated they "permit" in their time-reverse symmetry, the exact opposite. There is some mechanism or some dynamic that is either a unique unknown or a collective consequence of all dynamics that gives rise to the "direction" of entropy and its affiliation with the procession of time.
That the dynamical laws are time-reverse symmetric yet the universe as a whole displays an overwhelming tendency to progress in one direction toward "increased" entropy is IMHO clear evidence of a fundamental principle that has been overlooked.

To bring this back to my OP and in keeping it relevant to this forum, I think there is a relationship between the direction of entropy and the time symmetry of dynamics that only becomes apparent when the principle of relativity is upheld in the observations of the time-reverse kinematics of a system.
For example: the motion of two bodies (constant linear) is relative. Neither can be defined as in motion with respect to any absolute frame of rest. Therefore the kinetic energy of the two bodies is also relative. If the principle of relativity is strictly adhered to in considering the mechanics of a collision between the two bodies, the resulting relative motion of the bodies (with respect to the observer's frame) must either break the symmetry of their relative motion and kinetic energy by presenting motion that upholds the second law of thermodynamics, or it must break the time-reverse symmetry of the dynamics of the collision.
In short, the frame of the observer dictates the dynamics observed in the kinematics after the collision.
If in one frame ALL the kinetic energy is attributed to one body (i.e., the observer is at rest wrt the other) the
direction and magnitude of the motion of the two bodies after collision must reflect the same dynamics.
This is not possible in both frames of reference forward and backward through time.

 

[JesseM]

Nor do the dynamical laws predict such a universal direction of entropy. In fact as you stated they "permit" in their time-reverse symmetry, the exact opposite. There is some mechanism or some dynamic that is either a unique unknown or a collective consequence of all dynamics that gives rise to the "direction" of entropy and its affiliation with the procession of time.

The underlying dynamical laws do allow you to derive the fact that, if you start from a low-entropy state and move forward in time, the system is overwhelmingly likely to increase in entropy in the forward direction. The reason there is no time-asymmetry here is that in a deterministic universe you can also project backwards from a given low-entropy state to "retrodict" what the system was like at earlier times, and in this case the same laws give the prediction that the system was overwhelmingly likely to have been at higher entropy at earlier moments than your chosen state as well. So if your starting state is an ice cube in an isolated box at room temperature, then you can derive the prediction that at later times the ice cube will melt into a puddle, but you also get the prediction that at earlier times there was a puddle which, due to a very unlikely statistical fluctuation, happened to congeal into an ice cube. In real life, of course, this backwards prediction is very unlikely--it's more likely that the ice cube got in the box because someone took it out of the freezer and put it there, and the entropy of the room with the box and the freezer in it was even lower at earlier times before the ice cube was placed in the box. Reasoning backwards this way, physicists think the asymmetrical "arrow of time" is related to the very low-entropy conditions of the universe shortly after the Big Bang, and that entropy has been continually increasing since then. Here is a discussion of this by physicist Roger Penrose, starting on p. 317 of his book The Emperor's New Mind:

We shall try to understand where this 'amazing' low entropy comes from in the actual world that we inhabit. Let us start with ourselves. If we can understand where our own low entropy came from, then we should be able to see where the low entropy in the gas held by the partition came from--or in the water glass on the table, or in the egg held above the frying pan, or the lump of sugar held over the coffee cup. In each case a person or collection of people (or perhaps a chicken!) was directly or indirectly responsible. It was, to a large extent, some small part of the low entropy state in ourselves which was actually made use of in setting up these other low-entropy states. Additional factors might have been involved. Perhaps a vacuum pump was used to suck the gas to the corner of the box behind the partition. If the pump was not operated manually, then it may have been that some 'fossil fuel' (e.g. oil) was burnt in order to provide the necessary low-entropy energy for its operation. Perhaps the pump was electrically operated, and relied, to some extent, on the low-entropy energy stored in the uranium fuel of a nuclear power station. I shall return to these other low-entrop sources later, but let us first just consider the low entropy in ourselves.

