In Christ all things are held together (Colossians 1:17). Since God is an intelligent and logical Being Who holds the universe together by His power, and since we are made in His image and have revelation from Him, it is possible for us to discover some of the logical patterns by which Christ holds His universe together. There are four fundamental forces in nature, each of which is an expression of the mathematical way God’s mind upholds creation. Each of these four forces is associated with quantum particles called gauge bosons. These gauge bosons are the glue that holds matter together. When we study these forces, we are learning something about the mind of God.
The Four Forces
What is a force? A force is something that causes mass to accelerate – to change the speed and/or direction of an object’s motion. There are four fundamental forces in this universe: the strong nuclear force, the weak nuclear force, electromagnetism, and gravity. We all have experience with gravity. It’s the force that causes objects to fall – to accelerate toward earth’s center. The sun’s gravity keeps the planets in orbit.
Most people also have experience with electromagnetism. The reason magnets stick to the refrigerator is due to this force. The electromagnetic force manifests in two ways: magnetism and the electric force. Think of these as two different expressions of the same underlying mechanism. The electric force is what keeps electrons bound in atoms. It is what causes atoms to stick to other atoms in a molecule.
The two other forces are not so easily experienced (at least not directly) because they have extremely limited range. In fact, they don’t extend much beyond the nucleus of the atom. These are the two nuclear forces: the strong force and the weak force. We already discussed the strong force in the articles on quarks, baryons, and mesons. The strong force is what keeps the quarks bound together in a proton and neutron, and indirectly keeps the proton and neutron bound together in the nucleus of an atom.
The weak force is what is responsible for certain kinds of particle decay. That is, it allows particles to change into other particles. The strength of this force is actually quite high, but is much less than the strength of the strong nuclear force. The weak force is “weak” only by comparison.
Each of the four forces has a type of “charge” which can be thought of as the source of that force. Consider an electron. This particle has an electric charge of -1. As such, the electron is surrounded by an electric field. Think of the electric field like an invisible cloud surrounding every electron. This “cloud” gets thinner and thinner as we get farther away from an electron. It never quite goes to zero, but at some distance it is so thin that for all practical purposes it essentially vanishes.
When another electron is placed in the electric field of any given electron, it senses this field, and moves away from its source. This is why electrons don’t need to be in direct contact in order to repel each other. Each electron is within the electric field of any nearby electrons, and it is the field that tells the electron how to move (namely, away from the other electron). When a positively charged particle is placed within an electron’s electric field, the positive particle will move toward the electron. With electromagnetism, like charges repel and opposite charges attract.
Likewise, the strong force has a type of charge associated with it: “color charge.” Leptons have no color charge (or if you prefer, they have a neutral color charge), and so they do not feel the strong force. But quarks and antiquarks have color charge, and therefore have a color field surrounding them. As with electromagnetism, like charges repel and opposite charges attract. But, it’s more complicated because there are six types of charges associated with the strong force (red, green, blue, anti-red, anti-green, and anti-blue) rather than the two associated with the electric force (positive and negative). In the previous article we explored how these six charges relate to one another. The weak nuclear force also has a type of charge, and it is repulsive for like charges and attractive for opposite charges – just like the electric and strong forces.
The “charge” associated with gravity is simply mass. All mass has a gravitational field surrounding it. But unlike the other three forces, like “charges” attract and opposite charges repel. A particle with positive mass will gravitationally attract another particle with positive mass. Theoretically, the gravitational force between a particle with positive mass and a particle with negative mass would be repulsive. But as far as we know, there are no particles with negative mass. So, gravity is always an attractive force.
Gravity is much weaker (by many orders of magnitude) than the other three forces. That’s why the magnet sticks to the refrigerator without falling. And yet, the largest structures in the universe (galaxies and clusters of galaxies) are held together by gravity as if the other forces didn’t even exist. Why? Of course, the two nuclear forces have very limited range. So, they cannot contribute to large-scale structures. But the electric force has unlimited range. So why does it not contribute significantly to large-scale structures like galaxies?
