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> In classical physics, the universe is predictable: If you know the laws that govern a physical system and you know initial state, you should be able to track

by nyc111 8y ago

> In classical physics, the universe is predictable: If you know the laws that govern a physical system and you know initial state, you should be able to track its evolution indefinitely far into the future. ... [According to physicist Demetrios Christodoulou:] "This is the basic principle of all classical physics going back to Newtonian mechanics. You can determine evolution from initial data." This is a famous mantra repeated by physicists but it is not correct. Newtonian physics cannot even predict the future positions of three body from their initial positions. And Newton knew and stated that his doctrines could not predict planetary orbits in long term and he invoked the very scientific and physical notion (or maybe footballers term) of Hand of God. Thus, Newton claimed his doctrine could not make accurate prediction not because they were wrong but because God erred to create the universe according to Newton’s doctrines. Consequently, according to Newton, God once in a while nudged the orbits to make them move correctly according to Newtonian doctrines. According to Newton himself initial states cannot predict long term behavior. So how come NASA can predict so accurately planetary motions by using the so-called Newtonian Mechanics? The answer is easy: by not using Newtonian mechanics. NASA uses sophisticated mathematical methods or numerical integration to calculate orbits. But since they use as a unit conversion factor the strategically named Newton's Constant of Gravitation as one of their mathematical terms they feel they are justified to declare that they use Newtonian mechanics to compute orbits. So what happened is that at some point, maybe in the 18th century this philosophical -not physical- assumption entered the physics literature and gained the status of truth after centuries’ of repetition. But if we question the mantra we see that the so-called classical theories do not claim that they can predict future states by the initial state. Phycists do.

jonathanyc 8y ago
What on earth? Not having a closed form for something is decidedly not the same as not being able to use it to predict anything. That’s like saying so-called computer programmers can’t actually predict anything about their programs will do.
- masteranza 8y ago
  Do not bother this guy. Apparently he is either crazy or ignorant. The solar system is stable in the sense of time periods necessary to make NASA their calculations and the Lyapunov are small - all that's needed can be deduced from either Newton or Einstein theories.
- pofilat 8y ago
  Any (non-pathological) terminating computer program (including a non-terminating program that includes a step to forcibly stop at a certain clock time) has a closed form, it's just phenomenally complex. :)
qubex 8y ago
I am quite stupefied by this statement. NASA and other organisations most certainly uses Classical mechanics (whether in its Newtonian, Lagrangian, or Hamiltonian formulations does not impinge upon the central issue) when simulating celestial motions and calculating trajectories. That there exists an acknowledged ”Three Body Problem” (i.e., that the trajectories followed by more than two bodies interacting gravitationally are in general not algebraic) matters not one iota for numerical simulations such as those performed by aforementioned organisations for aforementioned purposes. Some kind of relativistic correction might be made for motions that occur within the orbit of Mercury, but again, those are numerical in nature. And as far as I know there are no exact solutions known for general-relativistic interactions between two gravitational objects, placing it at an even greater ’disadvantage’ compared to the ’Newtonian’ mechanics you erroneously deplore.
- AstralStorm 8y ago
  The general relativistic two body problem is hard mostly because the topological maths get really tough real quick symbolically. In 2D space, this problem is solved, but not in 4D. The topology involved makes string theory look easy...
- nyc111 8y ago
  > matters not one iota for numerical simulations such as those performed by aforementioned organisations for aforementioned purposes. So you agree that planetary orbits are computed by numerical simulation as I claim. Then why do you object at what I'm saying?
Strilanc 8y ago
> Newtonian physics cannot even predict the future positions of three body from their initial positions. You're confusing chaotic systems with random systems. Chaotic systems are still deterministic. [1] > according to Newton, God once in a while nudged the orbits to make them move correctly according to Newtonian doctrines Newton thought that because he didn't know perturbation theory. Perturbation theory doesn't change the laws, it reformulates them as "simple thing + small tweaks + more complicated even smaller tweaks + ...". This allows you to quantify how stable the solar system is. 1: https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory "these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved"
jcranmer 8y ago
> Newtonian physics cannot even predict the future positions of three body from their initial positions. Uh... yes it can. We don't have a closed-from solution [1] for the three-body problem, but we do have existence proofs that, for any initial condition that does not result in a collision, there is a well-defined, unique solution for the motion of bodies given that initial condition. (This kind of uniqueness/existence proof is quite hard in differential equations, hence why you win $1 million if you can prove the same thing for Navier-Stokes equations). [1] Actually, reading on Wikipedia, we do have a series expansion for the 3-body problem. It's just a really, really, really slow converging series.
n4r9 8y ago
As others have pointed out there is an important distinction to be made between determinism and predictability. However, "Norton's dome" is a good example of a situation in which Newtonian mechanics might arguably be non-deterministic: https://www.pitt.edu/~jdnorton/papers/DomePSA2006_final.pdf https://www.pitt.edu/~jdnorton/papers/DomePSA2006_final.pdf https://en.wikipedia.org/wiki/Norton%27s_dome https://en.wikipedia.org/wiki/Norton%27s_dome