Where indeed does our own low entropy come from? The organization in our bodies comes from the food that we eat and the oxygen that we breathe. Often one hears it stated that we obtain energy from our intake of food and oxygen, but there is a clear sense in which that is not really correct. It is true that the food we consume does combine with this oxygen that we take into our bodies, and that this provides us with energy. But, for the most part, this energy leaves our bodies again, mainly in the form of heat. Since energy is conserved, and since the actual energy content of our bodies remains more-or-less constant throughout our adult lives, there is no need simply to add to the energy content of our bodies. We do not need more energy within ourselves than we already have. In fact we do add to our energy content when we put on weight--but that is not usually considered desirable! Also, as we grow up from childhood we increase our energy content considerably as we build up our bodies; that is not what I am concerned about here. The question is how we keep ourselves alive throughout our normal (mainly adult) lives. For that, we do not need to add to our energy content.

However, we do need to replace the energy that we continually lose in the form of heat. Indeed, the more 'energetic' that we are, the more energy we actually lose in this form. All this energy must be replaced. Heat is the most disordered form of energy that there is, i.e. it is the highest-entropy form of energy. We take in energy in a low-entropy form (food and oxygen) and we discard it in a high-entropy form (heat, carbon dioxide, excreta). We do not need to gain energy from our environment, since energy is conserved. But we are continually fighting against the second law of thermodynamics. Entropy is not conserved; it is increasing all the time. To keep ourselves alive, we need to keep lowering the entropy that is within ourselves. We do this by feeding on the low-entropy combination of food and atmospheric oxygen, combining them within our bodies, and discarding the energy, that we would otherwise have gained, in high-entropy form. In this way, we can keep the entropy in our bodies from rising, and we can maintain (and even increase) our internal organization. (See Schrödinger 1967.)

Where does this supply of low entropy come from? If the food that we are eating happens to be meat (or mushrooms!), then it, like us, would have relied on a further external low-entropy source to provide and maintain its low-entropy structure. That merely pushes the problem of the origin of the external low entropy to somewhere else. So let us suppose that we (or the animal or mushroom) are consuming a plant. We must all be supremely grateful to the green plants--either directly or indirectly--for their cleverness: taking atmospheric carbon dioxide, separating the oxygen from the carbon, and using that carbon to build up their own substance. This procedure, photosynthesis, effects a large reduction in the entropy. We ourselves make use of this low-entropy separation by, in effect, simply recombining the oxygen and carbon within our own bodies. How is it that the green plants are able to achieve this entropy-reducing magic? They do it by making use of sunlight. The light from the sun brings energy to the Earth in a comparatively low-entropy form, namely in the photons of visible light. The earth, including its inhabitants, does not retain this energy, but (after some while) re-radiates it all back into space. However, the re-radiated energy is in a high-entropy form, namely what is called 'radiant heat'--which means infrared photons. Contrary to a common impression, the Earth (together with its inhabitants) does not gain energy from the sun! What the Earth does is to take the energy in a low-entropy form, and then spew it all back again into space, but in a high-entropy form. What the sun has done for us is to supply us with a huge source of low entropy. We (via the plants' cleverness), make use of this, ultimately extracting some tiny part of this low entropy and converting it into the remarkable and intricately organized structures that are ourselves.

He goes on to explain why the visible light photons coming in have lower entropy than the infrared ones radiated back out (basically just because the infrared ones have lower energy so there must be more of them, which means the energy is spread out over more 'degrees of freedom' when it goes out than when it came in, which implies higher entropy). He also explains that the low entropy of the sun must be due to the contraction of an even lower-entropy nebula, and that ultimately the existence of diffuse collections of gas such as nebulas can be traced back to the initial smoothness of the distribution of matter and energy shortly after the Big Bang.

That the dynamical laws are time-reverse symmetric yet the universe as a whole displays an overwhelming tendency to progress in one direction toward "increased" entropy is IMHO clear evidence of a fundamental principle that has been overlooked.

The issue certainly has not been overlooked, many physicists have debated the reasons for the smooth low-entropy Big Bang. You can also find more discussion of this issue on this recent thread:

https://www.physicsforums.com/showthread.php?t=244736

For example: the motion of two bodies (constant linear) is relative. Neither can be defined as in motion with respect to any absolute frame of rest. Therefore the kinetic energy of the two bodies is also relative.

Of course, kinetic energy is relative in both relativity and Newtonian mechanics.

