Sunday, October 19, 2014

Relativity Denial: The Importance of Dimensional Analysis

From the comment stream for the post Scott Rebuttal. I. GPS & Relativity this little goodie was flagged by the blogspot spam filter from an anonymous poster:
"The Engineering manager for GPS states that there are no corrections for relativity used in GPS, only a correction for gravitational potential (which has nothing at all to do with GR). If you want to discuss real errors with relativity you should check the mathematics of Einstein in GR for errors, because the whole lot is mathematically seriously flawed leading to all kinds of false conclusions!"
It also included a link to a site claiming relativity is flawed but not a link with documentation of the specific claim in the comment (and I already have plenty of links from this site to that site, so I don't need another).  I therefore regarded the comment as link-spam (Wikipedia) and have dumped it. 

However, it did make a couple of comments that I thought worthy of addressing and clarification.

The statement about the "Engineering manager for GPS" was made with no reference.  However, I have heard this term used to indicate the authors of the paper discussed in the main article, Scott Rebuttal. I. GPS & Relativity, "GPS and Relativity: An Engineering Overview".  Therefore I suspect the commenter actually mean the very same paper that was discussed in the main post.  One point of my original post was to point out that because of the "An Engineering Overview" paper, with the statement of no GPS effects, an additional experiment was actually conducted (again) and found the predicted relativistic effects.  Clearly the commenter either didn't read, or didn't understand the information.

Then there is this statement:
"there are no corrections for relativity used in GPS, only a correction for gravitational potential (which has nothing at all to do with GR)"
Let's see, Newtonian gravitation involves gravity, so we expect to see G.  It involves the mass of objects, so we expect to see M, and it involves positions, so we expect to see some representation of position, such as radial distance from a center, R.  Masses and positions are the main inputs for the theory.  This is true for Newtonian gravitation, as well as General Relativity. 

The gravitational potential for a point mass is G*M/R in Newtonian gravity.  The gravitational potential has units of energy per mass (joules/kilogram) which is dimensionally the same as velocity squared (meters/second)^2.

General relativity involves the very same quantities of G, mass, and position.  Being an extension of special relativity, the energy of the gravitational field must also be a component, since it also contributes to the mass of the system.  Therefore we expect a gravitational representation of energy in General Relativity.  With the quantities we have available, only one combination comes close to units of energy, and that is G*M/R, the same as the Newtonian gravitational potential.

Therefore basic dimensional analysis EXPECTS a quantity like the gravitational potential to appear in General Relativity in some form.  Very often, researchers will recast the full relativistic solution into a form using the classical gravitational potential to facilitate comparison of other derivations to the Newtonian solution.

So how can the commenter claim that the gravitational potential can have nothing to do with General Relativity?

The commenter's statement exhibits an incredible lack of understanding of not just general relativity, but basic physics and the importance of dimensional analysis.  These types of errors can be dangerous, expensive, or even fatal.  Dimensional analysis is a powerful tool that can often be used to find errors in analysis and is a vital tool in engineering.

Additional Resources on the Importance of Units and Dimensional Analysis

1 comment:

sjastro said...

The relevance of the gravitational potential in General relativity can be illustrated through a weak field approximation.
In a weak gravitational field the components of the Lorentz metric are perturbed. One can show the perturbation corresponds to the gravitational potential.
In fact Einstein's field equations for a vacuum reduce to LaPlaces equation for the gravitational potential.
On a different note how do relativity deniers explain the Pound-Rebka experiment if GR plays no role in GPS corrections?