The Nature of Relativistic Mass
by
Edmond S. Miksch
ed_miksch@yahoo.com
(412) 373-4919
First Copyright: April 19, 2008
Latest Copyright: November 9, 2008
Contents
- Contents
- Prerequisites
- Terminology and Conventions
- Introduction
- The Total Relativistic Mass of the Entire Visible Universe
- Calculation of the Relativistic Mass Density of the Gravitational Field
- Calculation of the Relativistic Mass Density of the Coriolis Field
- The Relativistic Mass Density in the Vicinity of Black Holes
- Relativistic Mass at the Dawn of Creation
- Relativistic Mass of the Nuclear Binding Force
- Does Gravitational Radiation have Negative Relativistic Mass?
- Conclusions
Prerequisites
Basic physics, including elementary mechanics and vector field operators, notably the divergence operator is a prerequisite, as well as familiarity with the theory of relativity.
Terminology and Conventions
We use the term "mass" to refer to the conserved quantity, and never use it for the rest mass of a particle, since rest mass is not conserved. The term "Mass" refers to relativistic mass. Relativistic mass has gravitational properties and inertial properties. We see no reason for questioning the equivalence of gravitational and inertial mass. Energy is viewed as comprising relativistic mass in any volatile form. Force, impulse and momentum are all vector quantities.
Vector quantities, which have both direction and magnitude, are denoted in the text by bold face characters. In the figures, they are denoted by overlying arrows. When the symbol for a vector quantity is not in boldface, it denotes the magnitude of the vector quantity. Asterisks are sometimes used to denote multiplication. Weight is considered to be a real force, as is centrifugal force and the Coriolis force. In this, we rely on the relativistic principle that we may view the universe from any coordinate frame we choose.
Measurements are always made by local observers. That is to say, a length anywhere in space is measured by a local measuring rod, such as a nearby atom that emits an electromagnetic wave of known wavelength. The atom may be bound to other atoms to reduce its recoil, as was done in the Harvard Tower Experiment. Time intervals between two nearby events are measured by a local clock, such as the frequency of a known electromagnetic wave from a nearby atom. Acceleration of an object is measured by local measuring rods and local clocks, and relativistic mass is defined by the negative of the source term of the gravitational field vector, in accordance with the vector form of Newton's law of gravity. Relativistic mass may also be determined by energy / c2 .
Introduction
At the outset, we understand that energy and relativistic mass are alternative views of the same thing. This fact is stated in Einstein’s famous equation: E = mc2 . It was presented in one of his famous papers, where he showed that the inertia of a body depends on its energy content. Thus, a charged capacitor or battery has more inertia (mass) than the corresponding capacitor or battery when it is discharged. If an object is heated, it has more thermal energy, therefore more mass, than when it is cold. An object that moves at high speed relative to an observer has more kinetic energy, therefore more mass (as determined by that observer), than when it is at rest relative to that observer.
The purpose of this web site is to present a number of reasons for seriously considering whether a negative density of relativistic mass can exist in some regions of space. It is believed that the physics community has many brilliant individuals, skilled in many aspects of physics, but that there is a near-universal belief that negative mass cannot exist. The purpose of this web site is to express the view that various regions of space can have a negative density of relativistic mass.
Various people have speculated concerning negative mass, but, unfortunately, many of these are closely related to the lunatic fringe. Some science fiction authors, for example, speculate that if a spaceship dives into a black hole, it may travel at superluminal speed through a ‘worm hole” to another black hole elsewhere in the universe. Such authors would employ negative mass to keep the mouth of the worm holes open. It may be that such wild speculations cause most physicists to view negative mass with suspicion.
Negative mass may also be in disrepute because it predicts some alarming instabilities. These instabilities may include runaway motions, runaway temperature flows, and gravitational radiation that becomes stronger as it interacts with matter. We take the view that instabilities are not a reason for rejecting the theory. There is no evidence that the universe is stable. In fact, it is generally viewed as having been exploding for the last several billion years. We take the view that the very fabric of spacetime – the very warp and woof of the spacetime continuum is unstable. Such instability is not inconsistent with the observations we have made on this very dynamic universe.
