The theory of quantum matter.
In order to show the possibility of a spatiomaterialist explanation of quantum
mechanics, I will describe one way that the relevant phenomena might be constituted
by space and matter as substances enduring through time. This will require
a refinement of the assumptions made thus far about the natures of both matter
and space. It is a refinement is a basic aspect, because it has to do with
how these substances endure through time.
Space and matter were postulated in Spatiomaterialism
as substances with essential natures that are opposite in a most fundamental
way. The parts of space all have essential natures that include geometrical
relationships to one another, so that the existence of one depends on the
existence of all the others. But the parts of matter can all exist independently
of one another. Being opposite in that way, it was possible to explain why
bits of matter have spatial relations to one another and how change is possible
by assuming that bits of matter exist together with space as a world by each
coinciding with some part of space or another. These are the basic assumptions
of spatiomaterialism, and it is possible to make further assumptions about
the natures of space and matter, as long as they are consistent with these
basic assumptions.
I made further assumptions about the nature of space and matter
in order to explain how the laws of classical physics are true. I assumed
that the nature of matter coincides with space in all the forms that are counted
by physics in its principle of the conservation of mass and energy: rest mass,
kinetic energy, two kinds of force-field matter (electric charges and gravitational
fields), and two kinds of waves of forces (electromagnetic waves and gravitational
waves).
I made another assumption about the nature of space and matter
in order to explain Einstein’s special theory of relativity ontologically.
I assumed that space has an inherent motion (or “ether”) which determines
the velocity of light), and that material objects suffer Lorentz distortions
as a function of their velocity relative to the inherent motion. (In order
to suggest the inevitability of the Lorentz distortions, I anticipated a conclusion
that I will defend here, namely, that material objects are constituted by
unit-like interactions that are equivalent to the two-way electromagnetic
interactions involved in the an interferometer.)
I made yet another assumption about the nature of space and
matter in order to explain Einstein’s general theory of relativity. I assumed
that centers of matter exert a force on the surrounding space that accelerates
the inherent motion (or ether) and, thereby, accelerates all the bits of matter
that coincide with space by way of it.
In order to explain ontologically the truth of the laws of quantum
mechanics, I will make further assumptions about both space and matter.
Space.
As we have already assumed, space has an inherent motion. This aspect of the
nature of space determines the velocity of light. This assumption about the
motion of electromagnetic waves (or photons) is crucial to the spatiomaterialist
explanation of relativity theory, because it is the motion of objects with
rest mass relative to the inherent motion that gives rise to the Lorentz distortions
which explain the phenomena of special relativity. And the acceleration of
the inherent motion itself relative to space is what explains the gravitational
phenomena covered by general relativity.
The inherent motion of space is what plays the role that the
ether was supposed to play in classical physics. The inherent motion mediates
all the motion and interactions among bits of matter, because it is the aspect
of space by which bits of matter coincide with parts of space. Since the inherent
motion goes both ways in every direction of three dimensional space, there
is a certain velocity at any point that is at “rest” relative to the inherent
motion itself (that is, at rest in the ether). Relative to that inertial frame,
light has the velocity, c, both ways in every direction in three dimensional
space. But rest relative to the inherent motion may not be rest relative to
space, because in gravitational fields, the inherent motion (or ether) is
in motion relative to space and even accelerating. That aspect of its nature
can, however, be set aside for now, because the inherent motion in substantival
space that is the relevant aspect in explaining the quantum nature of matter.
To make it concrete, consider what the inherent motion must involve in order to explain electromagnetic waves. It must exist at every location in space at every moment. It must always have the same velocity in space (except, of course, for the changes that occur in gravitational fields). In each part of space, it must sweep through space in every possible direction, that is, both ways in every direction in three dimensional space. And it must be able to carry electromagnetic waves of every possible wavelength and every possible phase of every wavelength across every point in space, preserving their wavelengths and phases. (And as we shall see, it must do this for photons of two kinds, one of each possible orientation of spin.)
Since the inherent motion
is sweeping through every part of space at the same time, what is sweeping
through any part of space in any given direction is like of a wave front.
The same motion sweeps through all the points in every two dimensional plane
of which it is part. Indeed, there is such a wave front sweeping in every
direction through every point of space.
Nor is it inappropriate to
speak of the inherent motion as having waves, since it carries every possible
wavelength of light, and as we shall see, the wavelengths of those wave fronts
make a difference in what happens. It takes a certain period time for a photon
(a complete cycle of electromagnetic radiation) to pass any given point, and
since the photon is carried along by the inherent motion, such a cycle marks
out a certain distance (its wavelength) over and over along its path. Indeed,
since this is always happening, there is always already a series of wavelengths
implicitly marked out in space by the inherent motion at any given wavelength,
each going through a cycle at the same time as all the others, that is, at
the present moment. This pattern holds for every wavelength and for every
phase of each wavelength both ways in every direction. And it holds both ways
in every direction for each point in space.
I elaborate this implication of postulating the inherent motion
in order to make explicit what all I will not try to explain about
the nature of space. By calling it an “inherent motion in space”, I mean that
it is an aspect of the nature of space itself. That means, at a minimum that
it is occurring at every location in space, whether there is any light there
or not. But what is more, it means that space is what causes light
to move as it does. The inherent motion at any location in space carries
light along with it, when matter of that kind happens to coincide with
that part of space. Unless the inherent motion of space were responsible for
the velocity of light, it would not be possible to explain relativistic phenomena
ontologically.
The inherent motion, therefore, marks out distances in space
according to any cycle of changes occurring locally as time passes. This is
to talk about the inherent motion as if it were a real set of events taking
place in space, and as I said earlier, it may be possible to formulate a simpler
spatiomaterialist explanation in which the inherent motion is merely a spatio-temporal
aspect of the nature of space as a substance, that is, a geometrical structure
about space and time. The inherent motion is, after all, basically
a relationship between distances in space and periods of time that are built
into the essential nature of space. That is to add a temporal aspect to the
spatial relationships that space was originally assumed to have in Spatiomaterialism
in order to explain the three-dimensional geometrical structure of space.
