Thought Experiments onRepulsiveGravity,
Negative Gravity

(2017 Feb blog post)
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INTRODUCTION : In the 2016  2017 time period (in my retirement), I have been reading many books on math and physics  including many books that try to explain Isaac Newton's Principia (which is very heavy reading)  and hence books that deal with gravity. Newton was very lucky to be living at a time when many new discoveries and events were coming together, such as
In addition, Newton benefited from recent experiments with magnetism  for example, work by William Gilbert  which showed that 'action at a distance' is possible. In other words, there can be forces in nature which act from one body to another with no (apparent) direct bodytobody contact taking place. Although Newton was tempted to seek some explanation for gravity in terms of magnetism, he apparently observed that magnetism is quite different from gravity. So he satisfied himself with showing how gravitational effects can be predicted mathematically  without actually knowing the 'causes' of those gravitational 'effects'. Near the end of the Principia, he declared that he was not going to 'feign hypotheses' about the mechanism (cause) of gravity. One notable difference between gravity and magnetism is that there is a 'north pole' and a 'south pole' of any magnetized body that has been studied. Furthermore:
Similar considerations apply when considering 'static electricity' phenomena. There are 'positive' and 'negative' effects  attracting and repelling effects  much stronger than gravitational force on similar sized objects. Thus, with static electricity, we have another example of 'action at a distance'  with both attractive and repelling forces involved. Is gravity attractiveonly? It appears that ever since the time of Newton (1642  1727)  in more than 250 years  no physicist has been able to explain gravity in terms of some sort of electromagnetic effect. In spite of this failure, one has to wonder ... with all the symmetries in nature ... such as ... 'north' magnetic poles and 'south' magnetic poles ... 'positive' charges and 'negative' charges ... and various symmetries at the molecular and quantum mechanical levels: Is there a gravitational symmetry?  other than Newton's 3rd law, which says that: For every (gravitational) force, there is an equal and opposite (gravitational) force. More specifically: Is there a 'repulsivegravity' as well as an 'attractivegravity'?
NOTE: So, to avoid confusion, I avoid the term 'antigravity'. The kind of 'repulsive' gravitation that I am talking may be called negative gravity (related to 'dark energy'?)  which might emanate from a negative mass (related to 'dark matter'?). This question could be phrased in different ways:
But those questions are just the same question using different namesofconvenience. The question really must get down to the operational level:
Is there 'repellinggravity' as well as 'attractinggravity'? 
That question 'what is mass?' is a doozy. It is probably best we skip over that for now. But a few words are in order: In more detail, the 3rd law says that, given two particles that exhibit a gravitational force (attractive) on each other, the change in 'momentum' in particle #1 due to particle #2's gravitational attraction is equal to the change in 'momentum' in particle #2 due to particle #1's gravitational attraction  where 'momentum' is measured by mass times 'instantaneous' velocity.
NOTE: The 3rd law (so far, in the human history of measuring physical phenomena) applies to many types of forces, including:
The puzzle of 'masses' that 'exude' a gravitational force prompts a couple of types of questions:
Someday, on another web page, I would like to consider the 'definitionversuslaw' logic issues in relation to 'massforcemomentum'  for various 'types of forces'. And I would like to consider the questions around identifying the masses that generate gravitational forces  where those forces MAY be 'postive' or 'negative'. But for now ... Rather than getting bogged down in these thorny issues, let us press on in (comparative) observations on gravity  in particular, 'repulsivegravity'.