There is one very responsible paper regarding negative mass that was published in 1957. Herman Bondi, who is well known in the field of relativity, showed that the laws of general relativity do not preclude negative mass. (Negative Mass in General Relativity: Reviews of Modern Physics: Volume 29, #3 July 1957 pp 423-428 )
An earlier paper on the subject was written by Dr. Edmond S. Miksch, who is the principal investigator of the present proposal. He wrote a bachelor’s thesis at Reed College in 1954 that was entitled “Negative Mass”. He derived the stress tensor of the gravitational field, and showed that if the net flux of the gravitational field vector points out of a region, there is negative inertial mass in the region. (Obviously, the gravitational mass is negative, if the net gravitational field points out of the region.) He presented the formula:
div g = - 4 π G Rho Equation RM1
Equation 1 expresses, in vector form, one aspect of the law of gravity, namely the effect of mass on the gravitational field. In the equation above, Rho is the mass density of the region of space in which g prevails and div g is the divergence of the gravitational field vector, g. The divergence operator, div, indicates whether the vector field on which it operates has a source or a sink at a point in space. For example, in a manure pile, or the core of a nuclear reactor, there is a positive divergence of the heat flow vector. Conversely, an ice cube in a glass of warm water causes a negative divergence of the heat flow vector. (The heat flow vector at the surface of the ice cube points into the ice cube.)
Dr. Miksch also put forth a formalism that, among other things, calculated a negative energy density (and hence a negative density of relativistic mass) for the gravitational field itself. The Physics professors at Reed did not like the theory, and grilled Miksch intensively for two hours. They could not, however, find any flaw in the theory, and passed it as a thesis – even though they disagreed with it.
In recent years, Dr. Miksch has developed the theory much further, and has published a number of web sites relating to negative mass, including:
- Negative-Mass.com
- EinsteinsElevator.com
- Time-Rate-Gradient.com
- CoriolisField.com
- Gravitational-Radiation.com
- Wilderwind.com
The total Relativistic Mass of the Entire Visible Universe
Dr. Miksch supports his views concerning negative mass from the following observations. First, it is known that distant galaxies are receding from our galaxy at an accelerating rate. Each of those distant galaxies may be thought of as a test mass which reveals the net gravitational field (as seen from our point of view) which prevails in those distant regions. Just as Sir Isaac Newton first speculated on the law of gravity when he reputedly saw an apple fall and accelerate toward the Earth, we should deduce an outward net acceleration field in the distant regions when we see the distant galaxies “fall” away from our galaxy. We are seeing, on average, for the entire visible universe, a positive divergence of the gravitational field vector. According to Equation RM1 above, this corresponds to a net negative mass density for the entire visible universe.
Figure RM1 which follows, illustrates the Earth and its gravitational field, and the contrasting Figure RM2 illustrates the net gravitational field of the entire visible universe. The arrows in these figures indicate the direction of the gravitational field.
Most scientists are so adverse to acknowledging negative mass that odd language is created to explain the accelerating recession of distant galaxies. The term “dark energy” is invoked for this purpose.
This term does have some appeal. It is our experience that energy tends to push outwardly. A solenoid carrying an electric current contains a magnetic field, and the magnetic field stores energy. The solenoid also experiences a force that tends to expand it. One can view the expansive force as an outward pressure exerted by the energy stored in the magnetic field.
In like manner, a sphere of metal, carrying an electric charge, produces an electric field in the space around it, and the electric field stores energy. The sphere also experiences an outward pressure due to the electric field. One can view the outward pressure as being due to the energy stored in the electric field.
For another example, a waveguide containing a high frequency electromagnetic field experiences forces that tend to expand it, and a box lined with mirrors containing light experiences outward forces due to the radiation pressure of the light as it is reflected from the mirrors.
In all these cases, the outward force on the structure is accompanied by electric, magnetic or electromagnetic fields which interact with the solid structures (solenoid, sphere, waveguide, or mirrors) in such a way as to push outwardly on the structures. But, when we observe distant galaxies, we see no such fields. We do not hear reports of unusual splitting of spectral lines due to the Zeeman effect caused by magnetic fields, or unusual splitting due the Stark effect caused by electric fields. The net outward force on distant galaxies does not appear to be due to electric or magnetic fields.