The reason is that there are an equal number of positive and negative charges in the universe. And since opposite electric charges attract, positive and negative charges are normally found very close together – such as the electrons that surround the nucleus of an atom. The net electric charge of most objects is therefore very close to zero. On the largest scales, the universe is electrically neutral. But gravity, even though it is much weaker than the electric force, is attractive for like charges. And since only positive mass exists, the effects of gravity are cumulative.
Forces and Particles
Each force has one or more quantum particles associated with it. These particles exist as a ripple or wave in the field associated with that force. Consider an electron and its surrounding electric field. If we rapidly wiggle that electron up and down, it will cause the electric field surrounding the electron to wiggle, which produces waves in the field that stream away from the electron. These are electromagnetic waves. When we detect these waves, we find that their energy levels are quantized, as if they are made of discrete particles. (Recall from the first article in this series that particles behave like waves at times.) These particles are photons – the same particles that make up light.
This is how radio works. Electrons are rapidly oscillated, which creates electromagnetic waves – radio waves. These waves travel away from the source. Some of them are intercepted by an antenna which causes the electrons in the antenna to oscillate in response to the oscillating electromagnetic field. This results in alternating electric current. When this current is put through a speaker, it produces sound waves. Radio waves are low-frequency photons.
The only difference between the photons associated with radio and the photons of visible light is their energy-level, which correlates with frequency and inversely with wavelength. The lowest energy photons associated with radio have the longest wavelengths. As we examine photons with progressively higher energy and shorter wavelengths, we go to microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. These are all electromagnetic waves made of photons.
Photons and Virtual Particles
Photons are spin-1 gauge bosons. “Gauge” refers to the fact that they are associated with a force – in this case the electromagnetic force. And being bosons, photons are not constrained by the Pauli Exclusion Principle; hence, multiple photons can exist in the same quantum state. This is what a laser is: multiple photons of identical energy and wavelength exist in the same place at the same time in a laser.
Photons have no electric charge and are their own anti-particle. They exist as a ripple or wave in an electromagnetic field. Photons have no rest mass. Any particle with no rest mass must travel at the speed of light in vacuum. Thus, photons must travel at the speed of light in vacuum. Since photons have no mass, they cannot decay into a less massive particle. Therefore, photons are stable. They will propagate through space forever until they impact a particle. There is only one kind of photon. Photons can have different kinetic energy levels from each other (resulting in different wavelengths), and they can be either spin-up (+1) or spin-down (-1), but in all other respects they are identical.
One of the strangest aspects of quantum physics involves virtual particles. Virtual particles are unobserved, temporary particles that arise from fields due to the Heisenberg Uncertainty Principle (HUP). A particle can form in a field by borrowing a little bit of energy from that field as long as it “pays back” the energy within a certain time limit. The particle then vanishes. The HUP gives the quantitative details. Basically, the more energy a particle borrows, the faster it has to pay it back, and hence the shorter its lifetime. Since photons are massless and therefore have no lower limit on energy, there is no upper limit on the lifetime of a virtual photon. Virtual particles can continually appear and disappear in a field. In some sense, the field surrounding a charged particle is the cumulative effect of all these virtual particles.
In an electric field, virtual photons can form and unform. These virtual photons can travel from one charged particle to another; this creates either an attractive force or repulsive force depending on the relative charges of the particles. Think of virtual photons as messengers between charged particles. They carry a simple message, either “come a bit closer,” or “move away a bit.”
Virtual particles explain why the electric force diminishes with the square of the distance. Two charged particles separated by a distance D will experience a certain force F. If these two particles are moved to twice the distance (2D), then they will receive only ¼ the number of virtual photons from the other charged particle. Hence, the force is reduced by the square of the distance.
It is important to note that virtual photons cannot be directly observed. (If observed, the photon would not be virtual). There is some debate about how “real” virtual particles are. Suffice it to say, the math works. That is, charged particles really do behave as if they are constantly exchanging undetectable photons, and this generates the force between them. Photons therefore mediate the electromagnetic force.
