Newton's Action at a Didstance

Discussion in 'Physics & Math' started by geistkiesel, Jul 6, 2011.

  1. Pete It's not rocket surgery Registered Senior Member

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    Ah... that makes sense. Charged particles in such an orbit must radiate, and that radiation carries angular momentum.

    But it's not quite analogous, is it, because the orbiting charged particles are accelerating, while orbiting masses are inertial (or are they? Way over my head.)

    I imagine the difference is in the EM and gravitational field equations and how they are quantised, which I'm not going to pretend to know anything about.
     
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  3. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

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    This was my first assumption too, but it would seem that the gravity field now at S is with local gradient pointing to J' i.e. S is a point on a constant gravitational potential circle with center at J'.

    However, I think angular momentum is conserved, and do not like Capbork's ideas that it all falls out of GR, which is probably true. I think the velocities are small enough that Clasical Mechanics must be able to explain a stable orbit despite the local gradient at S pointing towards J' - probably some thing like I suggested in my post 38.

    As a start on butting some math bones on this idea, I recall from geometry that when a diamater bisects a chord the products of the two parts of the diameter equals half the chord squared. Thus it is convenient* to let the diameter be 5 units, 4 of which are on one side of the chord. I.e. 4x1 = 4 and thus each half of the chord is o length 2. Then the angle from chord end S to the barycenter is such that the tangent of it is (2.5 -1)/2 = 3/4. This allows simple computation of the component of the force component directed towards the barycenter.

    That force on S from J' is 4 units away, in stead of 5 that reache across the full diameter. So the "stronger force" is (5/4)^2 stronger and we want the component of it towards the barycenter. I must stop here now. Perhaps someone else will continue to see how this compares with the force of instaneous gravity 5 units away but all directed towards the barycenter.

    *But with this choice of geometry, it is not very likely that the speed of gravity implicitedly assumed is that of light. If it should turn out that ONLY light-speed gravity is able to make a self consistent story, that would be more than just "interesting."

    Well past my bed time - perhaps more tomorrow.
     
    Last edited by a moderator: Jul 11, 2011
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  5. przyk squishy Valued Senior Member

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    I'm confused here: why is everyone still assuming that a mass should be drawn gravitationally directly to where another mass was? Not only is this not the case in electrodynamics - despite the fact the electromagnetic field also has a finite propagation velocity - but the idea really doesn't play well with the relativity principle (as James R more-or-less pointed out earlier).
     
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  7. Pete It's not rocket surgery Registered Senior Member

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    What if the objects are accelerating, such as two charged particles orbiting each other?
     
  8. CptBork Valued Senior Member

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    The question emerged as to whether Newton's laws with a speed-of-light time delay would make for a viable theory of gravity, so we're just going over some of the problems with that approach. I've actually wondered a few times why gravity couldn't have simply been modified in an analogous manner to Maxwell's equations, but I suppose one major factor is that the inertial mass varies between reference frames, whereas total electric charge doesn't.
     
  9. CptBork Valued Senior Member

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    I believe that even when you have static charges and currents, the fields they generate can contain angular momentum. There's an example I recall from Griffiths' Intro to Electrodynamics where you've got a constant electric current flowing through a battery of some sort, then you switch off the battery and the contraption starts to rotate.

    Well in this case we were imagining that we threw GR out the window and replaced it with a time-delayed variant on Newtonian gravity, so in such a picture, gravitational acceleration would be the same as acceleration caused by any other force.

    In GR there's a fundamental difference in how the two forces are treated. Like I mentioned to przyk, I don't think you could fit even a time-delayed version of Newton's law into the Relativity picture, because of the differences in masses and forces as measured in different reference frames. Besides, Einstein constructed his GR approach more than a decade before the first theory of quantum electrodynamics had been developed, so the reason he chose not to follow Maxwell's electrodynamic approach couldn't have had anything to do with quantization.
     
  10. Farsight

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    Sounds like the Einstein de-Haas effect.
     
  11. JJM Registered Senior Member

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    Howdy....Hello....Dywyddyr #9 7-07-11@ 9:03 AM....."Nope, it's drivel".....Do you not understand terms? h/v you don't understand? wave and fld you don't understand? pp' pressure density you don't understand? geo geometry you don't understand? square functions you don't understand? * opposite, not anti, you don't understand? The concept at #8 defines the act of 2Gmm'. Simplistically. I was told not to communicate with you, but I want you to know that this is measurable, quantitatively, qualitatively.
     