If the principle of relativity is strictly adhered to in considering the mechanics of a collision between the two bodies, the resulting relative motion of the bodies (with respect to the observer's frame) must either break the symmetry of their relative motion and kinetic energy by presenting motion that upholds the second law of thermodynamics, or it must break the time-reverse symmetry of the dynamics of the collision.
In short, the frame of the observer dictates the dynamics observed in the kinematics after the collision.
If in one frame ALL the kinetic energy is attributed to one body (i.e., the observer is at rest wrt the other) the
direction and magnitude of the motion of the two bodies after collision must reflect the same dynamics.
This is not possible in both frames of reference forward and backward through time.

There are no inertial frames of reference which disagree on which direction in time is +t and which is -t. You could construct a coordinate system which labeled +t and -t the opposite way, but this wouldn't be related to normal inertial frames by the Lorentz transformation and so it wouldn't be a valid inertial frame itself. All valid inertial frames will agree about whether entropy increases or decreases in a collision.

 

[Chrisc]

You have come full circle in this discussion and apparently missed the point.
Please look at the diagram attached. Consider the mechanics in context of the principle
of the laws. Please do not invoke the previous diversion of elastic and inelastic collisions.
What is being considered here is the principles of Newton's laws and the principle expressed
by the second law of thermodynamics that the forward direction of time is associated with increased entropy.
If it helps consider the bodies as theoretical mass points, as what is being considered is the theoretical
mechanics that test the principles of the laws with respect to the theoretical mechanics they define.

I have labeled the momentum and set it and the motion with respect to an observer initially at
rest (indicated by the small, downward pointing arrow) with each mass.
If there is an explanation for why 2D is valid and 2E is not, please let me know.
If you think that 2D is simply a question of probability you must remember that if such mechanics
were to occur even once in the history of the universe, they would invalidate Newton's laws.
If you think 2E represents the mechanics that follow from 2C you must remember such mechanics
violate the second law of thermodynamics and break the time-reverse symmetry of 2A.

 

[JesseM]

You have come full circle in this discussion and apparently missed the point.

What is the point? Could you spell it out? Are you claiming that the 2nd law can be violated in one inertial frame but not another inertial frame?

Please look at the diagram attached. Consider the mechanics in context of the principle
of the laws. Please do not invoke the previous diversion of elastic and inelastic collisions.

Sorry, if it's relevant to the discussion I'll have to invoke them.

What is being considered here is the principles of Newton's laws and the principle expressed
by the second law of thermodynamics that the forward direction of time is associated with increased entropy.

In the diagrams, you calculated the momentum before and after the collision but completely ignored the energy! In 1A the total kinetic energy before the collision is 4 kg*m^2/s^2 while in 1B the total kinetic energy after is 3 kg*m^2/s^2, a decrease in kinetic energy in frame 1 (in the forward-time direction). Likewise in 2A the total kinetic energy before the collision is 2 kg*m^2/s^2 while in 2B the total kinetic energy after the collision is 1 kg*m^2/s^2, so there was also a decrease in kinetic energy in frame 2 (in the time-forward direction). Therefore there must be two possibilities here:
1. If there was not an increase in some other form of energy other than linear kinetic energy (such as heat), then your scenario violates conservation of energy and must be completely impossible according to the dynamical laws.
2. If there was an increase in some other form of energy to balance out the decrease in total linear kinetic energy of the two bodies, then presumably this was in the form of heat or electromagnetic waves, meaning this was an inelastic collision where entropy increased.

You also misuse the word "dynamics" in your discussion in the diagram--the second law is not part of the fundamental dynamics, it is a statistical consequence of the underlying dynamical laws. And again, it only appears asymmetric in its statistical predictions because we live in a universe which, for reasons not yet well-understood, started off in a very low entropy-state. If we imagine an isolated system which already reached maximum entropy at some point, and then at a later time t we observe the system in a lower state of entropy due to a random statistical fluctuation, then in this case our statistical predictions would by time-symmetric--we'd predict that the lower entropy at time t was the minimum of the statistical fluctuation (since smaller spontaneous decreases in entropy are always more likely than larger ones), and thus that the entropy was higher both slightly after t and slightly before it.

If it helps consider the bodies as theoretical mass points, as what is being considered is the theoretical
mechanics that test the principles of the laws with respect to the theoretical mechanics they define.

