Does Planck length and irrational solutions mean time can't be reversed?

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Discussion Overview

The discussion centers around the implications of Planck length and irrational solutions in equations related to particle positioning, particularly in the context of time's reversibility. Participants explore concepts of quantization in space and time, and how these might relate to theories in physics, including those from general relativity and quantum mechanics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether the Planck length implies a loss of information as time progresses, suggesting that if particle positions are rounded to multiples of the Planck length, this could affect the reversibility of time.
  • Another participant argues that irrational solutions can be made rational through appropriate unit selection, challenging the necessity of rounding to the Planck length.
  • Some participants discuss the idea of space being quantized, with one suggesting that if space were quantized, it would lead to indistinguishable points at the Planck scale.
  • There is mention of loop quantum gravity as a theory that quantizes space-time, with a participant noting their limited understanding of such theories.
  • Concerns are raised about the implications of quantizing space-time on fundamental symmetries like rotational and Lorentz invariance.
  • One participant expresses a preference for a quantized and finitely computable theory of the universe, reflecting a background in computer science.

Areas of Agreement / Disagreement

Participants express differing views on the quantization of space and time, with some supporting the idea while others question its implications and feasibility. The discussion remains unresolved regarding the relationship between Planck length, irrational solutions, and the reversibility of time.

Contextual Notes

Limitations include varying interpretations of quantization, the dependence on definitions of space and time, and the unresolved nature of mathematical implications regarding irrational solutions.

TylerH
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If there is an irrational solution to an equation for where a particle should be, for example from an ODE, then what effect does Planck length have on that? Does the actual position of the particle get rounded to an a multiple of the Planck length? If it does, wouldn't that imply there is a loss of information as time flows forward, making it impossible to go back?

Thanks for your time,
Tyler
 
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The plank length is just a unit to measure distance with (although it is nice in the fact that in plank units G=c=h=1), any irrational solution could easily be made to be rational by picking units that make it rational so irrationality doesn't really matter. Why would things have to round up to a multiple of the plank length?
No standard theories quantise distance.

I could be misinterpriting what you're trying to ask here however
 
No, you seem to be interpreting what I said correctly. I assumed that since between Planck length, two points are indistinguishable, then space is quantized.
 
Thanks for the explanation. I need to really learn physics before I try to disprove time travel, apparently. :)
 
No problem buddy :D
If theories were to quantize space then the plank units would be the perfect candidate to quantize it as (but then results derived from these theories would have explicitly quantised results so you wouldn't bump into the problems you described). There's also been thoughs about the plank length being lorentz invariant and I believe that loop quantum gravity quantizes area in units of plank length squared, but I really know very little about these theories.

In terms of the results of your standard run of the mill quantum mechanics, as it is now, there is no quantization of time or space
 
I'm not that well educated on the standard theories of higher physics. I know there are ODEs for the relation between the change in time and some function of gravity and speed; with gravity itself really being a function of position and time, and speed being a function of time. Which I think are from Einstein's theory of relativity...

What I was thinking is that maybe spacetime was actually quantized itself, as in it actually rounded somehow to quantize to the Planck length. (Even subatomic particles would be centered around an integral of the grid. I just found out this is called a lattice gauge theory, I think.) I tend to think like a computer scientist, since that is my favorite area of study. Hence my tendency towards a quantized and finitely computable theory of the universe.
 
I can't think of any way of quantizing space-time without breaking the concept of rotational invariance and Lorentz invariance. If we assume each grid cell has the same shape, it seems to me that the grid cell needs to be some 4d variant of cubic or hexagonal closest packing. Hexagonal grid cells would limit you to rotation by 60 degrees, which totally diagrees with measurement.
 
Loop quantum gravity, one of the major hypotheses for unifying general relativity and quantum mechanics, quantizes space-time.
 

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