On 4/11/2016 6:17 PM, Jonathan Day wrote:
John Clark: Or maybe nothing tells the quantum foam how to behave; after all, why does every event have to have a cause? This is one of the key questions in physics. Causality forbids effects without causes and physicists are extremely keen on causality.
Since Born, physicists have pretty much given up on causality. Otherwise they'd never get beta particles to tunnel out of nuclei.
Singularities also have the potential for causality violations and I needn't say how many brain cells have been sacrificed, burned out beyond recognition, by the greatest minds trying to prevent things like the information paradox arising. I tend to assume, therefore, that causality must apply absolutely everywhere, that if violations of the conservation of information can't arise behind an event horizon, then it can't arise in quantum foam either. However, one could argue that the sum total information in quantum foam over classical scales of space and time will always come out at zero. If the sum is zero, then perhaps no violation is possible no matter what. Now, your other point about real numbers is also important. The idea I was toying with pre-supposes that most real numbers don't exist, that there are universal constants that can be generated at arbitrary precision but that all else is subject to the precision of one Planck unit of spacetime. (This creates an interesting problem. If the fundamental scale of the universe is the Planck distance, then is the universe made of bubbles? You can't tessalate spheres, so are the spaces inside the universe or outside?) The idea is to circumvent the problem of precision. A universe with finite accuracy loses accuracy. I don't see any way to avoid that unless there's something that effectively goes beyond the minimum physical scale. This feeds back round to computer simulation. A computer simulation cannot handle genuinely real numbers of any kind. So if arbitrary real values exist, then the universe is not a simulation. It's an interesting test.
Dispersion of gamma rays from distant novae show that if spacetime is discrete is must be at a scale far finer than the Planck scale.
If the universe is an emergent phenomenon resulting from pure mathematics, then real numbers of all kinds can genuinely exist at infinite precision even if the physics is quantized.
How does that follow? Why can't the universe emerge from integer mathematics (which is what Bruno claims).
Brent
If the universe does not have a mathematical or computational substrate, then there should be a recursive phenomenon with short enough cycles where the loss of precision would be measurable. This set of experiments would classify what sort of universe we have.
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