4 ms·

"In gravity's rainbow, space does not exist below a certain minimum length, and time does not exist below a certain minimum time interval" Does this imply that

"In gravity's rainbow, space does not exist below a certain minimum length, and time does not exist below a certain minimum time interval" Does this imply that neither space nor time can go below the given threshold independently? I.e.: could a situation be imagined where time remains above the minimal interval, but space is below? Also, would those answers be different depending on the observer's time / position?

phn 12y ago
I had never head of anything like this. Does that mean that space and time are somehow discrete instead of continuous?
- marktangotango 12y ago
  This idea kind of ties into the idea of a 'computable' universe: I'm no expert but this article gives some ideas[1]. [1] http://en.wikipedia.org/wiki/Digital_physics#Criticism http://en.wikipedia.org/wiki/Digital_physics#Criticism
- jarin 12y ago
  For all practical purposes, they kind of appear to be: https://en.wikipedia.org/wiki/Planck_length https://en.wikipedia.org/wiki/Planck_length https://en.wikipedia.org/wiki/Planck_time https://en.wikipedia.org/wiki/Planck_time
- tjradcliffe 12y ago
  They have a scale. They are not "discrete" in the sense that pixels are discrete because there is no grid (no orientation, no preferred direction, etc). Think of it like the resolution of a microscope: you can only see objects down to scales of 1 micron, say. That doesn't make what you are looking at discrete at the 1 micron level. It makes it blurry (invisible, or in the case of space and time, non-existent) below that level.
  - PaulHoule 12y ago
    How it shows up depends on the model. Superstrings are objects of (usually) Planckian size, so if the particles are the size of the "grain" then that is one way a scale could manifest. In other models like loops quantum gravity you can only ask questions about loops in space and not about points so that is another way the scale manigests.
- duaneb 12y ago
  Discrete is probably not the best way of looking at it; instead, think of it as the smallest scale across which space can change. From this perspective, it's not possible to discern between a quantized and continuous spacetime.
laxatives 12y ago
I'm definitely not an expert, but I was under the impression that both space and time are already thought to be discrete and have minimum quanta, Planck length (10^-36 m) and Planck time (10^-44 s). I guess this new theorem suggests that not only do they have minimum values, they don't exist between these points. Sort of like how pixels aren't really sized objects, but they sort of fill the space between them -- this might be a terrible analogy.
- pavel_lishin 12y ago
  I thought that it was the opposite - you can't draw half a pixel on a screen. (Perhaps a better analogy would be that you can't represent every real number as a floating point integer.)
mrfusion 12y ago
So does discrete space and time also solve zenos paradox? (or was that already solved classically?)
- Retric 12y ago
  Yes. But Zenos paradox has a simple solution; Time. It takes k(1) * 1/x time to reach k(2) * 1/x location assuming constant velocity. Basically moving an infinitely small distance takes an infinitely small unit of time.
  - gohrt 12y ago
    Zeno's paradox assumes less than "constant velocity". It assumes that there is a minimum finite velocity, or that an infinite number of moments in time must be experienced, not skipped over. Zeno's paradox is about our casual/informal passing between the continuous and the discrete. If in reality there is some planck-length-like discrete grid structure to the universe, there is no paradox.
    - Retric 12y ago
      There are two options that are intuitively acceptable. Discrete space, or continuous space and time. You can travel through infinite points in finite time iff time is infinitely divisible.

phn 12y ago

I had never head of anything like this. Does that mean that space and time are somehow discrete instead of continuous?

marktangotango 12y ago
This idea kind of ties into the idea of a 'computable' universe: I'm no expert but this article gives some ideas[1]. [1] http://en.wikipedia.org/wiki/Digital_physics#Criticism http://en.wikipedia.org/wiki/Digital_physics#Criticism
jarin 12y ago
For all practical purposes, they kind of appear to be: https://en.wikipedia.org/wiki/Planck_length https://en.wikipedia.org/wiki/Planck_length https://en.wikipedia.org/wiki/Planck_time https://en.wikipedia.org/wiki/Planck_time
tjradcliffe 12y ago
They have a scale. They are not "discrete" in the sense that pixels are discrete because there is no grid (no orientation, no preferred direction, etc). Think of it like the resolution of a microscope: you can only see objects down to scales of 1 micron, say. That doesn't make what you are looking at discrete at the 1 micron level. It makes it blurry (invisible, or in the case of space and time, non-existent) below that level.
- PaulHoule 12y ago
  How it shows up depends on the model. Superstrings are objects of (usually) Planckian size, so if the particles are the size of the "grain" then that is one way a scale could manifest. In other models like loops quantum gravity you can only ask questions about loops in space and not about points so that is another way the scale manigests.
duaneb 12y ago
Discrete is probably not the best way of looking at it; instead, think of it as the smallest scale across which space can change. From this perspective, it's not possible to discern between a quantized and continuous spacetime.

laxatives 12y ago

I'm definitely not an expert, but I was under the impression that both space and time are already thought to be discrete and have minimum quanta, Planck length (10^-36 m) and Planck time (10^-44 s). I guess this new theorem suggests that not only do they have minimum values, they don't exist between these points. Sort of like how pixels aren't really sized objects, but they sort of fill the space between them -- this might be a terrible analogy.

pavel_lishin 12y ago
I thought that it was the opposite - you can't draw half a pixel on a screen. (Perhaps a better analogy would be that you can't represent every real number as a floating point integer.)

mrfusion 12y ago

So does discrete space and time also solve zenos paradox? (or was that already solved classically?)

Retric 12y ago
Yes. But Zenos paradox has a simple solution; Time. It takes k(1) * 1/x time to reach k(2) * 1/x location assuming constant velocity. Basically moving an infinitely small distance takes an infinitely small unit of time.
- gohrt 12y ago
  Zeno's paradox assumes less than "constant velocity". It assumes that there is a minimum finite velocity, or that an infinite number of moments in time must be experienced, not skipped over. Zeno's paradox is about our casual/informal passing between the continuous and the discrete. If in reality there is some planck-length-like discrete grid structure to the universe, there is no paradox.
  - Retric 12y ago
    There are two options that are intuitively acceptable. Discrete space, or continuous space and time. You can travel through infinite points in finite time iff time is infinitely divisible.