The Millenium Run: Gravitational N-body problem with $N \sim 10^{10}$.
Imagine that each atom of the Earth is communicating with each atom of the Sun by exchanging force carrying particles named gravitons through which a gravitational force is established between each such pair of atoms (neglecting internal gravitation for simplicity).
The number of atoms in the Earth is estimated to be around $10^{50}$ and that in the Sun around $10^{57}$, which gives a number of pairs much larger than a $googol = 10^{100}$, while the total number of atoms in the Universe may be of order $10^{80}$.
To store the total set of gravitational forces between the Earth and the Sun, thus would require a hard disk much heavier than the Universe, and there would be no place for the gravitational force between the Earth and the Moon, to name one example.
Do you now start to feel that there is something strange about the standard model of gravitation, which is precisely the one described above?
Do you now start to feel that the very idea of each atom of the Universe making its presence felt to all other atoms of the Universe by creating a gravitational field extending over the entire Universe, is very strange or more precisely describes a complete impossibility?
Do you now start to feel that the Millennium Run with $10^{10}$ particles interacting by gravitation requires way to much computational work to represent physics?
Do you now start to think that maybe, maybe, it is the other way around; that is that the gravitational potential $\phi$ and gravitational field $\nabla\phi$ is primordial and that matter with density $\rho$ is generated locally formally by differentiation as $\rho =\Delta\phi$?
If so, then you are starting to develop a New View.
Inlägg
I hardly think that the Millenium Run involved actual individual atoms. The reasonable thing would be to compute on a conglomerate acting as a "particle". Compare with a continuum model like fluid mechanics.
SvaraRaderaFurther, you must be aware that the interaction between two bodies, like the Sun and the Earth, of course doesn't need to be calculated with regard to every single atom since they can be perfectly represented as point particles in the center of mass, thats like first semester mechanics... :-)
You are missing the point which is that the physical model assumes particle-particle interaction, which is impossible.
SvaraRaderaWhy should the nature of reality have anything to do with what is easy or feasible to compute? If it was established that reality was in fact a big computer simulation, I could see your point. But the amenability to computation could be arbitrarily low for a reality that is indifferent to the needs and wants of humans.
SvaraRaderaReal physics must be some form of computational process, since if not it can only be magical.
SvaraRaderaReal physics must be some form of computational process, since if not it can only be magical.
SvaraRaderaThis is of course a trivial truism if we are to be able to do physics at all.
Hence it is completely void of information of the nature of such computation.
It must be as Rickard writes, such a computation could very well be intractable for humans.
Instant action at distance is an example of a process which cannot be realized as a physical process of the same form as an explicit time-stepping computational algorithm and thus is not physical. This statement is not void of information.
SvaraRadera