Mach's principle
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In theoretical physics, particularly in discussions of gravitation theories, a Mach principle is one of several dozen alternative formulations of vague hypothesis first suggested by the physicist and philosopher Ernst Mach in 1893.
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Mach's principle
Mach's idea can be stated like this:
"The inertia of any system is the result of the interaction of that system and the rest of the universe. In other words, every particle in the universe ultimately has an effect on every other particle."
According to Mach, a single object (for example, the Earth) in an otherwise empty Universe would feel no inertial forces. It would be impossible to determine whether that object is rotating or not. According to Mach, the inertial forces on that object are caused by the sum of the gravitational forces from cosmic bodies such as the distant starsTemplate:Fn; the rotation of that object only makes sense relative to these other objects. For an example of the inertial forces on that object, see Coriolis force.
In this sense, at least some Mach principle's are related to philosophical holism. Mach's suggestion can be taken as the injunction that gravitation theories should be relational theories.
The above version of the principle is largely due to Albert Einstein, who brought the principle into mainstream physics whilst working on general relativity. Indeed it was Einstein who first coined the phrase Mach's principle. There is much debate as to whether Mach really intended to suggest a new physical law since he never states it explicitly.
The writing in which Einstein found inspiration from Mach was "The Science of Mechanics", where the philosopher criticized Newton's idea of absolute space, in particular the argument that Newton gave sustaining the existence of an advantaged reference system: what is commonly called "Newton's bucket argument".
In his Philosophiae Naturalis Principia Mathematica, Newton tried to demonstrate that one can always decide if he is rotating with respect to the absolute space, measuring the apparent forces that arise only when an absolute rotation is performed. If a bucket is filled with water, and made to rotate, initially the water remains still, but then, gradually, the walls of the vessel communicate their motion to the water, making it curve and climb up the borders of the bucket, because of the centrifugal forces produced by the rotation. Newton says that this gedankenexperiment demonstrates that the centrifugal forces arise only when the water is in rotation with respect to the absolute space (represented here by the reference frame solidal with the earth, or better, the distant stars), instead, when the bucket was rotating with respect to the water, no centrifugal forces were produced, this indicating that the latter was still with respect to the absolute space.
Mach, in his book, says that the bucket experiment only demonstrates that when the water is in rotation with respect to the bucket no centrifugal forces are produced, and that we cannot know how would the water behave if in the experiment the bucket's walls were increased in depth and width, until they became leagues big. In Mach's idea this concept of absolute motion should be substituted with a total relativism in which every motion, uniform or accelerated, has sense only in reference to other bodies (i.e., one cannot simply say that the water is rotating, but must specify if it's rotating with respect to the vessel or to the earth). In this view, the apparent forces that seem to permit to discriminate between relative and "absolute" motions should only be considered as an effect of the particular asymmetry that there is in our reference system, between the bodies which we consider in motion, that are small (like buckets), and the bodies that we believe as still (the earth and distant stars), that are overwhelmingly bigger and heavier than the formers. It is then not clear, in the passages from Mach just reminded, if the philosopher intended to formulate a new kind of physical action between heavy bodies. This physical mechanism should determine the inertia of bodies, in a way that the heavy and distant bodies of our universe should contribute the most to the inertial forces. More likely, Mach only suggested a mere "redescription of motion in space as experiences that do not invoke the term `space'" (see BarbourTemplate:Fn) What is for sure, is that Einstein interpreted Mach's passage in the former way, originating a long-lasting debate.
Mach's principle was never developed into a quantitative physical theory that would explain a mechanism by which the stars can have such an effect.Template:Fn Although Einstein was intrigued by Mach's principle, his general relativity does not fully agree with it. There have been attempts to formulate a theory which is more fully Machian, such as Brans-Dicke theory, but none have been completely successful.
Dicke's form of the Mach Principle:
- The gravitational constant should be a function of the mass distribution in the universe.
Note
- Template:Fnb Julian Barbour, Mach's principle: from Newton's bucket to quantum gravity Boston: Birkhauser 1995.
- Template:Fnb Max Born, Einstein's Theory of Relativity Dover 1962, a translation of Born's 1924 book in German, which explained Relativity in non-mathematical terms.
- Carl H. Brans, The root of scalar-tensor theory: an approximate history. arXiv:gr-qc/0506063 v1, June 2005.
See also
- Democratic principle (one possible "Mach principle")
- Equivalence principle
- Newtonian physics
- General relativity
- Inertial frame
- Absolute space
- Luminiferous aether
- Newton's bucket
- Frame-dragging
References
- Template:Cite web An important review explaining the multiplicity of "Mach principles" which have been invoked in the research literature (and elsewhere).
- Template:Cite book (Einstein studies, vol. 6)
- Template:Cite book This book advocates a somewhat plausible "Mach principle" which unfortunately resists a covariant statement, leading to somewhat confused writing in places, but this book is valuable nonetheless.
- Template:Cite book This classic textbook discusses Mach's principle in section 21.12. See also the facsimile of Einstein's 1913 letter to Mach in Fig. 21.5, in which he mentions his expectation that in his forthcoming theory of gravitation, inside a rotating thin spherical shell, the spin axis of a gryoscope should be "dragged" as if by a Coriolis pseudoforce, an effect which was later confirmed theoretically by Lense and Thirring, and is currently being tested by Gravity Probe B.
- Template:Cite book Dennis Sciama helped renew interest in Mach's principle with his writings in (among other places) this textbook.
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