  12. CptBork Valued Senior Member

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    Hmmm... Not really, in my opinion. That effect is almost entirely due to the actual spins of the electrons, not the angular momentum contained in the electromagnetic fields themselves. Still a nice effect though, lots of useful implications.
     
  13. Farsight

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    IMHO you shouldn't separate the two. We use pair production to create an electron out of an electromagnetic wave, a "quantum field variation". There's no point particle at the heart of a radio wave, and no surfaces or hard and fast boundaries. In similar vein there's no point particle at the heart of an electron, which of course has a wavelike nature and can be diffracted. A whirlpool analogy can be handy to conceptualize this, particularly a Falaco soliton. It's just rotating water, this rotation being part of what it is. In similar vein the electron's electromagnetic field is part of what it is.
     
  14. CptBork Valued Senior Member

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    Well if you looked at it that way, there'd be no point to distinguishing particles or physical quantities of any sort whatsoever. Even though they can be converted from one to the other at the quantum level, electrons and EM fields have some very distinct properties and characteristics, and the forms of angular momentum they carry can be distinguished.
     
  15. geistkiesel Valued Senior Member

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    If you use a speed of light constraint for the transfer of force from one stellar body to another, say sun and earth, the trajectory of your earth orbit will be erroneous. When Newton remarked that as to action at a distance he had no comment he was referring to inwstantaneous 'transfer' of the force of gravity.
     
  16. geistkiesel Valued Senior Member

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    Calculate the orbit of the earth-sun system using Newton's force equation and include the relativity delay in the calculation and your resulting trajectory will not be verified by observation.
     
  17. geistkiesel Valued Senior Member

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    The sun has been determined by some to be moving at approximately 200kim/sec. When a gravity 'pulse' leaves the sun it does not arrive until some 8 minutes later and the reaction force will not arrive back atthe sun until another 8 minutes. Using this reality the calculated trajectory will not be as observed.
     
  18. geistkiesel Valued Senior Member

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    James R, Calculating planetary trajectories using Newton's force term will produce a verifiable trajectory. Using a relativity constraint of the speed of light for forces - the action and reacdtion forces - will not produce a verifiable trajectory.
     
  19. geistkiesel Valued Senior Member

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    Yes, and when considering the reaction forces it seems inescapable that the same result of the mutual orbit will be observably equivalent where diff cannot be explained by experimental error considerations. Each delayed action reaction pair will drive the orbit of trajectories to a gross difference regarding Newton's presumed instantaneous problem.
     
  20. geistkiesel Valued Senior Member

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    It would probably be an ever growing error as compared to the Newton's formulation for the gravity forces. Remember, the delay would be amplified for the few billions of years since the BB. Likewise, the inflationary expansion of the BB was supposed to have the effect of maintaining the perfect equivalent state of the energy of all the universe's mass [in order to prevent a premature collapse] - the inflationary expansion was claimed to be a monetary reversal of the force of gravity, where the force pushed instead of pulled. This is Guth's opinion
     
  21. geistkiesel Valued Senior Member

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    The bold notice is not substantiated. How can it be that the delayed gravity forces will always arrive and return without a deelayed error in position due to the linitation associated with the delay?

    I suggest that Eddington's last sentence can be easily checked. Feynman has an example of making such a calculation using Newton's force expression. I will risk a correction that when comparing the GR and Newtoin's of trqajectory calculations differences should be apparent. See Fynman's Lectures on Physics Vol. 1 Section 9-6 where he has calculated and tabulated twenty points of the trajectory (1/2 orbit). He solves the equations mv(x)/dt = - GMmx/r^3 and mv(y)/dt = - GMny/r^3.
     
  22. geistkiesel Valued Senior Member

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    A\nalyze the problem with the assumed error growing for the 5 billion yearas the earth-sun system has been in operation.
     
  23. AlphaNumeric Fully ionized Registered Senior Member

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    Relativity is more than just a time delayed Newtonian force, so your claim is, aside from being unjustified, irrelevant.

    That is a massive over simplification of what would be done. Anyone familiar with electromagnetism will have seen calculations involving advanced and retarded waves. The superposition of all of these is what leads to the end result. In electromagnetism specific electromagnetic waves, even down to individual photons, can be modelled and the results verified. In GR the interactions aren't modelled as single gravitons, instead they are wave fronts in space-time geometry. They don't come in discrete packets, they are constantly being emitted, as an ongoing process. Hence this "pulse from Sun to Earth and then Earth to Sun" is a massive over simplification.

