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Einstein repeatedly noted that the his theory didn't preclude negative mass-energy. He wrote that he wouldn't elaborate on it in a physical theory since it had not been physically observed. His predilection for a net density of 0 can be seen in his writing as is his almost plaintive admission that "this does not appear so." He never wavered in his disallowing of physical singularities and could he have known of their popularity soon after his death he likely would be especially receptive to a possibility that would preclude them and provide tests for which data might (and did) soon appear.

Model of Universe Allowing Probability of Creation of Particles

This model holds that all existing particles have non-zero probabilities for creation and annihilation (Pc, Pa) and these same probabilities exist for particles of like observable descriptors except that the mass is negative and equal in quantity---- |m-| = |m+|. (Pc=particles/time-cubic three space, Pa = particles/time. Probabilities operate in proper space-time).

In laboratory of m+ matter observation of E/M interactions between m- and m+ matter inhibited by lack of m- matter. This lack of perception within the laboratory produces difficulty in conceiving of possible E/M interactions between m+ instruments in the laboratory and m-matter at large distance. m- collections thus appear transparent, unusually devoid of m+ matter.

The probability for creation of neutrons apparently being considerable, this is the only probability considered here. Particles of one type of mass will tend to collect gravitationally and repel oppositely massed particles. M(sum of m+ minus sum of m- within a radius r) divided by |M|( sum of m- plus sum of m+) tends monotonically to zero as r increases about any point. Likely GR will agree that E/M and other physics of m- matter are similar to that for m+ matter.

A collapsing m+ neutron star will speed clocks of m- matter . These "clocks" acting thru Pc preclude developed black hole: the formulas below relate to neutrons entering a sphere of radius R(inside neutron star) at velocity dr/dt.

Density at its surface is D(finite number).

dm/dt, R, D are observed, measured far from star.

dm+/dt = 4 xPi x Rsquare x D(R) x dr/dt < 4 x Pi x Rsquare x D x C (light speed=1)

dm-/dt > Pc x 4/3 x Pi x R^3 (1+ M/2R)^3 over 1-2M/R.

M = D x volume of sphere of radius R. Note that when integrating IntD/r over this sphere to get metric-- ruler-clock expansion factor, the largest r between any mass element and any 3space element for which we desire the factor is 2R. Thus actual expansion factor greater. Note we are ignoring mass outside the sphere.

If R is such that M(R)/2R is close enough to 1 that dm-/dt > dm+/dt (note that expansion of rulers goes to 2) that is:

Pc x 4/3 x Pi x 2^3 R^3 over 1-M/2R > 4 x Pi x R^2 x D

or Pc x 8/3 R over 1-M/2R > D --- then

net mass within radius R does not increase. The alternative to the above "If" is that there is no R such that M / 2R approaches one. m- neutrons appearing within high enough density of m+ neutrons will annihilate with m+ neutrons(QM extrapolation)

Very large collections of m+ matter containing much hydrogen will present high energy(fusion energy) and low particle density which decreases probability of annihilation of m+ and m- matter and thus escape of m- matter. Local region of order 10^10 Ly possibly artifact of prior collapse of region of this order and subsequent fusion-excursion expansion. Or, local region of apparently expanding m+ results from prior collapse of m- region with subsequent productin of core of m+ which produced m+ core that initially maintained integrity and pressure for large scale fusion energy until it could repel m- collapsed matter. Again producing observed expansion through globs of m-.

A large region of relatively constant density m- matter containing a smaller void(perhaps due to presence of m+ matter there) can be handled in the elementary physics classroom by imagining the region to have no void but have imbedded in the m- dominated region a small region of m+ matter of absolute density equal to the "average" density of the voided region of m- matter. A void induced by an m+ galaxy in a large m- region could be approximated as a sphere of m+ matter of radius of order of the galaxy. As the gravitational(centripetal) effect of this incompressible imaginary matter would proceed from 0 at r=0 to maximum at the surface, far observation would show that the outer reaches of the galaxy suffer a higher central attraction(and velocity) than more central matter. This effect is superimposed on the effect of the visible(m+) matter Resulting angular velocity of far-off matter would approach a constant versus r. Matter near center would exhibit usual mv^/r = mM/r^2 velocity

A compact enough galaxy cluster could induce above Elem. Phy. void of cluster size thus effecting the dynamics of peripheral galaxies within the cluster more than central ones in their co-orbiting. Individual galaxies would not exhibit the appearance of higher central attraction for peripheral matter. Individual galaxies in less compact clusters would exhibit combination of above dynamics.