by nyc111 8y ago

jonathanyc 8y ago

What on earth? Not having a closed form for something is decidedly not the same as not being able to use it to predict anything. That’s like saying so-called computer programmers can’t actually predict anything about their programs will do.

masteranza 8y ago
Do not bother this guy. Apparently he is either crazy or ignorant. The solar system is stable in the sense of time periods necessary to make NASA their calculations and the Lyapunov are small - all that's needed can be deduced from either Newton or Einstein theories.
pofilat 8y ago
Any (non-pathological) terminating computer program (including a non-terminating program that includes a step to forcibly stop at a certain clock time) has a closed form, it's just phenomenally complex. :)

qubex 8y ago

I am quite stupefied by this statement. NASA and other organisations most certainly uses Classical mechanics (whether in its Newtonian, Lagrangian, or Hamiltonian formulations does not impinge upon the central issue) when simulating celestial motions and calculating trajectories. That there exists an acknowledged ”Three Body Problem” (i.e., that the trajectories followed by more than two bodies interacting gravitationally are in general not algebraic) matters not one iota for numerical simulations such as those performed by aforementioned organisations for aforementioned purposes. Some kind of relativistic correction might be made for motions that occur within the orbit of Mercury, but again, those are numerical in nature. And as far as I know there are no exact solutions known for general-relativistic interactions between two gravitational objects, placing it at an even greater ’disadvantage’ compared to the ’Newtonian’ mechanics you erroneously deplore.

AstralStorm 8y ago
The general relativistic two body problem is hard mostly because the topological maths get really tough real quick symbolically. In 2D space, this problem is solved, but not in 4D. The topology involved makes string theory look easy...
nyc111 8y ago
> matters not one iota for numerical simulations such as those performed by aforementioned organisations for aforementioned purposes. So you agree that planetary orbits are computed by numerical simulation as I claim. Then why do you object at what I'm saying?

Strilanc 8y ago

> Newtonian physics cannot even predict the future positions of three body from their initial positions. You're confusing chaotic systems with random systems. Chaotic systems are still deterministic. [1] > according to Newton, God once in a while nudged the orbits to make them move correctly according to Newtonian doctrines Newton thought that because he didn't know perturbation theory. Perturbation theory doesn't change the laws, it reformulates them as "simple thing + small tweaks + more complicated even smaller tweaks + ...". This allows you to quantify how stable the solar system is. 1: https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory "these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved"

jcranmer 8y ago

> Newtonian physics cannot even predict the future positions of three body from their initial positions. Uh... yes it can. We don't have a closed-from solution [1] for the three-body problem, but we do have existence proofs that, for any initial condition that does not result in a collision, there is a well-defined, unique solution for the motion of bodies given that initial condition. (This kind of uniqueness/existence proof is quite hard in differential equations, hence why you win $1 million if you can prove the same thing for Navier-Stokes equations). [1] Actually, reading on Wikipedia, we do have a series expansion for the 3-body problem. It's just a really, really, really slow converging series.

n4r9 8y ago

As others have pointed out there is an important distinction to be made between determinism and predictability. However, "Norton's dome" is a good example of a situation in which Newtonian mechanics might arguably be non-deterministic: https://www.pitt.edu/~jdnorton/papers/DomePSA2006_final.pdf https://www.pitt.edu/~jdnorton/papers/DomePSA2006_final.pdf https://en.wikipedia.org/wiki/Norton%27s_dome https://en.wikipedia.org/wiki/Norton%27s_dome