Re: Why Einstein geometrized away Newton's "force of gravity"

Daryl McCullough wrote:
pmb says...
I'll put this [something about "inertial forces"] into
tensor form in the future.

I just don't understand what *benefit* there is in talking
about inertial forces. Mathematically, the difference is
a triviality: In the equation
m (d/dtau U^u + Gamma^u_vw U^v U^w) = F^u
you can, if you like, move the Gamma term to the other side
of the equation to get:
m d/tau U^u = F^u - m Gamma^u_vw U^v U^w
Then you can call the right side F_total^u.
but what is the advantage of doing that?

I don't see any advantage to this algebraic manipulation. But there is a major loss: the equation no longer reflects the underlying symmetry of the theory. The original equation was written in terms of tensors (before projecting it onto some coordinate system's basis), was manifestly invariant under coordinate transforms, and directly and manifestly displayed that symmetry of the theory. This last equation loses that completely -- no term in it represents a tensor (i.e. obeys the underlying symmetry of the theory), except the original F^u. This set of equations is not covariant under coordinate transformations.

And also: calling the gamma term "inertial forces" does not meet pmb's definition of them -- the connection coefficients from spherical coordinates are included, but he has said several times those aren't "inertial forces" (he is attempting to make a distinction without a difference, but that's not worth the argument).

And I repeat my objection to the entire notion "inertial force" -- it is a historical, inappropriate, and misleading name given to these quantities before physicists understood that they are merely artifacts of a HUMAN coordinate choice, and cannot possibly model any physical phenomena [#]. Remember, please, that the primary purpose of science is to construct theories that accurately model the world we inhabit, and obfuscations like this are not helpful to that process.

[#] Yes, pmb has mentioned what he thinks might be a possible
process. But it requires nature to be clairvoyant; I'm pretty
sure that in GR such clairvoyance prevents the field equation
from determining the geometry of the manifold, and thus
destroys the basic structure of the theory (quantum theory is
completely different in this sort of thing). I doubt very
much that it is an admissible process, and it certainly is an
outrageous process (in the context of this CLASSICAL theory).


Tom Roberts
.

Relevant Pages

  • Re: Why Einstein geometrized away Newtons "force of gravity"
    ... tensor form in the future. ... about inertial forces. ... the underlying symmetry of the theory), ... bathroom scale, relative to Earth coordinates. ...
    (sci.physics.relativity)
  • Re: Why Einstein geometrized away Newtons "force of gravity"
    ... My argument is that "inertial forces" cannot possibly be models of ... It's not a "wrong" frame of reference, it's just one that has non-zero ... Newtonian physics so please stop repeating it. ... What most people fail to realize is that Christoffel symbols are components of a *tensor*, ...
    (sci.physics.relativity)