Each part of space has not only an essential geometrical relationship
to every other part of space at the present moment, but also an essential
relationship to future and past moments in the existence of every other part
of space. To be sure, the past and future states of parts of space do not
exist, because nothing exists but what exists at present, if substance endure
through time. That means that one location’s relationship to future or past
states of another location is a temporally complex property of space, which
determines the maximum velocity with which what happens in one part of space
and affect what happen in other parts of space. But that temporally complex
property corresponds to a temporally simple relationship that actually exists
among the parts of space as time passes. That is what I mean to emphasize
by talking about the wave patterns set up in space by the inherent motion
sweeping though every part of space, both ways, in every direction. These
patterns may be nothing more than simply how all the parts of space endures
through time, but speaking of these patterns as being laid out by the inherent
motion in real time dramatizes the role they play in explaining the regularities
described by quantum mechanics. And at this point, clarity about what is being assumed
is more important than simplicity, since it is not necessary to have the simplest
ontological explanation in order to show that there is such an explanation.
Matter.
In order to give a deeper explanation of the nature of matter, we must distinguish
between two kinds of matter, which I will call “force-field matter” and “quantum
matter.” Three of the six forms of matter that were distinguished in order
to explain the truth of classical mechanics are forms of force-field matter
(electric fields, gravitational fields, and gravitational waves), and three
are forms of quantum matter (rest mass matter, kinetic energy matter, and
photons). Force-field matter has already been explained ontologically as involving
a property (or temporally variable condition) of parts of space (though there
is more to be said about it). And it is the nature of quantum matter that
will bear the major burden of this ontological explanation of the quantum
mechanics.
Force-field
matter. By “force-field matter,” I mean forms of matter that are constituted
by a changeable property or condition of parts of space. The property of space
acts like a force, because it changes the way in which bits of matter coinciding
with that part of space move and interact. Consider the three forms of force-field
matter:
Gravitational fields. Gravitational matter is one kind
of force-field matter, and we can set it aside, because it has already been
explained. Gravitational matter is the matter that exists as the force field
that gravitating bodies impose on the surrounding space, accelerating the
inherent motion (the ether) toward themselves. Like any form of potential
energy, the quantity of matter involved in a gravitational field is already
counted in the rest masses of the objects exerting the forces. That is, their
rest masses decline as the bodies attract one another, acquiring kinetic energy
at the expense of potential energy (though as we shall see, force-field matter
is not actually converted to kinetic quantum matter until the material
objects acquire kinetic energy relative to the inherent motion by colliding
with other material objects near the center).
Gravitational waves. Since gravitation is a force that
propagates with the inherent motion of space, gravitating bodies can set up
gravitational waves, which exist independently of material objects with rest
mass, for example, from binary stars, which are in orbit around one another.
But this is still a form of force-field matter, not quantum matter, because
the gravitational force propagating at the velocity of light acts on space,
not on bits of matter directly. It is by accelerating the inherent motion
in the parts of space it encounters that gravitation accelerates bits of matter,
not by interacting with bits of matter directly.
Electric fields. An electric charge also imposes a force field on the space surrounding the material objects that has the charge, and that is another form of force-field matter. The electric field is another property (or variable condition) of space which affects other material objects with electric charges. Electromagnetic matter contained in electric charges is already counted in the rest masses of the objects that have the charge, and matter is conserved, because as we have seen, the consumption of potential energy is counted as a negative quantity.
The electric field is more complex than the gravitational field, as we have seen, because changes in the electric field cause magnetic forces. But that connection between electric and magnetic forces, which is described by Maxwell’s equations, can be explained as another aspect of the nature of space. That is, changes in the electric field caused by the motion of an object with rest mass propagate as a result of the inherent motion in space, and thus, the electromagnetic interactions are relative to the inherent motion (as we have assumed in explaining Einsteinian relativity).
Quantum electrodynamics is the gauge field theory that is currently accepted by physics as an explanation of the electric charge and its behavior, and such a theory lends itself to a spatiomaterialist ontological explanation, because it portrays forces as being exerted by the exchange of particles, called the "boson" of the gauge field. In this case, it is a virtual photon. The electric charge is described as having a certain orientation in a complex vector plane, and the forces exerted on the charged particle by the virtual photons are just what is required for the orientation of the charge to be unchanged in that complex vector plane by its change of location. Those forces turn out to the forces described by Maxwell’s law. But since the force field is explained as virtual photons emerging from space as a result of the charged particle's motion at its location in the field, the gauge field theory is the kind of explanation that can be given an ontological explanation by spatiomaterialism. (More will be said about the nature of the electric charge and the gauge bosons that mediate interactions among charged particles as required as we go along and, more completely, when we take up the basic particles. See Change: Basic Objects.)
Quantum
matter. The nature of quantum matter is the basis of this ontological
explanation of quantum mechanics, and the remaining three forms of matter
(rest mass matter, kinetic energy matter, and electromagnetic waves) are all
forms of quantum matter. Like the new assumption about the nature of space,
this new assumption about quantum matter recognizes a temporal aspect to the
nature of matter, though it is a temporal property suited to the opposite
nature of matter.
Parts of space are all connected geometrically, and since the
inherent motion connects them all temporally as well, the endurance of space
through time is characterized by the inherent motion (or the spatio-temporal
geometry) described above. Much the same way of enduring through time also
characterizes force-field matter, since force-field matter is spread out continuously
in regions of space through which the inherent motion is constantly flowing.
But since bits of matter can exist independently of one another, there is
another way in which they can have a further temporal aspect to their nature.
The new assumption is that quantum matter is just a series of
cyclic events that occur over time. That is, bits of quantum matter endure
through time as a series of unit-like events whose cyclic nature entails that
each event gives rise to another event of the same kind (unless it interacts
with another bit of matter in some way and another kind of cyclic event ensues).
Since these events follow one another as time passes, cycles of events (of
the same kind) are a way of counting time, much as the inherent motion in
space allows periods of time to be counted by the distance it crosses. These
events will be called “quantum event,” because these are the smallest changes
that can take place in a spatiomaterialism world (except for the inherent
motion itself in smaller parts of space). Quantum events cannot be divided
up in to smaller events, and so they are elementary units. But since they
are cyclic events, each gives rise to another event, and since they
reproduce in time, they explain the endurance of bits of (quantum) matter
through time. The way that matter endures through time as a series of cyclic
quantum events is mainly what the “quantum” in quantum mechanics is referring
to, according to this spatiomaterialist explanation of quantum mechanics.
