What is Mach’s principle? Well, lots of people have given lots of versions of this principle, and protracted debates have taken place about it. Its simplest expression is: Inertial reaction forces are produced by the gravitational action of everything that gravitates in the universe. But back in 1997 Herman Bondi and Joseph Samuel, answering an argument by Wolfgang Rindler, listed a dozen different formulations of the principle. Generally, they fall into one of two categories: “relationalist” or “physical”. In the relationalist view, the motion of things can only be related to other things, but not to spacetime itself. Nothing is said about the interaction (via fields that produce forces) of matter on other matter. The physical view is different and more robust as it asserts that the principle requires that inertial reaction forces be caused by the action of other matter, which depends on its quantity, distribution, and forces, in particular, gravity, as well as its relative motion.
The simplest “physical” statement of the principle, endorsed by Einstein and some others, says that all inertial reaction forces are produced by the gravitational action of chiefly the distant matter in the universe. Note that this goes a good deal farther than Einstein’s Equivalence Principle which merely states that the inertial and gravitational masses of things are the same (and, as a result, that all objects “fall” with the same acceleration in a gravity field), but says nothing about why this might be the case. Mach’s principle provides the answer to: why?
Guided by Mach’s principle and Luchak’s Newtonian approximation for gravity – and a simple calculation done by Dennis Sciama in his doctoral work for Paul Dirac in the early 1950s – it is possible to show that when extended massive objects are accelerated, if their “internal” energies change during the accelerations, fluctuations in their masses should occur. That’s the purchase on gravity and inertia you need. (Ironically, though these effects are not obviously present in the field equations of GRT or electrodynamics, they do not depend on any novel coupling of those fields. So, no “new physics” is required.) But that alone is not enough. You need two more things. First, you need experimental results that show that this theorizing actually corresponds to reality. And second, you need to show how “Mach effects” can be used to make the Jupiter masses of exotic matter needed for stargates and warp drives. This can only be done with a theory of matter that includes gravity. The Standard Model of serious physics, alas, does not include gravity.
A model for matter that includes gravity was constructed in 1960 by three physicists of impeccable credentials. They are Richard Arnowitt (Texas A and M), Stanley Deser (Brandeis), and Charles Misner (U. of Maryland). Their “ADM” model can be adapted to answer the question: Does some hideously large amount of exotic matter lie shrouded in the normal matter we deal with every day? Were the answer to this question “no”, you probably wouldn’t be reading this. Happily, the argument about the nature of matter and the ADM model that bears on the wormhole problem can be followed with little more than high school algebra. And it may be that shrouded in everyday stuff all around us, including us, is the Jupiter mass of exotic matter we want. Should it be possible to expose the exotic bare masses of the elementary particles that make up normal matter, then stargates may lie in our future – and if in our future, perhaps our present and past as well.