Point masses don't have heat energy, because in statistical mechanics an increase in heat in a macroscopic body is really an increase in kinetic energy of all the molecules that make it up (but with different molecules moving in random directions so this does not contribute to the linear kinetic energy of the body). So again, that would leave us with option 1), where energy is not conserved and your scenario is completely impossible.

If there is an explanation for why 2D is valid and 2E is not, please let me know.

Both are dynamically valid if there is a change in heat energy to balance out the change in kinetic energy. One is statistically more probable to see in the real world than the other because we live in a universe which started in a low-entropy state (in 2C the kinetic energy was 1 kg*m^2/s^2, in 2D it's 2 kg*m^2/s^2, in 2E it's 3/4 kg*m^2/s^2, so if these changes in kinetic energy are balanced by changes in heat, 2C to 2D represents a spontaneous decrease in heat, which the 2nd law says is very improbable, while 2C to 2E represents a spontaneous increase in heat).

If you think that 2D is simply a question of probability you must remember that if such mechanics
were to occur even once in the history of the universe, they would invalidate Newton's laws.

No they wouldn't, not if the increase in linear kinetic energy was balanced out by a spontaneous decrease in heat (statistically improbable in the real world, but it wouldn't violate Newton's laws, in fact one could pick out a particular set of initial conditions for the random velocities of all the molecules in the objects where a decrease in entropy would follow deterministically from these initial conditions according to Newton's laws).

If you think 2E represents the mechanics that follow from 2C

There is no single set of mechanics that follows from 2C, not if you allow the collision to be an inelastic where some energy is lost to heat. There would be many different possible continuations of 2C, which would occur would depend on things like the nature of the materials the two masses are made of, their stickiness, the detailed topography of each one's surface, etc.

 

[Chrisc]

1. If there was not an increase in some other form of energy other than linear kinetic energy (such as heat), then your scenario violates conservation of energy and must be completely impossible according to the dynamical laws.

You seem unwilling, even in principle, to consider the principle of conservation of momentum in an event unless you can simultaneously consider the conservation of heat energy in the same event.
It is true a "single" point mass does not posess heat energy, nor does a "single" molecule, or in principle a single anything. It is the collective distribution of kinetic energy of a "single" entity's constituents that defines the heat energy of the entity as a whole.
But how do you propose to arrive at a collective distribution of kinetic energy if you consider the collision of any two constituents "completely impossible according to the dynamical laws"?

It seems from this same reasoning you think that the second law of thermodynamics is not observed in the collision of two masses, but only on some greater number of masses. This is not true. A change in the distribution of momentum during the collision of two masses will not display a spontaneous "increase" in the total momentum of the system. i.e. a spontaneous "decrease" in entropy. The system will display either no change in entropy while conserving the total momentum, or an increase in entropy while conserving the total momentum. Where the latter simply means the total momentum of the system is more evenly distributed between the masses, i.e. the momentum of the system approaches equilibrium.

If I had presented an example that had a complete disregard for the laws of conservation I could understand your objections. But I have not. I have presented a simple two-mass event that considers the principle of conservation of momentum in context of the principle of relativity as a set of frame dependent observations that will both break or violate the second law of thermodynamics and uphold it, depending on the frame of the observer.

What is the point? Could you spell it out?

The point I have rephrase and paraphrased numerous times is:
The time symmetry of the "principle" of relativity is broken by the time asymmetry of the second law of thermodynamics.
Or, because this is a frame dependent dynamic, it can be stated in the inverse as:
The time asymmetry of the second law of thermodynamics is broken by the time symmetry of the principle of relativity.
This arises from the relativity of observation presenting frame dependent dynamics, which shows there is a preferred or privileged frame(one where the observer is initially at rest with the smaller mass) in which one can uphold both the time symmetry of dynamical laws and the time asymmetry of the second law of thermodynamics. It is a preferred or privileged frame "because" the only other frame in the system (initially at rest with the larger mass) will not uphold both but must break either one in order to uphold the other.

 

[JesseM]

You seem unwilling, even in principle, to consider the principle of conservation of momentum in an event unless you can simultaneously consider the conservation of heat energy in the same event.

All that matters is that total energy is conserved, it doesn't matter whether there's any heat energy present or not. Weren't you supposed to be discussing the question of whether a given situation is a violation of the dynamical laws? Well, any situation where total energy isn't conserved violates the known dynamical laws and is thus physically impossible according to the known laws of physics.