An “event” has both a spatial and a temporal dimension. It begins
at some place and time and ends at some place and time. What happens in a
quantum event is that a force is exerted and change is caused. The force may
cause a change in another force, as illustrated by the photon, in which electric
and magnetic forces are coupled in cycles. Or the quantum event may be a force
that changes the motion of an object with rest mass, as we shall see holds
in the case of the motion of an object with rest mass.. Different forms of
quantum matter are constituted by different kinds of quantum events, as we
shall see. But since they are elemental events, they all have the same, smallest
size. That size is what is represented by “Planck’s constant”, h.
Planck’s constant is a certain size in a parameter called “action”.
Though action was recognized early in the Newtonian era as one kind of physical
quantity, it has nearly dropped out of contemporary physics (except for the
constant h), apparently because
it need not be mentioned in describing efficient causes. Action is, however,
defined in terms of a certain physical quantities that are mentioned as efficient
causes (such as spatial relations, mass, force, velocity, acceleration, momentum,
and energy). For our purposes, the most useful way to think of action is as
the product of force times distance times time, as if a force were
acting on something (such as a unit mass) for a certain distance over a certain
period of time.
In units that physicists take to be basic, action has the dimensions of mass times distance squared per unit time (or mass times distance squared per unit of time squared, all times time). And in addition to thinking of it as force times distance times time, it can be seen as momentum (or mass times velocity) times distance (that is, as the integration of a change in momentum over the distance it occurs). Alternatively, it can be seen as energy (mass times velocity squared) times time (that is, as the integration of a change in energy over the period of time it occurs).
In speaking of momentum and kinetic energy, I assume that we are talking about matter that is nearly at rest in the ether, where Newtonian laws hold and momentum is approximately equal to mass times velocity and kinetic energy is approximately equal to one-half of mass time the square of velocity. This is not quite true, because according to the special theory of relativity, mass increases with velocity. However, by starting with rest mass as the quantity of matter constituting particles at rest in the inherent motion, it will be possible to explain why mass increases with velocity, because we will be able to explain the extra mass as the matter making up its kinetic energy.
The idea is, therefore, to interpret the quantum of action as
an event, that is, as a change of
some kind that takes place in the world as a result of something being done.
This may be a little vague, but remember that we are taking now about the
most basic elements of what exists in the world, and the nature of quantum
events can be made clear only by considering their various kinds. But since
action is measured in units that include both space and time, it is possible
to think of these events as having determinate boundaries in space and time,
that is, as beginning at some place and time and ending at some place and
time. That gives these events determinate locations in the geometry of space
and time as determined by the velocity of light, that is, by the inherent
motion.
Planck’s constant is a certain size of action, and we can explain
why it appears in all the equations of quantum theory, if we assume that quantum
events have an all-or-nothing character about them. Bits of quantum matter
endure, we assume, because they are constituted by quantum events with a cyclic
nature. Although cycles of quantum events may follow one another continuously
in time and space, there is a unit-like nature about them, so that either
a whole quantum event occurs, or it does not occur at all. This means, on
the one hand, that nothing can happen that involves less than a unit of action
(except possibly the inherent motion), and on the other, that everything that
does happen to quantum matter is made up in some way of a certain number and
kinds of these elemental units of action.
The assumption that quanta all have the same amount of action
is not as restricting as it may seem, because quanta have widely varied temporal
and spatial dimensions. They can take place in a short distance in a brief
period of time, if the force is great enough, or they can take place over
a longer distance in a longer period of time, when the force is weaker. But
in order to spell out the assumption that they have a unit-like nature, let
us think of quanta as having end points in space and time, so that quantum
events can be fit together as complete cycles in the spatio-temporal geometry
of the inherent motion of space in different ways. This model may be too crude.
It is unlikely that quantum events have anything as abrupt as definite points
at which one cycle ends and another begins. But that is a way of keeping in
mind the unit-like nature of these events, even if it is just a place-holder
to be replaced by a better explanation of where and how one quantum event
ends and another quantum event begin.
For example, a better model of their unit-like nature would,
perhaps, be one in which interactions between different bits of matter can
occur only when whole cycles of the different bits of matter are lined up
somehow according to the spatio-temporal geometry of the inherent motion in
space. That is, given their precise locations in space and time, the points
at which quantum cycles stop and start would depend on what they are interacting
with and the direction from which they are interacting, so that different
starting points and stopping points might hold if they were interacting with
quantum cycles of bits of matter from different directions in space, of different
kinds, or with different phases to their cycles. (Lining particles up in this
way could be, as we shall see, the role of their intrinsic spin and its magnetic
moment in mediating interactions of bits of quantum matter.)
Matter is a substance, because it exists continuously over time,
never coming into existence nor going out of existence. We are assuming that
one form of matter can be converted into another, including conversions between
quantum matter and force-field matter (that is, between potential and kinetic
energy). But when matter exists in the form of quantum matter, the endurance
of bits of matter through time is explained by the cyclic nature of the quantum
events that constitute their existence. That is, given that the quantum event
starts at some place and time, there is a certain place and time where the
cycle is complete, and at that point, another quantum event begins. Since
quantum events are related cyclically, they can reproduce themselves in time.
However, quantum cycles succeed one another not only temporally, but also
spatially, so that nothing is flitting about discontinuously from place to
place in space. Other things being equal, quantum events give rise to other
quantum events of the same kind and dimensions as themselves.
Bits of matter do, however, interact. I will say more about how
they interact in a moment, but in general, what happens is either the conversion
of matter between quantum forms and force-field forms of matter and/or changes
in the kinds of quantum matter. Force-field matter is laid out in space, changing
its shape with the motion of the material objects that are imposing the forces.
And since material objects, their motion and photons are just cycles of quantum
events reproducing themselves in time, what changes are the kinds, numbers,
and dimensions of the quantum events constituting them.
