Newtonian Gravity Pressure Equation

Reader's Note: The Sister Texts To This One Might Be "Matter", Which Is An Electromagnetic Model Of Mass At: http://www.johnkharms.com/matter.htm And "Antimatter": http://www.johnkharms.com/antimatter.htm . See Also "Gravitation" At: http://www.johnkharms.com/gravitation.htm . This Picture Of Mass Was Derived Mainly Through The Author's Thoughts About Gravity At The Link Above. The Author Calls This Set Of Ideas, The "Pressure" Model Of Mass. This Text Was Conceived And Completed In Early September, 2001.

What Is Mass; The Characteristics We Associate With Matter?

Does Mass Have Two Sub-Components That Are Associated With Pressure?

The Quantified Newtonian Radiation Pressure Gravitational Equation

Related Topics Concerning Mass

By: John K. Harms

Email: harmsjk3@earthlink.net

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Abstract:

This model gives the equation for a pressure model of gravity. This can be understood to be an adaptation of Newtonian gravity, where mass is defined by the difference in pressures of the vacuum, but also on the internal pressures associated with matter itself. Several consequences can be derived from this model.

Key Words: Mass, Gravity, Pressure, Mass Increase, Mercury's Mass

Introduction

What is mass? How does mass cause gravity? These questions along with many others will be addressed by this text. Gravitation is the basis of this model of mass. The author's previous work on gravity at the links below led to the ideas contained in this model.

Mass And The Newtonian Gravity Equation

The author would like to propose in this text that what we call mass is actually the difference in pressures between the vacuum energy and that of the negative value associated with the radiation pressure of matter. So, mass has primarily two pressure subcomponents.

The logic behind this proposal is symmetrically-based and is as follows:

A difference in the radiation pressure (leading to gravity) depends upon two essential factors; as in a low pressure storm known as a hurricane, the strength of the hurricane's winds depend upon the outer local atmospheric pressure as well as the strength of the low pressure within the eye of the storm. Thus, in essence, it is the difference in pressures between the surrounding "high" and the internal "low" that matters most!

So, for there to be gravity in the pressure viewpoint, the strength of gravity must depend upon the average local vacuum radiation pressure as well as the amount of matter present. This quantity of matter can be measured by the strength of the "low" or the negative pressure associated with the mass in question. Therefore, gravity may depend upon the local average negative vacuum radiation pressure (call this P1) added to the negative pressure associated with the amount of matter present (call this P2).

Hence, P1 + P2 can be understood to be the two subcomponents that compose what we call mass. Mass, therefore, must be equal to P1 + P2. Therefore, in the standard Newtonian equation for gravity given by:

F = G x (M1 x M2) / d^2

This can then be rewritten as:

F = G [A(P1 + P2) x B(P1 + P2)] / d^2

Where: F = The Force Of Gravity

G = The Gravitational Constant (As Deduced By Experiment)

"A" And "B" Are The Two Different Bodies

P1 = The Average Local Positive Radiation Pressure Of The Vacuum (This May Be "Locally" A Constant).

P2 = The Negative Radiation Pressure Of A Piece Of Mass (This Varies Only With The Amount Of Matter That Is Present). So, All Matter Of The Same Quantity Has The Same Negative Pressure And, Therefore, An Identical P2.

d^2 = The Distance Between Bodies A And B Squared

It can then be understood by substitution from Newton's equation that:

M1 (or the mass of the first body) = P1 + P2

And: M2 (the mass of the second body) = P1 + P2

Since P2 varies negatively with the amount of matter present, the bigger is the mass, the higher is the value for P2. So, M1 and M2 can be different (and usually are) and this is reflected by the two different values of P2 for both A and B.

It is interesting to note that P1 is a "local" pressure value for the vacuum. Thus, P1 may vary in different regions of the solar system, galaxy and/or throughout the Universe. So, gravity in this picture may vary. Hence, if P1 locally rises, this may give bodies the appearance of being more massive than they actually are. The force is, therefore, greater between any two objects. More about this below.

The observed rotational difficulties of galaxies (now explained with dark matter) might be understood as the local vacuum radiation pressure environment of these galaxies being very (or even extremely) high. Therefore, all objects that exist in this high radiation pressure environment would tend to have a stronger gravitational attraction toward each other. Thus, galaxies may be allowed to rotate faster than the conventional Newtonian gravity allows. This is what is observed presently by astronomers. Thus, Newtonian gravity may vary when the local radiation pressure environment P1 is different in different regions. Our own solar system's radiation pressure environment must be comparatively low; creating the conditions necessary for our own existence.

Furthermore, the planet Mercury, which has a non-elliptical orbit that the author agrees is explained well by Einsteinian gravity, has yet another difficulty; its mean density. That is, although the planet Mercury appears to be much like the Moon in its overall composition, the Moon has a mean density of around 3.34 g / cm^3, whilst Mercury's mean density is close to 5.42 g / cm^3 (Audouze & Isreal, 1988). So, Mercury is more dense than the Moon, although there is no compelling reason why it should be. To explain this, planetary scientists must place a quite huge core composed of 70 % iron within Mercury (Krisciunas & Yenne, 1989).

