Is space "discrete" or "continuous"? In other words, can a particle be in only "set" positions or is there an infinite number of positions that it can be in. (At a very small scale, a particle could be in an infinite number of positions, or... it can only be in a discrete number of positions)

I claim that space is NOT continous.

It instead is discrete. This discreteness thusly leads to the (in-exceedable) speed of light.

So, if we have discreteness, then all interactions/computations can only reach a certain distance. For example, two particles next to each other can interact (it may well be a huge number distance away, but still there is a FIXED MAXIMUM distance in which particles and interact). This maximum rate of the movement of interactions (a particle can only react with another only so far away) is in essence the speed of light.

Well, let's say that space is continous--there is an infinite number of positions that a particle can be in. This means that information/computation/interaction can move at ANY conceivable speed, which means no speed of light as a MAXIMUM allowed rate.

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Originally posted by brum:
First of...

Is space "discrete" or "continuous"? In other words, can a particle be in only "set" positions or is there an infinite number of positions that it can be in. (At a very small scale, a particle could be in an infinite number of positions, or... it can only be in a discrete number of positions)

I claim that space is NOT continous.

It instead is discrete. This discreteness thusly leads to the (in-exceedable) speed of light.

So, if we have discreteness, then all interactions/computations can only reach a certain distance. For example, two particles next to each other can interact (it may well be a huge number distance away, but still there is a FIXED MAXIMUM distance in which particles and interact). This maximum rate of the movement of interactions (a particle can only react with another only so far away) is in essence the speed of light.

Well, let's say that space is continous--there is an infinite number of positions that a particle can be in. This means that information/computation/interaction can move at ANY conceivable speed, which means no speed of light as a MAXIMUM allowed rate.

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This is an idea that has been floating around for quite some decades now. However, the big problem is that it is very difficult to build Lorentz-invariant dynamics on a discrete spacetime. Nobody has yet done it fully convincingly...

I don't think your idea in your last paragraph really follows.

David

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Originally posted by Brad_Ad23:
As for constructing Lorentz invarient dynamics on a discrete background, some of the new work within loop quantum gravity shows immense promise in heading in that direction.

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Indeed it does show promise, but we're not there yet. This is why I said "nobody has done it yet fully convincingly" rather than saying it hasn't been done at all.

In fact one of the big hurdles LQG has faced for the past decade has been its lack of Lorentz invariance - something I spoke with Lee Smolin about recently. In his words, he was "just confused about it for a decade".

David

Indeed if space were discrete then how would we say what lay between the lattice points?
Nothing?

In that case nothing would exist between the points and we would again have continous space.

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Originally posted by ObsessiveMathsFreak:
But this would mean that particles would have to "jump" from point to point on a certain lattice.

Indeed if space were discrete then how would we say what lay between the lattice points?
Nothing?

In that case nothing would exist between the points and we would again have continous space.

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Yes, between would be nothing--vacuum.

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It's not that a particle could jump from this point all the way over to this point. It's instead more like a cellular automata. Basically, "information" can only "move" to "have an influence over" or "cause something" at some other place at a certain rate. An event that happens in point A, for example, cannot be "felt" or have any effect on anything else outside of it's influence (or how far the cellular automata reaches--whether it be only the nearest neighbors or any points <= 9 points away or 1 million points away, whatever it may be). In other words, information can only travel so quickly because, since it's discrete, information can move only at a maximum, fixed amount of points away at a time.

1 dimensional example:

XXOOXOXOXOOOXXXOXXOXOOOXOXXOXO
^an event happening at this point here

can first have an effect on each point on either side
then, the information from that inital point (the 2nd X) can then have an effect on the NEXT 2 points (nearest neighbors, aka either side)
then, the next 2 neighbors
then, the next 2 neighbors
.
.
.

there is a "unit" of time between each step---it may be one second, millisecond, whatever

We can get different "speeds of light", or maximum rate of information travel in an example such as the above one, by changing the rules that the cellular automata follows--- i.e. instead of nearest neighbors, we could have NEXT-nearest neighbors as well. This would mean that an event could have influence over the 2 cells on either side at each step.

=========================

One thing to realize -- I'm not explaing the speed of light just as a particle moving through space, but rather information in general (can include particles) moving through space.

quote:

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Originally posted by brum:
First of...

Is space "discrete" or "continuous"? In other words, can a particle be in only "set" positions or is there an infinite number of positions that it can be in. (At a very small scale, a particle could be in an infinite number of positions, or... it can only be in a discrete number of positions)

I claim that space is NOT continous.

It instead is discrete. This discreteness thusly leads to the (in-exceedable) speed of light.