Since the quantum events have a unit like nature, what happens
to bits of quantum and force-field matter in space involves fitting quantum
events together in space and time according to certain laws as if the endurance
of the world through time were the result of building a brick wall into the
future. Some bricks are simply stacked on top of one another, as quantum cycles
reproduce themselves in time. But when bits of matter interact, the bricks
fit together in more complex ways, changing the sizes and locations of the
bricks in the next row. The space on which the wall is being built also plays
a role, because the sizes of the brick may also change with their locations
(as in force fields), and the effects of space on their sizes changes with
the locations of the bricks affecting space (as in changing location in a
force field). Nature is a master mason, never failing to lay in the next layer
of bricks according to fixed rules, and thus, there are regularities about
change as the brick wall is built into the future. And the structures formed
by them can be quite stable over time.
In order to spell out the details of these “rules of quantum
masonry,” I will describe each of the forms of quantum matter and then take
up the issue about how they interact with one another. Some of the quantum
puzzles will be explained along the way, and in the end will, we will see
how their interactions explain the structure of the atom, the Heisenberg uncertainty
principle, and the Bell correlations.
To explain the endurance of matter by the cyclic nature of quantum events may, however, make it seem that matter is not a substance at all. If quantum events are ultimately just the exertion of a force in some part of space making some other event occur that is also constituted by forces, it is conceivable that quantum matter is just a property of parts of space, much like force-field matter. Could matter be entirely reducible to space? This is not what we assumed when we took spatiomaterialism as the foundation for this ontological way of doing philosophy.
The reduction of matter to space is, however, something that
ontologists should welcome, if it is possible, for it would be just as complete
as spatiomaterialism, but a simpler, and, thus, better ontological explanation
of the natural world. It is more or less what Einstein was trying to do during
the latter part of his life in attempting to construct a unified field theory.
He wanted to describe matter another kind of curvature of spacetime, along
with gravitation. If something like that comes of this ontological explanation,
then spatiomaterialism will turn into spatialism.
However, I will put this possibility aside. In the first place,
we would be getting ahead of ourselves to assume at this point that spatialism
is true. We have yet to see how matter can be explained by cycles of quantum
events. And second, even if an ontological explanation of quantum mechanics
like this stands up in the end, it does not seem to me that that would make
spatialism true. You may be able to reduce the inherent motion in space to
spatio-temporal geometry, but the unit-like nature of quantum events will
keep them from being reducible to properties in space. Each quantum event
occurs over a period of time, and since quantum events cannot exist unless
the whole event occurs, to postulate their existence is tantamount to holding
that what exists includes entities with a temporal dimension to their essential
nature. Bits of matter-time may be less problematic than spacetime, but in
a world in which nothing exists but the present moment, they are, strictly
speaking, not possible. Thus, this unit-like nature can be explained only
by postulating the existence of a substance with a part-whole relationship
of some kind that make it appear to be made up indivisible cycles of events.
Whatever its nature, it basically different from the essential nature from
space. Space is incapable of explaining the unit-like nature of quantum events,
because it must exist only at the present moment in order to have an inherent
motion that flows continuously. The only plausible way of explaining the all-or-nothing
character of quantum events is to postulate another kind of basic substance,
distinct from space, which can coincide with parts of space, for in that case,
we can believe that, despite seeming to have a temporal dimension to their
nature, quantum events also exist only at the present moment. There is, however,
no need to settle this issue now.
Forms of
quantum matter. I will focus first on the nature of quantum matter, since force-field matter
depends on the existence of the bits of quantum matter constituting a particle
with rest mass in nearby parts of space and it is fairly clear how it can
be explained. Quantum matter includes electromagnetic waves, material objects
with rest mass, and their kinetic energy.
The total matter is ultimately equal to the total quantum matter. Force-field matter is already counted in the masses of the objects exerting the forces, and gravitational waves eventually die out as they are converted into other forms of matter.
The quantity of quantum matter in any region of space is measured by the number of quantum events per unit time, for that is equal to the quantity of energy, given the definition of “action.” Since we will assume that all quantum matter is constituted by quantum events, the equivalence of energy and mass by Einstein’s equation, E = mc2, implies that each unit of mass must be equivalent to a certain number of quantum events per second.
The quantity of force-field matter involved in constituting the
electric charge can be measured as potential energy, that is, in terms of
the number of quantum events per second that can be converted from it, and
that quantity must be subtracted from the total quantum cycles constituting
rest mass.
After describing the nature of each form of quantum matter, I
will take up the nature of electromagnetic interactions, bringing force-field
matter back into the picture. But along the way, I will point out how this
theory explains the peculiar nature of matter at the scale of the quantum
and solves certain quantum puzzles.
Light. Light is the easiest form of matter to explain on the assumption that “quantum”
refers to elementary events with the size indicated by Planck’s constant,
for light can be explained as being made up of photons, each of which is the
size of a quantum.
Light was understood as a wave in classical physics. According to Maxwell’s equations for electromagnetism, the change in the electric force has as its effect a magnetic force, and the change in the magnetic force has as its effect an electric force. Thus, the two forces interact, and their interaction can couple them in cycles of changing electric and magnetic forces that propagate through space at a fixed velocity, the velocity of light. Its wave-like nature is apparent in such phenomena as diffraction and interference.
As we assumed in explaining Einsteinian relativity, the velocity of light is explained ontologically by the velocity of the motion inherent in space itself. Let us, therefore, think of the electric and magnetic forces involved in electromagnetic waves as being carried along with the inherent motion in some direction. That will allow us to explain electric and magnetic forces as properties of parts of space, except for the way that they are coupled together in units as photons (or rather aspects of the inherent motion in space).
The particle-like nature of light waves can be explained on the assumption that each cycle of electric and magnetic forces is a single quantum event that occurs as a whole, if it occurs at all. Since these quantum events are cyclic, when one event does occur, it is followed, other things being equal, by another quantum event of the same kind. But since these quantum events coincide with space by way of the inherent motion, the next cycle of electric and magnetic forces occupies the next part of space in its direction. As the cycles reproduce themselves in time, therefore, they move across space, constituting an electromagnetic wave in time and space.
This ontological explanation of light accounts for the quantum equations used to describe the energy and momentum of photons. Energy is proportional to the number of quantum cycles per unit time, and that is what the equation for the photon’s energy says: E = hf (where f is the frequency of the light). The shorter the period of each quantum cycle, the more units of action that can occur in a unit of time, and thus, the more energy it carries.