Consequently, if photons did not exist, then there could be no electric force. Of course, we couldn’t see anything either. But that would be the least of our problems. With no electric force, atoms could not exist, and biological life would be impossible.
The W and Z Bosons
Although there is only one particle that mediates the electromagnetic force (the photon), there are three particles that mediate the weak nuclear force. These are the W+, the W–, and the Z0. Like the photon, these are elementary spin-1 gauge bosons. Unlike the photon, they have mass, and quite a bit of mass. The two W bosons each have a mass of 80,433 MeV/c2. The Z is slightly heavier with a mass of 91,188 MeV/c2. The only heavier elementary particles are the top quark and the Higgs boson.
As implied by the notation, the Z0 boson has no electric charge. The W+ and W– have an electric charge of +1 and -1 respectively, and are anti-particles of each other. The Z0 boson is its own antiparticle. None of these three bosons have any color charge and therefore are not influenced by the strong force.
W and Z bosons are unstable; they decay into pairs of fermions. And since all elementary fermions are less massive (except the top quark), there are many possible decays. The W bosons can decay into a lepton and anti-lepton pair, with one of the two having the same electric charge as the W, and the other being a neutrino. Alternatively, they can decay into a quark-antiquark pair with a total charge matching that of the W. For example, a W+ could decay into an up quark and a down antiquark.
Z0 bosons decay into two fermions that are anti-particles of each other. They most commonly decay into quark-antiquark pairs. But they can also decay into lepton-antilepton pairs, such as an electron and positron, or a neutrino and antineutrino.
The weak nuclear force is mediated by virtual W and Z bosons. And since these bosons have quite a lot of mass, they must pay back their borrowed energy in a very short time according to HUP. As such, they cannot travel very far before they are reabsorbed. This is why the weak force has extremely short range.
The strong nuclear force is mediated by gluons. Gluons are spin-1 gauge bosons, much like photons. Gluons have no electric charge. And they are thought to be massless – again like photons. However, gluons do have color charge. Recall that all quarks have one of three color charges: red, green, or blue. And antiquarks have one of three color charges: anti-red, anti-green, or anti-blue. Gluons have both. Each gluon has one of the positive-type color charges (red, green, or blue), and one of the negative-type color charges (anti-red, anti-green, and anti-blue) at the same time.
As such, there are eight types of gluons. Six of these types consist of a color and a non-opposite anti-color. These are (1) red and anti-blue, (2) red and anti-green, (3) green and anti-blue, (4) green and anti-red, (5) blue and anti-red, and (6) blue and anti-green. What about combinations like red and anti-red? These color-neutral gluons cannot exist in isolation, but they can exist in an indeterminate, mixed state. There are two mathematical ways in which this can occur, and there really is no easy way to illustrate these. Suffice it to say these are the seventh and eighth type of gluon.
The exchange of virtual gluons is what holds the quarks together in a hadron. Consider a baryon such as a proton or neutron. Each nucleon is made of one red quark, one green quark, and one blue quark (top panel in the figure). Suppose the red quark emits a gluon that has the red and anti-blue combination. To conserve color charge, the red quark must turn into a blue quark (middle panel). When “added” to the gluon, the blue in the quark cancels the anti-blue of the gluon, leaving only red. So, there is no change in the net color of the nucleon – it is still color neutral. This gluon is then absorbed by another blue quark, transforming it into a red quark (bottom panel). The two quarks swap color charge, and this results in an attractive force between them. The overall color of the nucleon is unchanged (and is neutral) since the two quarks have merely swapped colors.
Since gluons are spin-1 bosons, a gluon exchange also swaps the spin states of the quarks. Suppose the quark emitting the gluon has an initial spin state of +1/2. The emitted gluon will have a spin state of +1, which flips the quark to -1/2 (so that the combined spin states still add up to +1/2). The gluon is then absorbed by a quark that has an initial spin state of -1/2. The gluon flips the quark to spin +1/2 since it “adds” +1 to the spin of the quark. The overall spin of the baryon is unchanged.
