Thought Experiments on

Repulsive-Gravity,

Negative Gravity,

Negative Mass

(2017 Feb blog post)

Some paragraphs or web-links or images may be added (or changed),
if I ever get back to this page.

Home > Blog menu > This page of 'thought experiments' on 'repulsive-gravity'.

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

  • Galileo's experiments with acceleration of falling bodies --- and bodies sliding down an inclined plane

  • Galileo's observations on pendulum motions --- the period seemingly (almost) independent of the amplitude of the swing

  • Galileo's planetary discoveries with newly developed telescopes --- especially the observation that moons rotate around Jupiter

  • Kepler's use of Brahe's celestial motions data to observe that planets seem to move in elliptical orbits and they seem to sweep out equal areas in equal times --- and an apparent cube-square relationship between orbital periods and orbital radiuses

  • Huygens' experiments and mathematical analysis on motions of pendulums --- and analysis of centrifugal force (an outward force rather than an inward force)

  • Boyle's experiments with making a vacuum --- and observing falling bodies, such as feathers, in a vacuum

  • England was undergoing Protestant resistance to Catholic dogmatism that was shutting down freedom of inquiry --- examples: Jesuits attempting to stop studies involving 'infinitesimals', and the Vatican suppressing the accumulating evidence that the Earth might not be the center of the Universe.

    (This was scaring the heck out of European philosophers, such as Descartes and Huygens, who saw what happened to Giordano Bruno and what almost happened to Galileo. So many 'natural philosophers' in Continental Europe tried to stay away from the Inquisitions and religious wars that were proceeding in Spain, France, Italy, and Germany --- and were careful about what they studied and published. England preferred their own Anglican church rather than the Catholic hierarchy --- even after the Protestants under Cromwell were overthrown and the English monarchy re-established. Hence there was a little more freedom of inquiry in England than in Continental Europe.)

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 body-to-body 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:

  • The 'north pole' of one magnetic body and the 'south pole' of another magnetic body are strongly attracted to each other --- much more strongly than two similar sized masses sitting near each other --- which seem to be oblivious to each other. That is, any gravitational attraction that exists is much, much weaker than the magnetic attraction between similar sized bodies.

  • The 'north poles' of two magnetic bodies (strongly) repel each other.

  • The 'south poles' of two magnetic bodies (strongly) repel each other.

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 we have another example of 'action at a distance' --- with both attractive and repelling forces involved.


Is gravity attractive-only?

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 electro-magnetic 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 'repulsive-gravity' as well as an 'attractive-gravity'?

    NOTE:
    On Wikipedia, 'anti-gravity' seems to be defined as an absence of gravity, rather than as a reversal of gravity. So, to avoid confusion, I avoid the term 'anti-gravity'. The kind of 'repulsive' gravitation that I am talking may be called negative gravity --- which might emanate from a negative mass.

This question could be phrased in different ways:

    Is there 'negative-gravity' as well as 'positive-gravity?
    Is there 'south-gravity' as well as 'north-gravity'?
    Is there 'black-gravity' as well as 'white-gravity'?

But those questions are just the same question using different names-of-convenience. The question really must get down to the operational level:

    Is there 'repelling-gravity' as well as 'attracting-gravity'? ---

    where 'gravity' is just a name for a type of force that is proportional to the 'mass' in an object or particle --- and where 'mass' is ... what?

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 definitions and laws get rather mixed together. Some physicists have noted that the definition of force in terms of a change in momentum (Newton's 2nd 'law') depends on a definition of mass --- and yet a definition of mass typically depends on the measurement of a force --- either an inertial force (resistance to motion) or a kinetic force (generation of motion) or a potential force (balance of motions).

The 3rd law (so far, in the human history of measuring physical phenomena) applies to many types of forces, including:

  • gravitational forces
  • magnetic forces
  • electric forces
  • contact forces between solid objects (atomic-sized and above)

Someday, on another web page, I would like to consider these types of forces in relation to mass-force-momentum definition-versus-law logic issues. But for now ...

