Motion

[Resha Caner]

Is motion discrete or continuous (mathematically speaking)?

 

[leftrightleftrightleft]

Is motion discrete or continuous (mathematically speaking)?

Continuous.

Take 2 points, A1 and B and say you move from A1 to B in a given time (t2-t1) where t2 is the time you reach B and t1 is the time you leave A1. Set t1=0 as an arbitrary reference and t2=t.

There's nothing mathematically that limits you from breaking up that motion from A1 to B into two segments: A1 to A2 and A2 to B (where A1<A2<B).

There's nothing mathematically that limits you from breaking up that motion from A1 to A2 to B into three segments: A1 to A2 and A2 to A3 and A3 to B (where A1<A2<A3<B).

There's nothing mathematically that limits you from going on and doing this an arbitrary number of times: A1 to A2 and A2 to A3 and … and A(n-2) to A(n-1) and A(n-1) to An, Where An=B and A1<A2<A3<…<A(n-2)<A(n-1)<An.

Now let n --> infinity and sum all the segments and divide by t:

 

[Resha Caner]

Sorry. Maybe I didn't state the question well. Let me try again.

I meant real, physical motion but I wanted to clarify "discrete" and "continuous" as being used in the mathematical sense - since those words got confused in a recent thread.

So, is real, physical motion discrete or continuous? IOW, when something moves though a space, does it pass through every infinitesimal point in that space, or does it step discretely by some quantum amount?

 

[Colter]

Sorry. Maybe I didn't state the question well. Let me try again.

I meant real, physical motion but I wanted to clarify "discrete" and "continuous" as being used in the mathematical sense - since those words got confused in a recent thread.

So, is real, physical motion discrete or continuous? IOW, when something moves though a space, does it pass through every infinitesimal point in that space, or does it step discretely by some quantum amount?

Throughout the movement with time objects have a fixed position, but this becomes greatly complicated by the fact that even objects that appear to be stationary are in motion through space.

 

[Chesterton]

So, is real, physical motion discrete or continuous? IOW, when something moves though a space, does it pass through every infinitesimal point in that space, or does it step discretely by some quantum amount?

Question from a non-mathematician: how many infinitesimal points are there between points A and B?

 

[Resha Caner]

Question from a non-mathematician: how many infinitesimal points are there between points A and B?

An infinite number. Hence the puzzle (Zeno's Paradoxes, etc.).

 

[quatona]

Sorry. Maybe I didn't state the question well. Let me try again.

I meant real, physical motion but I wanted to clarify "discrete" and "continuous" as being used in the mathematical sense - since those words got confused in a recent thread.

I´m neither a mathematician nor a physician, but I´m pretty sure that physical events are expected to model mathematical abstractions.

So, is real, physical motion discrete or continuous? IOW, when something moves though a space, does it pass through every infinitesimal point in that space, or does it step discretely by some quantum amount?

Are mathematical points supposed to exist in physical reality?

 

[Armoured]

Discrete. However the divisions are extremely small (Planck lengths and quantised energy) so for all practical purposes, it's continuous. Einstein trumps Zeno.

 

[Chesterton]

An infinite number. Hence the puzzle (Zeno's Paradoxes, etc.).

In that case, motion is discrete.

 

[Resha Caner]

Are mathematical points supposed to exist in physical reality?

My opinion is no, but some may differ with that.

 

[Resha Caner]

Discrete. However the divisions are extremely small (Planck lengths and quantised energy) so for all practical purposes, it's continuous. Einstein trumps Zeno.

In that case, motion is discrete.

So one could say the object ceases to exist centered at point A, and begins to exist at point B some discrete time later. If that is the case, how does the material centered at A get to B? Or is it the same material?

 

[quatona]

My opinion is no, but some may differ with that.

The digital revolution has a great impact, apparently.

 

[Chesterton]

So one could say the object ceases to exist centered at point A, and begins to exist at point B some discrete time later. If that is the case, how does the material centered at A get to B? Or is it the same material?

It digs a quantum tunnel.

 

[Resha Caner]

It digs a quantum tunnel.

I don't know if that's meant to be a joke or not.

Quantum tunneling refers to a particle moving through a potential barrier. I'm not quite sure how "nothing" is a potential barrier. Even more so I don't see quantum tunneling as an explanation for how the particles moves beyond the barrier, but more a determination of when it can happen based on the probability distribution of the particle and the potential of the barrier.

So, I would have the same questions for tunneling as I do for simple motion.

 

[Chesterton]

So, I would have the same questions for tunneling as I do for simple motion.

We all do.

 

[Loudmouth]

Is motion discrete or continuous (mathematically speaking)?

If my understanding of physics is correct . . .

According to quantum mechanics, motion is uncertain in specific situtations. If I am remembering Q-chem correctly from 20 years ago, if the DeBroglia wavelength for an object becomes dominant, then the position of an object at any one time is described by a probability in the form of a wave function.

Wave nature of electron

It is a bit like the famous Schroedinger's cat, where it is both dead and alive at the same time, and only becomes one of those things when observed. Therefore, an object would be both here and there at the same time, only appearing here or there when observation collapse the wave function.

 

[essentialsaltes]

*If* space is quantized, then it would be necessarily discrete. Nobody knows if space is quantized.

Quantum effects obviously add their own weirdness. An electron can use quantum tunneling to go through a barrier it can't classically go through.

Does that mean it teleported through the barrier and its motion is 'discrete'?
Does that mean the wavefunction is 'real' and the electron should be identified with the wavefunction and the wavefunction does pass continuously through the barrier? So motion is continuous?

I don't know. Time to consult the philosophers again.

 

[variant]

I don't know if that's meant to be a joke or not.

Quantum tunneling refers to a particle moving through a potential barrier. I'm not quite sure how "nothing" is a potential barrier. Even more so I don't see quantum tunneling as an explanation for how the particles moves beyond the barrier, but more a determination of when it can happen based on the probability distribution of the particle and the potential of the barrier.

So, I would have the same questions for tunneling as I do for simple motion.

Quantum tunneling also relates to how the electron is thought to exist with it's position being a probability in the various places surrounding the nucleolus of an atom.

If the electron moved classically (from A to B) it could not breach the barrier because the physics of repulsion don't allow it, but since it simply exists as a probability which has some (often small) chance of being across the barrier quantum tunneling can happen.

The electron would (at least some of the time) move the same way through space as it does through the barrier, discreetly.

 

[KCfromNC]

The original question looks like a case of making up artificial bins that reality must fit into (discrete vs. continuous) rather than looking at reality and explaining what we see - in this case, wave nature of particles, the uncertainty principle, and so on.

 

[Loudmouth]

*If* space is quantized, then it would be necessarily discrete. Nobody knows if space is quantized.

Quantum effects obviously add their own weirdness. An electron can use quantum tunneling to go through a barrier it can't classically go through.

I could be wrong, but I think that quantum tunneling is thought to be the mechanism that allows for nuclear decay.