It is similar with mesons. Recall that mesons are made of one quark and one antiquark of opposite color. Suppose we have a red quark and anti-red antiquark. The red quark could emit a gluon that is red and anti-blue. This will flip the quark to blue to conserve color charge. When the gluon is absorbed by the antiquark, the red cancels the anti-red, and the remaining anti-blue is absorbed by the quark, transforming it to anti-blue. The meson is still color-neutral because one quark is now blue and the other is anti-blue. Mesons are always color neutral; but their quarks and antiquarks are constantly changing color charge by exchanging gluons.
Unlike photons, gluons possess the very type of charge that they mediate. In other words, photons mediate the electric force, but are themselves electrically neutral. So, photons don’t attract or repel each other. But gluons both mediate color charge and possess color charge. Therefore, gluons can attract or repel other gluons! They have a tendency to group into long tubes. This makes the strong force far more complicated than the electric force. Since gluons interact with each other, the strong force does not diminish with distance in the same mathematical way as the electric field or gravity. It diminishes much faster, and can even become repulsive at extremely short distances (for particles that are normally attractive). This prevents the three quarks in a nucleon from being in exactly the same location, which results in imperfect cancelation of the three colors at the outer surface of the nucleon, which allows pions to form and mediate the residual strong force. And without the residual strong force, no atoms other than hydrogen could exist.
The extreme strength of the strong force is such that the energy needed to separate the quarks in a baryon exceeds the energy of the quarks themselves. Therefore, any attempt to separate the quarks would result in the formation of new quarks from the energy, resulting again in a color-neutral hadron. This is called “color confinement” and is why composite particles are always color-neutral. This, along with the fact that gluons interact with each other, is why the strong force has such a short range.
The color field of the strong force has so much energy, that not only virtual gluons form within it, but virtual quarks and antiquarks as well. To conserve baryon number, quarks and antiquarks always form in pairs – a temporary meson. And they can only exist for a very short time since they must “pay back” the energy they borrowed from the field. These are sometimes called “sea quarks” as opposed to the three permanent “valence” or “constituent” quarks. Since sea-quarks always form in quark-antiquark pairs with opposite charges and spin, they do not change the overall charge or spin state of the baryon. They do affect the mass. And this is why the constituent mass of quarks is greater than their current mass. The virtual mesons that form just outside a proton or neutron of an atom (due to imperfect cancellation of color charge) are responsible for the residual strong force which holds together the nucleus of all atoms (except hydrogen).
Many physicists believe that the remaining fundamental force, gravity, is mediated by gauge bosons called gravitons. Unlike the other gauge bosons, gravitons have not been observed or detected in any experiment. They remain theoretical. Furthermore, gravity can also be explained in an entirely different way – without appealing to quantum particles. The science of general relativity developed by Einstein correctly predicts gravitational interactions by computing how mass affects the curvature of spacetime. Most physicists believe that gravity on quantum scales requires a quantum explanation, perhaps one that will be fully compatible with the large-scale successful predictions of general relativity.
In any case, although gravitons have not been detected experimentally, we can compute many of their properties using math on the basis of what gravity does. This is only possible because the universe is upheld by a mind – the mind of God – that thinks rationally and mathematically. We know, for example, that gravitons have no rest mass – just like photons. If they had any mass whatsoever, then the range of gravitation could not be infinite. Yet, the motions of galaxies in clusters show that gravity works on a universal scale. Being massless, gravitons must travel at the speed of light.
Furthermore, gravitons must be spin-2 bosons. As with all bosons, they ignore the Pauli Exclusion Principle. A spin-2 boson results in a force that is attractive between like charges. This stands in contrast to the other three fundamental forces, mediated by spin-1 bosons, and in which like charges repel. As such, the graviton is the only spin-2 elementary particle.
