"Go back to First Principles" is a common request of pedants and managers.
Okay, let's do it.
Imagine a universe containing a single Point. It has no structure, no mass, no energy, or any property of any sort: it's just a Point. Only there is no point to a single Point. It exists, as we have defined it; but that's all: it only exists. It has no position, as there is no frame of reference for it to have a position in. Without position there can be no motion. It's a very lonely, very boring Point.
*Pop* and a second point exists. Now there is a frame of reference - the other Point. Assuming the universe containing these points is a lawful one, then each point now experiences Distance.
A universe without motion is not only dull, it's improbable. Change is possibly the only 'universal' constant. Thus our Points can move. Thus they also experience Time.
No matter how complex their motion might appear to external observers like ourselves, the Points are only able to notice change in the distance between themselves. Which may vary from infinitesimally small to infinity minus an infinitesimal. There motion may be smooth or rhythmical or complex, or all of these in turn.
If Time and Distance are infinitely smooth, then there are an infinite number of possible variations in the distance between these Points; but if Time has a definite tick and distance a minimum step (which must occur together: there cannot be one without the other) then the number of variations is finite. At some 'point' in time, the sequence of variations would be repeated.
So an imaginary universe of just two imaginary points already exposes one of the key challenges of modern physics.
First Principles have there limits :-)
Okay, let's do it.
Imagine a universe containing a single Point. It has no structure, no mass, no energy, or any property of any sort: it's just a Point. Only there is no point to a single Point. It exists, as we have defined it; but that's all: it only exists. It has no position, as there is no frame of reference for it to have a position in. Without position there can be no motion. It's a very lonely, very boring Point.
*Pop* and a second point exists. Now there is a frame of reference - the other Point. Assuming the universe containing these points is a lawful one, then each point now experiences Distance.
A universe without motion is not only dull, it's improbable. Change is possibly the only 'universal' constant. Thus our Points can move. Thus they also experience Time.
No matter how complex their motion might appear to external observers like ourselves, the Points are only able to notice change in the distance between themselves. Which may vary from infinitesimally small to infinity minus an infinitesimal. There motion may be smooth or rhythmical or complex, or all of these in turn.
If Time and Distance are infinitely smooth, then there are an infinite number of possible variations in the distance between these Points; but if Time has a definite tick and distance a minimum step (which must occur together: there cannot be one without the other) then the number of variations is finite. At some 'point' in time, the sequence of variations would be repeated.
So an imaginary universe of just two imaginary points already exposes one of the key challenges of modern physics.
First Principles have there limits :-)
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