Where is information of motion stored?

Question

I've asked variations of this question a few times to a few people. My physics professor answered it with: "if no forces act on an object why should it stop, start, or do anything else?" But that doesn't do it for me, because it doesn't (seem to) address my question. Maybe this is a bad question and I'm lacking some fundamental understanding about motion that would simply put me right, but I haven't found that yet, so here it goes...

Let's take two practically identical objects and place them in an empty frictionless universe at rest with respect to each other. We apply a force to one of the objects, say the rightmost one, and it starts off moving to the right. The energy of the force looks to be stored within the object itself in the form of its momentum, which is dependent on mass and velocity. To conserve the energy in momentum, the relationship between mass and velocity should result in some constant. Typically, objects don't fluctuate in mass, so velocity stays constant and the object proceeds at constant velocity forever.

We, the experimenters, sit in some Olympian position to view all of this. We look in detail at the particles of the leftmost object in its own inertial frame, look in detail at the particles of the rightmost object in its own inertial frame, and compare notes. When we created the universe, both objects started out physically identical, and after we accelerated the rightmost object, they still remain physically identical. Yet, the rightmost object moves at constant velocity, maintains constant momentum/obeys energy conservation, and thus somehow stores information about the force that acted on it in the past. Yet, no change happened to the objects' make-up.

Question: Where/how is this information stored? How do objects “know” and tend to their motion? I appreciate any answer, but I would more easily understand an answer in layman terms.

My thoughts surrounding this question (may disregard):

Physically, where the heck is this information? Somewhere in the matter, in space-time itself? I've never heard of quanta of momentum (momentum particles—well, what keeps those going? More momentum particles?). My fear is that the answer to this question reduces down to some inherent property of spatial dimensions. I'm not saying that such an answer or an other shouldn't be correct—if it is, then it is. Again, I'm approaching this with the base assumption that I'm lacking a crucial understanding. But, if the cause of motion in matter is just unphysical, what confounds and frightens me is how something with no physical manifestation may orchestrate all motion in the universe.

Thank you for your time.

Answer 1

both objects started out physically identical, and after we accelerated the rightmost object, they still remain physically identical

That’s just wrong. Whether you use classical mechanics or quantum mechanics, they are in completely different dynamical states. The only thing identical about them is their properties in their rest frames. The only reason you are confused about motion is that you are refusing to consider motion as part of the state!

As for “where” the information about motion is “stored”, this is similar to asking “where” the non-motion properties are “stored”. Where is the mass or charge or spin of an electron “stored”? In mainstream physics these are irrelevant questions. Current physics does not model reality as an information-processing machine with localized storage.

The notion that every electron independently “stores” its mass, charge, and spin is simply the wrong way to think about electrons. The one universal electron field, of which all electrons are quanta, has a particular mass, charge, and spin, but that information is “stored” only in the equations describing the field.

Answer 2

It seems to be very common misconception that the correct way to analyze an object is with respect to "its own reference frame", which apparently means a reference frame in which it's at rest.

That's the wrong way to understand reference frames. The right way is that you can pick any reference frame to solve any problem, since they are all equivalent. The best choice is whatever makes the problem easiest. That may in some cases be an inertial frame in which some object is at rest, but it can also be a center-of-mass frame in which nothing is at rest.

In this case, if you pick any particular inertial frame, you'll find that your two objects have different velocities. If you pick a different frame, the velocities will have different values, but they'll still be unequal. The fact that they're unequal is an invariant property that has actual physical meaning.

If you measure the velocity of one object in one inertial frame, and the velocity of another in a different inertial frame, and compare the resulting numeric values, you're comparing apples and oranges. It's like measuring one temperature in Celsius and another in Fahrenheit. If the results are numerically equal, it doesn't follow that the objects have the same temperature. You have to work consistently in one unit system (or convert consistently between the multiple unit systems that you use) if you want comparisons between measured quantities to be meaningful.

Answer 3

How do objects “know” and tend to their motion?

The object doesn't have to "know", and it actually shouldn't once it is moving with a constant velocity. As far as it is concerned, it is not moving, and the other particle is moving.

Velocity is all relative, and once the objects stop accelerating, they are both inertial reference frames, and the rules of physics can apply the same to both.

The information about the previously applied force is stored in the relative motion of the particles. The particle that was accelerated notices that the "stationary" particle is moving relative to it's own frame of reference. The "stationary" particle sees the accelerated particle moving relative to it's own frame of reference as well.

Neither are wrong. Velocity requires a reference frame, and the laws of physics can apply equally in different inertial reference frames.

The information about motion gets stored by the relative movement between the two, not in either particular object.

Answer 4

The answer to your question is the wavefunction. The wavefunction (squared modulus) is the probability distribution of the particle's position (or having a given momentum) in space.

A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. In Born's statistical interpretation in non-relativistic quantum mechanics,[8][9][10] the squared modulus of the wave function, |ψ|2, is a real number interpreted as the probability density of measuring a particle's being detected at a given place – or having a given momentum – at a given time, and possibly having definite values for discrete degrees of freedom.

https://en.wikipedia.org/wiki/Wave_function

I actually asked a question about this.

The state of microscopic object can be described, as well as its future behaviour can predicted with a high degree of precision by introduction of the abstraction called wave function. So the wave function, namely its parameters, itself defines microscopic state. Hence information about its parameters infered through macroscopic measurement is stored in the observer's dataset.

Where is the info of the wavefunction stored at?