Is Zeno's Paradox Relevant in Understanding Digital and Real-World Motion?

[p764rds]

Here is an ultra short repeat of the Zeno Paradox, but please google it for a longer version with pictures etc:

Think of a moving arrow.
In an instant of time an arrow cannot move (bc its an *instant*).
An arrow's movement is given by the sum of the movements at every instant. But since in anyone instant it cannot move then it follows that it cannot move at all. Zeno was laughed out of court at the time.

In a digital 3D virtual world pixels can only *jump* from one digital coordinate to another. There is no such thing as *continuous* movement in a computer game. The fastest speed possible is determined by the computer's clock. A screen pixel can only jump from one coord to another. Similarly every curve zooms into show reality is not curved rather rectangular pixellation.

I posit that there can be only discrete *jumps* in the real world too, not only in energy but in movement as well, and that Zeno had it correct in 500 BC :)

What do you think?

 

[atyy]

Yes, there conceivably can be discrete jumps in the real world too, as a solution to Zeno's paradox. However, another solution is that spacetime is smooth - so we first imagine discrete jumps, but we are able to take the discreteness as small as we please using the mathematical notion of a limit. So both of these would solve Zeno's paradox, essentially incorporating the discrete jumps idea with or without a limit.

As far as we can tell through experiments, the limit idea is more useful at the moment, because our spacetime has Lorentz symmetry, which is a smooth symmetry. If Lorentz symmetry is found not to be exact, one possibility could be that spacetime or a more fundamental structure is discrete.

Here is a recent review of the experimental tests of Lorentz invariance:

http://arxiv.org/abs/1304.5795
Tests of Lorentz invariance: a 2013 update
Stefano Liberati
Class. Quantum Grav. 30 133001 doi:10.1088/0264-9381/30/13/133001

 

[bhobba]

You must remember physics is a model.

Obviously an arrow does move, the solution to Zeno's paradox being since we can never know what happens in an instant we break it up into smaller and smaller units of time and take a limit (as Atyy also explains). The physical assumption is the limit exists. In this way what's going on in an actual instant is avoided - which isn't a problem really - since we can't observe an actual instant.

Thanks
Bill

 

[humbleteleskop]

Ok, one solution is that space is digital rather than analog, where time can be either I guess. But does it work the other way around? Do we have a solution if space is continuous and only time is composed of discrete steps? I think not, but I don't see a way to properly grasp it.

 

[p764rds]

Both time *and* space must be digital. As regards 'in the limit' the area under a curve is a numerical issue.
Area is the sum of small squares under a curve. Also note that Pi is infinite precision - its has to be because the area of a circle cannot be comprised of an infinite number of squares (to make a *real* curve possible).
I mean its *physically* impossible to have a perfect circle because it implies an infinite number of squares to make up the circle.

All curves must be pixellated when zooming in. That includes space-time.

We all went wrong when Zeno showed that objects cannot move if space were continuous.

The in-the-limit idea is a monstrous fudge!

 

[humbleteleskop]

I'm afraid I don't follow, possibly because I don't know what are you referring to by "in-the-limit idea". You also don't seem to be talking about time.

Can you use Achilles and tortoise to formulate explanation?

 

[humbleteleskop]

The fastest speed possible is determined by the computer's clock.

Given enough computer speed, it's display refresh rate that is limiting factor, assuming objects are not supposed/allowed to skip pixels. So on a display with refresh rate of 60 frames per second maximum speed would be 60 pixels per second. Little computer people would call it the speed of light.

It's only logical then to conclude refresh rate of our universe is 299,792,458 frames per second. Great refresh rate and amazing resolution, playing us must be real fun.

 

[Dale]

I posit that there can be only discrete *jumps* in the real world too,

There is no evidence for this. Thread closed.