The momentum of the photon can be explained in a parallel way,
except relative to the direction of space in which the photon is moving. The
dimensions of the quantum as a unit of action implies that the momentum of
a quantum cycle is proportional to the number of quantum cycles per unit distance
(in the direction of motion), and that is what the equation for the momentum
of the photon says: p = h/l, where l is the wavelength of the light and 1/l is
the number of cycles per unit length). In other words, the momentum is inversely
proportional to the wavelength. Photons with shorter wavelengths have more
momentum.
Since the velocity of light is constant, fl = c (where
c is the velocity of light), and thus,
the energy and momentum of the photon are proportional to one another: E = pc. In other words, the shorter
the photon’s quantum cycle in time and space, the higher its energy and momentum,
respectively. But since it is still the size of a quantum, the decreased size
of the event in space and time means that the forces involved in each cycle
are greater (since action is the product of force, space and time).
Since each cycle of electric and magnetic forces is a quantum
event, no part of it can exist unless the whole cycle does. This unit-like
nature to the events that constitute the existence of a photon is explained
ontologically by how bits of matter coincide with space, and so it depend
as much on the nature of space as it does not the nature of matter. (More
precisely, the energy of the photon depends on the bit of matter apart from
space, whereas its momentum also depends on space, because momentum is a result
of the interaction of electric and magnetic forces being carried along by
the inherent motion.) This suggests a straightforward ontological explanation
of the phenomena that led to the recognition that light is made up of particle-like
units.
Planck. What Planck discovered about blackbody radiation
can be explained ontologically as a discovery about how photons coincide with
the same part of space. What he discovered is that photons of different frequencies
can all coincide with the same part of space as long as there their frequencies
differ from one another by at least one quantum of action per second. This
limitation on the frequencies that can exist in the same part of space avoids
the so-called ultraviolet catastrophe, that is, why the total energy of photons
at higher frequencies does not become infinite.
On this ontological explanation, what coincides with space are not just the changing electric and magnetic forces of electromagnetic waves, but rather complete cycles of such forces. And since the inherent motion contains each quantum of action is part of a wave pattern of a certain size that extends though the space in its direction, this limitation is a minimum difference that holds for the sizes of the wave patterns that can exist in that region of space.
Though this is a limitation on the variety of possible photons
that can coincide with any part of space, the inherent motion in space is
still handling a lot of different kinds of photons. In addition to all the
frequencies of light in any direction that can exist at any part of space,
photons of each frequency can have different phases (that is, different points
in space where the cycle begins) as well different orientations of spin. Not
only must the inherent motion be able to carry photons of all these kinds
at once in any given direction, but it must also be able to carry the complete
variety of photons in every direction
in three-dimensional space. Indeed, at any given location it must be able
to carry photons of all kinds both ways
in every direction, and it must do so at
every location in the region
of space all the time. That
is just how the parts of space are connected (though the inherent motion itself
may be moving across space and being accelerated in a gravitational field).
Einstein. Einstein’s explanation of the photoelectric
effect was that in order for light to free electrons from matter, the light
had to have a high enough frequency, because the electron had to receive all
the energy it needed to overcome the force binding it to the atom from a single
photon. Lots of low frequency photons would not work.
This particle-like behavior of light is just what would be expected,
if light is constituted by cycles of quantum events, because in order for
light to interact at all, a whole quantum event of one kind must become a
quantum event of another kind, in this case, it is the kind of quantum event
that constitutes kinetic energy. And a single photon can supply the force
needed to accelerate the electron, because photons with a higher frequency
have smaller temporal and spatial dimensions and, given that each photon is
a quantum of action, the forces constituting them must be correspondingly
greater.
Compton. When a photon does interact, it is the whole
photon that interacts. When a photon is scattered by an electron, for example,
a whole photon is absorbed and a whole new photon is generated (one that is
180o out of phase with the original). The Compton effect has a
straightforward ontological explanation, because the scattering of the high
energy photon by an electron, like an elastic collision between two material
objects, conserves both energy and momentum. The mass of the electron limits
how much energy and momentum can be carried away, and that can be confirmed
by measuring the direction and wavelength of the reflected photon.
Rest
mass. Material objects with rest mass are another form of matter that
was recognized in explaining the truth of classical physics, and our reason
for thinking that rest mass is just another form of the substances that are
counted in the principle of the conservation of energy was the equivalence
of mass and energy (E = mc2)
entailed by Einstein’s special theory of relativity. But having set aside
force-field matter, we are now explaining those forms of matter as forms of
quantum matter, and that requires us to hold that material objects with rest
mass are constituted by quantum events in some way. And there is an obvious
way to do so.
The rest mass of a particle can be explained as the number of cycles of quantum rest mass events per second, just as for the energy of photons. Such quantum cycles would, of course, have to coincide with space in a different way from photons, because objects with rest mass can remain at rest (or more precisely, have a constant velocity relative to the inherent motion in space). The simplest way to explain why such objects can be at rest is to hold that the quantum cycles constituting them go around in circles (or some such closed path), instead of moving across space with the inherent motion like photons. Moreover, since such quantum events would follow a closed path, like a circle, which brings the action back to where it began to start the next cycle, it is clear how quantum rest mass cycles can succeed one another in time.
In order to show that objects
with rest mass can be explained as form of quantum matter, it will be necessary
to show how all the basic particles recognized by physics can be explained
by quantum rest mass cycles in this way. But that is a task that will not
be taken up until the next chapter on contemporary physics, Cosmology:
Basic Objects. For purposes of explaining quantum mechanics proper,
we shall need only three kind of basic particles with rest mass: electrons,
protons and neutrons. They are the near basic constituents of ordinary material
objects of all kinds, and together with the electromagnetic force, including
the photon, they can explain all the processes that occur in ordinary objects,
from atoms to human beings. That is the range of phenomena covered by the
quantum mechanics of electromagnetism.
Such ordinary phenomena do
not include, of course, the sun, radioactivity, nuclear power and the like.
These other phenomena depend on interactions among more basic particles than
nucleons and their electromagnetic interactions with electrons. These more
basic particles are recognized by physics, and they must all be explained
as cycles of quantum events (and how quantum cycles coincide with space) in
order for this ontological explanation of quantum matter to be complete. There
is a way of doing that in which even the electron does not turn out to be
basic, as explained in Cosmology:
Basic Objects.
For the present, we shall
simply take it for granted that electrons and nucleons can be explained ontologically
as objects constituted by quantum rest mass cycles.
