Physics majors early on learn to appreciate the role of symmetry in nature's scheme of things. The existence of antimatter is one such remarkable symmetry translation seen in nature involving the transposition of electric charge between oppositely charged particles. Thus, every known particle has a counterpart with opposite charge and/or spin (the antiparticles of the neutron, along with other neutral particles have only their spin reversed). A more subtle and complex symmetry translation is embodied in the hypothetical magnetic monopole in which the roles of the electric and magnetic components of the electromagnetic field are transposed. Such particles, in theory, would carry quantitized units of magnetic charge, and would possess an electric dipole field with the same configuration as the dipole magnetic field seen in ordinary electrically charged particles.
There seems to be a trend here, and the curious student might well ask if even higher order symmetry translations are part and parcel of nature's inventory of possibilities. If the intrinsic charge of a field, and the components of a field, may interchange their roles, might not some of the four fundamental fields of nature - the electromagnetic, strong, weak, and gravitational - also be able to exchange roles with one another, leading to the creation of novel forms of matter with extraordinary characteristics? This makes all the more sense in light of the widely held assumption that all these forces are manifestations of a single underlying superforce. Of nature's four forces two have infinite range, while the other two are confined to the nucleus. It seems natural to suppose that any role interchange would preferentially occur between fields within the same category.
The electromagnetic and gravitational fields are both long range and fall off by the inverse square law, but otherwise exhibit quite different properties, not least of which is their enormous disparity in coupling strength. Every High School physics student learns that the electrostatic force between two stationary particles - say an electron and proton - is 39 orders of magnitude stronger than the gravitational force between them. Suppose you could switch the roles of these forces so that the gravitational force took on the role of the electrostatic force, and the electrostatic force acquired the role of gravity, how would particles with such a transposition of forces behave?
The first apparent consequence of this symmetry transformation is that such hypothetical particles would be endowed with quantitized units of gravitational charge (as will be explained shortly, this assumption of gravitational charge is a first order approximation, and not quite on the mark). Like electrically charged particles these gravitationally charged quantum particles (we'll call them G-particles) would possess two opposing polarities. The force of gravitational attraction between two G-particles of opposite polarity would be 39 orders of magnitude greater than the universal electric type force of attraction experienced by these particles, which would acquire the role of gravity as we experience it in our universe (this notion of 'electric' mass is also a first order approximation). Presumably a gravitationally charged particle of one polarity would be attracted to mass in our universe, and the other polarity would be repelled. While such denizens of the particle world have never been detected, with certain modifying assumptions they still may be a factor in our everyday world, as will be become evident later on.
Assuming Newton's equation for the force between two gravitating bodies is applicable here, the force of attraction or repulsion between our type of matter and gravitationally charged matter must be approximately proportional to the square root of the force of attraction between two electrically charged particles (or two gravitationally charged particles). To express it differently, it would be 19.5 orders of magnitude stronger than the force of gravity between two ordinary particles of matter. A charged G-particle would thus couple to ordinary matter 32 billion, billion times more strongly than ordinary matter to itself. For a neutral G-atom the gravitational Van deer Waals force would, undoubtedly, still be quite potent in relation to normal matter. Nevertheless, it would fall short of the normal Van deer Waals forces between molecules by a factor of 19.5 powers of ten.
On further reflection, it's apparent that quantum particles possessing gravitational charge, as an analogue to electric charge, pose a major puzzle. The movement of ordinary electrically charged particles leads to the evolution of a magnetic field as described in Maxwell's equations. What then, would be the nature of the secondary field associated with the movement of gravitationally charged particles? On first blush it would seem that it would simply be a gravitational force. But that evidently is a flawed argument since by analogy electric and magnetic forces, while they are intimately connected, are quite distinct. For example, while two electric charges of opposite polarity will attract each other along the line connecting them, and two magnetic monopoles of opposing polarity will do likewise, the same would not be the case between a magnetic monopole and electric charge.
However, there is a very sensible solution to this paradox, which is quite profound, especially if nature really allows such particles to exist. The train of logic goes like this: There is a symmetry inherent in both the gravitational field and electromagnetic field in our universe, that revolves around the speed of light. Any electromagnetic wave - radio wave, light wave, gamma ray - is constrained to the speed of light by the interplay of the electric and magnetic components of that wave as Maxwell deduced and quantified 137 years ago. In similar fashion, the force of gravity in General Relativity arises from the warpage of space-time, and it is the interplay of these two components - space and time - that constrains the propagation of any space-time disturbance (like gravity waves) to the speed of light.
Hermann Minkowski recognized the inseparable and unified nature of space and time in Einstein's Special Relativity, which he described as the space-time continuum. Space-time is spoken of as a four dimensional continuum, but in Minkowski's formulation the dimension of time enters into the equations of relativity on a very different basis than the three dimensions of space. The time component is always factored with the imaginary number i - the square root of minus one. In calculating an absolute space-time interval the square of the time dimension is, subtracted from the sum of the squares of the three space dimensions, which is at variance from the Pythagorean rule for calculating distance between points in Euclidean space. The time component, then, is clearly distinct from the three components of space in the space-time continuum.