Gravitons must have no electric charge, otherwise they would interact with electric fields. Gravitons have no color charge, and therefore ignore the nuclear strong force. Gravitons are stable since there is no lighter particle into which they could decay. Since they do not interact with the strong force, the weak force, or the electromagnetic force, gravitons are exceptionally difficult to detect. They really only respond to gravity, and gravity is orders of magnitude weaker than the other forces. This accounts for why these particles have not been detected as yet.
The Higgs Boson
One elementary boson stands apart as the only elementary boson that is not a gauge boson; that is, it does not mediate any force. This is the Higgs boson. The Higgs boson is a spin-0 boson, and the only known elementary particle that has no spin. It has no electric or color charge. But it is massive, weighing in at 125,350 MeV/c2. This is the second most-massive elementary particle; only the top quark is heavier.
Just as the photon, the 8 gluons, and the W and Z bosons are each associated with a field, so the Higgs boson is associated with the Higgs field. Recall that the fields associated with the strong and weak nuclear forces have extremely limited range, whereas the force of gravity and electromagnetism have infinite range – but their force diminishes with distance. We think of them as a cloud that gets thinner as we move away from the source. The Higgs field, however, permeates the entire universe equally, and is not diminished anywhere. The Higgs boson is then a wave in this field.
But unlike the other fields, the Higgs field does not produce any force. Instead, it produces mass. The mass of a particle is determined by how strongly that particle “feels” the Higgs field. Particles like photons, gravitons, and gluons do not interact at all with the Higgs field. They cannot detect it, and so they remain massless. Particles like the top quark interact very strongly with the Higgs field and thereby are very massive. Even the Higgs boson itself strongly interacts with this field, causing its high mass. The Higgs field was proposed in 1964 to explain why the W and Z bosons had mass. The Higgs boson was detected experimentally in 2012.
The Higgs boson is sometimes called the “The God Particle” due to a 1990 popular book of the same name written by physicist Leon Lederman. The particle “rules” over all others in that its field sets their mass. However, most physicists do not use that nickname. The Higgs field is apparently the mechanism that God uses to set the mass of all particles in the universe. Without the Higgs field, all particles would be massless, and would therefore travel at the speed of light. Obviously, chemistry and biology would not be possible in such a universe.
Lessons from the Quantum World
We have seen that there are exactly 12 elementary fermions (six quarks and six leptons), along with their 12 antiparticles. And there are exactly 14 elementary bosons., Thus, everything in the universe is made of some combination of these 38 particles. But most quantum particles have a fleeting existence; they are created and decay in a fraction of a second. Only three of these particles form physical, massive substances with long-term stability (either alone or in combination). Namely, the up and down quarks form all protons and neutrons, and the electrons “orbit” a nucleus in roughly equal numbers to the protons. This results in a universe that is electrically neutral on the whole, and determines the properties of all chemicals.
However, we have seen that many of the transient, short-lived particles are essential in holding matter together. The interaction of gluons in a proton or neutron holds the three quarks together. And mesons forming around nucleons mediate the residual strong force, holding the protons and neutrons together in an atom’s nucleus. Virtual photons keep the electrons orbiting the nucleus of atoms by mediating the electromagnetic force. And gravitons apparently mediate the force of gravity, which keeps the earth’s atmosphere from escaping into space, and keeps the earth orbiting the sun.
A slight change to any of these essential particles and the properties or the rules they obey, and the physical universe as we know it could not exist. Just imagine the intelligence necessary to think through the logic of how all particles must behave in order for the universe to be right for biological life. Secularism has no answer for this. And so, the first lesson we learn from quantum particles is that only the infinite mind of the Lord can think through all the infinite combinations of particles and rules to arrive at a solution that allows for the properties of this universe.