This observation might be better explained as Mercury simply appearing to be more massive because the radiation pressure environment (P1) closer to the Sun is significantly greater. Since P1 is added to P2 as a factor of Mercury's mass (in the radiation environment around Mercury), Mercury appears to be more massive and dense than it actually is. If Mercury were farther out from the Sun's radiation, Mercury's density would appear to be less and Mercury would appear (gravitationally speaking) lighter i.e., less massive.

It might also be the case that the gaseous Jovian planets actually contain more mass within them than we now believe (to maintain the orbits that they presently occupy). Hence, the outer planet's P2 value, associated with the quantity of matter they contain, may be higher than we have deduced from Newton's equation. Farther from the Sun, their P1 (the radiation environment) may be less than closer to the Sun. It is important, therefore, to understand that P1 and P2 are the different components of mass. Hence, Newtonian gravity tends to overestimate the densities of the planets closer to the Sun, whilst underestimating the density of planets farther away.

One might estimate this pressure background near the Sun in the following fashion:

If we assume that the Moon and Mercury are of a relatively similar composition throughout -- the Moon and Mercury do very strangely resemble each other, so this assumption may not be too outlandish. Then we compare their densities:

Mercury: 5. 42 g / cm^3

Moon: 3. 34 g / cm^3

If we now then assume that their densities are in actuality very close to each other and that it is actually Newton's definition of mass that is faulty, we can then perform the following calculation:

5. 42 / 3. 34 = approximately 1. 62

So, it may be the case (and admittedly this is only a rough estimate--given that the densities of these planets are actually about the same) that the vacuum radiation pressure P1 near the planet Mercury (in its orbit around the Sun) may be about 1. 6 times greater than the radiation pressure environment P1 near the Moon in its orbit around the Earth. To the author, none of these estimates or assumptions appear to be unreasonable.

Therefore, P2 is in essence associated with the quantity of matter in the body. P2 may change, but only when the quantity of matter in the body changes. All objects of the same amount of matter must always have the same P2 value. Matter disturbs the vacuum radiation and this disturbance is essentially a lowering of the radiation pressure of the vacuum. One might picture this as matter being composed of photon "holes". See the "Matter As Photon Holes" text on the index page for further information. However, there are also other methodologies of viewing matter as the negative pressure of space that may also be valid. Where possible, the author has noted these options and generated these proposals.

Admittedly, it is difficult to gauge the precise values of P1 and P2, although the Casimir experiment demonstrates that P1 must be an actual effect. In fact, the Casimir experiment demonstrates essentially three effects; ( 1 ) that both a negative value for vacuum radiation is possible (P2--in the author's view this is within matter), ( 2 ) this negative vacuum is attractive like gravity and ( 3 ) that there may be a significant amount of energy in the vacuum of space (P1). Thus, the Casimir force between two metal plates is in effect a kind of measurement of the energy of the vacuum.

So, it must be the case that if the radiation pressure of the vacuum does vary, that Casimir might measure somewhat different values than it does at present here on Earth. Hence, in a lower pressure vacuum, perhaps, farther out from the Sun, the pressure on the metal plates (in the Casimir experiment) due to vacuum radiation should be somewhat different. Therefore, a small spacecraft package with a small Casimir experiment on board may show a somewhat different result farther away from the Sun than is does here on Earth. Since the background radiation pressure may vary, the results of the Casimir effect may indeed be different.

Moreover, the values of P1 and P2 might be deduced if one of the values could be measured with precision. For example, if:

M1 = P1 + P2

Then Algebraically: P1 = M1 - P2

Or Similarly: P2 = M1 - P1

Therefore, the radiation pressure of the vacuum or the negative pressure within any mass could be deduced by measuring precisely the values of either P1 or P2. M1 is simply the mass (or energy given by mc^2) of any given object and this is known with great precision as its weight. Weight = Mass x The Force of Gravity. It's interesting that by substitution that one arrives at a somewhat different defination of weight: Weight = (P1 + P2) x Force Of Gravity.

Picturing The Pressure Model Of Mass

The author's picture of mass as pressure can be understood in the following image:

It should be noted in the above image that the positive and negative vacuum pressures associated with matter and antimatter respectively are strictly averages and can only be defined locally.

The author will now describe the above image as it related to mass as a pressure effect. One can see a matter wave on the left and an antimatter wave on the right. Hence, they are equivalent, except they are precisely out-of-phase with each other. So, they cancel each other when they meet and are identical, emitting light energy as a result of a structural wave collapse. At any one point, they fluctuate back and forth from matter to antimatter and back. However, this is not what waves do.

If one were "at absolute rest" with respect to these waves, one could watch them change from matter to antimatter and back again over and over. One would know if one was at absolute rest if one was observing this phenomenon taking place. However, since this is never observed because we are in essence riding the crest of these waves as they are moving along with us, perhaps, Einstein and Mach are correct that only relative motion in the Universe matters. Therefore, one may not be able to be at rest in an absolute sense with respect to the matter waves that surround us. This remains a matter for further speculation.

