What Is Motion and How Is It Defined in Modern Physics?

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Motion is defined in modern physics as the change in position of an object. It is not quantized, meaning it can occur in a continuous manner without discrete steps. Additionally, motion cannot be explained without the concept of spacetime, as spacetime provides the framework for determining an object's position in both space and time. Understanding these principles is crucial for grasping the fundamentals of physics. The discussion highlights the integral relationship between motion, spacetime, and the continuity of movement.
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I have couple of question related to what motion is;


1) What is the definition of motion in today's physics?

2) Is motion quantized? If it is; what are the effects of it?

3) Can motion be explained without spacetime?
 
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1. Motion is a change in position of an object.

2. No, motion is not quantized.

3. Absolutely not, as spacetime is what allows us to label an objects position in both space and time.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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