Rather than getting bogged down in these thorny issues, let us press on in (comparative) observations on gravity --- in particular, 'repulsive-gravity'.


If there were 'repulsive-gravity', what would it be like?

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 the paragraph:

    "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 right-hand 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:

  • an expanding universe

  • galaxies whose rotational velocities at the outer parts of the galaxy are much higher than expected

  • force effects from regions in which no force-source has been detected

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: No agglomeration of RGP's.

    Since the RGP particles repel each other, they cannot congregate together like 'attractive-gravity' particles --- and so they cannot form large bodies like planets and suns and black holes.

    In fact, such particles would probably be the size of sub-atomic 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 sub-atomic particles in the Standard Model of sub-atomic 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 space-time --- a singularity from which emanates one or more types of force field.


OBSERVATION 2: One-over-R-squared force from RGP's.

    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 one-over-R-squared 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 inverse-square 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:
      One could perform computer numerical-integration experiments to model the motions of any collection of AGP and RGP particles --- just as computers are used to integrate systems of differential equations that describe 2-body, 3-body and N-body (where N is very large) problems --- that involve only 'AGP' particles.

      For example, on pages 45 - 62 of the 1967 book 'FORTRAN for Physics', by Alfred M. Bork, (QC 20.2.8734) there is code for doing a 3-body simulation --- the 'attractive' gravity problem. This kind of 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 2-body 'attractive' inverse-square force problem (for a large mass and a small mass) results in an elliptical trajectory, for many initial conditions.

      It seems that the 2-body '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 electro-magnetic 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 attractive-gravity particles.

    (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 planet-sized 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:
    How do RGP's and AGP's interact?
    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                           Magneto-statics           Electro-statics
                (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 magnetic-pole force fields and electric-charge 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 magnetic-and-electric 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 AGP-RGP (row1-col2) and RGP-AGP (row2-col1) 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:

    • ? is -     (a repulsive force)
    • ? is +     (an attractive force)
    • ? is 0     (zero, a neutral effect, no force)

    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 --- for an RGP and AGP with equal 'mass' (gravity size).

    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

    • huge clusters of AGP's --- with relatively few RGP's scattered throughout

    • expanding fogs of RGP's that cannot be accomodated by the clusters of AGP's --- because of there being equal numbers of RGP's and AGP's, and because of the limited take-up of RGP's by AGP's.

    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 AGP's --- the visible universe.

    I am inclined to reject the '+' case --- the case of attraction between any pair of RGP and AGP particles.


    Observation3 - Case3   (? is 0):

    Could there be a 'middle-ground' --- a 'mutual stand-off' --- a 'non-action' --- 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 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

    • huge clusters of AGP's --- with extremely few RGP's scattered throughout

    • expanding fogs of RGP's that cannot be accomodated by the clusters of AGP's --- because of there being equal numbers of RGP's and AGP's, and almost nil distribution of RGP's among AGP's --- because of no attraction of the RGP's to the AGP's, attraction of AGP's to each other, and RGP's repelling each other.

    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 this:

                  Gravity                           Magneto-statics           Electro-statics
                (Gravitons?)                           (poles)                    (charges)
                                                      
                   AGP   RGP                          North  South                Pos   Neg
                   ---   ---                          -----  -----                ---   ---
            AGP     +     -                    North     -     +            Pos    -     +
            RGP     -     -                    South     +     -            Neg    +     -
             

    So in the magnetic-and-electric tables, 'opposites attract' --- but in the gravity table 'opposites repel'.

    It seems to me that this could lead to questions about the elusive graviton, such as:
    Are there to be 2 types of gravitons --- attractive and repulsive gravitons?


Observation 4:

    At this point, I have (temporarily) run out of observations to make on 'repulsive gravity'. I retire until another day --- when I might have more to add on these matters.


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 that I 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, which is of interest to me.


For further information :

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Page was posted 2017 Feb 20.
Page was changed 2017 Feb 21. (Added a section on numerical integration.)
Page was changed 2017 Feb 26. (Added to the Observation-3 section.)