Yet, God is creative as well. Some of His creations are perhaps not essential for life, and yet they display His majesty. To my knowledge, the top quark is not necessary for life, or for chemistry, physics, or astronomy to be the way these disciplines are. Yet, particles like the neutral kaon (which may not be necessary for life), have opened up new arenas in physics by behaving in unexpected ways. They give us insight into the creativity of the Lord.
Since mankind has been made in God’s image, as if a shadow of His nature, we have at least a limited capacity to discover and understand the way God upholds His universe. God has revealed Himself to us. So, we know something about Him. Since God’s mind upholds all creation, and since God is logical and mathematical, the laws of nature are logical and mathematical. Mathematics is a mental exercise in the logic of numbers, which are concepts of quantity. And yet the universe obeys logic and mathematics because it is upheld by the mind of God. Secularism has no answer for this. It cannot account for the success of science, nor the effectiveness of mathematics in the formulation of physical laws. But the biblical worldview can. Indeed, many of the quantum particles that have been experimentally discovered were predicted to exist on the basis of mathematics! And this is the second lesson.
A Nested Hierarchy
A third lesson concerns the way particles are classified. We have seen that quantum particles fall neatly into certain families. There are composite particles that are made of smaller particles, and there are elementary particles that are indivisible. Of the elementary particles, there are 12 that are fermions (and 12 antiparticles), along with 14 bosons. The 12 fermions fall into two families: quarks and leptons. Each of these two families has exactly six members called flavors. Furthermore, there are two flavors in each of three generations. Quarks always group to other quarks or antiquarks forming a hadron. And there are two types of hadrons: baryons (which are fermions) and mesons (which are bosons).
The elementary bosons come in two broad varieties: gauge bosons, and the Higgs. The Higgs is the only member of its class (as far as we know). But there are four families of gauge bosons: one for each of the four fundamental forces. There is only one type of photon, and one type of graviton. But there are three particles mediating the weak force (W+, W–, and Z0), and there are 8 varieties of gluons. How do we account for this logical pattern?
Furthermore, particles can be classified by different criteria as well. For example, particles that have positive rest mass and travel slower than the speed of light are called bradyons. Particles that have zero rest mass and travel at the speed of light are called luxons. Particles that travel faster than the speed of light are called tachyons. All quarks, leptons, and hadrons are bradyons. So are the W, Z, and Higgs bosons. Photons, gluons, and gravitons are luxons. And as far as we know, there are no tachyons.
Hence, all particles on the quantum level can be classified into a hierarchy within a hierarchy. This is called a nested hierarchy. There are many nested hierarchies in nature. But there is one in particular that is often brought up in debates on origins. Namely, biological organisms fall into a nested hierarchy. Biologists classify organisms by the Linnaean taxonomy: kingdom, phylum, class, order, family, genus, and species.
And what is responsible for this hierarchy? How do we account for it? Evolutionists have argued that this hierarchy of organisms is the result of evolution. Organisms are said to have similarities because they share a common ancestor. Gradual, infinitesimal changes are said to have accumulated over millions of years of mutations, eventually resulting in the wide variety of life. Some evolutionists have even argued that evolution is the only explanation for this nested hierarchy.
However, quantum particles refute this notion. We have seen that quantum particles also fall neatly into a nested hierarchy. Yet, it would be absurd to say that this is because they have gradually evolved from a common ancestor. It’s not like the electron reproduced a slightly more massive electron, which gave rise to a slightly more massive version until the electron evolved into a muon.
Unlike animals, quantum particles can change into other particles – they decay. But this process is instantaneous and never results in a new type of particle. Rather, any particle decay will always result in some combination of the 38 elementary particles that God created. Furthermore, the way in which particles decay is strictly governed by the conservation laws. Particles cannot change into anything other than various combinations of the 38 particles that the Lord allows to exist in His universe.
