Time quantization in classical physics

[hclatomic]

Hello,

It is considered that the time is continuous in classical physics, but it sounds paradoxal to me, let me explain.

Let a particle inside a galilean frame of reference. This particle can only be measured either at rest, either in motion, but never simultaneously at rest and in motion. Therefore calling $t_0$ the last time when the particle can be measured at rest, and $t_1$ the first time when it can be measured in motion, we must have $t_0 \neq t_1$. It can not exist a time $t$ verifying $t_0 < t <t_1$, because at such a time the particle would be simultaneously at rest and in motion. We are then led to consider that the time must be quantized in classical mechanics, the quantum of time being $\Delta t = t_1 - t_0$.

Of course the situation is different in quantum mechanics, but my point is only concerning the classical mechanics for which it is usually accepted that the time is continuous.

Don't you think there is a paradox here ?

 

[Ibix]

Don't you think there is a paradox here ?

No. It's a variant on Zeno's Paradox, and is therefore thoroughly answered by stopping using verbal reasoning and starting using calculus.

 

[hclatomic]

No. It's a variant on Zeno's Paradox, and is therefore thoroughly answered by stopping using verbal reasoning and starting using calculus.

As far as I can read I used the calculation in my question. I am talking about physics and you tell me about philosophy, stated 500 BC. I am aware of the differential calculation, I think you refer to this, but there are the mathematics and the philosophy, and there is the physics.

So in practice, not in mathematics nor in philosophy, can a particle be at the same time at rest and in motion, in classical mechanics ?

 

[dextercioby]

Your reasoning can be summed as: what is the next real number in increasing order after 2? Good luck finding it. :)

 

[hclatomic]

Your reasoning can be summed as: what is the next real number in increasing order after 2? Good luck finding it. :)

In mathematics you would be right, but I am talking about classical physics.
So my question stands, not in mathematics nor in philosophy, but in clasical physics : can a particle be at the same time at rest and in motion ?
Did anyone measure such thing ?

 

[Nugatory]

$\Delta{t}=t_1-t_0$ can be made arbitrarily small. This implies that $t$ is continuous even though $t_1$ is never equal to $t_0$ and even though (as you point out above) an object cannot be moving and not moving at the same time.

Thus, the answer to your original question is that there is no paradox here. This thread is closed.