Another reason for rejecting the “dark energy” explanation is that electromagnetic energy would exert an outward pressure that does not depend on the mass that reacts it. A uniform pressure would tend to blow away wispy portions of galaxies, and not affect dense portions of galaxies as much. Hence, when we observe a distant galaxy, we would not see wispy portions. Also, how would the pressure of the “dark energy” be reacted in the vast spaces between galaxies?
Furthermore, if we suppose that “dark energy” is on our side of the distant galaxies and none or less on the other side, aren’t we supposing a geocentric theory? Didn’t we bury the geocentric theory a while back?
We believe, do we not, that an observer on such a distant galaxy would be unaware of any great force accelerating his galaxy away from ours. Don't we expect that every type of mass in that distant galaxy, including atomic nuclei, electrons, positrons, and even photons moving transversely to the acceleration vector to experience the same acceleration away from our galaxy? (In addition to the acceleration due to all the local forces between entities in the distant galaxy.) That observer would see our galaxy to be accelerating away from him. Isn't this exactly the way that a gravitational field or acceleration field would work? Aren't we seeing that the entire observable universe has a net positive divergence of the acceleration field vector – and therefore a net negative mass density?
Now, about the psychology of the situation: If distant galaxies were found to be slowing in their outward motion, or if they were accelerating toward us, physicists and astronomers alike would have taken the inward acceleration as indicative of the total relativistic mass of the universe. Such an inference is made all the time. The masses of Jupiter and other planets is known because the moons of those planets are seen to move orbitally around the planets, which shows a gravitational inward acceleration that balances the centrifugal acceleration due to their orbital motion. The inward gravitational acceleration is interpreted as being due to gravitational attraction caused by the positive mass of the planet.
We wish to point out the inconsistency of taking an inward gravitational field as indicative of positive mass, but taking an outward gravitational field as indicative of something other than negative mass. To be consistent, we would do well to accept the outward acceleration of distant galaxies as being indicative of a net negative mass density for the entire visible universe.
Calculation of the Relativistic Mass Density of the Gravitational Field
Another indication that relativistic mass can have a negative mass density is provided by the gravitational field itself. We have calculated the mass density of the gravitational field by a thought experiment in which a gravitational field is generated in a certain region of space, while the gravitational fields elsewhere in space are left unchanged. An energy balance comparing the situation before and after the field is generated then provides the energy density of the gravitational field, and hence the relativistic mass density.
A gravitational field, g is generated at a point outside the sphere of massy particles at a point a distance R from the center of the sphere, according to the law of gravity. It’s magnitude equals GM/R2 , where G is Newton’s gravitational constant. It is commonly understood, and may be shown by simple integration, that inside the sphere of massy particles, the field g is zero.
We then permit the shell of massy particles to contract to a smaller radius, RL, shown in phantom in Figure RM3. The configuration after the contraction is illustrated in Figure RM4. In Figure RM4 the heavy circle is the shell of massy particles contracted to the smaller radius, RL. The circle shown in phantom in Figure RM4 shows the location of the shell before the contraction. We obtain energy from this movement, just as we obtain energy in hydro power systems by permitting water to go from a high elevation to a lower elevation. After the contraction, the region of space between the inner radius, RL and the outer radius, RG, has a gravitational field.
The equations underneath the figures give the magnitude of the gravitational fields in the three regions. The first region is the entire universe outside the larger sphere. The second region is the space between the radii of the two spheres, and the third region is the space inside the smaller sphere.
Outside the larger sphere, the gravitational field at every point is unchanged as a result of the contraction. Inside the smaller sphere, it is everywhere zero and, hence, is unchanged. However, a gravitational field is created in the space inside the larger sphere and outside the smaller sphere. Since we obtained energy when we created a gravitational field in a region of space, while leaving fields elsewhere unchanged, conservation of energy requires that the gravitational field has a negative energy density. We obtain:
Energy density = -g2/(8πG) Equation RM2
If SI units are employed, with distance measured in meters, time in seconds and energy in joules, the gravitational constant, G equals 6.67 * 10-11.