Visible light is made up
of photons with frequencies of about 1015 cycles per second and
energies about a few electron volts. Electrons have an energy of about one
half million electron volts, and thus, the frequency of its quantum rest mass
cycles must be on the order of 1021 cycles per second. And since
protons have a rest mass about two thousand times that of electrons (or about
938 million electron volts), the frequency of their quantum rest mass cycles
must be on the order of 1024 cycles per second. However, nucleons
have a complex structure, and on this ontological explanation of them, their
quantum rest mass cycles do not follow a circular pathway. It is a more complex
pathway that may involve three or six quantum events to complete.
Electrons and protons carry
an electric charge, as well as rest mass. The conservation of electric charge
is explained by the gauge field theory for electromagnetism, and though what
I will say about the electric charge is compatible with that theory, I will
not try to explain it until we take up the basic particles. (See Change:
Basic Objects: Gauge Field.) We shall just take the electric charge
for grated.
Kinetic
Energy. The assumption that kinetic energy is a
form of matter was made in order to explain ontologically the basic laws of
classical physics. We explained the principle of the conservation of mass
and energy ontologically by the endurance of material substance, and that
forced us to recognize that kinetic energy is a form of matter. What needs
to be shown here is how kinetic energy matter can be explained as a form of
quantum matter.
The received view is that the motion of a material object is
nothing but its change of location in space over time. But that is not possible
for an ontological explanation of the world that explains change by the endurance
of substances through time, that is, as “real change,” because it must assume
that nothing exists but what exists at the present moment. However, if nothing
exists but the present moment, material objects are never in motion, and so
wherein does its motion consist? To call motion “instantaneous velocity” is
merely to name what needs to be explained.
Thus, ontology must recognize that the motion of objects with rest mass is not just their change of location over time, but rather is due to another form of matter that endures through time. That is, we must think of motion as an additional bit of matter that coincides with the material object and the part of space where the object is located. But it is a different form of matter, because it coincides with space in a way that moves the rest mass along in a certain direction at a certain rate.
This is to resurrect the notion that inertia is a kind of force
that keeps the object with rest mass moving, and it explains, as we shall
see, the difference between the rest mass of a material object and its inertial
mass. But since heat is known to be the kinetic energy of material objects
at the micro level, it is also, in effect, to vindicate the notion that heat
is a caloric fluid, as we shall see in explaining Material
global regularities.
De Broglie’s equation. Kinetic energy can be explained in terms of quantum cycles by supposing that there are quantum events that change the locations of material objects by a certain distance in a certain time. Newton’s first law of motion requires that material objects in motion continue in motion, and in order to explain why that law is true, we assumed that kinetic energy matter endures through time like any other form of material substance. But now we are explaining how quantum matter endures through time by the cyclic nature of quantum events, and so we must explain kinetic energy as a series of cyclic changes, each step of which can exist only as a whole. Let us call them “quantum kinetic cycles.” They will explain ontologically the truth of the de Broglie equations for the momentum and kinetic energy of particles with rest mass, which parallel the equations for photons.
De Broglie first proposed that particles with rest mass have
a wave-like nature, much like photons. His equation, p = h/l, which was derived from
the equation for photons, described the momentum of the particle as being
inversely proportional to its wavelength, and that can be explained ontologically
by the nature if the cyclic quantum events that constitute kinetic energy.
The wavelength of the particle can be explained ontologically as the distance
that the quantum kinetic cycle moves the particle during each kinetic cycle.
And we can explain ontologically why the de Broglie equation is true, if we
assume that for a unit mass, the length of the quantum kinetic cycle in the
direction of its motion is inversely proportional to the momentum of the material
object. Like photons, therefore, momentum is proportional to the number of
quantum kinetic cycles that occur within a unit of space (in the direction
of motion).
Just as the momentum is related to the spatial dimensions of
the quantum events constituting kinetic energy matter, so the kinetic energy
itself is related to their temporal dimension. The kinetic energy of the particle
is inversely proportional to the period of its quantum kinetic cycle, so that
its kinetic energy would be proportional to the number of cycles that occur
in a unit of time, also like photons. In this case, E = hf, where f is the frequency
of the kinetic cycle, or the inverse of its temporal size.
In sum, the faster the particle with rest mass moves, the shorter
the distance covered by each quantum kinetic cycle, and the shorter the period
required for each quantum kinetic cycle that moves it across space. But since
each quantum kinetic cycle is a quantum of action, the shorter its temporal
and spatial dimensions, the stronger the force that is acting to move the
rest mass across space in each cycle, that is, the more inertia it has.
Quantitative relationship of momentum and kinetic energy. The cycles of quantum events that are responsible for the motion of objects with rest mass explain their momentum and energy, therefore, in much the same way as the momentum and energy of photons. But there is an important difference. In photons, there is a constant relationship between energy and momentum (described by the Einsteinian equation, E = pc), but no such relationship holds for particles with rest mass. Unlike photons, rest masses can have various velocities in any direction, and their momentum and kinetic energy do not have a constant relationship. On this ontological explanation, that means that the temporal and spatial dimensions of the quantum kinetic cycles by which the rest masses change location in space do not have a constant relationship.
From the equations for classical physics, we know that the momentum
of a moving object is proportional to its velocity (p = mv),
while the energy of its motion is proportional to the square of the velocity
(E = ½mv2), and as promised when the laws of classical
physics were being reduced to spatiomaterialism, this kinetic theory of matter
explains why momentum and energy are related in this way.
For example, if the velocity of a unit mass is doubled, the wavelength of each quantum kinetic cycle is cut in half. But that means that the period of each quantum kinetic cycle must be one-fourth as long as the previous quantum kinetic cycles, for otherwise the object will not travel twice as far in the same period of time.
Thus, the way kinetic quantum events must fit together in space
over time in order to explain the motion of particles with rest mass explains
why the kinetic energy increases with the square of the velocity, while momentum
increases directly with velocity. It is a result of how the change in the
spatial dimensions of quantum kinetic cycles must affect their temporal dimensions
in order for momentum to be inversely proportional to their de Broglie wavelength.
(And the reason that the kinetic energy of a particle is not equal to the
frequency of its quantum kinetic cycles, but only half, is that only half
that much energy is required to accelerate a particle to that “frequency.”