Thank you for your consideration,

John Shoemaker

Model of Universe Allowing Probability of Creation of Particles

This model holds that all existing particles have non-zero probabilities for creation and annihilation (Pc, Pa) and these same probabilities exist for particles of like observable descriptors except that the mass is negative and equal in quantity---- |m-| = |m+|. (Pc=particles/time-cubic three space, Pa = particles/time. Probabilities operate in proper space-time).

In laboratory of m+ matter observation of E/M interactions between m- and m+ matter inhibited by lack of m- matter. This lack of perception within the laboratory produces difficulty in conceiving of possible E/M interactions between m+ instruments in the laboratory and m-matter at large distance. m- collections thus appear transparent, unusually devoid of m+ matter.

The probability for creation of neutrons apparently being considerable, this is the only probability considered here. Particles of one type of mass will tend to collect gravitationally and repel oppositely massed particles. M(sum of m+ minus sum of m- within a radius r) divided by |M|( sum of m- plus sum of m+) tends monotonically to zero as r increases about any point. Likely GR will agree that E/M and other physics of m- matter are similar to that for m+ matter.

A collapsing m+ neutron star will speed clocks of m- matter . These "clocks" acting thru Pc preclude developed black hole: the formulas below relate to neutrons entering a sphere of radius R(inside neutron star) at velocity dr/dt.

Density at its surface is D(finite number).

dm/dt, R, D are observed, measured far from star.

dm+/dt = 4 xPi x Rsquare x D(R) x dr/dt < 4 x Pi x Rsquare x D x C (light speed=1)

dm-/dt > Pc x 4/3 x Pi x R^3 (1+ M/2R)^3 over 1-2M/R.

M = D x volume of sphere of radius R. Note that when integrating IntD/r over this sphere to get metric-- ruler-clock expansion factor, the largest r between any mass element and any 3space element for which we desire the factor is 2R. Thus actual expansion factor greater. Note we are ignoring mass outside the sphere.

If R is such that M(R)/2R is close enough to 1 that dm-/dt > dm+/dt (note that expansion of rulers goes to 2) that is:

Pc x 4/3 x Pi x 2^3 R^3 over 1-M/2R > 4 x Pi x R^2 x D

or Pc x 8/3 R over 1-M/2R > D --- then

net mass within radius R does not increase. The alternative to the above "If" is that there is no R such that M / 2R approaches one. m- neutrons appearing within high enough density of m+ neutrons will annihilate with m+ neutrons(QM extrapolation)

Very large collections of m+ matter containing much hydrogen will present high energy(fusion energy) and low particle density which decreases probability of annihilation of m+ and m- matter and thus escape of m- matter. Local region of order 10^10 Ly possibly artifact of prior collapse of region of this order and subsequent fusion-excursion expansion. Or, local region of apparently expanding m+ results from prior collapse of m- region with subsequent productin of core of m+ which produced m+ core that initially maintained integrity and pressure for large scale fusion energy until it could repel m- collapsed matter. Again producing observed expansion through globs of m-.

A large region of relatively constant density m- matter containing a smaller void(perhaps due to presence of m+ matter there) can be handled in the elementary physics classroom by imagining the region to have no void but have imbedded in the m- dominated region a small region of m+ matter of absolute density equal to the "average" density of the voided region of m- matter. A void induced by an m+ galaxy in a large m- region could be approximated as a sphere of m+ matter of radius of order of the galaxy. As the gravitational(centripetal) effect of this incompressible imaginary matter would proceed from 0 at r=0 to maximum at the surface, far observation would show that the outer reaches of the galaxy suffer a higher central attraction(and velocity) than more central matter. This effect is superimposed on the effect of the visible(m+) matter Resulting angular velocity of far-off matter would approach a constant versus r. Matter near center would exhibit usual mv^/r = mM/r^2 velocity

A compact enough galaxy cluster could induce above Elem. Phy. void of cluster size thus effecting the dynamics of peripheral galaxies within the cluster more than central ones in their co-orbiting. Individual galaxies would not exhibit the appearance of higher central attraction for peripheral matter. Individual galaxies in less compact clusters would exhibit combination of above dynamics.

Thank you for your consideration,

John Shoemaker

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