    You strike me as someone who doesn't know how the calculations are done in the mainstream community. I also have some vague memory of a previous thread where it was determined your maths skills are very poor. This "Add a time delay to Newtonian force" is not how GR works, it is not how the calculations are done and your description of it on a qualitative level doesn't match how such a calculation would be done properly.

    Perhaps you'd like to show us all your calculations? Can you demonstrate GR does not predict the right dynamics for the solar system? Doing the time dependent calculations in GR are extremely difficult, they cannot be solved analytically and unless you use very complicated numerical methods even a computer can't do them without serious issues to do with numerical stability and non-linearity. Fortunately there are people who know how to handle such things and numerical calculations for the dynamics of things like the orbit of the GPS network around the Earth or Gravity Probe B, which required precise modelling of the interactions between it, the Earth, the Moon, the Sun and probably the other planets too. They do match experimental results.

    Hence I request that you present your work. If you haven't used GR but some idea you made up to do with adding a time delay to Newton then your complaints are irrelevant as you aren't addressing the models used. If you haven't done the calculations then you have no right to make the claims you do.

    I know you won't provide them, I know you haven't done them. I just want to see you make laughable excuses or perhaps, if we're lucky, you attempt to do some mathematics so laughably wrong it'll be comedy gold. So, you going to fess up or end up digging yourself in further?

    Newtonian gravity, including time delay or not, cannot model inflation. No one who understands the models in question would ever make that conceptual mistake. Newtonian space-time is rigid and locked, it does not bend or twist or warp or inflate. You seem to have a fundamental lack of understanding of even basic conceptual issues in mainstream physics. The fact you've had these for years is all the more worrying. You seem to devote massive amounts of time to whining about these things yet zero time finding out what they actually say. How can you disprove what the mainstream says when you don't know what they say?

    Of course there are, else they'd be the same model.

    This just illustrates my comments about you not understanding the maths. What you're referring to is the motion of the \(\theta = \frac{\pi}{2}\) orbital plane, which is equivalent to the z=0 plane in Cartesians. If you convert the spherical coordinates' radial \(m\ddot{r} = - \frac{GMm}{r^{2}}\) equation into Cartesians (x,y) you get \(m\ddot{x} = - \frac{GMmx}{r^{3}}\) and \(m\ddot{y} = - \frac{GMmy}{r^{3}}\).

    The fact you didn't even manage to copy the expression for a derivative correctly speaks volumes. Trying to throw in mathematics when you don't understand it always ends badly. Even Farsight has the good sense to stay away from equations, seeing as he couldn't pass a high school exam on the stuff. It never went well for Reiku either.

    Altering that equation to include a time delay is a non-trivial thing. You have to consider infinitely many interactions back and forth, so what you have to end up doing integrals, compute the expressions which determine the actual resultant force in terms of the delayed force and then numerically solve them. That's basically the advanced/retarded wave problems of electromagnetism. If you can't even write down a derivative properly I'd say they are out of your league. Just like basic arithmetic and sanity.

    No one would ever do such a calculation. Firstly there's no need to know the precise location of the Earth 5 billion years ago today. Secondly, it would require knowing all the gravitational effects the solar system has experienced in that time. A passing star would cause changes to orbits for instance. Thirdly even if gravity were instantaneous and the equations nice it is known that a 3+ body gravitational system is chaotic. Any error, no matter how small, will eventually overwhelm the predictions of the model. This is not a problem with the model but an inherent mathematical fact for certain classes of dynamical systems. As such, even if we knew every interaction the Earth has had in the last 5 billion years it is beyond the bounds of the numerical accuracy of modern computers to model a chaotic system for 5 billion years.

    Instead the analysis would be done by showing that the behaviour of the Earth-Sun system is stable to small perturbations and remains in certain regions of its phase space. In chaotic systems it might be impossible to analytically say the state at a particular time in the future but you can still say a lot about whether the system will be well behaved.

    Newtonian gravity is fine for short term, approximate modelling. Want to put a rocket into orbit or send a probe to Mars? Newton works fine. Want to do timings to billionths of a second and measure space-time warping due to the Earth's rotation? Relativity is needed. And it's thoroughly examined. Sure, that doesn't mean it is perfect (it is only an approximation to quantum gravity) but the sort of hypothetical problems you're talking about are not real problems. Relativity is not Newton + time delay, it is a complete reformulation of gravity which happens to have Newtonian gravity as a weak field limit (as it should) but it does that limit in a very particular way.

    I suggest you spend a little more time trying to understand that Feynman book you have, rather than just copying the squiggles from page to forum without understanding them.
     

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