Thus, even though we normally think of curved space-time associated with gravitation as a 4 dimensional entity, it could with equal justification be considered a 2 component field, as long as we keep in mind that one component refers to the three physical dimensions of space. In fact, we can go a step further in this analogy. There is no logical reason why space-time cannot be treated as a field with the same legitimacy as the electromagnetic field - an assumption central to the arguments to follow. Both fields have mutually interdependent components, although they differ radically in their behavior and characteristics. The 'reality' of the field components for these forces - electric/magnetic for the electromagnetic, and space/time for gravity - can be considered to possess an equal validity, despite the fact that one field - space-time - provides the arena upon which the other - the electromagnetic - plays out. Their respective properties can be measured at different points with suitable test probes. Additionally, the existence of either field is meaningless in the absence of matter/charges. However, it should be emphasized that this is not implying a return to the ether concept.
We see therefore that gravity, like the electromagnetic field, can be treated as a two component field. Thus, it is not gravity, per se, that would be transposed with the electromagnetic field, but the space-time field. If space is assigned the role of electric charge in the proposed transposition of fields then the answer to the question of the nature of the secondary field in 'gravitationally' charged quantum particles is evident. The secondary field in these exotic particles must be related to time. In these space charged G-particles time must adopt the exact role of the magnetic component in Maxwell's electromagnetic field theory. To reiterate, the full and proper symmetry transformation between electrically charged quantum particles and 'gravitationally' charged quantum particles involves the transposition of the electro-magnetic field with the space-time field.
From these arguments it follows that the electromagnetic field transforms into a ten component tensor field in G-matter, exactly like space-time is formulated in our universe. Space in a G-universe would acquire 'electric' characteristics. Time, in turn, would adopt a 'magnetic' character to it. In short, the fabric of space-time in a G-universe would have 'electric-magnetic' properties. How to interpret such concepts will be addressed later. For now, it's vitally important to emphasize that these perceptions of 'electric' space and 'magnetic' time are from the perspective of an observer made of normal matter. For a person made of G-matter residing in a G-universe all the laws of physics would be indistinguishable from what we perceive in our universe.
The issue of perspective is so important in this analysis that it has to be regarded as a fundamental axiom. Indeed, contrary to a basic tenet of Special Relativity, the laws of physics will not be the same as viewed from every reference frame, when considering G-matter. There is a distinct divide between observers made of each type of matter observing his own matter, or the other type. However, this division would be perfectly symmetrical. Thus a G-person would perceive the space-time fabric associated with our matter as having electric-magnetic properties.
In G-matter the space-time field (Einstein's field) becomes a local gauge field, exactly like Maxwell's electromagnetic field in our universe. Essentially space and time maintain separate, but interwoven roles in G-matter, and behave precisely like the electric and magnetic components in Maxwell's electromagnetic equations (to a G-person). A current of G-electrons in a length of wire made of G-matter would induce lines of temporal flux (to a person in our universe) whose direction would always be perpendicular to the G-electron current in exact analogy to an electric current induced magnetic field. And, as with a magnetic field, these temporal flux lines would have a defined vector direction determined by the familiar left-hand rule of thumb. The presence of such a conductor in our universe would have dramatic effects on our matter and space-time. But exactly how the enormously intense temporal component of this 'spatiotime' field might affect our environment as seen from our perspective, will be tackled further on.
The field transformation that leads to the existence of G-matter is assumed to be perfectly symmetrical. Therefore, for every normal particle there would be a corresponding G-particle which, to a person made of G-matter in a G-universe, would possess identical properties to the corresponding particle in our universe. In keeping with the convention adopted for the electromagnetic field the direction of the flux lines for the spatial field emanating from G-particles will flow from G-protons to G-electrons. The charge associated with these particles will be dubbed positive or negative spatial charge. Similarly, the flow direction of the temporal field (the equivalent of the magnetic field in electromagnetic theory), will flow from the corresponding north pole to the south pole of spatially charged particles.
In spatially charged G-particles where the space field lines diverge it seems logical to expect that a repulsive force would be experienced with respect to ordinary matter (more on that later). Conversely, where the space field lines converge an attractive force would presumably be experienced with ordinary matter. For all intents and purposes these forces of attraction and repulsion would, to us, be indistinguishable from gravitation, except for their vastly greater intensity. For this reason the nomenclature to describe the Maxwell field in G-matter could be prefixed with gravito, and the provisional name would be gravitotime field. Also, gravito rhymes suitably with electro - the prefix for Maxwell's electromagnetic field, and the component of Maxwell's field that it substitutes for. The prefix spatio is technically the more accurate term, but it's a tongue twister.
