Butterfly effect or is it due to seagulls.

[sjastro]

 

[SelfSim]

Yep .. good video.

The rubber meets the road at the 5:00 minute mark where she points out: 'whether the real butterfly effect occurs for any equation that describes nature is unclear ... {Navier Stokes eqns} ... no-one knows'.

Also, whether or not equations actually describe nature, is always only ever under perpetual scrutiny in physics, at best ..

 

[sjastro]

Yep .. good video.

The rubber meets the road at the 5:00 minute mark where she points out: 'whether the real butterfly effect occurs for any equation that describes nature is unclear ... {Navier Stokes eqns} ... no-one knows'.

Also, whether or not equations actually describe nature, is always only ever under perpetual scrutiny in physics, at best ..

I don't agree with Sabine's statement that because quantum mechanics is a linear theory it is not subject to butterfly effects.
While this is true for quantum mechanics the implication is that any linear theory is not subject to the butterfly effects.
Newton's theory of gravity is a linear theory and when applied to a two body or Keplerian system is a predictable non chaotic system.
Add a third body and the ternary system does become chaotic recognized as early as 1890 by Poincare.
In this case the evolution to a chaotic system is slow as one can make reasonably accurate predictions that span centuries.

 

[SelfSim]

I don't agree with Sabine's statement that because quantum mechanics is a linear theory it is not subject to butterfly effects. While this is true for quantum mechanics the implication is that any linear theory is not subject to the butterfly effects.

I'm not sure she was explicitly implying that in what she actually said though(?) :
She says: 'The equations of quantum mechanics do not have butterfly effects because they are linear. Then again, no one would use quantum mechanics to predict the weather, so that's a rather theoretical answer'.

Newton's theory of gravity is a linear theory and when applied to a two body or Keplerian system is a predictable non chaotic system.
Add a third body and the ternary system does become chaotic recognized as early as 1890 by Poincare.
In this case the evolution to a chaotic system is slow as one can make reasonably accurate predictions that span centuries.

So, I think this again illustrates the real butterfly effect ... whereas assuming that determinism for the three body a system is somehow also 'a given', just because Newton's equations for the two body system are .. is not at all what actually 'determines' the behaviour as it evolves ..

 

[sjastro]

I'm not sure she was explicitly implying that in what she actually said though(?) :
She says: 'The equations of quantum mechanics do not have butterfly effects because they are linear. Then again, no one would use quantum mechanics to predict the weather, so that's a rather theoretical answer'.

It's not just the equations that are linear.
Quantum mechanics is built around the mathematics of Hilbert spaces which is a linear vector space where the quantum wavefunctions are a linear combination of vectors.
(Hilbert incidentally was the mathematician who informed Einstein that energy was not conserved globally in GR.)

So, I think this again illustrates the real butterfly effect ... whereas assuming that determinism for the three body a system is somehow also 'a given', just because Newton's equations for the two body system are .. is not at all what actually 'determines' the behaviour as it evolves ..

Chaos theory ultimately tells us that for any dynamic macroscopic system, a physics model can only be predictive for as long as the system does not evolve into a chaotic system.