Newton's gravity vs. Einstein gravity

[edguy99]

I am new here, so hopefully this is an appropriate post for the speculations section. This is about the first principles of gravity and the differences between Newton's version and Einstein's version. When looking at the effects of the two versions, the differences are obvious.

 

Newton used the inverse square law where the force you feel from another mass is inversely proportional to the square of the distance you are from it. Go twice as far away and you feel 1/4 the force. When modelling planetary orbits, you always end up with an elliptical orbit that never precesses. Unfortunately for his theory, the orbit of Mercury precesses. Newton was wrong. Einstein's is quite different. You have precessing orbits, gravitons and curved space (among other things). What are the differences in the fundamental assumptions that make the two different? After doing some research, consider the following:

 

Newton: A note from Newton's Principles definition #4 in 1687: Impressed Force - This force conflicts in the action only; and remains no longer in the body when the action is over.

Einstein: In Einstein's second paper on relativity in 1905, he explicitly concludes: "Radiation carries inertia between emitting and absorbing bodies". It is important that not only does something receive a "kick" from the momentum of the energy, but the internal inertia (i.e., the inertial mass) of the body is actually increased.

Newton's base assumptions clearly conflict with Einstein.

To model Einstein, start with a model of repulsion. Say we take a machine gun and shoot it a lump of lead. The bullets hit the lead and get stuck inside. They provide both a kick to the lead to make it move a little faster as well as they increase the mass of the lead ball by sticking inside it.

The illustration demonstates this and you immediately see that the blob of lead will never go quite as fast as the bullets no matter how many you shoot at it. The first few bullets speed the lead blob up quite a bit, but as it gets heavier and faster, the bullets have less effect. You can get the blob of lead going to 99% of the speed of the bullets or even 99.9999% of the speed of the bullets, but the blob will never go as fast as the bullets.

Now let's reverse this to model attraction. Instead of shooting bullets at the lump of lead, we suck the bullets out. Sucking out the bullets speeds up the lump of lead but again we see that the lump of lead cannot get to the speed of the bullets as it will always be slower then the bullets that are being sucked out. In addtion, the lump of lead will eventually simply disappear as all the bullets get sucked out of it.

Finally, if we assume the bullets are gravitons travelling at the speed of light and the lump of lead is our normal view of "mass" we get Einstein's gravity with all the wierd things associated with it.

 

Comments?

[swansont]

Energy is a property, not a substance, so "speed of energy" is nonsensical.

 

Newtonian physics deals with precession. The unexplained effect on Mercury is quite small.

 

GR is a classical theory. There are no gravitons in it.

 

"Radiation carries inertia between emitting and absorbing bodies" says that light has momentum (incidentally, saying "second paper" is far less helpful than a title, or better yet, a link). In "DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT? ", where he derives E=mc^2, it is for an object at rest — the radiation is emitted in opposite directions, so the object's momentum remains zero. There is no clear indication that he ever considered mass to be a proxy for total energy, only for energy in the objects rest frame. That paper is part of special relativity, with no mention of gravity.

[edguy99]

Thanks for the comment. "Speed of energy" is short for "speed of massless particles" like gravitons and photons, assumed to be the speed of light.

 

Newtonian physics does NOT deal with precession. Using Newtons force laws on 2 bodies that are rotating around each other like the Sun and Mercury will ALWAYS produce an ellipse that does NOT precess. You cannot produce a precessing orbit with Newtons laws. Also, although I agree the precession on Mercury is very small, the discovery that it did precess was a very important historical observation that led to doubt about Newtons gravity. For large masses that are much closer then Mercury and the Sun, precession becomes the dominent feature of their orbit. You can see some dramatic examples at mathpages.com and the history and mathmatical derivation of their orbits here.

 

Both of these orbits would be non-rotating ellipses if Newton's laws were used.

 

I agree with you comment on GR, but, every force has its field, including the gravitational force. The graviton is simply the quanta of that field. We are simply quantizing this gravitational field, and everything which is quantized has its quanta, which in this case is the graviton. The only thing different when someone talks about the graviton is that the G force is not smooth, but rather comes in discrete lumps. Also, no one has ever "seen" the graviton, so we can't say with certainty that it even exists. Hence I posted in the "speculations" section of your forum.

 

Finally, the "repulsion" animation works for "quanta of energy" like a photon hitting something, but the "speculation" is using the "attraction" animation to model gravity and the graviton.

 

Best wishes.

 

 

[Strange]

We are simply quantizing this gravitational field, and everything which is quantized has its quanta, which in this case is the graviton.

If it could be done "simply" we would already have a theory of quantum gravity. We don't because this is not a simple problem.

Finally, if we assume the bullets are gravitons

 

That is not how gravitons would mediate the gravitational force.

[swansont]

Newtonian physics does NOT deal with precession.

 

...

 

You cannot produce a precessing orbit with Newtons laws.

 

 

So nobody knows how tops work?