It is true a "single" point mass does not posess heat energy, nor does a "single" molecule, or in principle a single anything. It is the collective distribution of kinetic energy of a "single" entity's constituents that defines the heat energy of the entity as a whole.
But how do you propose to arrive at a collective distribution of kinetic energy if you consider the collision of any two constituents "completely impossible according to the dynamical laws"?

The collision of any two pointlike constituents is not "completely impossible", it's just that the only type of collision between pointlike entities which the dynamical laws allow is one where their kinetic energy is conserved. For any pair of initial velocities for the two particles, it is always possible to find a unique set of post-collision velocities such that both momentum and kinetic energy are conserved (and this is what is known as an 'elastic collision'). As an example, in your scenario 1A, you had the 2kg mass initially moving at 2 m/s while the 1 kg mass was initially at rest, prior to the collision. Well, if there is no change in heat energy in this collision, then the only possible set of post-collision velocities would be the 2 kg mass moving at 2/3 m/s and the 1 kg mass moving at 8/3 m/s. In this case the total momentum both before and after the collision will be 4 kg*m/s, while the total kinetic energy both before and after the collision will be 4 kg*m^2/s^2. Assuming there is no change in some other form of energy like heat energy, then this is the only set of post-collision velocities which are allowed by the dynamics (if you set up the equations (2 kg)*v1 + (1 kg)*v2 = 4 kg*m/s and (1/2)*(2 kg)*v1^2 + (1/2)*(1 kg)*v2^2 = 4 kg*m^2/s^2, you can solve these equations and see that there are only two possible sets of solutions for v1 and v2, one of which gives the velocities before the collision and one of which gives the velocities after).

It seems from this same reasoning you think that the second law of thermodynamics is not observed in the collision of two masses, but only on some greater number of masses.

What do you mean by "two masses" vs. a "greater number of masses"? If we have a collision between two macroscopic balls which are themselves made up of many molecules, would you call this "a greater number of masses"? Are you using the term "two masses" to refer exclusively to something like point masses which are not composed of multiple parts? If so, it's true that there can be no change in heat energy in the collision between two point masses, and the basic dynamics demand that total energy (and total momentum) must be conserved in every collision. This doesn't necessarily mean there can be no change in entropy in the system at all, since the entropy of some combination of velocities for the point masses might be higher than others, although to talk about changes in entropy you have to have some macro-parameters such that there are multiple possible microscopic states (microscopic states means a precise set of values for the position and momentum of each particle) compatible with a single value of the macro-parameter, with the entropy of a given value of the macro-parameter being proportional to the logarithm of the number of possible microscopic states associated with it, and I'm not sure what kind of macro-parameter you could define for a system consisting of only two point particles. I have my doubts that you could define one such that a collision would involve any change in entropy (though I'm pretty sure you could define one for an isolated system with three parts, like three particles in a closed universe or two particles in a box).

This is not true. A change in the distribution of momentum during the collision of two masses will not display a spontaneous "increase" in the total momentum of the system. i.e. a spontaneous "decrease" in entropy.

You can never have a spontaneous increase or decrease in total momentum, not even in situations where entropy changes. The momentum vector of a composite object made of many molecules or other parts is just the sum of the momentum vectors of all the parts, so a pair of composite object can't balance out a decrease in momentum for the centers of mass of the two objects by an increase in the total momentum of all the parts that make them up. On the other hand, the kinetic energy of the center of mass of a composite object is not the sum of the kinetic energies of all the parts making it up, so it is possible to have a decrease (or increase) in the sum of the kinetic energies for the two centers of mass be balanced out by an increase (or decrease) in the sum of the kinetic energies of all the parts that make up the larger masses.

The system will display either no change in entropy while conserving the total momentum, or an increase in entropy while conserving the total momentum. Where the latter simply means the total momentum of the system is more evenly distributed between the masses, i.e. the momentum of the system approaches equilibrium.

In order to make this statement well-defined you'd need some parameter which defines how "evenly distributed" the momenta are...I suppose you could use the sum of the squares of the momentum for each particle, a parameter which decreases as the momentum becomes more evenly distributed, but this would essentially just be the sum of kinetic energies multiplied by a constant.

If I had presented an example that had a complete disregard for the laws of conservation I could understand your objections. But I have not.

