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

1. Mar 20, 2012

### TylerH

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?

Tyler

2. Mar 20, 2012

### genericusrnme

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

3. Mar 20, 2012

### TylerH

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.

4. Mar 20, 2012

### TylerH

Thanks for the explanation. I need to really learn physics before I try to disprove time travel, apparently. :)

5. Mar 20, 2012

### genericusrnme

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

6. Mar 20, 2012

### TylerH

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.

7. Mar 23, 2012

### Khashishi

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.

8. Apr 12, 2012

### TylerH

Loop quantum gravity, one of the major hypotheses for unifying general relativity and quantum mechanics, quantizes space-time.