Time quantization in classical physics

In summary, the conversation discusses the concept of time in classical physics and whether it is continuous or quantized. The participant argues that there is a paradox in the idea of a particle being both at rest and in motion at the same time, but the other participant points out that this is a variation of Zeno's Paradox and can be solved using calculus. The discussion also touches on the role of mathematics and philosophy in understanding this concept. Ultimately, it is concluded that while time may appear quantized, it is actually continuous and can be made arbitrarily small. Therefore, there is no paradox in classical physics.
  • #1
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 [itex]t_0[/itex] the last time when the particle can be measured at rest, and [itex]t_1[/itex] the first time when it can be measured in motion, we must have [itex]t_0 \neq t_1[/itex]. It can not exist a time [itex]t[/itex] verifying [itex]t_0 < t <t_1[/itex], 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 [itex]\Delta t = t_1 - t_0[/itex].

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 ?
 
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  • #2
hclatomic said:
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.
 
  • #3
Ibix said:
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 ?
 
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  • #4
Your reasoning can be summed as: what is the next real number in increasing order after 2? Good luck finding it. :)
 
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  • #5
dextercioby said:
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 ?
 
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  • #6
##\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.
 

1. What is time quantization in classical physics?

Time quantization in classical physics refers to the idea that time is not continuous, but rather is made up of discrete, indivisible units. This concept suggests that time is not infinitely divisible, but rather has a smallest possible unit of measurement.

2. Why is time quantization important in classical physics?

Time quantization is important in classical physics because it helps to explain certain phenomena that cannot be understood using continuous time. For example, the stability of atoms and the behavior of particles at the quantum level can only be explained by considering the discrete nature of time.

3. How does time quantization affect our understanding of motion?

Time quantization can affect our understanding of motion by introducing the concept of a minimum time interval. This means that the speed and position of an object can only be measured accurately to a certain degree, and there may be limits to how accurately we can predict the future position of an object.

4. Can time quantization be observed in the real world?

Currently, there is no direct evidence or experimental proof for time quantization in the real world. However, some theories, such as loop quantum gravity, suggest that the fabric of space-time is quantized at the smallest scales. This is an area of ongoing research and debate in the field of physics.

5. How does time quantization differ from the concept of Planck time?

Planck time is the smallest possible unit of time that can be measured, according to the theory of quantum mechanics. It is related to the Planck length and the Planck mass, and is much smaller than the time interval suggested by time quantization in classical physics. While time quantization suggests that time is made up of discrete units, Planck time is a specific value that is derived from fundamental constants in physics.

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