Talk:One man's look at the arrow of time

Repulsive electromagnetic force and two electrons

(To be incorporated later in some form.)

In the article (later to be corrected), I considered a thought experiment in which we have two electrons and only the electromagnetic force, no other forces, especially no gravitational force and no other attractive force. (Electromagnetic force can be attractive e.g. for an electron and a proton, but not for two electrons.) As the initial state, I took the electrons to be at rest (zero velocity) and at a fixed distance, say, 1 meter. Then, as I let the system develop in time (or press play/run on a simulation), the electrons start to move away from each other and never return. I thought this shows an arrow of time: if the electrons are moving away from each other, the film someone took of them is moving forward, if they are moving toward each other, backward.

But this seems wrong. It is true if we fix the initial condition, that is, if we know that the system (or our little universe) started with the two electrons being at rest. But how can an observer know the initial condition? If we, by contrast, assume the initial condition to be unknown, the film being played backward seems plausible/compatible with the repulsive force. Since, the film starts with the electrons moving toward each other with a non-zero speed (their speed vector is exactly the opposite of the one at the end state of the simulation run forward) and they slow down as a consequence of the repulsive force, eventually becoming at rest, which is where the movie played in reverse ends. (If this continued, which is not part of the reverse movie, they would start moving away from each other.) Thus, the observer does not know that the movie is being played backwards. But if the observer knew the initial condition was the two electrons being at rest, the observer would in fact know: it would be impossible for the electrons to find themselves moving toward each other.

As an aside: if we take time to have a start and no end, then a system with an initial condition of the two electrons moving toward each other will spend only finite time in them moving toward each other but infinite time in them moving away from each other. An observer whose goal would be to determine the unknown direction of the film could argue that it is much more probable for electrons to be moving away from each other than toward each other, and that if we see electrons moving toward each other, our best guess (if we have to make it) is that the film is moving backward.

Not knowing the initial condition is plausible enough if we consider the observed system to be a universe, something causally isolated from everything else (but still being able to be observed). If we take humans as observers of our universe, we are observing the universe process somewhere in the middle; we do not directly observe or know the initial condition.

This thought experiment is made using classical physics: the two electrons are electrically charged infinitely thin points (having no extension) having a precise location in space; there is no Einsteinian/relativistic limit on velocity and there are no quantum mechanical effects. --Dan Polansky (discuss • contribs) 07:33, 31 October 2024 (UTC)

Two initially not moving Newtonian point masses approaching their mutual center of mass

I am now unclear about what happens to two initially not moving Newtonian point masses, both having the same mass. For instance, let them start 1 meter apart at rest, each having the mass of 1 kg. They start moving toward each other, but what happens as they approach their mutual center of mass? From the formula of the Newtonian gravitation force, the force would approach infinity as the points approach each other, and thus, the acceleration would approach infinity. It seems that the moment of meeting would be some kind of singularity. It is not clear to me whether this would result in arbitrarily large speeds near the shared center of mass. (I am not that good at calculus and systems of continuous time, having studied computer science and not physics at a university level.)

Of course, real particles have also electrical charge, and there are repulsive forces that get very strong as particles get very close to each other. Moreover, Newton is superseded by Einstein. And perhaps the concept of a particle is not particularly apt either and should rather be replaced with something like an entity with a dual particle-wave character, and quantum mechanics should kick in. But that is not the analytical exercise here. The question is what happens in a purely Newtonian system that has only the Newtonian force. Thus, in a sense, the question is more mathematical than physical.

Links:

• Two-body problem, wikipedia.org
• newtonian mechanics - Infinities in Newtons law of gravity (for point particles), physics.stackexchange.com
• newtonian gravity - Singularity in Newton's gravitational law, physics.stackexchange.com

--Dan Polansky (discuss • contribs) 07:14, 3 November 2024 (UTC)