At a point on the Earth where the gravitational field has a magnitude of 9.8 m/sec, the energy density of the gravitational field is therefore:
Energy Density = - 9.8 * 9.8/( 8 * π * 6.67 * 10-11 ) = - 5.73 * 1010 Joules per cubic meter
Noting that e = mc2, we have for the relativistic mass density of a gravitational field of strength g the following:
Mass density = -g2/( 8πGc2 ) Equation RM3
Where c is the speed of light, 2.997 * 108 . At a point on the Earth where the gravitational field has a magnitude of 9.8 m/sec, the mass density of the gravitational field is therefore:
Mass Density = - 9.8*9.8/( 8 * pi * 6.67 * 10-11 * 2.997 * 108 * 2.997 * 108 ) = - 6.38 * 10-7 Kilograms per cubic meter
By combining Equation 1 with Equation 3, we obtain the interesting relation:
div g = g2/(2 c2) Equation RM4
Equation RM4 expresses the nonlinearity of the gravitational field. It tells us that the gravitational field is a source of the flux of the gravitational field, and hence that it has a negative mass density.
The Relativistic Mass Density of the Coriolis Field
The Coriolis field is a curious matter that combines the mystery of gravity with the mystery of magnetism. It derives its name from a French mathematician, Gaspard de Coriolis (1792-1843), who noted that in a rotating coordinate frame, for example, a frame attached to the rotating Earth, a mass moved in a direction oriented at an angle relative to the axis of rotation of the coordinate frame tends to accelerate in a direction perpendicular to its motion, and perpendicular to the axis of rotation.
For example, a wind in the Northern Hemisphere, away from the equator, blowing toward the north, tends to veer toward its right, hence toward the east. Likewise, a wind in the Southern Hemisphere, blowing toward the south, tends to veer toward its left, hence also toward the east. This causes the prevailing westerly winds (which blow toward the east) in the temperate zones both north and south of the equator. Both the Gulf Stream and the Japanese Current are in the Northern Hemisphere, flow toward the north, and veer toward the east due to the Coriolis Field. Likewise, north of the equator, air flowing toward a low pressure region tends to veer towards its right and this creates a counterclockwise flow around the low pressure region. Thus, tornadoes and hurricanes in the Northern Hemisphere rotate counterclockwise around their low pressure regions. The opposite is true in the southern hemisphere.
In latitudes away from the equator, at high altitudes where terrain does not interfere with air flow, air does not flow from high pressure to low pressure. Instead, air flows in a direction perpendicular to the pressure gradient, hence, parallel to the isobars. Force to react the pressure gradient comes from the wind interacting with the Coriolis field of the Earth.
In a science museum, one may see a pendulum that is free to move back and fourth in any vertical plane passing through its center of support. One observes that the plane in which it moves slowly rotates, or precesses, as the day proceeds. This, also, is an effect of the Coriolis field. If a spinning flywheel is exposed to a Coriolis field, its bearings experience a torque that is perpendicular to the Coriolis field and perpendicular to the axis of the flywheel. A turn signal in an airplane operates by this principle to measure the magnitude of the vertical component of the Coriolis field seen by the airplane, thus showing the rate at which the airplane is turning.
We inquire about the mass density of the Coriolis field because an observer who sees a Coriolis field always sees it to be accompanied by a centrifugal acceleration field, which points outward. In contrast, the Earth has an acceleration field, which we call the gravitational field, which always points inward. According to the general theory of relativity, there is no physical distinction between an acceleration field seen by an observer and a gravitational field seen by that observer. A centrifugal acceleration field may, therefore, be regarded as a gravitational field. In the language of vector algebra, the Earth is associated with a negative divergence, or sink of the acceleration (or gravitational) field vector. A Coriolis field, conversely, is associated with a positive divergence, or source of the acceleration (or gravitational) field vector.
It is instructive to rewrite Newton's law of gravity in differential form as follows, where MV is the mass density of space, div is the divergence operator, g is the gravitational field vector, and G is the gravitational constant, which equals 6.672 * 10-11. Equation RM5, below, is a rewritten version of Equation RM1, above.
