Why two mass attracts each other?

I probably didn't say that very well. It just turned out that the first physics I studied was GR. Even that was different because that initial text is an undergraduate text that focused on using the metric to evaluate the physics and I was in my late 40's. That's still the most revealing book I've read and I was able to start it after just learning calculus [big 'just' for me].

 

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Both "Universal Gravitation" and "Newtonian orbits" refer to the inverse-squared law central force where: \(\vec{F} = - \frac{G m_1 m_2}{r^2} \hat{r}\).

Tach's page describes aphysical speculation by Newton so that he would better understand his own theory.

Specifically, if F₁(r) is universal gravitation, F₂(r) is universal gravitation plus an unphysical cubic term that looks like this:
\(\vec{F}_{\tiny 2} = \left[ - \frac{GM m}{r^2} - ( k^2 - 1 ) \frac{L_{\tiny 1}^2}{m r^3} \right] \hat{r}\)

However, in Universal Gravitation, k=1, k²=1, F₁ = F₂, and there is no precession in the two-body problem.

Finally, Newton used his non-physical mathematical exploration to try to explain the more complicated behavior of matter when there is more than 2 bodies.

But even as Newton was developing perturbation theory, he limited himself to geometrical means of exploring the math, and his success was limited.
http://en.wikipedia.org/wiki/Lunar_theory

But for the two-body problem in universal gravitation, elliptical orbits do not precess.

http://archive.org/texts/flipbook/flippy.php?id=anelementarytre04godfgoog

 

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That was the only type of proof considered valid in Newton´s day. Just as some current mathematicians do not consider a computer proof "by exhaustion" (all possibilities calculated) to be valid.

Everyone with the slightest interest in physic or math, should spend at least a couple of hours actually reading (no make that studying) his Principles of Mathematics just to see how powerful, complete and detailed geometric proofs can be in the hands of a real genius!

 

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... and can read Latin...

 

Nice post. Pretty interesting. I like to wonder what Newton would have discovered if he knew what Maxwell would discover in the distant future.

 

At this point the cosmological constant is the 'dark energy'. WMAP results confirm the predictions of Guth's Inflation model. I always like saying that, LOL. Personally I really like the way that turned out [so far]. Regardless what Einstein said it turns out 'even' the prediction he thought was wrong was right. Science is 'one thing' the human race got right.

 

I could in high school, but not well. I read it in English translation. I did as practice of my German, in college, by reading Das Kapital in the original, but I had an English translation in the other hand, used when confused.

 

Perhaps so. What is it the way that turned out that you like?

 

Inflation turned cosmology into a testable science. I followed Guth's idea since shortly after he wrote his non mathematical book on cosmology and his inflation idea. It turns out it evolved into testable cosmology. What's not to like. The weirdest thing is after 30 years of it's 'known existence' very few non practicing cosmologists know anything about it. You'd think it would be a big deal in forums like this but instead most still believe all the matter in the universe was stuffed into a singularity and was spewed out when it popped it's load.

 

No, it is the geometry of space-time around the sun which determines the orbits.

 

Immediately from calculus to DG is quite a big leap. Especially since you skipped Newton.

Oops. I should have said "What do you like about the way that it turned out?" Not enough sleep LOL.

To the layman, inflation sounds the same as "spewing out". Many also confuse it with the accelerating universe. Also, it's always been pictured as some kind of "bell-shape".

 

When you start using terms like "sounds the same as..." and "confuse it with..." for what people think then it just means nobody actually did any homework on the subject before having a confused opinion. I do it all the time just not when discussing science. The accelerating universe is a [possible] further consequence of the original inflation event. Where the vacuum expectation value didn't fully reach minimum at the end of the original inflation event and is finishing up as we observe in the present. Finishing up probably isn't the best analogy.

 

One problem I have with space-time explanations of mass attraction, is you begin with a variable that lacks substance, instead of using substantial things like mass and energy. We can't store time or space-time in a bottle and run experiments on a just a pure sample of space-time. We can do that with mass. Space-time is always indirectly measured by means of changes observed within tangible things. Red shift is a tangle change in energy, used to infer something you can't save in a bottle; emperors new clothes?

Let us ask science questions like, is it possible to measure space-time, in a vacuum without any tangibles, to make sure space-time is self standing and not just a mental construct that stems indirectly from measurable substance? If we can't isolate space-time, isn't this just game engine science? Game engine science is where you move math instead of substance to create magic tricks. The scientific method should require we isolate a sample of space-time to use as a standard. It avoids this why?

I was trained as an engineer so I understand practical utility and how this can fool some into reading too much into the practical utility of a procedure. I remember an old timer who did chrome plating. He was the best and his personal secret was he used to spit chewing tobacco into the vat. From a pure chemistry POV this made little sense to me. But from an applied science POV his unique ability to plate things so well made that claim seem real enough for other to assume it was true. Is space-time the chewing tobacco in the vat of substantial variables?

 

Deleted.

 

This makes no sense, since GR uses the stress-energy-momentum tensor as the source term of gravity; that tensor is a representation of mass and energy.

So is energy. Or momentum. Or potential. Or any number of other concepts in physics.

Actually, no. The scientific method only requires us to extract numerical predictions from the model as a whole, and then compare it to experiment and observation. The scientific method does not actually concern itself with the specific mechanisms of the model; you could, if you wanted to, write a model which explains gravity in terms of microscopic pink unicorns - so long as all predictions of that pink-unicorn explanation line up with experiment and observation, you'd have a valid model of gravity, until such time as a contradiction or a wrong prediction surfaces. The scientific method simply goes : Ask a question - formulate a hypothesis - extract predictions - test those against observation - analyse the outcome, and amend the hypothesis if necessary.
So far as predictions and observations go, GR does a pretty good job in explaining the effects of gravity.

 

Quasi-phyiscal = gravity and virtual particles?

"geometry is the science of patterm"..Fuller

A friend reminded me that it was the shape--- patterned outline ---of the vehicle that affected the air-flow, however, the vehicle was made of molecules erg atoms.

This above by "geometry of space-time" seems to be very similar to the "shape/geometry of", however, in the case of the vehicle, it is the associated molecules/atoms, whereas in Markus's above, there is only the geometry of space-time( gravity ) aka gravitational spacetime.

Quasi-physical--- beyond our detectability --- space-time or spacetime = gravity = mass-attraction = bosonic force = ultra-micro graviton assumed to be exchanged between mass A/Sun and mass B/planet.

Metaphysical subcatagory of mathematics called geometry, pattern, shape like a spiral, or a triangle or square etc.....i.e. the metaphysical pattern/shape is not the medium of mass or the force exchanged between massess.

Yes, the metaphysical shape/patterned outline of a vehicle affects the air-flow, but ionly via the inter-actions/relationships with atoms/mass.

It appears very clear to me, that, there exists an ultra-micro force of gravitational spacetime( gravitons ) far beyond our ability to ever quantize ergo focus in any practical( mechanistic ) way, as we do with EMRadiation( photons ) which we do quantize via the electron( mass ).

Lee Smolin predicted humans would quantify gravity by around the year 2015 via geometry. I think he was way too optimistic.

r6

 

Although the space distortion by mass POV is probably better discription for accurate calculations, it is not an answer to the Why question. My joking answer of many pages back does as well as any (I think) attempt to answer the why question:

"Inanimate love" is as good an answer as any to the why question.

 

Inanimate love between two masses, the attraction?

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Can you explain the difference between 'effect of force on a mass' and 'effect of curvature(or geometry) of space-time on a mass'?

 

My claim is based on "observable fact".