If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
This seems unlikely for a number of reasons.
This doesn't mean spacetime is a nice even grid, but it does suggest it comes in discrete lumps of something, even if that something is actually some kind of substrate that holds the information which defines relationships between lumps.
> If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
This would be true if objects existed at perfectly local points. However we know that a perfectly localised wavefunction has spatial frequency components that add up to infinite energy. Any wavefunction with finite energy is band-limited. At non-zero temperature the Shannon-Hartley theorem will give a finite bit rate density over frequencies, and since the wavefunction is band limited it will therefore only have the ability to carry a finite amount of information.
This and the comment under it are making my point for me. Relativity assumes spacetime is continuous. Quantum theory implies that quantum phenomena are bandlimited and therefore the information spacetime can hold is limited.
The difference is we know what the quantised components of field theory are. We don't have any idea what the quantised components of spacetime are supposed to be, or how they operate.
The various causal propagation theories (like causal dynamical triangulation) may be the first attempts at this, but it's going to be hard to get further without experiments that can probe that level - which is very difficult given the energies involved. Without that, we're just guessing.
I often wonder if we simply constructed math the wrong way around.
People tend to mentally construct the natural numbers from set theory, wholes from naturals, rationals from wholes, reals from rationals and so on.
But what if there is some universe (in the math sense), which is actually complete and decidable, it's just that the moment you take discrete subsets of it, you also remove the connections that make it consistent or complete.
The very act of formalising mathematical concepts into words and paper is a quantisation step after all, because both are symbols.
Maybe there are proofs that can be inuitioned about (assuming brains are continuuous in some sense) but neither verbalised nor formalised.
How do you know arithmetic is not complete or consistent? In ZFC arithmetic is complete and arithmetic is consistent. This assumes that ZFC is consistent. The second order Peano axioms are categorical so I assume you mean only the first order theory.
At any rate, what does any of this have to do with information capacity in the universe? Is the information capacity of the universe related to the consistency/completeness of arithmetic?
> If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
Even if space is continuous, that doesn't mean we can get information in and out of it in infinite precision.
Look at quantum physics. Maxwell's equations don't suggest existence of photons (quantized information). But atoms being atoms, they can only emit and absorb in quanta.
Obviously that "something" is the float type used to calculate the simulation. Probably some ultra dimensional IEEE style spec that some CPU vendor intern booked anyways. ;)
Someone else asked about their hand moving in a pixelated versus continuous way in reality, and it occurred to me that if spacetime were discrete that would be a good reason for entanglement, intuitively speaking. Otherwise there wouldn't be an obvious way for information to be transferred across the discrete points? Maybe I'm wrong about this but it seems that way on first thought.
That doesn't mean anything has to be a particular way, but it at least would be intuitively consistent to me.
When I think about that, I wonder if that 'quantization of space' is what determines the speed of light. And perhaps explains why inertial and gravitational mass are identical.
Since gravity is the curvature of spacetime, quantizing gravity would mean quantizing spacetime (or quantizing geometry) also, which would lead to their being smallest units of space and time, perhaps somewhere around the Planck length and Planck time.
If you look at it with the analogy of vinyl records and digital representations of that music. You can reach a point in which you are quantizing something that equally can represent the original in a way that is not discernable in difference (maybe 192khz 32 bit float for some but still quantized).
You equally, hit limits in human perception and technology/physics limitations more so.
Maybe the universe is always N+1 with N being the best sampling rate known to man. Sure we can infer, but when you want to know the answer to the exact decimal point, sometimes you have to accept that 1/3 is 1/3 and never exactly 0.333333333333 however much recurring you have.
That was my point, just because you can only perceive at one limit, does not mean there is nothing beyond that like Ultrasound. Anyhow, was analogy about perception and sample rates and what your measuring. Clearly didn't make it that clear and sorry for that.
If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
This seems unlikely for a number of reasons.
This doesn't mean spacetime is a nice even grid, but it does suggest it comes in discrete lumps of something, even if that something is actually some kind of substrate that holds the information which defines relationships between lumps.
> If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
This would be true if objects existed at perfectly local points. However we know that a perfectly localised wavefunction has spatial frequency components that add up to infinite energy. Any wavefunction with finite energy is band-limited. At non-zero temperature the Shannon-Hartley theorem will give a finite bit rate density over frequencies, and since the wavefunction is band limited it will therefore only have the ability to carry a finite amount of information.
