Lecture on Newtonian spacetime

[Dale]

Note: this thread is a fork from https://www.physicsforums.com/threa...s-nobel-laureate-stanford-university.1067929/

I saw a rather interesting lecture recently that showed how Newtonian spacetime followed from taking Newton’s first law seriously (ie as something applicable to the real world and not as a special case of the 2nd law). In the resulting Newtonian spacetime there was a concept of absolute time and absolute space, but even so there was not a notion of the velocity of space.

 

[gmax137]

I saw a rather interesting lecture recently that showed how Newtonian spacetime followed from taking Newton’s first law seriously (ie as something applicable to the real world and not as a special case of the 2nd law). In the resulting Newtonian spacetime there was a concept of absolute time and absolute space, but even so there was not a notion of the velocity of space.

Sounds interesting, @Dale . Is the lecture available online or ?? Thanks!

 

[Dale]

Sounds interesting, @Dale . Is the lecture available online or ?? Thanks!

Yes, this is lecture 9 by Dr Schuller at the Heraeus International Winter School on Gravity and Light. It is all quite good, but lecture 9 was the one I was specifically referring to.

 

[gmax137]

Thank you @Dale . Parts of that lecture were over my head but the professor is doing a very good job. I think I will start with Lecture 1 and see what I can learn.

 

[Dale]

I did the same for the same reason!

 

[cianfa72]

@Dale Lecture 9 referenced in your post #10 is basically the Newton-Cartan theory ?

ps. very interesting his point of view about Newton I law/axiom: basically it defines what physically/geometrically an uniform straight line is.

 

[Dale]

@Dale Lecture 9 referenced in your post #10 is basically the Newton-Cartan theory ?

I would say it is the spacetime of Newton-Cartan theory, but in that lecture he didn't develop the theory further. I.e. no description on how matter curves Newton-Cartan spacetime other than the restrictions on the connection that he mentions.

ps. very interesting his point of view about Newton I law/axiom: basically it defines what physically/geometrically an uniform straight line is.

I agree. The other alternatives I have seen are:

1) Treat it as a special case of the second law
2) Treat it as the definition of an inertial frame

His third approach

3) Treat it as the definition of a straight line in spacetime

Has some benefits. I think the other two are still viable, but I see the appeal of the third way.

 

[cianfa72]

1) Treat it as a special case of the second law
2) Treat it as the definition of an inertial frame

His third approach

3) Treat it as the definition of a straight line in spacetime

I think 1) isn't useful since it is contained in the Newton's second law.

Btw, as he pointed out, to be applicable the first law actually requires knowing when/in which circumstances there is "no-force" acting on a particle (viewing/including gravity as a force).

As far as I understand, what he says about Laplace's idea was to "overcome" this difficulty (basically a "circular" argument) by attempting to treat gravity as curvature of just space (gravity is no longer a force) turning the second law in an autoparallel equation. It turns out that in space alone isn't possible, yet in spacetime it is.

 

[Dale]

Btw, as he pointed out, to be applicable the first law actually requires knowing when/in which circumstances there is "no-force" acting on a particle (viewing/including gravity as a force).

Yes, and that is why making gravity not a force is so useful. Then you can just attach an accelerometer. If it reads 0 then the particle is free. It makes the theory empirically clear.

Laplace's idea was to "overcome" this difficulty (basically a "circular" argument) by attempting to treat gravity as curvature of just space (gravity is no longer a force) turning the second law in an autoparallel equation. It turns out that in space alone isn't possible, yet in spacetime it is

I wonder historically why that didn’t occur to Laplace.