The notion of some kind of evolution through imperfect replication from a common ancestor is a non-starter for particles. They just don’t work that way. So, what will account for the nested hierarchy of particles? Quantum particles can be classified into a logical hierarchy because their existence is determined by a rational Mind. The Triune God of Scripture is the basis for the logical pattern of similarities and differences that exist in the universe. God Himself is one in nature, and three in Persons. Thus, there is unity (all three divine Persons are the one God) and a type of diversity (e.g. the Father is not the same Person as the Son, Who is not the same Person as the Holy Spirit) within the Godhead. God therefore rules nature in a way that expresses both unity and diversity. And this is what makes taxonomic classification possible.
Thus, electrons, muons, and tau particles are all classified as leptons because they are all spin ½, and have an electric charge of negative 1. But they differ in mass, and are therefore distinct members of this one family. In the same way, dogs and cats both have bones, fur, and four legs; both give live birth, and nurse their young. They are both in the class of mammals. But they differ in anatomical details and are therefore in different families. The Christian worldview can explain why not only animals, but many other aspects of nature can be classified into a nested hierarchy. It is not due to Darwinian evolution. It is due to the sovereignty of the triune God of Scripture.
Quantum physics is a complex topic. We have only scratched the surface in this short series, covering the types of elementary particles that are known or inferred to exist and some of their basic properties. It takes years of study to master the mathematics necessary to calculate quantum phenomena. Even many of the concepts are difficult. We have seen particles that behave like waves, or exist with indeterminate compositions. The counterintuitive nature of this topic stretches our mind. Yet, all of these strange properties are what allow chemistry to work in such a way that biology is possible. It is amazing to consider how the Lord thought of all this. Furthermore, it is God’s mind that upholds all creation. It is His thoughts that control every particle in the universe. Our response should be to praise Him.
 However, the way negative mass responds to force is opposite to the way positive mass responds to force in terms of the direction of acceleration. This is because F = ma (the net force equals mass times acceleration). So, when mass is negative, the direction of acceleration is opposite the direction of the force! (If you push negative mass away from you it will move toward you.) So, imagine we had two planets next to each other – one made of ordinary mass, and the other made entirely of an equal magnitude of negative mass. The gravitational force between them would be negative, and so the positive-mass planet would begin to accelerate away from the negative-mass planet. The negative-mass planet also experiences a repulsive force (away from the positive planet), but it responds to that force backwards – by accelerating toward the positive-mass planet. The two planets would spontaneously accelerate with the negative-mass planet always maintaining the same distance from the positive-mass planet. Strangely, this violates no laws of physics because the total kinetic energy of the system remains zero (the negative-mass planet would have negative kinetic energy).
 Only positive mass exists in isolation. The mass defect associated with bound particles is negative, but is always less than the positive mass of the system. As far as we know, negative mass is never found in isolation.
 The reasons for this are given in my book, The Physics of Einstein.
 It is important to note that virtual particles do not come from nothing. They come from fields that permeate space, and are reabsorbed into those fields.
 This is why the electric force has infinite range.
 This is much like the neutral pion which has an indeterminate composition. This is discussed in the previous article.
 Since gluons are massless, the theoretical range of virtual gluons is infinite. But color confinement effectively limits the range to nuclear scales. So, the strong force and the weak force have limited range for entirely different reasons.
 Alternatively, there may be only 9 unique elementary anti-fermions depending on the reason why neutrinos have mass. In some models of quantum physics, neutrinos are their own anti-particle. Such a scenario would mean that lepton number is not a conserved quantity.
 This includes the hypothetical graviton.
 These include anti-particles. The graviton, photon, Higgs, and Z0 are each their own anti-particle. The antiparticle of any gluon is just another gluon, and the anti-particle of the W+ is the W–.
 Of course, only the Lord knows for certain. We cannot think through all of the implications of certain particles existing or how that would affect laws of nature, partly because we do not know all the laws of nature.
 The decay of neutral kaons was the first known violation of a principle called CP (charge-parity). The details go beyond this article. However, scientists previously thought that CP could not be violated. The discovery that neutral kaons violate CP has led to entirely new ways of thinking in physics.
 See Eugene Wigner’s excellent paper on this topic: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”