MV = -div g/(4πG) Equation RM5
If we wish to apply Equation RM5 to the acceleration field, denoted a, associated with the Coriolis field, we first calculate the divergence of the centrifugal acceleration field a. It is well known that if an observer rotates at an angular rate of Ω radians per second, that observer will see a centrifugal acceleration field equal to Ω2 r, where r is the cylindrical radius vector from the axis of rotation of the observer to any point in space, and a is the magnitude of the acceleration vector at that point. Applying the divergence operator in cylindrical coordinates, we obtain:
div a = 1/r(d/dr(ra)) = 1/r(d/dr(rΩ2r)) = 1/r(2Ω2r) = 2Ω2
Simplifying the equation, we obtain the following for the divergence of the acceleration field vector, a due to a Coriolis field Ω:
div a = 2Ω2 Equation RM6
Combining Equation RM1 with Equation RM6, we obtain the following for the mass density of a Coriolis field that has a strength of Ω.
MV = - Ω2/(2πG) Equation RM7
We now note, with astonished consternation, that not only is the mass density of the Coriolis field negative, it is also enormous! If we consider a unit Coriolis field, which corresponds to a rotation rate of one radian per second, and insert values into Equation RM7, we find that the mass density of that modest Coriolis field is about -2.385 billion Kilograms per cubic meter. Hence, if I just turn in my swivel chair, I fill the entire universe (as seen from my reference frame) with a negative mass density of billions of kilograms per cubic meter!
So what good is this? Shouldn't I learn my lesson and never view the universe from a frame of reference that sees a Coriolis field? Well, here's the problem. According to the theory of relativity, moving masses generate Coriolis fields in their vicinity. This is sometimes referred to as "frame dragging" or the "Lense-Thirring effect". A satellite is now in orbit, the Gravity Probe B, which contains four spinning quartz spheres, held in position by superconductors, to reveal precession caused by the Coriolis field caused by rotation of the massy Earth. Note that this is not the Coriolis field that is of concern to meteorologists. That Coriolis field is due to rotation of the observer relative to distant galaxies, and does not depend on the mass of the Earth.
The Coriolis fields generated by moving masses are non-uniform. Hence, I cannot select a coordinate frame for which the Coriolis field is everywhere zero. I must accept the Coriolis field as a reality that I cannot avoid, and I may need to consider the mass density of the Coriolis field.
Various investigators refer to the Coriolis field by a variety of terms. These include the gravimagnetic field, the kinemassic field, the gravinetic field, the gravnetic field, gravomagnetic field, gravitomagnetic field, gravitomagnetism, and the magnetic-like gravitational field. In the following section, we provide an explanation of the origin of the Coriolis fields due to moving masses.
Figure RM5 illustrates a pair of plates of massy material that are moving in opposite directions, both at velocity U, relative to a first observer. Indicia on the plates deliniate equal areas of the plates. The indicia seen by Observer 1 are separated by a distance L. The plates are assumed to have equal mass between indicia, as seen by the first observer, and that mass is denoted M. There is no gravitational field in the space between the two plates because the masses per unit area on the plates are equal and the gravitational fields of the two plates cancel in the intervening space.
Figure RM6 illustrates the plates as seen by a second observer who moves toward the right at velocity V, at the same velocity as point P. When the second observer considers the lower plate, he reckons that it is moving relative to him at a velocity of U + V. (We assume that U and V are both much less than the speed of light. If either was near the speed of light, we would use the addition of velocities formula.) Because of the increased velocity of the lower plate, as seen by Observer 2, that observer sees a greater mass between indicia on the lower plate than that seen by Observer 1. The increased mass between indicia is denoted MB. It is emphasized in Figure 4 by the heaver lines with which the upper plate is drawn. Furthermore, the distance between indicia, LB is smaller than the distance between indicia, L that is seen by Observer 1. Therefore, the mass per unit area on the lower plate is greater, as seen by Observer 2 than the mass per unit area seen by Observer 1.
Conversely, when the second observer considers the upper plate, he reckons that it is moving relative to him at a relative velocity of U – V. that is smaller than the relative velocity of U + V of the lower plate. Therefore, the upper plate has a smaller mass between indicia, MT, as seen by Observer 2 than the mass between indicia, MB seen by observer 2 on the lower plate and the distance, L T, as seen by Observer 2 is greater than the distance between indicia, LB that he sees on the lower plate. Therefore, the mass per unit area on the upper plate is less, as seen by Observer 2, than the mass per unit area he sees on the lower plate.