Do you acknowledge that conservation of energy is one of the "laws of conservation", separate from conservation of momentum. Do you acknowledge that in your scenario, the sum of kinetic energies of the centers of mass of the two objects is different after the collision than it was before? If so, you should agree that unless there is a change in some other form of energy (like heat) in your scenario, then your scenario does disgregard the "laws of conservation".

I have presented a simple two-mass event that considers the principle of conservation of momentum in context of the principle of relativity as a set of frame dependent observations that will both break or violate the second law of thermodynamics and uphold it, depending on the frame of the observer.

If your scenario obeys the laws of conservation, it must involve a change in some other form of energy besides the kinetic energies of the centers-of-mass, like heat. All valid inertial frames will agree on whether the heat increases or decreases after the collision, so there is no disagreement on whether the 2nd law of thermodynamics is upheld or violated. I suppose if we consider a situation where there is no change in heat, like the one I suggested where the post-collision velocities were 2/3 m/s and 8/3 m/s, then for some sufficiently weird choice of macro-parameter one might be able to show that a collision took the system to a value of the macro-parameter with higher entropy in one frame while it took the system to a value with lower entropy in another frame, though as I said earlier I have my doubts that this is possible for a system with only two parts. But in any case, if one chooses the usual macro-parameters which are normally used to define entropy in thermodynamics, like temperature and pressure, I'm pretty sure an increase in entropy in one inertial frame would mean an increase in every inertial frame.

The point I have rephrase and paraphrased numerous times is:
The time symmetry of the "principle" of relativity is broken by the time asymmetry of the second law of thermodynamics.

Where do you get the idea that the principle of relativity requires that the laws of physics be time-symmetric? It doesn't, time-symmetry is a separate postulate. And the apparent asymmetry of the second law is not a violation of time-symmetry, again because it is ultimately just a consequence of the initial conditions of the universe near the Big Bang, not of the laws of physics themselves. The particular arrangement of matter and energy in spacetime can be asymmetric even if the laws of physics are symmetric; as another example, the laws of physics exhibit rotation symmetry meaning there is no preferred direction in space, and this would continue to be true even if we imagine that all of space happened to be filled with some magnetic material that allowed everyone to orient themselves in the same direction using a compass.

This arises from the relativity of observation presenting frame dependent dynamics, which shows there is a preferred or privileged frame(one where the observer is initially at rest with the smaller mass) in which one can uphold both the time symmetry of dynamical laws and the time asymmetry of the second law of thermodynamics. It is a preferred or privileged frame "because" the only other frame in the system (initially at rest with the larger mass) will not uphold both but must break either one in order to uphold the other.

Please be explicit about the change in entropy that you think is happening in different frames in your scenario--are you suggesting that in 1B the entropy has increased beyond what it was in 1A, while in 2B (which is just 1B viewed in a different frame) the entropy has decreased from 2A? If so you're wrong, the only way your scenario could be consistent with the laws of dynamics would be if the heat energy increased after the collision, and it would have to increase in both frames. You're free to pick a different scenario where the sum of kinetic energy for the centers-of-mass is conserved and so there is no need for a change in heat (like my scenario which starts the same as 1A, but after the collision leaves the 2 kg mass moving at 2/3 m/s and the 1 kg mass moving at 8/3 m/s in that frame), but in this case if you want to assert that there's some change in entropy before and after the collision, you'll have to specify what macro-parameter(s) you're using to define entropy.

 

[DrGreg]

I wonder, Chrisc, do you think that when two bodies bounce off each other, conservation of momentum alone predicts a unique outcome? Do you think that, in your example, your outcome is the only possible outcome that conserves momentum? If you do, you are wrong. There are an infinite number of different possible outcomes, in all of which momentum is conserved. We have to consider something else, e.g. energy, to work out which one of all the momentum-conserving potential outcomes actually occurs. (See post #39.)

So your example is one specific choice of solution where kinetic energy is converted into some other form of energy, e.g. heat or sound, and if we reverse time on your solution, that energy would have to be converted from heat or sound into kinetic energy.

If we insist in no loss of kinetic energy (which applies if the two "bodies" are fundamental particles), your solution is not the correct one; the correct one is time-reversible.

(By the way, this entire thread hasn't really got anything much to do with the theory of relativity, as exactly the same issue arises in Newtonian mechanics (Galilean relativity).)