More energy is required to accelerate objects at higher velocities, as we
noted in explaining why the gravitational time dilation varies with altitude
in a gravitational field, not with the strength of the force.)
Rest mass. This description of quantum kinetic cycles has assumed that the particle being moved has one unit of rest mass, but particles of different kinds have different masses and according to classical physics the mass of the particle helps determine its momentum. Its momentum is the product of its mass and velocity. For example, when two material objects have the same velocity, but one has twice the mass of the other, the one has twice the momentum and twice the kinetic energy of the other object. This can be explained ontologically on the assumption that the particle’s motion is due to quantum kinetic cycles, but it will require us to take into account the relationship between the quantum cycles making up the rest mass and the quantum cycle constituting its motion.
We are assuming that the rest mass of a particle is proportional to the frequency of the quantum cycles constituting its rest mass. In an object with twice the rest mass, there are twice as many quantum rest mass cycles per second. Though rest mass and kinetic energy are both a series of cycles of quantum events, and though the total matter is equal to the total of both kinds of quantum cycles per second, they are different forms of matter and each has an existence that is distinct from the other. But in order to explain the role of rest mass in determining momentum, we must assume that the quantum rest mass cycles determine a scaling factor for quantum kinetic cycles. For example, when two material objects have the same velocity, but one has twice as many quantum rest mass cycles as the other, the one must have quantum kinetic cycles whose wavelengths and periods that are half the other object.
This scaling factor would explain why the momentum and kinetic energy of particles is proportional to the rest mass. But it is only a scaling factor for the quantum kinetic cycles required to move the object across space. The period of its rest mass cycles are not changed by the motion of the particle with rest mass. Quantum kinetic cycles are additional quantum events whose size depends on how many rest mass cycles occur during each unit of time as well as how far the object is moved during each unit of time.
Inertial mass. This is only a first approximation to the
explanation of how the size of the quantum kinetic cycles depend on mass as
well as velocity, because kinetic energy is an additional quantity of matter
that coincides with the object with rest mass and that kinetic matter must
itself be moved along with the object with rest mass. Thus, since the total
number of quantum cycles per second that is being moved along by the kinetic
matter includes both the quantum rest mass cycles and the quantum kinetic
cycles of the objects, the scaling factor for quantum kinetic cycles must
depend not only on the total rest mass cycles but also on the total quantum
kinetic cycles. Let us call that combined total quantum cycles the “inertial
mass” of the material object, to distinguish it from the rest mass. And let
as refine our ontological explanation of momentum and kinetic energy to make
them proportional to the inertial mass of the material object, rather than
its rest mass.
The rate for the conversion of matter between mass and energy is given by Einstein’s formula, E = mc2, and the simplest explanation is that it describes the rate at which additional quantum kinetic cycle contribute to the scaling factor. That fixes the number of quantum rest mass cycles for each unit of mass and constrains the explanation of rest mass by quantum cycles.
[However, the relationship may be more complex. It is possible that the quantum rest mass cycles constituting particles have a special nature (presumably because of how they depend on weakons and neutrinos and the unique structures that result), and each quantum rest mass cycle contribute more to total mass than a single quantum kinetic cycles. Let us proceed, however, on the simple assumption.]
[There is, however, no reason to doubt that the quantum kinetic cycles are simply added to the quantum rest mass cycles in determining the total mass (or energy, if you will) of the object. To be sure, the Einsteinian formula, E2 = p2c2 + mo2c4, suggests that the contributions of rest mass ( mo2c4) and the object’s motion (p2c2) to the total energy (E2) is more like orthogonal components of total energy as a vector sum. But this formula represents the object’s motion in terms of its momentum, that is, its spatial aspect, not its total energy. Energy is the temporal aspect of the quantum cycle, and both kinds of energy are included in this total. Furthermore, this equation merely describes the dynamic invariant that holds among inertial frames corresponding to the kinematic separation s (where s2 = c2t2 – x2, and the parallel is mo2c4 = E2 - p2c2). But on the spatiomaterialist explanation of special theory of relativity, the tradeoff between total energy and momentum (in the temporal and spatial dimensions) that makes inertial frames equivalent in this way is just an appearance. Not only rest mass, but also the total energy and momentum have absolute values, though they cannot be determined empirically, that is, measured.]
This ontological explanation of inertial mass would account for the Lorentz distortion in the masses of material objects with a high velocity relative to the ether, or what is called the “relativistic mass increase” (which was promised in Change: Special theory of relativity). The reason that inertial mass increases with velocity is that the total mass of the material object includes both its rest mass (the quantum cycles constituting its mass when it is at rest relative to the inherent motion) and the mass of its kinetic energy (the quantum kinetic cycles that give the object a velocity relative to the inherent motion).
Thus, not only is more energy required to accelerate a material
object by a fixed amount at higher velocities relative to the ether because
of the laws of classical physics (with higher velocity the force has to be
applied over a longer distance in the same period of time to increase its
velocity the same way), but more energy is required to accelerate a material
objects by a fixed amount at very high velocities because of the relativistic
mass increase entailed by Einstein’s special theory of relativity (with very
high velocities, the mass of the kinetic energy that must be accelerated along
with its rest mass becomes significant). As the material object approaches
the velocity of light, the mass of the kinetic energy matter (and, thus, the
inertial mass) becomes infinite.
Interference phenomenon. Finally, this explanation of
kinetic energy as a form of quantum matter affords an explanation of interference
phenomena (and diffraction) with material objects, that is, the phenomenon
that most clearly demonstrates the wave-like nature of particles.
In order for quantum kinetic cycles to explain the wave-like nature of moving material objects, we must take into account the role of the inherent motion. Quantum kinetic cycles move objects with inertial mass relative to the inherent motion in space, but they are usually much slower than the motion that sweeps each point both ways in every direction. Let us assume, therefore, that as that motion sweeps through a material object in any direction, it picks up the wavelength of its quantum kinetic cycle and lays out, in the space beyond it, waves with the same wavelength (until it runs into another object). Since the wavelength varies inversely with the product of the inertial mass and velocity, the waves laid out in space by the inherent motion, in effect, broadcast information about the particle’s momentum and phase of its quantum kinetic cycle in every direction in the ether. (Since the inherent motion flows in all directions, waves are laid out in all directions indicating its momentum in each direction, including those opposite to the direction of the particle itself.)
