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Suppose you have the power to take a snapshot of an object containing all its information. Say a ball was thrown to a direction to your right and you took a snapshot of it. This snapshot contains all information about the ball in that very specific moment of time.

  • How would you know where the ball is going given the snapshot which is a frozen state of its all information?

  • Is inertia somehow stored in the configuration of the fundamental particles of an object?

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    $\begingroup$ Classically, the information you require to describe the state of an object is its position and momentum. In the hypothetical situation you describe you only have the position so it is an incomplete description of the system. $\endgroup$ – S V Jun 13 at 15:14
  • $\begingroup$ Quantum mechanically you need "less information" to get the evolution of the system. You could store the state vector at some given time, and then the Schrödinger equation could tell you exactly how that evolves at a later time. But to me that sounds like a cheat, because you are storing the complete mathematical object that describes it extrinsically (it would be as if you froze the classical object, but you stored the value of its momentum, when you unfreeze it you just plug in that value and voilà, everything works) $\endgroup$ – S V Jun 13 at 15:22
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I already posted what I think in the comments, but I want to post a full answer for two reasons. First, I want to be more precise in the physical arguments. And second, I want to point out that I believe the question is misleading and why.

In classical mechanics the state of a particle is determined completely by its position $\mathbf x$ and its momentum $\mathbf p$ (I am not going to talk about solid objects because a full description of those would require continuum mechanics and the complexity of that would obscure the answer). Such a system evolves through the equations of motion, these have three equivalent forms, due to Newton, Lagrange and Hamilton. All of those equations would take us from $(\mathbf{x}, \mathbf{p})$ to $(\mathbf{x}(t), \mathbf{p}(t))$.

When you say (emphasis mine):

Suppose you have the power to take a snapshot of an object containing all its information.

It is very misleading. Saying "a snapshot" sounds like you are talking about just looking at the position of the particle(s), but storing only its position by no means captures "all its information", it is an incomplete description of the system and therefore you cannot know how it can evolve afterwards.

What you can do is store the complete information of the mathematical description of the system $(\mathbf{x}, \mathbf{p})$ and then try to experimentally reproduce those conditions (which in practice can be very hard to achieve).

If you "zoom in" you have that your physical system is really quantum mechanichal, but there the idea of a "snapshot" is even more shady than the one you proposed with the ball, I can't even imagine what that would be. But you can still do what you did in the classical case: you take your mathematical description, the state vector $\mathbf \Psi$ and evolve it through the equations of motion to $\mathbf \Psi (t)$ (again, in practice this can be very, very complicated).

The bottom line is that a "snapshot of an object containing all its information" is not at all like a photograph, but they do exist, they are precisely the mathematical objects we use in our theories. What may be confusing you is the concept of mass and how it keeps objects from changing their state of motion, but there have already been a lot of very good discussions of that subject.

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This snapshot contains all information about the ball in that very specific moment of time.

As @S V has already pointed out, the snapshot only provides you with information on the position of the object.

How would you know where the ball is going given the snapshot which is a frozen state of its all information?

You wouldn't, because you don't have sufficient information. Two snapshots while recording the time for each would give you at least the average velocity between the snapshots.

Is inertia somehow stored in the configuration of the fundamental particles of an object? Inertia is a property of matter that resists a change of velocity

Yes, inertia is a property of matter that causes it to resist changes in velocity, according to Newton's first law. You can say the quantity of inertia possed by an object is proportional to its mass.

Hope this helps.

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I think the question really has nothing to do with photos. Instead, I think the question is about inertia and where it is located with respect to an object. E.g., is it in the object's gravitational field? Is it in the magnetic field if the object is a charged particle? Etc.

I think there is not a clear and definite answer to your questiin. Arguments have been made to the effect that kinetic energy, rest mass, momentum, and inertia are prooerties of fields (primarily gravitational and electromagnetic), but there is not yet a convincing particle model that provides fields having the right properties. The present philosophy is to ignore the question of where inertia resides.

That said, it might be worthwhile to think about what kinds of practical experiments might provide an answer. IF inertia resides in fields, what sort of experiment could prove it?

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