If there were 'repulsivegravity', I mentioned above that I have been reading physics and math books in my retirement. One of those books is Great Calculations by Colin Pask. On page 160 of that book (in Chapter 7, titled 'The Universe'), in talking about observations  by physicists Perlmutter, Reiss, and Schmidt  that the rate of expansion of the universe is actually increasing, Pask presents a paragraph of sentences including: "The suggested solution to this dilemma is to postulate the existence of something called dark energy, which contributes a density and has the weird fluid property that its pressure is negative so that the righthand side of [the Friedmann equations] becomes positive. Dark energy is somehow driving an acceleration in the rate at which the universe is expanding. It acts something like a repulsive gravitational force. ... The 'dark' refers to the fact that this dark energy has not been seen (detected) in other ways, and here is an incredible mystery for future cosmologists to come to grips with." It is considerations like these:
that motivate one to ponder what would happen if there were particles that have a 'repulsive force proportional to their matter'  for short, 'repulsive gravity particles'  RGP's. Here are several observations that I make (so far)  on hypothetical 'repulsive gravity particles' (RGP's):
OBSERVATION 1: Since the RGP particles repel each other, they cannot congregate together like 'attractivegravity' particles (AGP's)  and so they cannot form large bodies like planets and suns and black holes. In fact, such particles would probably be the size of subatomic particles  quarks or smaller  so they would be dispersed and extremely small  very hard to detect. Some comments on gravity 'particles' (as used here): In this discussion, I am not thinking about the specific variety of subatomic particles in the Standard Model of subatomic particle physics, but rather, I think of a general (vague, if you want to call it that) notion of a particle which has a 'mass' property which indicates its size, in a gravitational sense. One could think of these 'particles' as being some kind of 'singularity' in 3D space or 4D spacetime  a singularity from which emanates one or more types of force field.
OBSERVATION 2: Just as with 'attractive gravity particles' (AGP's), one would expect that the influence (the force field) of 'repulsive gravity particles' (RGP's) would fall off in a oneoverRsquared manner  because, just as with 'normal' gravity, one would expect the force intensity to be spread out over a spherical surface emanating from the RGP, so the force would be spreading out over a 4*pi*R^2 surface area  just as Robert Hooke and Isaac Newton discussed in letters to each other more than 250 years ago  about an inverse square law. Under this inversesquare force, the repulsive force of each RGP would die off to miniscule levels as the RGP's separated from each other. They could form large clouds of RGP's that are 'slowly' expanding.
NOTE: For example, on pages 45  62 of the 1967 book 'FORTRAN for Physics', by Alfred M. Bork, (QC 20.2.8734) there is FORTRAN code for doing a 3body simulation  the 'attractive' gravity problem. This kind of computer code could be changed (by simply flipping some algebraic signs) to model the motion of 3 'repulsive gravity particles'  for given initial conditions (initial locations and velocities). As Newton and followers showed, the 2body 'attractive' inversesquare force problem (for a large mass and a small mass) results in an elliptical trajectory, for many initial conditions. It seems that the 2body 'repulsive' problem (for 2 equal sized masses, say) may typically result in a hyperbolic trajectory of the 2 masses, with the 2 masses diverging and approaching an 'asymptote'. Has anyone addressed this problem? I do not remember any mathematical treatments of this type of problem in all my reading in physics  but I have not done much reading in electromagnetic mathematical physics, where repulsive forces between particles/bodies may have been considered, and rigorously described or simulated mathematically.
OBSERVATION(s) 3: (Interaction of RGP's with AGP's) As their name implies, RGP's (repulsive gravity particles) would repel each other. Hence they could not cluster together like AGP's do. If they could conglomerate together in large quantities, they would become easily detectable. There could be planetsized bodies made up of RGP's. And, we know that AGP's (attractive gravity particles) attract each other. They constitute the 'ordinary' matter that we see in planets and suns and moons and asteroids  and in particle accelerators.
A question arises: In other words, it becomes a matter of filling out a table of two rows and two columns  an RGP and an AGP row  and an RGP and an AGP column. 