In order to explain how the inherent motion picks up the wavelength of the quantum kinetic cycle, we must assume that it interacts with the quantum kinetic cycle as a whole. It is as if the inherent motion timed how long it took to pass through the whole kinetic cycle and laid down a mark in space each time the same period had passed again. But notice that this period is not the period of the quantum kinetic cycle itself. The material object takes much longer to cross the distance covered in a single quantum kinetic cycle than the motion inherent in space, and thus, the inherent motion will take many trips across the distance covered by each quantum kinetic cycle before it is succeeded by another quantum kinetic cycle. This effect on the inherent motion would not be possible, if the kinetic cycle did not have a quantum nature, existing as a whole or not at all, for it must interact with both ends of the path across which the material object is being moved during each cycle. In other words, the kinetic energy, which is inversely proportional to the period of the quantum kinetic cycle, is not broadcast to other regions of space by the motion inherent in space. Only the momentum is. And that is fitting, since momentum is the spatial aspect of quantum kinetic cycles, whereas energy is the temporal aspect.
In order to explain the interference phenomenon exhibited by objects with inertial mass in the two-slit experiment, we must recognize that the inherent motion sweeping through a material object in each direction, picking up the wavelength of its quantum kinetic cycle, is part of a wave front. When particles with a certain velocity are moving toward the barrier with two, closely spaced slits, some particles pass through, and their collisions with the wall lying beyond the barrier indicates that the two pathways are interfering with one another like waves. The particles collide with the distant wall only along certain fringes, and not between them. This would be just what is expected, if we assume that the particle tends to move along the path of waves that have been laid out by the inherent motion. The wave fronts broadcast by the particle are intercepted by the barrier except for the two slits. The inherent motion stops laying out wavelengths in space where it is intercepted by the barrier, but it continues laying them out where it flows through the slits. Thus, on the other side of the barrier, there are two wave fronts laying out the same wavelengths, one emanating from each slit, and they interfere with one another like light waves. Assuming that the particle tends to fall in step with the waves that have always already been laid out in the space between the barrier and the distance wall, therefore, its path is diverted away from paths on which the wave fronts interfere destructively toward those paths on which the wave fronts interfere constructively. That is, the particle always tends to be where its wave front is strongest.
If we use the crude picture of quantum cycles as having a definite starting point and ending point, we can think of the particle as being subjected to a force at the completion of each quantum kinetic cycle, if it finds itself in a position where the waves being laid out from the two slit are interfering destructively, which changes its direction slightly. But when it ends a quantum kinetic cycle where the waves from the two slits interfere constructively, it simply goes with the flow. Thus, the effect is to channel the particle along a certain path way. The actual path will vary from particle to particle with the same momentum depending on the direction its emerges from the slit it passes through, and so it results in a fringe of more and less likely points of interception by the distant wall.
In other words, in both photons and material objects, the cause
of interference phenomena is the inherent motion. In the case of photons,
the inherent motion carrying the relevant wavelength goes through both slits
setting up a pattern of spacetime cells where they interfere constructively,
and the direction of the photon is diverted slightly in those regions. It
is the same in the case of particles with inertial mass, except that the relevant
wavelength is due to the quantum kinetic cycles of the particle. In both cases,
therefore, the interference phenomena also occurs when particles (photons
or objects with rest mass) are sent through the slits one at a time. It depends
on the geometry of the inherent motion moving in certain directions laying
out a waves of a certain length in space. And in both cases, if one of the
slits is blocked — or even if an apparatus is set up that can detect which
slit a particle goes through — the interference effects disappear.
Schrödinger’s equation.
The quantitative adequacy of the wave pattern laid out by the inherent
motion to explain interference and similar quantum phenomena has already been
demonstrated, in effect, by David Bohm (1993), for this role of the inherent
motion is an ontological explanation of what he calls the “quantum potential.”
What happens in these experiments on particles with rest mass
can be described by the Schrödinger wavefunction, and Bohm shows mathematically
how such a wavefunction can be divided into a part that is due to the causally
relevant factors described by classical physics and another part which he
calls the “quantum potential.” The quantum potential is a rather strange force,
because unlike classical forces, its strength does not decline with distance.
The quantum force can be quite strong, but its casual role does not come from
its strength, but rather from its spatial structure. Bohm describes the quantum
potential as “active information,” for he assumes that the particle moves
with its own energy and momentum, while the quantum potential merely informs it about how to do so in detail.
The particle has a definite position and momentum at each moment, but its
classically determined path is affected by the quantum potential that exists
along with it. The Schrödinger wavefunction holds for all particles with the
same momentum in the two-slit experiment, but the effect of the quantum potential
on any particular particle cannot be predicted, because it depends on a so-called
“hidden variable”.
The quantum potential is the key to Bohm’s explanation of how the Schrödinger wavefunction can be understood as referring to a fully deterministic process, and this ontological explanation of interference phenomena is an example of how spatiomaterialism would interpret what Bohm means by the quantum potential. The quantum potential describes the waves laid out in space by the inherent motion for any relevant wavelength of kinetic quantum cycles or photons. The effect of the waves laid out by the inherent motion makes the quantum potential look like “active information” (or a “pilot wave,” as de Broglie called it), because the particle follows the nearest path to its classically determined path in which the waves coming from various directions reinforce, avoiding those in which they cancel out. But to explain the quantum potential by the inherent motion is to disagree with Bohm on one point, for he holds that the quantum potential is simply a manifestation of a “nonlocality” about what happens that simply exists in the quantum system and does not depend on anything traveling across space over time. But on this ontological theory, it is due to the inherent motion.
Furthermore, the inherent motion explanation of the quantum potential makes it possible to hold that the hidden variable, which determines how any particular particle is affected by the quantum potential described by the wavefunction, is the particular phase of its quantum kinetic cycle. That is, any particular particle has a definite position and momentum at the beginning and end of its quantum kinetic cycle, and the Schrödinger wavefunction describes precisely what happens to it as a result of the quantum potential. But it is not possible to measure which phase any particular particle has, and since that wavefunction also describes what happens to all other possible particles with the same momentum (the complex numbers enable it to take all the different possible phases into account), the outcome can be predicted only probabilistically.