 

https://en.wikipedia.org/wiki/Precession#Classical_.28Newtonian.29

 

Here's an article that specifically mentions orbital precession

https://en.wikipedia.org/wiki/Newton%27s_theorem_of_revolving_orbits

 

And there's this

"Newton's theory had predicted an advance only half as large as the one actually observed. Einstein's predictions exactly matched the observation."

 

http://physics.stackexchange.com/questions/26408/what-did-general-relativity-clarify-about-mercury

 

And the mathages site you linked to (only the top level, though) has an entry on Newtonian orbital precession

http://www.mathpages.com/home/kmath280/kmath280.htm

 

"This again is the equation of an ellipse, except that the period of the radial function is not exactly equal to the period of the angular position q. The angular travel necessary to go from one apogee to the next (for example) is not 2p, but rather 2p(1+PQ). Hence the ellipse precesses by the amount 2pPQ radians per revolution. In the case of our oblate gravitating body we have P = MJ/h² and Q = M/h², so the orbit precesses by 2p(M/h²)²J radians per revolution. "

[edguy99]

Sure tops precess, no argument there. You can also make an orbit precess by adding in a third planet or by deforming or spinning one of the masses.

 

The math you quoted is under the section starting with "However, in actual physical situations, the gravitating body may not be exactly spherical."

 

There was a great historical effort to account for Mercurys precession by other planets farther out, maybe a planet on the other side of the sun we cannot see, maybe a distortion in the internal mass of the Sun, maybe the spinning of the Sun or maybe a tiny planet in close to the sun. All of these effects were calculated and failed to account for Mercury's precession and Einstein's version of gravity won out. The early part of the linked article goes through all of these efforts:

 

It isn't simple to work out these effects, and unfortunately there is no simple analytical solution to the n-body problem in Newtonian mechanics, but using the calculational techniques developed by Lagrange, Laplace, and others, it is possible to determine that the effects of all the other planets should contribute an additional 532 arc seconds per century to the precession of Mercury's orbit. Combined with the precession of our equinox reference line, this accounts for 5557 arc seconds per century, which is close to the observed value of 5600, but still short by 43 arc seconds per century. The astronomers assure us that their observations can't be off by more than a fraction of an arc second, so there seems to be a definite problem here.

 

It is a definite fact that a 2-body system will form a non-precessing ellipse under Newtonian gravity. Certainly other things can cause precession. The crowning achievement of Einstein's equations was to account for this precession.

[swansont]

Sure tops precess, no argument there. You can also make an orbit precess by adding in a third planet or by deforming or spinning one of the masses.

Thank you for admitting that you were wrong before.

 

So now we're back to Newtonian physics being able to account for most, but not all, of the precession, and GR picking up the last bit (to within measurement uncertainty). Now that we've dispensed with this, can you explain the point you were trying to make in more detail i.e. can you give a more mathematically-based model of your idea of gravity using exchange particles?

[MigL]

Einstein's gravity, GR, reduces to Newton's gravity in the low space-time curvature limit.

IOW where space-time is relatively flat ( absence of deep gravitational potential wells ), Newton's gravity is essentially equivalent to GR.

If Mercury wasn't so deep in the potential well of the Sun, its precession would be ( almost ) completely accounted for by Newtonian gravity. Even light travels in what are essentially straight lines in the absence of space-time curvature ( as Newton predicts ).

[edguy99]

Thank you for admitting that you were wrong before. ...

 

Nothing new here, if you want a list of things I am wrong about, just ask my wife.

[Mordred]

shorter list is what we married men are right about.

[edguy99]

Relativity calculations are done by professionals using ADM equations or a thing called BSSN, unfortunately, above my payscale. For details, there is a good video here. This post is about speculations.

 

To make the point with a more mathematically-based model of gravity using exchange particles, consider an animation with grid spacing of 10 kilometers and time intervals of about 9 hours. Between each frame, the forces on all objects (Sun and Earth in this case) are calculated using Newtons inverse square law. The force is added to the motion of the the object, the motion of the object is added to the location of the object and the scene is re-displayed. If you stop and step the animation at the right time, you can see that it calculates a pretty accurate orbit time (just over 365 days and 6 hours) and gets the aphelion and perihelion pretty close.

http://www.animatedphysics.com/planets/Earth_Orbit_v1.htm

 

To have a look at precession, we need an orbit that is not circular. Using different momentum for the earth at the start of the animation produces a very eliptical orbit for the earth, but no matter the starting positions or momentum of the Sun and the Earth, we always end up with an elliptical orbit that does not precess.

http://www.animatedphysics.com/planets/Earth_Orbit_v2.htm

 

To calculate force under Newton, we use F = G0*Mass/R^2, where G0 is the gravitational constant and R is the distance between them. To add the force of the exchange particle being sucked out of the planet, assume force is related to the inverse of R, ie. F = G0*Mass/R^2 + G1*Mass/R. Right away we see that we get precession and the amount of precession depends on G1. Ie. we can reverse engineer the orbit of Mercury by using the right value of G1 that produces the proper amount of precession.

http://www.animatedphysics.com/planets/Earth_Orbit_v3.htm

 

No one is saying that adding G1*Mass/R to the force is correct, only that adding the exchange force can produce precessing orbits and infact can produce "butterfly" type orbits posted above if you aim the earth in close enough to the sun.