So, if we have discreteness, then all interactions/computations can only reach a certain distance. For example, two particles next to each other can interact (it may well be a huge number distance away, but still there is a FIXED MAXIMUM distance in which particles and interact). This maximum rate of the movement of interactions (a particle can only react with another only so far away) is in essence the speed of light.

Well, let's say that space is continous--there is an infinite number of positions that a particle can be in. This means that information/computation/interaction can move at ANY conceivable speed, which means no speed of light as a MAXIMUM allowed rate.

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Well it can be easily proofed that your argument is wrong.

You suppose that the speed of light is just the speed of the smallest unit of lenght in the smallest unit of time.

If that would be correct, the speed next close to it would be exactly half the speed of light, then one third the speed of light, etc.

But we have measured speeds that are between half the speed of light and the speed of light. In a discrete space /time that would be impossible.

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Originally posted by heusdens:
Well it can be easily proofed that your argument is wrong.

You suppose that the speed of light is just the speed of the smallest unit of lenght in the smallest unit of time.

If that would be correct, the speed next close to it would be exactly half the speed of light, then one third the speed of light, etc.

But we have measured speeds that are between half the speed of light and the speed of light. In a discrete space /time that would be impossible.

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I was talking about a basic unit of time, not "the smallest unit of time." In other words, I was talking about a fundamental, theoretical unit of time, not so much something from the "actual world".

Also, you were talking about 1/2 the speed of light, 1/3, ...
But I was just using the simple example of the rule of nearest neighbors only (or the cells adjacent), however in the real world it may very well be much larger. How large this is --> speed of light. (How far information can travel, aka how far a particle's influence affects other particles, per the unit of time leads to the speed of light). I.E. if, at every unit of time, we tracked the influence of a particle at the farthest particle it can reach (say, 79 away at maximum) the information that is sent at 79 cells away PER unit of time is the speed of light. A particle cannot affect a particle 80 cells away (in keeping with this example of the max. being 79).

==============================
so, would this mean that in the real world we would see "jumps" in the time it would take to send information to another particle say, 80 cells away when the maximum distance a particle can influence is just 79

i.e.
To affect a particle 79 cells away would take "1 unit of time"
To affect a particle 80 cells away would take "2 units of time"

Or maybe this "unit of time" that im theorizing is so short that this situation above ^^ would not be seen since the "unit of time" is so insignificantly short

Hurkyl

What if the speed of the particles is set to one lattice point per hour?

How does the particles "know" when to move?

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Originally posted by ObsessiveMathsFreak:
But how would lesser speeds exist in this lattice.
What if a particle traveled 25 lattice points in two unit seconds. How far did it travel in one unit second.

What if the speed of the particles is set to one lattice point per hour?

How does the particles "know" when to move?

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I wouldn't put the word "seconds" onto this fundamental unit of time that Im talking about here because that makes us try to compare it to real-life, big sized objects rather than theoretical entities n' stuff.

How far did it travel in one second? Well, you can say that the average is 14.5 per second, but that contradicts the whole "discrete points" idea--you can't move .5 cells. Instead, we have only whole number rates (no halves, thirds, ...) which means you can only move information either A) 2, 4, 6, 8 ... cells away or B) 1 cell every 2,3,4,5 ... seconds)

In other words the A) from above would be y=2x y=4x y=6x ...
and B) would be y=1/2 x y = 1/3 x

if you think of the movement of information as a 2 dimensional graph

(The line of the graph is the rate at which the information can move throughout the space)

tell me to explain things in a different way if I didn't explain myself clearly enough

I'm sure they're are plenty of flaws to seek out

quote:

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Originally posted by brum:
I claim that space is NOT continous.

It instead is discrete. This discreteness thusly leads to the (in-exceedable) speed of light.

---

quote:

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Originally posted by heusdens:

Well it can be easily proofed that your argument is wrong.

You suppose that the speed of light is just the speed of the smallest unit of lenght in the smallest unit of time.

If that would be correct, the speed next close to it would be exactly half the speed of light, then one third the speed of light, etc.

But we have measured speeds that are between half the speed of light and the speed of light. In a discrete space /time that would be impossible.

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Do you know little about digital information system? About binary system in particular? Then you should know that "n" bit allow to get 2 ^ n combination. If speak of velocitie that quantum of space Qs = 10 ^ -20 m allows to get 2 ^ 20 importances of the velocity which smaller than velocity of light. Such accuracy of the slicing can provide ANY importance of the velocity from zero to "c".

Try this link to a simulation of John Conway's "Game of Life".

–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–

Extremes in politics are dangerous and should be avoided.

Remaing neutral on all subjects is an extreme.