Hence, waves carry energy on down the line in the direction of motion. Indeed, if they are in our frame of reference, we travel with them. This energy, therefore, exists exclusively as matter or antimatter at all times as it is always in motion (as we are). Only relative motion matters. So, mass exists as a wave on down the line as a fluctuation of space where P1 + P2 (which are the flutuations) are added together. It is the same for antimatter. P1 + P2 equals the mass of a piece of antimatter.

Note for matter that negative pressure P1 + P2 yields the gravity effect (as mentioned in the previous sections), but for antimatter it may be the case that a piece of antimatter has antigravity. This may be the positive radiation pressure associated with antimatter. Since gravity is inward pressure, antigravity may be an outward push. Admittedly, the model presented here is not precisely clear on this point, so this idea unfortunately is conjecture at best. However, this proposal remains a theme in the "Antimatter" text. See the link below for further details.

It should be noted that antimatter is a rarity in nature, perhaps, due to the fact the Universe appears now to have a positive Cosmological Constant. So, we may not have a negative vacuum pressure (in the lower right hand corner of the image above), a negative Cosmological Constant. For this reason (that we live in a positive Cosmological Constant Universe which is observed to be increasing its expansion over time), antimatter may be somewhat scarce in the Universe. This idea becomes the "pressure" model of antimatter and can at least offer a reason why antimatter may be seen to be a rarity.

Related Topics

Other substitutions (and algebraic manipulations) are also possible with this new picture of mass.

For Force:

Force = (P1 + P2) x Acceleration, For F =ma

Or: P1 + P2 = Force / Acceleration

Or: Acceleration = Force / (P1 + P2)

For Momentum:

Momentum = (P1 + P2) x Velocity, For P = mv

Or: P1 + P2 = Momentum / Velocity

Or: Velocity = Momentum / (P1 + P2)

It is notable that in the above (first) momentum equation [ P = (P1 + P2) x V ] that as a massive body increases its speed close to c, that P1, the vacuum pressure, may tend to resist a further increase in acceleration. Hence, vacuum particles may cause a resistence to a further increase in speed and this may result in an addition to the value of P1. Perhaps, vacuum radiation may accumulate in front of a body adding to P1. So, mass, the total of P1 and P2, increases as the body approaches the speed of light. P2 (a measure of the amount of matter in the body) does not change as one approaches the speed of light. Thus, the actual quantity of matter in a body does not change with speed.

For Einsteinian Mass / Energy Conversion:

Energy = (P1 + P2) c^2, For E = mc^2

Thus, For Mass We Have: P1 + P2 = Energy / c^2

So, this equation may relate the energy of radiation with both the radiation pressure of the vacuum and that of a piece of matter. Mass, thus, appears to be transformed into a different form of energy -- pressure. One can now see why mass is energy!; mass is pressure -- a form of energy. Mass may, therefore, fundamentally be a pressure effect similar to gravity. One simply cannot have mass in the absence of gravity and vice versa -- at least this has never been demonstrated in a laboratory. Mass and gravity always exist side by side.

It is worthy of note that in general relativity, Einstein recognized that pressure on a mass gives rise to a gravitational field. That is the case here as well. Gravity does depend in part upon the inward radiation pressure exerted by the vacuum on a mass, however, there is another component that should be mentioned here. That is, what is the negative pressure of the mass itself? Einstein did not consider that pressure (which in this viewpoint has two fundamental components) is mass!

So, the conventional Higgs mechanism for assigning mass to a piece of matter may be invalid. Instead, mass may arise (as does gravity) by a difference in the pressures of the vacuum verses that within a piece of matter. As mentioned above, one does not have a mass without gravity and vice versa. Antimatter has gravity as well, although it might be (as discussed above) opposite or antigravity. A massless particle such a photon does not have a rest mass because photons are the carriers of the pressure associated with radiation pressure. Hence, the massless particles carry forces. At rest, force carrying particles have a mass of zero.

Conclusion

There is one major prediction of the pressure model of mass:

1) The most important prediction of the pressure model of mass is that Newtonian gravity varies with the background radiation pressure. So, planets closer to the Sun have a somewhat higher background pressure P1. A sensitive Casimir experiment sent to the outer solar system would, therefore, measure a less dense background of radiation there. Thus, planets closer to the Sun (such as Mercury) are actually less massive (based upon the amount of matter they contain) than they appear as measured by Newtonian gravity. Farther away from the Sun, the Gaseous Jovian planets are actually more massive (based upon the amount of matter they contain) than is predicted now by Newton's equation. This is consistent with the inverse square relation of radiation away from the Sun. So, mass = P1 + P2; see above for details.

See also the links above the title for further elaboration on these ideas.

References

Audouze, J., Isreal, G., 1988, The Cambridge Atlas Of Astronomy, Second Edition, Cambridge University Press, France, P. 50-53

Krisciunas, K., Yenne, B., 1989, The Pictorial Atlas Of The Universe, Brompton Books Co., Spain, P. 44

Reader's Note: Proper References And/Or Acknowledgments To This Text Are Appreciated.