This and the comment under it are making my point for me. Relativity assumes spacetime is continuous. Quantum theory implies that quantum phenomena are bandlimited and therefore the information spacetime can hold is limited.
The difference is we know what the quantised components of field theory are. We don't have any idea what the quantised components of spacetime are supposed to be, or how they operate.
The various causal propagation theories (like causal dynamical triangulation) may be the first attempts at this, but it's going to be hard to get further without experiments that can probe that level - which is very difficult given the energies involved. Without that, we're just guessing.
People complain about infinite information, but the theory of real fields is complete and consistent, while arithmetic is not:
https://en.wikipedia.org/wiki/Decidability_of_first-order_th...
I often wonder if we simply constructed math the wrong way around.
People tend to mentally construct the natural numbers from set theory, wholes from naturals, rationals from wholes, reals from rationals and so on.
But what if there is some universe (in the math sense), which is actually complete and decidable, it's just that the moment you take discrete subsets of it, you also remove the connections that make it consistent or complete.
The very act of formalising mathematical concepts into words and paper is a quantisation step after all, because both are symbols. Maybe there are proofs that can be inuitioned about (assuming brains are continuuous in some sense) but neither verbalised nor formalised.
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How do you know arithmetic is not complete or consistent? In ZFC arithmetic is complete and arithmetic is consistent. This assumes that ZFC is consistent. The second order Peano axioms are categorical so I assume you mean only the first order theory.
At any rate, what does any of this have to do with information capacity in the universe? Is the information capacity of the universe related to the consistency/completeness of arithmetic?
8 replies →
> If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
Even if space is continuous, that doesn't mean we can get information in and out of it in infinite precision.
Look at quantum physics. Maxwell's equations don't suggest existence of photons (quantized information). But atoms being atoms, they can only emit and absorb in quanta.
> If spacetime is continuous you effectively get infinite precision -> information density - at every point (of which there are an infinite number).
Without some smallest resolution, we'd need infinite amounts of information to track point particle displacement in one dimension.
Obviously that "something" is the float type used to calculate the simulation. Probably some ultra dimensional IEEE style spec that some CPU vendor intern booked anyways. ;)
Your mistake is that you didn't pony up for the "double" feature in your personal universe.
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Care to to enlighten us these number of reasons?
That there is a cosmic speed limit may imply one unit of space per one unit of time. Nothing faster.
Someone else asked about their hand moving in a pixelated versus continuous way in reality, and it occurred to me that if spacetime were discrete that would be a good reason for entanglement, intuitively speaking. Otherwise there wouldn't be an obvious way for information to be transferred across the discrete points? Maybe I'm wrong about this but it seems that way on first thought.
That doesn't mean anything has to be a particular way, but it at least would be intuitively consistent to me.
If it were discreet, why would that be a good reason for entanglement? Could you explain your idea more?
If it's true that the Planck length (1.616e-35 meters) is the smallest possible Length, [https://futurism.com/the-smallest-possible-length] then so far as we'll ever know, space is quantized.
When I think about that, I wonder if that 'quantization of space' is what determines the speed of light. And perhaps explains why inertial and gravitational mass are identical.
https://en.wikipedia.org/wiki/Cutoff_(physics)
Since gravity is the curvature of spacetime, quantizing gravity would mean quantizing spacetime (or quantizing geometry) also, which would lead to their being smallest units of space and time, perhaps somewhere around the Planck length and Planck time.
If you look at it with the analogy of vinyl records and digital representations of that music. You can reach a point in which you are quantizing something that equally can represent the original in a way that is not discernable in difference (maybe 192khz 32 bit float for some but still quantized).
You equally, hit limits in human perception and technology/physics limitations more so.
Maybe the universe is always N+1 with N being the best sampling rate known to man. Sure we can infer, but when you want to know the answer to the exact decimal point, sometimes you have to accept that 1/3 is 1/3 and never exactly 0.333333333333 however much recurring you have.
Hint: 44100 Hz is plenty to exceed any human's perceptual resolution.
That was my point, just because you can only perceive at one limit, does not mean there is nothing beyond that like Ultrasound. Anyhow, was analogy about perception and sample rates and what your measuring. Clearly didn't make it that clear and sorry for that.
And yet I can flash an LED that fast, then turn my head from side to side and see the modulation ....
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