Substantiating the equivalence principle
v. 6 n. 21
Cover image caption: Equal but separate.
The equivalence principle has been employed recently with Newton's gravity, as in general relativity, equating gravity to acceleration or inertial effects. Familiarity aside, gravity and acceleration are actually rather vague concepts. Gravity is more a phenomenon (without completely satisfying explanation). Acceleration seems to depend on matter to be accelerated; can there be acceleration without matter to accelerate?
Popularly, gravity is just matter "simply" attracted to other matter. With relativity, matter curves space, and "things slide down gravity wells" in two-dimensional drawings of abstract four-dimensional theoretical occurrences, whatever that really means. Why does matter curve space? Beyond these familiarities there is really no satisfying explanations of gravitation and acceleration effects.
The equivalence principle is an axiom, not a proven law of physics, regardless of experiments to date. However, if it can be shown that gravity and acceleration effects, inertia, are two terms for the same thing -- an identity -- then the equivalence principle could be a corollary of a law. An equivalence can be conditional, while an identity is unconditional. General relativity at small acceleration is equivalent to Newton's gravity only under certain conditions, as near the surface of the Earth (where the equivalence principle was conceived). See Figure 1.
Clusters of galaxies are imbedded in space in that accelerated expanding space is separating these clusters. Therefore, each fundamental or point-like particles such as the electron and quark, normal matter, making up these clusters is imbedded in space. Focusing on a single free electron imbedded in space midway between two clusters of galaxies, in which general direction is it moving, if at all, or what is the net force on this electron?
This "free" electron would be accelerating with the rest of the Universe, being imbedded in accelerating expanding space at about 10^-14 m/s^2 (barring local effects), as discussed. It makes no difference whether this electron is being accelerated or the space one meter away from this electron is being accelerated; matter and space are being accelerated at the same rate in this vicinity. The electron is imbedded in this space, and work must be done on it to stop it from accelerating; this electron has position; similarly, the space one meter away from this electron is accelerating at the same rate and work must be done on it to stop the acceleration.
Certainly, this free electron has inertia; it has mass. But does the space one meter away from this electron have inertia? Does space have mass? Does it make any difference in an accelerating region consisting of this electron and surrounding space?
If this free electron is a gravitational sink instead of a source, it would have no mass at the point it would be said to exist; its mass(-energy) would be everywhere else in its gravitational field extending to infinity. Part of its mass, then, is in the location one meter away in space. Similarly, this arbitrary location in space houses a portion of the gravitational fields of all the other condensed matter in the Universe, and can be said to "have mass," even though it has only parts of the mass of all the other condensed matter. This arbitrary point in space beside the free electron has mass, it has inertia. This arbitrary region of space has mass and inertia that cannot be distinguished. Gravitational and inertial effects are seen as identical, and the equivalence principle might be a corollary. Aside from this, according to general relativity the ambient gravitational field cannot be distinguished from space; no field no space.
Related material:
A. Einstein, Relativity, Crown, New York, 1961, p.155
Cover image (less text and weights): Balance scale by Colourful Minds | TPT ( teacherspayteachers.com )
Neti neti.
Retired Mechanical Engineer
1 个月Nice Warren! Here's my take on the Equivalence Principle: https://physicsdiscussionforum.org/viewtopic.php?p=19142#p19142
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1 个月Since the experience of “gravitation” depends on an intertial reference point I would say yes (same thing)! Every “thing” that matters is moving and shifting always and there’s then the stillness as the empty space zero as voids in-between they too expanding and contracting, so what else would there need to be? Gravity seems to me an experience of these phenomena as measured from some point in reference to another.
Aren't all forces equivalent to acceleration? Electromagnetism for example deforms the respective quantum field creating wells which dictate how particles affected by that force should move.