"Truth is one; the sages just speak of it in different ways."
Berkeley should have stuck to chasing the ghosts of departed quantities.More seriously, is there a place where Berkeley addresses Newton's argument from inertial force?
Well, I haven't gone into these issues in any depth, so my suggestion is tentative, but doesn't his "take the fixed stars" as the background for inertial force suffice? (And, again, I'm very tentative about wading into these waters without much more study, but: Hasn't exactly Berkeley's suggestion been put forward in modern physics? [I seem to recall it has.])
I've always seen that argument attributed to Mach. (Perhaps he got it from Berkeley?) But in the first place, it is a little exotic to think that what happens with the rotating bucket (to take Newton's example) is dependent on the situation of distant stars. Second, and much more devastatingly, "the fixed stars" can be regarded as fixed only by way of approximation; they are constantly in motion relative to one another.
"But in the first place, it is a little exotic to think that what happens with the rotating bucket (to take Newton's example) is dependent on the situation of distant stars."Well, not as exotic as thinking that there is some absolute space independent of all things in that space!"Second, and much more devastatingly, "the fixed stars" can be regarded as fixed only by way of approximation; they are constantly in motion relative to one another."Come, come, that is not devastating at all: they are certainly "fixed" for the amount of time you are swinging the bucket around. Again, very tentative, but I seem to remember the idea is that it is their combined gravitational effect which creates the "illusion" of absolute space. And that combined effect is only going to be an average of all of their positions, which surely doesn't change much during the time any inertial phenomenon of interest takes place!
Everyone is entitled to his own priors, but to me it seems passing strange to posit that inertial force depends on the average location of certain distant bodies in relative motion to one another.
Julian Barbour's The End of Time is a masterful exposition of the history of time and how to think about it. (Barbour advances the thesis that time does not exist, in the sense that it is reducable to non-time concepts, and that all of physics can be conducted without reference to it.)In particular, he talks about the long conflict between Newton and Leibniz over whether space is absolute or purely relative. Barbour concludes that Leibniz was ultimately correct, but that the particulars of our place in the cosmos (at least as observable in the 17th century) allow it to look like a universe with absolute space.Barbour's answer to the bucket (and related) problem(s) is, following Mach's Principle, that the rest of the universe forms an inertial frame that determines when acceleration forces are felt. Under this view, you would not be able to tell the difference between a) looking up at the stars and spinning around, vs. b) the rest of the universe spinning around you (modified by the speed of light constraints) so as to produce the same apparent path of stars -- both produce the same forces, and this shows up in the General Relativity equations. (You could, of course, differentiate the two to the extent that you can know you caused yourself to spin around via your feet.)Here is an excellent introduction to Barbour's timeless physics.
Silas, I don't quite know what to say! Your comment is polite, to the point, very informative, and doesn't claim I have failed at something! Has someone taken over your account?:-)
Hmm, did my earlier reply disappear?Silas Barta,I haven't read Barbour's book (thanks for the reference), but that solution seems pretty close to what I'm saying. What is a universal inertial frame, if not absolute space by another name? And GTR actually supports my argument for substantival (albeit not exactly absolute) space—but I was reluctant to invoke it, as it is badly out of step with quantum mechanics.
@Gene_Callahan: Thanks!@PSH: It makes a pretty big difference. For example, in a universe with absolute space, you would feel the centrifugal forces when everything in the universe rotates together.Barbour also claims to have reconciled General Relativity with QM, basically by taking the time-independent Schrodinger equation as universal and then using the concept of a "minimum fundamental distance between configurations" wherever you would normally use "time" in describing observations. (Requires a longer explanation than I'm ready to give here.)