Gravity Magnetostatics Electrostatics
(Gravitons?) (poles) (charges)
AGP RGP North South Pos Neg
     
AGP + ? North  + Pos  +
RGP ?  South +  Neg + 
where '+' indicates 'mutual attraction' and '' indicates mutual repulsion. For comparison, I have added tables for magneticpole force fields and electriccharge force fields, in addition to an (incomplete) table for gravity fields. Note that, even though we have not filled out the gravity table yet, it is clear that there will be a major difference between gravity fields and magneticandelectric fields. To put it briefly, with magnetic and electric fields, 'likes repel' (and 'opposites attract')  whereas, for AGP gravity particles, 'likes attract'  and for RGP gravity particles 'likes repel'. Now we ask ... what goes in place of the question marks of the gravity table? In other words, in the gravity table, what do opposites do? We would expect the AGPRGP (row1col2) and RGPAGP (row2col1) entries to be the same, because, whatever the effect, we would expect a 'Newton 3rd law' type of situation: the effect of particle #1 on particle #2 to be the same as the effect of particle #2 on particle #1. If we accept that, then there are at least 3 cases to consider:
Let us consider some implications of each case. Observation3  Case1 (? is ) : It seems likely that the '?' (question mark) should be ''  a mutually repulsive force  keeping the RGP's from collapsing onto AGP's. In that case, "clouds of RGP's" could persist  as they may be now  causing an expansion of the visible (AGP) universe. Observation3  Case2 (? is +): Would putting a '+' in place of the question marks be an option? That is, could RGP's be attracted to AGP's, and vice versa? And  could "clouds of RGP's" persist in that case? In the '+' case, the attractive force of an AGP on an RGP could be expected to be equal to the attractive force of an RGP on an AGP. Imagine then a huge cluster of AGP's (like a planet or sun). It could have a huge attraction to individual RGP's  and yet since the RGP's repel each other, there could be RGP's in a cluster of AGP's  but they would be scattered  much less dense than the AGP component of the big cluster. Now imagine a huge cluster of RGP's (which would be like a fog, diminishing in density over time, since they repel each other). The fog could have a huge attraction to individual AGP's, and since the AGP's attract each other, the AGP's would infiltrate the fog of RGP's and eventually accrete together in large bodies like planets or suns  with relatively few RGP's scattered throughout that accretion. So in either scenario  start with a huge cluster of AGP's or start with a huge cluster of RGP's  it seems like the end result would be huge clusters of AGP's  with relatively few RGP's scattered throughout the mass of AGP's. So it seems like the RGP's would eventually be scattered quite thinly throughout AGP clusters  and expanding 'fogs' of RGP particles might exist  but they would be attracted to AGP clusters, in this '+' case. If, initially, there are an equal number of RGP's and AGP's, then it seems like the universe might migrate toward
One problem with this '+' case (RGP's and AGP's attracting each other) is that the AGP's could permeate through fogs of RGP's  and this would not seem to be compatible with the 'expanding visible universe' scenario  and, then, certainly not compatible with the 'accelerating expanding visible universe' scenario. In other words, there would be a tendency toward collapse  at least of the selfattracting AGP's  in the visible universe. I am inclined to reject the '+' case  the case of attraction between any pair of RGP and AGP particles. However there may be a case for the AGP's being the 'raisins' in an 'expanding pudding' of RGP's (???)  the AGP's being carried along in a fog of selfrepelling RGP's. Observation3  Case3 (? is 0): Could there be a 'middleground'  a 'mutual standoff'  a 'nonaction'  between a pair of RGP and AGP particles? In other words, should we put '0' (zero) in the table in place of the two question marks (?)  where zero means an AGP and an RGP do not have any effect on each other (a sort of cancelling of the attractive power of the AGP and the repulsive power of the RGP)? Is there some sort of logic that would eliminate that possibility? Imagine a huge cluster of AGP's (like a planet or sun). It would have no attraction to individual RGP's  so one would expect to see way fewer RGP's among AGP's than in the '+' case above. Furthermore, since the RGP's repel each other, what few RGP's might be in a cluster of AGP's would be scattered. So there would be very, very small amounts of RGP's among AGP's. Now imagine a huge cluster of RGP's (which would be like a fog, diminishing in density over time, since they repel each other). The fog could have no attraction to individual AGP's, and yet AGP's attract each other. AGP's could infiltrate the fog of RGP's  but not nearly as aggressively as in the '+' case  and eventually accrete together in large bodies like planets or suns  with relatively few RGP's scattered throughout that accretion. So in either scenario  start with a huge cluster of AGP's or start with a huge cluster of RGP's  it seems like the end result would be huge clusters of AGP's  with few RGP's scattered throughout the mass of AGP's. So it seems like the RGP's might eventually be scattered extremely thinly throughout AGP clusters  and expanding 'fogs' of RGP particles might exist  but the fogs would NOT be attracted to AGP clusters, in this '0' (zero) case of no attraction or repulsion between a pair of RGP and AGP particles. Nor would the RGP fogs be repelled from the AGP clusters. If, initially, there are an equal number of RGP's and AGP's, then it seems like the universe might migrate toward
One problem with this '0' (zero) case (for RGP's and AGP's) is that the fogs of RGP's would not repulse the AGP's  and this would not seem to be compatible with the 'accelerating expanding visible universe' scenario. I am inclined to reject the '0' (zero) case  the case of neither attraction nor repulsion between any pair of RGP and AGP particles. Conclusion to Observation 3: Hence I am inclined to accept the '' case and a gravity table like the following. 