Observer 2, therefore, finds himself disposed between two plates having different mass per unit area, and therefore experiences a gravitational field, g2 that is directed from the less massy plate toward the more massy plate. Since the acceleration, g2 of the moving point P is due to the velocity V, and is perpendicular to it, Observer 1 sees point 2 to experience a Coriolis acceleration. We anticipate similar results for the case in which point P moves in the direction from one plate towards the other. Thus, Observer 1 sees a Coriolis field in the space between the two relatively moving mass streams of the two plates.
A similar analysis for the Coriolis field inside a rotating hollow cylinder made of massy material indicates a Coriolis field that is parallel to the axis of the cylinder.
Because moving matter creates local Coriolis fields, I cannot choose a coordinate system that everywhere eliminates the Coriolis field. I will see some regions of space to have Coriolis fields. Such regions must have centrifugal acceleration fields, and, hence, if no other mass is present, a negative mass density.In the web site: www.CoriolisField.com, it is shown that the time rate of change of the Coriolis field caused by an accelerating mass assists mass to accelerate. In electromagnetism, Lenz’s law states that the emf induced by a changing electric current opposes the change in the current. In the gravitational-Coriolis case, a similar law states that if a mass flow changes, an induced gravitational field tends to assist the change in the mass flow.
Relativistic Mass in the Vicinity of Black Holes
Since the gravitational field has a negative density of reltivistic mass, we inquire as to whether the space near a black hole, outside of the event horizon, has a negative mass density. We employ a thought experiment in which we attempt to form a black hole by placing massy particles in a spherical shell surrounding a point in otherwise field-free space. We will release the particles to fall towards their center point due to their mutual gravitational attraction. The experiment would be done on such an enormous scale that as the mass particles come together, the pressures generated overcome the ability of the particles to resist compression.
We will permit this process to continue until the particles are moving at speeds approaching the speed of light. It may be that a black hole, with an event horizon, can never be formed in this manner, because as the particles come together, producing a deep gravitational well, time in the vicinity of the particles is slowed by the increasingly negative gravitational potential of the particles. (This effect is referred to as gravitational time dilation. It is based on the fact that clock at a high elevation indicates more elapsed time than a clock at a relatively low elevation. It was observed in the famous Harvard Tower Experiment by Pound and Rebka, and has been measured with accurate atomic clocks.) It was first observed in the spectra of white dward stars. We view the event horizon as something that may be approximated as the particles approach a critical radius from the center, which they may never actually reach due to the slowing of time as they approach the critical radius.
In order to observe the particles we postulate a stationary frame of reference in the space surrounding the center point of the shell of particles. Before releasing the particles we attach instruments to the reference frame. (Since this is a thought experiment, we will ignore the fact that the massy particles falling on the instruments would destroy them.)
After the particles have been released, and begin to acquire velocity, relative to the instruments, each particle has a greater mass than it had at the beginning of the experiment, when the particles were not moving. This is due to the well-known increase of mass with velocity. Instruments at lower and lower elevations on the frame see greater and greater velocities for the particles, and hence, greater and greater masses for the particles.
If we evaluate readings from instruments at a radius where the velocity of the particles is the square root of 3, divided by 2 times the speed of light, we find that at that velocity, the mass of the particles has doubled, compared to their mass before being released. If the total rest mass of all the particles is M, then when they reach the above velocity, their total mass is 2M. Conservation of mass then requires that the mass of the gravitational field outside the shell of particles, but inside the radius of the original shell is equal to –M.
If we evaluate readings from instruments at a radius where the velocity of the particles is 0.99 times the speed of light, the mass of the particles as measured by the instruments is over 7 times as great as it was before the particles were released. Conservation of mass then requires that the mass of the gravitational field outside of the shell of particles but inside the radius of the original shell be -6M.
As the velocity of the particles, as measured by instruments in their vicinity gets closer and closer to the speed of light, as seen by instruments in their vicinity, the mass of the particles increases without limit, and the mass density of the gravitational field outside the shell of particles becomes increasingly negative without limit.