To further emphasize the exact correlation between the gravitotime field in G-matter and the electromagnetic field in normal matter, I thought an even more appropriate designation would be the gravitochronetic field. Chronetic rhymes nicely with magnetic, and is a derivative of the Greek word chronos for time. Gravitochronetic has exactly the same number of syllables as electromagnetic, and rolls off the tongue with the same cadence, further underlining the exact parallel between the two fields. To save space I will frequently abbreviate the gravitochronetic field as the GC field. Also, the word temporal will be used interchangeably with chronetic, since the meaning of this word is understood in the popular lexicon.
Now we address the really tricky question - what is the operational meaning to a human observer of the spatial (length) and temporal components of the GC (length-time) field? We have already suggested that a diverging spatial field will mimic a repulsive gravity field, and a converging spatial field will mimic an attractive gravitational field. But this was an intuitive guess, and the challenge is to see if this result can be supported with more logical arguments.
The possible properties of the spatial and temporal components of the GC field to a human observer can be narrowed down somewhat by recourse to symmetry principles. In particular, we know that both the electric and magnetic components of the electromagnetic field are bipolar. We should therefore expect the same property in both the spatial and temporal components of the GC field. In the case of the temporal (chronetic) component of the GC field bipolarity must logically imply two temporal directions of flow; that is, into the future, as well as into the past. It seems self evident that a bipolar temporal field could accommodate this behavior in two ways.
One way would be for each equipotential cross section of the field to correspond to a fixed moment in time. Consequently, the closer a test probe of ordinary matter approached a chronetic field source the further into the past or future the test probe would be shifted. A chronetic field of one polarity would shift test objects made of normal matter into the future, while a chronetic field of the other polarity would shift test objects into the past. As with a magnetic field (or electric field) the polarity of the chronetic field is to be defined by whether the field lines are diverging or converging (in the case of a uniform chronetic field, like in the middle of a solenoid, there must be a stasis effect - but more on that later). It's important to realize that test objects immersed in these fields would be shifted into their own future or past. The shift in time would be affected only on a local basis, rather than a global basis, where global refers to the rest of the universe.
The other interpretation would be for each equipotential cross section of a bipolar chronetic field to correspond to a particular degree of temporal expansion or contraction in either the forward or reverse temporal directions (traditionally the word dilation is used to indicate slowing of time in discussions of relativity, but expansion is a more appropriate antonym for contraction, and has the identical linguistic intent). Again test objects of normal matter would be shifted into their own future or past depending on the polarity of the field, but with a crucial difference. In this instance immersion in the field would lead to continuous slowing or acceleration of time in the forward or reverse sense depending on the strength and polarity of the field where the test probe is situated.
Having the degree of temporal expansion or contraction be dependant on the magnitude of the field source is more in the spirit of relativity, where a gravitational field slows time to an extent proportional to the strength of the gravity field. Important differences between gravitational time dilation and a bipolar chronetic field are that the latter would accelerate time as well as slow it, and in two temporal directions. Also, in a bipolar field there must, in principle, be an intermediate region (or null plane) where the passage of time stops altogether, or is frozen. In practice, this null plane would always be shifted off the physical centerline between two opposite chronetic charges, by the preexisting state of the space-time continuum of our universe at a particular location. Another major difference is that a chronetic field would possess an intrinsic strength some thirty-two billion, billion times stronger than gravitational time dilation.
Further clarification of the properties of chronetic fields should clearly be gained by understanding the significance of a solitary quantum of temporal charge for an observer in our universe (which through symmetry considerations should simultaneously lead to an associated definition for a quantum of spatial charge). A single quantum of temporal charge would be the gravitochronetic field equivalent of the hypothetical magnetic monopole in electromagnetic field theory. As with magnetic monopoles there would be two opposite polarities of temporal quanta, which we will designate as north and south chronetic monopoles.
For the first interpretation of the meaning of a chronetic field where each equipotential slice is some moment in the future or the past, the extreme or ultimate state of such a field must correspond to the beginning of time, or the end of time in our universe. If we imagine a sphere centered on a chronetic monopole (which can be treated as a point charge in analogy with the electron), the magnitude of the field will be equal over the sphere's entire surface. If we shrink the sphere down in size until it is coincident with the point charge this equipotential field will rise to infinite intensity. In essence, a chronetic monopole of one polarity would correspond to a singularity of time at the genesis of our universe, while a chronetic monopole of the other polarity would correspond to a singularity of time at the universe's final moment.
Extrapolating this concept to the spatial charges of a GC field, however, leads to seemingly illogical results. A spatial charge of one polarity must correspond to a singularity of space at the birth of our universe, and the other polarity must correspond to a singularity of space at the universe's final demise. But if two spatial charges of opposite polarity were placed a few feet apart in our universe each equipotential cross section of the field between them must correspond to the entire spatial extent of the universe at that stage in its history. Accordingly, the total field between any two opposite spatial charges, by this definition, would embrace the entire spatial evolution of the universe - a curious result. Intriguingly, this concept echoes the quantum mechanical notion of a particle's wave function in which the entire potential history, future and past, of the particle is encompassed, as well as the notion that every particle in the universe is connected through an underlying hidden domain to the rest of the universe.