Gravity Magnetostatics Electrostatics
(Gravitons?) (poles) (charges)
AGP RGP North South Pos Neg
     
AGP +  North  + Pos  +
RGP   South +  Neg + 
So in the magneticandelectric tables, 'opposites attract'  but in the gravity table 'opposites repel'. However, I have not totally ruled out the possibility that the RGP's and AGP's mutually attract. It seems to me that this idea of RGP's and AGP's could lead to questions about the elusive graviton, such as: Are there to be 2 types of gravitons  attractive and repulsive gravitons?
Observation 4: The Einstein equation E = m * c^2 implies that 'where there is energy, there is mass' and 'where there is mass, there is energy'. Gravity is a force that creates energy. This suggests that 'where there is gravity, there is a graviton' and 'where there is a graviton, there is gravity'. Another variation: 'where there is dark energy, there is dark mass' and 'where there is dark mass, there is dark energy'. Yet another: 'where there is repulsive gravity, there is repulsive mass' and 'where there is repulsive mass, there is repulsive gravity'. Another: 'where there is negative gravity, there is negative mass' and 'where there is negative mass, there is negative gravity'. Observation 5:
At this point, I have (temporarily) run out of observations to make on 'repulsive gravity' and RGP's and AGP's  and 'dark energy' and 'dark matter' and 'gravitons' and 'quarks' and ... I retire until another day  when I might have more to add on these matters. I hope to do numerical integration experiments someday to simulate 3 or more RGP and AGP particles interacting with each other  for a variety of inital conditions (positions and velocities in 2space or 3space)  and for various values of 'gravitational constant' for repulsive gravity as well as the known constant for attractive gravity. I intend to do those numerical experiments using the TclTk scripting language that I have used to make 'tkGUI' scripts for physics simulations, such as I have many, many projects  but I hope to get around to those simulations someday  after doing some initial coding for 2D and 3D 3body motion simulations for 'AGP' masses. Doing such numerical experiments may help me clarify the discussions in Observation#3 above  to settle questions in trying to fill out the little 2x2 AGPRGP gravitational attraction/repulsion table. CONCLUSION : There is no conclusion to this web page. I hope to continue adding observations and notes and links to this page  until my ashes are spread to mix with the atoms of the universe. I feel I must add that I know that there are physicists who are *WAY* more capable and experienced than I (a nongenius, 'degreed' mathematician) in considering these matters. Someone may have already made (or rejected) observations like these. I simply use this page as a place to collect my thoughts (and the thoughts of others) on this subject area  a subject area which is of interest to me. 
For more information : For further information on these 'repulsivegravity' issues  which are motivated by observations of an accelerating expansion of the universe and questions on the high rotating velocity of galaxies  which suggest there may be influences from unknown sources that are nicknamed 'dark matter' and 'dark energy': Here are some links to WEB SEARCHES on keywords related to this topic. After the search window appears with an intial page of 'hits', you can change or add keywords to hone the search to what you are looking for. 
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