In the limit, we anticipate a black hole having an event horizon and an infinite mass within the event horizon, and a gravitational field with an infinite negative mass density surrounding it. Viewed from a great distance, the black hole has a mass of M, which was the original mass of the particles. If the event horizon never forms, due to time dilation, that structure, nevertheless, becomes approximated more and more as time continues.
Relativistic Mass at the Dawn of Creation
Modern cosmological theories generally take the view that the entire universe started in a “big bang” in which all the mass of the universe came into being along with space and time. The early universe is pictured as incredibly dense, incredibly hot with all the mass of the universe in a tiny, expanding volume.
If we apply the laws of physics as we know them, we would expect such an enormous mass, compacted into a small volume, to constitute a black hole. How could time ever proceed at any point given the time dilation effect of so much nearby mass? How could any outward movement occur against an infinite gravitational field that prohibits even light from escaping?
Some other element must be present to enable time to proceed, and to reduce the gravitational field to finite values so that expansion can occur. That element must have a positive divergence of the gravitational field vector, and that would therefore be negative mass.
Relativistic Mass of the Nuclear Binding Force
It is well known that the binding energy that holds protons and neutrons together to form atomic nuclei is negative. If a wave or particle that moves back and forth between two nuclear particles binds them together, then it must have negative mass. For example, if two ice skaters toss a ball back and forth, the repeated reaction force as the ball is tossed and as it is received causes the two skaters to accelerate apart. For the process to draw the skaters together, the ball must have negative mass.
Does Gravitational Radiation Have Negative Mass?
Electromagnetic radiation may be viewed as a consequence of Coulomb’s law and the transformations of the theory of relativity. The law of gravity is similar to Coulomb’s law. Electromagnetic radiation comprises crossed electric and magnetic fields. Maxwell’s equations present the basis of electromagnetic fields. In those equations, the Curl of the electric field, E is accompanied by a time derivative of B . Likewise, the Curl of the magnetic field B is accompanies by a time derivative of E . An electromagnetic wave comprising perpendicular E and B fields is capable of traveling across the universe, far from the charges that created the electric and magnetic fields.
Gravitational radiation comprises, among other things, gravitational fields and Coriolis fields. There are other aspects as well, such as time rate gradient effects caused by the gravitational fields. We believe that gravitational waves can likewise travel across the universe, far from the masses that created the gravitational and Coriolis fields.
Because gravitational fields and Coriolis fields have negative mass densities, it is reasonable to inquire as to whether gravitational radiation carries negative mass. However, one might ask “If gravitational waves carry negative energy, how can they do any work on matter, such as moving a mirror of a gravity wave detector such as LIGO or LISA? The answer is that the wave gains negative energy as it gives positive energy to the mirror. We expect that all the matter in the universe that is free to move acts as an amplifier for gravity waves. The reasons that we do not see catastrophic amplification is that the universe is mostly empty space, the amplification effects are very weak, and, as the wave tavels, it is continually shifted toward longer wavelengths, as are all waves.
Conclusions
Although we have found no kind of matter that is capable of independent existence and that is capable of being at rest, or at less than the speed of light, we believe that various force fields, which are bound to matter, or which can be liberated as radiation travelling at the speed of light can exist. We should lay aside our aversion to negative mass, but accept it as such when we find it. We may find it in several ways:
- When we find a positive divergence of the gravitational field vector, as seen by a certain observer, then we should acknowledge that that observer sees negative mass.This is consistent with the law of gravity written in vector form (Equation RM1 above.)
- When a mass balance is made of a process and conservation of mass requires that for mass to be conserved, a negative density of relativistic mass must exist in a region of space, then, so be it. Negative mass exists in that region of space. The process illustrated above in Figures RM3 and RM4 is an example.
- If we create a theory in which binding or attractive forces between a pair of bodies are communicated by the momentum of massy particles travelling between the bodies, then the massy particles must have negative mass.
- If we consider a process wherein enormous positive mass is present in a small region of space, as in a black hole, or in the big bang, so that time totally stops, and yet the process proceeds, then some form of negative mass must be present to enable time to proceed.
- If we ever find a particle that is capable of travelling at less than the speed of light, and which accelerates as it passes through matter, then we should investigate further to see whether it has negative mass.
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- Negative-Mass.com