Computer guy likes the idea that physics is a computer. What a surprise.
Like literally nothing distinguishes this idea in boldness from other ideas except that its not the current mainstream view. Also, no experimental verification.
If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models without some other compelling experimental means of determining its presence. I believe folks are trying to figure this out, but at present, my money remains on spacetime being continuous. I don't know shit, but I expect good quantum gravity theories will need to be scale free.
In general I think this CA stuff is much less deep than it seems to be. You can, of course, approximate continuous differential equations with discrete difference equations, which is, fundamentally, what all this boils down to, in the end. It isn't surprising that with appropriate rules one can reproduce smooth mechanics at scales way above the discreteness scale.
> If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models
A computational universe does not strictly imply discrete spacetime. You can most certainly still have a continuous universe—at least from the perspective of the beings that inhabit it. By way of analogy, consider the fact that ZFC proves the existence of uncomputable real numbers yet itself has a countable model (presuming it is consistent).
> I find it very appealing to consider the idea that the world is not somehow running “hidden mathematics”, somewhere and somehow, to solve some complicated equations in a seemingly magical way, but rather, that things are radically simpler, in that the world is simply implementing a set of trivially simple rules. The world is not concerned with, or made with mathematics, mathematics just emerges, with inherent and irreducible complexity, from extreme simplicity.
Wouldn’t those simple rules be mathematics? It’s very hard for me to see how the world isn’t made of math. Then again, I am a Pythagorean.
There is a distinction between "What the universe is made of or how it works just happens to be really compatible with how math describes things" and "The universe is just "running" math and we discovered that math and use it for other things"
But like, words stop working at these levels of rigor.
What the hell does "The universe is made of math" mean? How can something be made of a field of study? Where is the "Addition" particle? How does 1+1=2 give rise to what we see as an electron?
Like it's bad enough dealing with "quantum fields" that might be "real" or maybe are just really nice mathematical objects that happen to be useful for calculating the future.
Does math take up space? Does space take up math? Does blue afraid of seven? Can I eat integrals or will they go straight to my thighs?
If the universe is "made of" math, what is the consequence? For example, the consequence of being made of "quantum fields" in my lay mind is that we get observations like entanglement and the hilarity of whatever is going on in the higgs field.
>Then again, I am a Pythagorean.
Ah, let me just move this sqrt(2) out of the way real quick :P
I want simple rules because I am a simple man, and if those simple rules happen to actually be math, that sucks for me because the "simple rules" are really hard math.
But it seems to me that the acid test, as always, is successful prediction. If one day a digital model makes a prediction that is experimentally demonstrated, and not accounted for via other models, then there might be more support for this approach.
Computer guy likes the idea that physics is a computer. What a surprise.
Like literally nothing distinguishes this idea in boldness from other ideas except that its not the current mainstream view. Also, no experimental verification.
If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models without some other compelling experimental means of determining its presence. I believe folks are trying to figure this out, but at present, my money remains on spacetime being continuous. I don't know shit, but I expect good quantum gravity theories will need to be scale free.
In general I think this CA stuff is much less deep than it seems to be. You can, of course, approximate continuous differential equations with discrete difference equations, which is, fundamentally, what all this boils down to, in the end. It isn't surprising that with appropriate rules one can reproduce smooth mechanics at scales way above the discreteness scale.
> If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models
A computational universe does not strictly imply discrete spacetime. You can most certainly still have a continuous universe—at least from the perspective of the beings that inhabit it. By way of analogy, consider the fact that ZFC proves the existence of uncomputable real numbers yet itself has a countable model (presuming it is consistent).
What about experimentally validating these models against reality? There is kinda a reason why we came up with the models we currently have.
> I find it very appealing to consider the idea that the world is not somehow running “hidden mathematics”, somewhere and somehow, to solve some complicated equations in a seemingly magical way, but rather, that things are radically simpler, in that the world is simply implementing a set of trivially simple rules. The world is not concerned with, or made with mathematics, mathematics just emerges, with inherent and irreducible complexity, from extreme simplicity.
Wouldn’t those simple rules be mathematics? It’s very hard for me to see how the world isn’t made of math. Then again, I am a Pythagorean.
There is a distinction between "What the universe is made of or how it works just happens to be really compatible with how math describes things" and "The universe is just "running" math and we discovered that math and use it for other things"
But like, words stop working at these levels of rigor.
What the hell does "The universe is made of math" mean? How can something be made of a field of study? Where is the "Addition" particle? How does 1+1=2 give rise to what we see as an electron?
Like it's bad enough dealing with "quantum fields" that might be "real" or maybe are just really nice mathematical objects that happen to be useful for calculating the future.
Does math take up space? Does space take up math? Does blue afraid of seven? Can I eat integrals or will they go straight to my thighs?
If the universe is "made of" math, what is the consequence? For example, the consequence of being made of "quantum fields" in my lay mind is that we get observations like entanglement and the hilarity of whatever is going on in the higgs field.
>Then again, I am a Pythagorean.
Ah, let me just move this sqrt(2) out of the way real quick :P
I want simple rules because I am a simple man, and if those simple rules happen to actually be math, that sucks for me because the "simple rules" are really hard math.
The concept does have a certain appeal.
But it seems to me that the acid test, as always, is successful prediction. If one day a digital model makes a prediction that is experimentally demonstrated, and not accounted for via other models, then there might be more support for this approach.