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We assume the centre of gravity of a mass as reference point for gravitational calculations. This assume a well defined directional component for gravitation. Could the uncertainty principle apply to gravity and if not why not?

Measurement of gravitation is quite inaccurate, ...

..so any quantum fluctuations would be very hard to measure. It is said that the gravitational constant G is the least accurately known fundamental constant.

Yes, the uncertainty principle applies to gravitational fields. Roughly, the uncertainty principle for the metric tensor says that delta (g_munu) = L*/L, where L* is the Planck length, and L is the size of the region in which we measure the metric tensor. If L is of the same order of magnitude as L*, then the metric tensor becomes totally uncertain.

Quote from: jeffreyH on 08/06/2014 23:18:51We assume the centre of gravity of a mass as reference point for gravitational calculations. This assume a well defined directional component for gravitation. Could the uncertainty principle apply to gravity and if not why not?I spoke to a friend about this who's a textbook author on the subject. In case you were asking about using the HUP with respect to the field and not a particle moving in the field he wroteQuoteYes, the uncertainty principle applies to gravitational fields. Roughly, the uncertainty principle for the metric tensor says that delta (g_munu) = L*/L, where L* is the Planck length, and L is the size of the region in which we measure the metric tensor. If L is of the same order of magnitude as L*, then the metric tensor becomes totally uncertain. Does that answer your question?

This question was in relation to a hypothetical graviton or gravitons plural.

Quote from: jeffreyH on 09/06/2014 20:11:59This question was in relation to a hypothetical graviton or gravitons plural.We don't know, since there isn't an accepted theory of gravitons. Presumably since they're quantum objects the uncertainty principle applies to them. Of course, some theories of quantum gravity are quite exotic, so in those cases maybe not.

Quote from: JP on 09/06/2014 20:15:49Quote from: jeffreyH on 09/06/2014 20:11:59This question was in relation to a hypothetical graviton or gravitons plural.We don't know, since there isn't an accepted theory of gravitons. Presumably since they're quantum objects the uncertainty principle applies to them. Of course, some theories of quantum gravity are quite exotic, so in those cases maybe not.Question: Since gravitons are the mediators of the gravitational field doesn't that make them virtual particles? Does the uncertainty principle hold for virtual particles? After all in order to apply the uncertainty principle you have to be able to detect the gravitons and if they're virtual particles they can't be detected.

Quote from: PmbPhy on 10/06/2014 01:43:17Quote from: JP on 09/06/2014 20:15:49Quote from: jeffreyH on 09/06/2014 20:11:59This question was in relation to a hypothetical graviton or gravitons plural.We don't know, since there isn't an accepted theory of gravitons. Presumably since they're quantum objects the uncertainty principle applies to them. Of course, some theories of quantum gravity are quite exotic, so in those cases maybe not.Question: Since gravitons are the mediators of the gravitational field doesn't that make them virtual particles? Does the uncertainty principle hold for virtual particles? After all in order to apply the uncertainty principle you have to be able to detect the gravitons and if they're virtual particles they can't be detected.Short answer: Yes, the uncertainty principle holds for virtual particles. Long answer: The uncertainty principle holds for all quantum particles, period. If they're particles that have wavelike properties, they necessarily obey uncertainty principles. The distinction between real and virtual particles is fuzzy because real means that a particle exists for all time. A virtual particle has a finite existence because it is emitted/absorbed at points in time. But really nothing exists for all time, so all particles are in a sense virtual. The reason we distinguish between them is that typically there are interactions that involve very short-lived particles and interactions that involve very long-lived particles without a lot in between, so it makes sense to categorize them as such. Because of the energy/time uncertainty principle a short-lived particle has a wide spectrum of allowed energies, whereas a long-lived particle has a narrow spectrum of allowed energies. This is why we say virtual particles can be off-shell (i.e. they can have energies not allowed for free particles):http://en.wikipedia.org/wiki/On_shell_and_off_shellhttp://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

I have just ordered "Numerical Relativity: Solving Einstein's Equations on the Computer" by Thomas W. Baumgarte. I am hoping that I can adapt some of this for my own use. May be a hard task.

Quote from: jeffreyHI have just ordered "Numerical Relativity: Solving Einstein's Equations on the Computer" by Thomas W. Baumgarte. I am hoping that I can adapt some of this for my own use. May be a hard task.Thanks, Jeff. It sounds like an interesting text so I decided to download it from the internet. I can down most textbooks off the internet. I found a place where I can download them for free!

It would be interesting to compare notes.

Quote from: jeffreyHIt would be interesting to compare notes.I printed it out yesterday and then glued the ends of the pages together to make sort of a binding. Tomorrow I'm going to put a makeshift cover on it. Then it will probably sit on the shelf for a long time. I'm currently engulfed in reviewing quantum mechanics. I do this every once in a while to stay fresh on the subject. I'm then going to study EM and then onto GR, both in much more depth and at higher levels. Then I plan on learning Java. Then I'll come back to this. Let me know what you're doing in the mean time. I want to watch what you produce. How will you display the results of the computations you get?

I haven't even considered how to display results yet. I have been looking into the open source Einstein Tools but that only runs on unix\linux based systems. I could run it on cygwin but will probably rewrite it or base something else on it. I am currently examining how they handle the Ricci calculations. I'll keep you posted on this as I progress.

Quote from: jeffreyHI haven't even considered how to display results yet. I have been looking into the open source Einstein Tools but that only runs on unix\linux based systems. I could run it on cygwin but will probably rewrite it or base something else on it. I am currently examining how they handle the Ricci calculations. I'll keep you posted on this as I progress.What are "Ricci calculations" and why are you so interested in them? Are you referring to how to calculate the Rici tensor? If so then why? Don't confuse the Rici tensor with a measure spacetime curvature because it isn't. People often make that mistake.

I am also looking at flat affine geometry. This also is not related to curvature but there are reasons for studying it. You do of course have affine curves.

Quote from: jeffreyHI am also looking at flat affine geometry. This also is not related to curvature but there are reasons for studying it. You do of course have affine curves.Yes. I see. And of course I’m intimately aware of these facts since I’ve been studying it for a very long time now.I recommend that you pick up the following textbookA General Relativity Workbook by Thomas Moore, Springer Press, (2012)If you want to really know general relativity as well as I think you do then this is the perfect textbook for you. I’m taking my own advice too since I just bought it.