What does Fermat's principle of least time mean for causality

[fando1234]

I have been reading some fairly mind bending stuff about the principle or least time (and those of least action) raising questions about causality and free will.

Can anyone explain this to me? Is this total 'woo woo' psuedo science, or are these philosophical questions widely accepted?

Thanks a lot guys. Really messing with my brain this one!

*I'm not a phycisist myself, just an interested laymen, so please bear that in mind as much as possible when answering.

 

[A.T.]

or are these philosophical questions widely accepted?

I don't know what it means for a question to be accepted, but philosophical questions are definitely off-topic here.

 

[fando1234]

I don't know what it means for a question to be accepted, but philosophical questions are definitely off-topic here.

I suppose what I mean is: is this established physics, and does it call into question causality? Or is this pure philosophy. Lagrangian mechanics and Fermats principle of least action are both physics concepts so I think this is still within the topic of general physics.

 

[Nugatory]

I have been reading some fairly mind bending stuff about the principle or least time (and those of least action)

If you could tell us what you've been reading, you'll likely get better answers. As is, we're just guessing whether it's reasonable stuff or what you call "total 'woo woo'" - there's a lot of both out there.

 

[fando1234]

Sure... here's one article: https://www.forbes.com/sites/chadorzel/2016/11/21/the-physics-that-got-left-out-of-arrival/ also alluded to in this video

 

[A.T.]

Sure... here's one article: https://www.forbes.com/sites/chadorzel/2016/11/21/the-physics-that-got-left-out-of-arrival/

I like this quote from the article:

"At the same time, though, there are physicists who note that this approach is basically just a slightly odd approach to specifying the boundary values for a problem-- somewhat loosely speaking, it amounts to specifying a starting position and an ending position and being amazed that the path is determined, but if instead you specified a starting position and starting velocity, the path is equally inevitable, but somehow that feels less magical."

Consider: https://en.wikipedia.org/wiki/Fermat's_principle

If you send light in all directions from point A through a variable propagation speed environment, it will reach point B from some direction first, which is orthogonal to the local wavefronts. So if you trace back along that direction from B, always orthogonally to the local wavefronts, you will get the locally fastest path. But that is also how directed rays of light propagate locally:

https://en.wikipedia.org/wiki/Huygens–Fresnel_principle

So it just follows from the local behavior of waves, and the crucial fact that you directed the ray such that it actually hits the other point.

 

[A.T.]

I suppose what I mean is: is this established physics, and does it call into question causality? Or is this pure philosophy. Lagrangian mechanics and Fermats principle of least action are both physics concepts so I think this is still within the topic of general physics.

Maybe it's easier to understand the principle of least action based on geodesics instead of light paths:

Consider a toy car with no steering, driving on a curved surface. Its path will be a geodesic (locally straight line, because no steering). To envision this start with a spherical surface, where geodesics are great circles.

If you pick two points A and B on that path, there is no nearby path, that is shorter than the geodesic one. But globally there might be shorter paths. So it's not like the car knows the globally shortest way. It just behaves locally such that it minimizes path curvature and thus also path length, so wherever it ends up, there is no nearby path that is straighter and thus shorter and leads to that same place. Any small perturbation of the path between A and B would make the connection longer.