On Tuesday, July 19, 2016 at 8:46:44 AM UTC+5:30, Steven D'Aprano wrote: > On Tue, 19 Jul 2016 10:36 am, Rustom Mody wrote: > > > I recollect — school physics textbook so sorry no link — > > that in the Newton gravitation law > > f = -GMm/r² > > > > there was a discussion about the exponent of r ie 2 > > And that to some 6 decimal places it had been verified that it was > > actually 2.000002 > > Because gravitational forces are so weak, it is very difficult to > experimentally distinguish (say) an exponent of 1.999999 from 2.000002 from > 2 exactly. > > Most physicists would say that an experimental result of 2.000002 is pretty > good confirmation that the theoretical power of 2 is correct. Only a very > few would think that the experiment was evidence that both Newtonian and > Einsteinian gravitational theory is incorrect.
Yes this was — if memory is right — the conclusion, viz.: Experimentally it looks like 2.000002 (or whatever) This is as good as we can measure So concluding its 2 seems to be reasonable with that 0.000002 relegated to experimental error Nevertheless my main point was that such a math (aka analytic to a layman) looking entity like 2, may for a physicist be a quantity for synthetic verification > > (Newton, for obvious reasons; but also general relativity, since Newton's > law can be derived from the "low mass/large distance" case of general > relativity.) > > But it's an interesting hypothetical: what if the power wasn't 2 exactly? May be related to the margin of error for G being quite high -- https://mail.python.org/mailman/listinfo/python-list
