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- Thread starter professor
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newtonian law of gravitation

[tex]g=G\frac{M}{r^2}[/tex]

gravitational acceleration

[tex]\vec{G}=g[/tex]

magnitude of gravitational field is equal to the magnitude of the acceleration due to gravity at a point.

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okay newtonian...yes

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perhaps where i might find some of einsteins origional text... that seems to be impossible... i cant get a near advanced description....and in that order- has anybody read gravitation by kip thorne... might that be what i am lookinhg for?

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um, warping of spacetime and such.

uses tensor calculus...past me for now...

uses tensor calculus...past me for now...

- #6

Gokul43201

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It's quite confusing to use the same symbol for field as you use for the Universal Gravitational Constant (G).yourdadonapogostick said:[tex]\vec{G}=g[/tex]

magnitude of gravitational field is equal to the magnitude of the acceleration due to gravity at a point.

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not the same. i used a vector symbol for the field and i stated that it was the field.

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EnumaElish

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In case you have not looked at these already: there are questions and answers that have been posted under other threads of this forum which may be of interest; see, e.g., threads entitled "spacetime as a rubber sheet" and "general relativity" (among others).professor said:

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professor said:

Try

http://math.ucr.edu/home/baez/einstein/einstein.html

note to EnumaElish - this has some notes about curvature, too.

This explains Einstein's equation (gravity in General relativity) at a moderate technical level of difficulty

Einstein's equation:

G_uv = 8 Pi T_uv

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- #13

ohwilleke

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professor said:

General Relativity is the dominant theory of gravity. Newtonian gravity is a special case of the General Relativity equations. Most astrophysics between stellar objects is effectively Newtonian in GR. Much of the astrophysics within stellar objects is not effectively Newtonian in GR.

General Relativity is a classical theory which means that it assumes that space-time is continuous and that the universe is deterministic. In contrast, quantum mechanics is a stochastic model of the universe and many quantum gravity models (especially the non-peterbative ones) assume that space-time is not continuous.

General Relativity differs significantly from Newtonian gravity in the case of masses which are moving relative to each other, in the impact that gravity has on photons, and in very strong gravitational fields where phenomena like black holes arise (to name the most common examples). GR also provides the framework for understanding a big bang interpretation of the universe and why the universe appears to be expanding and doing so at an increasing rate.

There are active efforts underway to integrate gravity into quantum mechanics. Thus far, those efforts have been failures. These efforts involve quantitizing time-space, quantitizing a graviton (which would have to be a "spin two" particle, the only such particle in the standard model) to carry the gravitational force, or both. In string theory (more accurately known as M-theory) extra dimensions are employed to help explain gravity. Loop quantum gravity tries to appeal to a discrete structure of space time to achieve results. Quantum gravity fields tend to more closely resemeble the QCD (quantum chromodynamics) which governs the strong force, than they do the electro-weak force.

The gravitational constant is the least accurately known non-contact force constant.

The luminious matter we observe with our telescopes merges with GR is not sufficient to explain the phenomena we observe in our telescopes. Galactic dynamics and lensing, for example, in galaxies and clusters frequently differs from a GR expectation. We also observe the accellerated expansion of the universe. These issues are commonly known as the dark matter problem and the dark energy problem. The mainstream approach to these issues is lambda CDM, which means the theory that there is a cosmological constant in the GR equations which represents "dark energy" of some sort (the lambda) and that the universe is full of slow moving, weakly interacting massive particles which are not protons or neutrons or neutrinos or electrons or other quark based particles which cluster in "halos" around certain galaxies and clusters to produce the observed behavior. But, such dark matter has not been directly observed.

Some scientists, a minority view, seek to explain dark matter and/or dark energy by modifying the GR equations. Milgrom and Bekestein's Tensor-Vector-Scalar model, and Moffat's Conformal Gravity model are the two most prominent of that type of theory. Both theories have gravity equations which make gravity stronger than expected in the weak field fringe around galaxies. The two theories differ significantly beyond that weak field galactic fringe.

Another area of active investigation is whether gravity behaves in any unexpected way at the 0.1 mm scale or less, and whether anomolies in the motion of probes like the Pioneer 10 probe have a fundamental gravitational cause. The suspicion would be that at very small scales gravity might be weaker than expected in GR, while at large scales like the Pioneer solar system scale that gravity might be stronger than expected. This is roughly analogous to QCD in which close objects are "asymptotically free" while distant objects are very strongly attracted to each other to the extent that they are "confined". But, in QCD this shift happens at microscopic scales, while in gravity you are talking about sub-millimeter and galactic or at least solar system scales.

If there are deviations from GR the obvious place to point a finger would be quantum gravity effects.

We are actively engaged in high stakes experiments to detect gravitational waves and certain kinds of "frame dragging" predicted by GR. The former experiments have not yet provided conclusive results but have set upper bounds on gravity wave size. The latter experiments are not yet complete.

Gravity is of course, intimimately tied up with matter. The standard model of particle physics doesn't tell us why particles have mass. It suggest that a "Higgs boson" may help particles interact with a scalar Higgs field in the universe to create interial mass. But the notion that there is both a Higgs field and a gravitational field which are both proprotionate to mass is notable. Physicists are actively searching for the Higgs boson, and their ability or inability to find it is a turning point that physicists are awaiting while the particle accellerators to do it are built.

Another big mass question is why the particles in the Standard model have masses of the magnitude that they do (as opposed to why they have mass at all).

Likewise, the recent discovery that neutrinos appear to have mass is notable. Of course, general relativity is also the source of the famous equation E=mc^2.

Einstein's equation: G_uv = 8 Pi T_uv relates two rank 2 tensors, the G tensor and the T tensor. Mathematically, a tensor looks like a matrix. Tensors are necessary because they, as a matter of form, make the solution independent of any coordinate system. The tensor T is the stress-energy tensor. Gravity is a function of the stress energy tensor.

I can't say it very articulately, but suffice it to say that the stress energy tensor involves more information than Newtonian gravity which relies on point masses at points in space. For example, in Newtonian gravity, gravity is not impacted by the degree to which particles are in motion with respect to each other, while in GR relative motion can impact gravitational effects.

According to Baez, the following plain English statment sums up Einstein's equation:

A photon which leaves a gravitational field will experience red shift.

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- #14

Phobos

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professor - it's not clear to me what you're asking for...why not just refer to a Physics textbook?

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well...because i dont own any - you are my textbooks :)

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