Exploring the Limits of Travel: Planck Lengths

[wolram]

Take a circle that can be (traveled) by some thing, then keep reducing it in
size until distinct Planck lengths are reached, does this mean that the traveler can not move any more, as there is no such thing as half a Planck
length ?

 

[Meir Achuz]

The Planck length is not a precise smallest length.
It is just a convenient dimensional length appropriate for some cases.
It would be like saying there is no half a nanometer.

 

[rbj]

The Planck length is not a precise smallest length.
It is just a convenient dimensional length appropriate for some cases.
It would be like saying there is no half a nanometer.

a hellava difference in order of magnitude between a Planck Length and a nanometer!

In fact, the Planck Length and Planck Time (or there abouts, some of us might view units with $4 \pi G$ normalized to 1 as more of a natural choice for "natural units" than just normalizing $G$ as in Planck Units) are not necessarily the discrete units of length or time of some discrete physics or cellular automa system that have been hypothesized by some. but there are some elegant reasons for some to think that it would be so, however such reasoning might be considered to be aesthetic, rather than science. since the Planck Length or Planck Time are so damn small, i don't foresee human beings ever being able to construct an experiment that would allow measurement in anywhere close to this scale. so if reality truly is discrete with something around the Planck Length and Planck Time as the size of cells in some kind of grid, i don't think that human beings will ever know.

 

[jasc15]

isnt the inplication still quite huge here, even if these incredibly small things are undetectable? the idea that time and length (and matter) are discrete rather than continuous quanities.

 

[AlphaNumeric]

Take a circle that can be (traveled) by some thing, then keep reducing it in size until distinct Planck lengths are reached, does this mean that the traveler can not move any more, as there is no such thing as half a Planck length ?

Sounds vaguely like how M theory in 11 dimensions can reduce itself in Type IIA string theory in 10 dimensions by letting the radius of it's compactified dimension go to zero in the non-perturbative limit.

The coupling strength is related to the string length, but having spent the last fortnight reading textbooks and papers on this stuff, the Planck length isn't mentioned often (though I might have just missed it, I skim a lot of things).

 

[Meir Achuz]

"however such reasoning might be considered to be aesthetic, rather than science"

 

[wolram]

isnt the inplication still quite huge here, even if these incredibly small things are undetectable? the idea that time and length (and matter) are discrete rather than continuous quanities.

This is part of my question, ie discrete rather than smooth, it surly makes a
BIG difference to how things work.

 

[jasc15]

We already know that fields like fluid mechanics and thermodynamics are incomplete in that they assume matter as being continuous rather than as discrete particles. the step from thermodynamics to the more complete statistical mechanics (or kinetic theory, I am not too sure of the difference as i haven't studied either of them) as i understand it is what led to quantum theory and the idea of the discrete atom. If matter is discrete, then why not time and distance? With the symmetry of the universe, this doesn't seem too far an assumption.