 

If you could produce an equation for the correct exchange force there are a couple of pretty interesting implications:

 

1/ Black holes would no longer be black holes. As objects with mass fall in closer to the event horizon, more and more mass would be sucked out in the form of gravitons and you would end up with a ball of energy (ie. gravitons) from which nothing, including light could escape. No need for wormholes or alternate universes to explain what is going on.

 

2/ Gravity would look very different on a large scale as in the orbits of entire galaxies. The force on stars close to the center of the galaxy would not change that much, but the force on stars on the outer edge of the galaxy would be greater then under the inverse square law and they would rotate faster then you would expect (maybe like this?). No need for dark matter to explain the orbit of galaxies.

[Mordred]

perhaps you had better study quantum geometrodynamics if you want to use gravitons. I can tell you properly using gravitons will not do the things your suggesting. Though the math is in and of itself complex. Honestly you should sit down with a good GR textbook.

 

However not many people can afford textbooks. So here is several decent articles.

 

http://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on Relativity by Mathius blau.

http://www.lightandmatter.com/sr/

 

The last is an open source textbook on SR. The math will give you a proper starting point to correctly develop a model your describing.

 

None of the math you've posted shows what you are describing.

 

For one thing gravitons would mediate the force aspects of gravity but will not add any force of its own. This is a guage vector boson. Another gauge boson being the photon for the electromagnetic. The photon mediates the charge but does not have a charge.

 

Ok lets do this Graviton modelling 101.

 

First the purpose of the graviton is to couple the stress tensor [latex] T_{\mu\nu}[/latex] to the gravitational field denoted [latex]h^{\mu\nu}[/latex] graviton having spin 2 statistics. k is the coupling constant of the graviton

 

The Langrene is [latex]L_{int}=-\frac{1}{2}k T_{\mu\nu}h^{\mu\nu}[/latex]

 

with field tensor [latex]g_{\mu\nu}=\eta_{\mu\nu}+kh_{\mu\nu}[/latex]

 

to correspond to Newton potential [latex]k^2=32\pi G[/latex]

 

Spin 2 requires the following

 

[latex]+2: h_{\mu v}=\epsilon_{\mu}^{+}\epsilon_v^{+}[/latex]

[latex]-2: h_{\mu v}=\epsilon_{\mu}^{-}\epsilon_v^{-}[/latex]

 

where

 

[latex]\eta \epsilon_\mu \epsilon_v=0[/latex]

and [latex]k^\mu \epsilon_\mu=0 [/latex]

 

There now you have the basics behind the graviton under GR. The above equations is the standard treatments of the Graviton as a spin 2 gauge vector boson. For the spin 2 a good study is the harmonic oscillator (deDonder gauge)

 

By the way gravitons are not sucked out of a planet.

are a couple of pretty interesting implications:

 

1/ Black holes would no longer be black holes. As objects with mass fall in closer to the event horizon, more and more mass would be sucked out in the form of gravitons and you would end up with a ball of energy (ie. gravitons) from which nothing, including light could escape. No need for wormholes or alternate universes to explain what is going on.

 

2/ Gravity would look very different on a large scale as in the orbits of entire galaxies. The force on stars close to the center of the galaxy would not change that much, but the force on stars on the outer edge of the galaxy would be greater then under the inverse square law and they would rotate faster then you would expect (maybe like this?). No need for dark matter to explain the orbit of galaxies.

Both one 1 and 2 are false gravitons aren't sucked out of the mass term. Blackholes, stars, planets etc do not lose rest mass due its interaction with other massive bodies.

 

2 because the inverse square law is a natural consequence of a force over a volume. "Essence of Astrophysics" has an excellent section on that. Secondly the dynamics your describing will still have the wrong mass distribution to account for galaxy rotation curves. (at least as you have described it above)

Edited October 28, 2016 by Mordred

[studiot]

Mordred is in his element gauge here. +1

 

[Mordred]

Thanks Studiot, there is one key property that would be difficult but not impossible to explain. I suspect the OP isn't explaining his ideas correctly though that is difficult to determine without the mathematical details. Though incorrect terminology is a strong indicator...

 

Dark matter has mass but the graviton is a massless particle. There is a peer reviewed article that applies a possible correction but you need to redefine GR.

 

http://www.google.ca/url?q=http://arxiv.org/pdf/1401.8191&sa=U&ved=0ahUKEwir0Z3z0P7PAhVGwWMKHSyjDdMQFggjMAQ&usg=AFQjCNFQDRY7wmfp_pE-tSf5F4-wxy37gw

 

This isn't the only attempt, others have tried different models to accomplish the same goal.

 

A key note, just because an article is peer reviewed. It doesn't mean it is correct. Only that it is a viable possibility. It also doesn't make it a mainstream model. That possibility requires further rigorous testing.

Edited October 28, 2016 by Mordred

[J.C.MacSwell]

shorter list is what we married men are right about.

For that you must answer the age-old question: If a man says something deep in a forest without his wife around to hear...is he still wrong?