Expanding Spacetime Theory

A Few Philosophical Comments

Here are a few reflections of a more philosophical nature. These musings were written at various times and I may reiterate some points. However, I have elected to leave them as originally put down and apologize for any overlap. It is my belief that the EST theory cannot be fully grasped and digested without a deeper appreciation of how it answers old riddles and revises our world-view. The teachings of modern science are like the polished veneer of an impressive structure whose foundation lies hidden in the contrails of history. We have to return to this foundation and start over by again asking ancient but fundamental questions hoping that today we are in a better position to answer them.

An ancient but fundamental riddle.

The celebrated paradox by Parmenides poses the following riddle:

Only being is - non-being is not. But, if only being is, there can be nothing outside this being that articulates it or could bring about change. Hence being must be conceived as eternal, uniform and unlimited in space and time. The changes we experience must thus only be illusion. - Parmenides.

We read these lines with a sense of awed respect for the deep perceptiveness reaching us from millenniums past. Have we in these hectic modern times forgotten to ask important fundamental questions, questions critical to our understanding of the world? As Einstein said:

“The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.”

Parmenides' riddle poses a challenge to any cosmological model. The Big Bang (BB) theory tries to circumvent the problem posed by the riddle by ascribing the changes we perceive as the progression of time to the expanding space. It creates an evolutionary history of the universe starting with an instant of creation ending either in the Heat Death or the Big Crunch. However, it does not address the first statement of the riddle: only being is - non-being is not. If non-being is not, how can being ever arise out of non-being? How can existence emerge from non-existence? Recently this question has motivated further, somewhat strained, speculation suggesting that our universe is an outgrowth of some pre-existing spacetime, a “baby universe” spawned from a “mother universe” suggesting eternal existence of many “universes”. However, this does not agree with the conception of the Universe as being all there is. The conclusion of the riddle that the progression of time is an illusion is seemingly confirmed by general relativity, which has no provision for modeling the progression of time. This is why Einstein agreed with Parmenides in thinking that what we perceive as the flow of time must be an illusion. Obviously something important is missing in our understanding of the world.

The EST theory offers a possible resolution to the riddle by suggesting that the unknown mysterious agent “outside” the universe that controls the progression of time is the cosmological scale. The expanding scale acts as a fifth dimension that ticks away the progression of time beyond the four spacetime dimensions. With this Parmenides paradox is resolved. Being could be eternal, unlimited in both space and time. There is no non-being; the problem with the paradox lies in the second statement. There actually exists something outside space and time that articulates change; it is the expanding scale. The four-dimensional universe never changes, but yet it is forever evolving. The only motion known to have this feature is circular, motion. Thus, the agent of change in the universe is cyclic motion in the form of vibrations of spacetime caused by the scale expansion. These vibrations create the sub-microscopic world of quantum mechanics and also generate the missing dark matter vacuum energy.

A basic idea of Greek philosophy is the assumption that everything in Nature is made from some fundamental substance. Thales of Miletos stated: “Water is the material first principle of all things”. The EST theory suggests that spacetime is the first principle of all things. Vibrations in spacetime can generate energy in the form of atomic particles. Varying the phase of these spacetime vibrations with spatial and temporal location can generate electromagnetic fields. It appears that everything could be made from vibrating spacetime. This is why wave mechanics so successfully model the sub-microscopic world.

Plato taught that the highest principle of the world is the Ideal consisting of ideal forms and ideas and that what we perceive through our senses merely are like shadows on the wall of a cave. The blinding light outside the dark world-cave in which we live conceals the true, beautiful workings behind our existence. Many modern physicists tend to agree with Plato's view of the world - the working of Nature seems to reflect a sublime intelligence often only describable in mathematical terms. One cannot help wondering why the world is such that its material features and dynamic processes most easily are described by mathematics. The EST theory provides a clue to this mystery by proposing that everything that exists is formed as part of the cosmological resonating, vibrating, ever changing, scale of spacetime. Spacetime is filled by vibrations at extremely high frequencies carrying out a complicated dance that sustains everything there is including our own existence. A modern electronic computer consists of electronic circuits carrying information coded in oscillating signals. Spacetime might be such a machine, or rather organism, of unthinkable processing speed with vibrations at frequencies exceeding a billion, billion, cycles per second. The shapes and intermingling of these oscillations carry the information that sustains the existence of particles and of all matter. Spacetime vibrations are present everywhere and in everything. One might perhaps wonder if we humans actually directly sense the presence of this energy field as the progression of time.

Conformal scale invariance and the mystery of time.

Conformal means “same form” or “same shape” and “invariance” as used in physics means the preservation of some physically observable characteristic. The most well known conformal relationship is scale invariance, which relates systems of different scale. But we know that a three dimensional scale models do not exhibit conformal invariance since the laws of physics do not scale with the dimension. However, if we also include time as a forth dimension we get conformal invariance - the universe looks and behaves the same in all respects if all four dimensions of spacetime were to change.

That this might be true may be realized from the following general argument. Consider the task of creating something, for example an apple, in a total void of emptiness with no external references, i. e. in nothingness. Without any references at all any size would do - we could make the apple the size of a pea or of a melon or even the Earth and scale everything else in relation to the scale chosen for the apple. If this were not true there must be something in the total void of nothingness that pre-determines the scale of things, but this would contradict the assumption that the void is empty. Therefore, a world created without references must be conformally scale invariant.

Scale invariance may also be deduced from general relativity. If the scale is changed so that the metrics in the line element of general relativity change by some constant factor, all the equations of general relativity remain the same. This means that the laws of physics as well as the form (geometry) of everything remain the same, which implies conformal invariance. Realizing that the universe is scale invariant we might ask what happens if the scale were to change with time. Exploring this possibility directly leads to the Expanding Spacetime theory by which the progression of time results from cosmological scale expansion.

What we call “time” actually has two different aspects and most of the confusion regarding the concept of time might be caused by not clearly differentiating these two aspects. The first is the progression of time, which we all feel is something very real that separates the past from the present. The expanding scale of spacetime, a “fifth dimension” beyond the four dimensions of spacetime. The second aspect of time is the fourth dimension of spacetime modeled by general (and special) relativity. According to general relativity the geometry for the four dimensions of spacetime determine the laws of physics, which govern the motion of particles in for example a gravitational field. By comparing records of the position of a particle in space (three coordinate dimensions) as a function of time (one dimension) with the predictions of general relativity we conclude that this theory accurately describes what actually happens, or rather happened, when a particle moved in a certain force field. The four dimensions of spacetime described by general relativity refer to a record of the past and can be used to predict the future with some certainty. Together with the three spatial dimensions it models the geometric relationships between space and time via the line element of general relativity but does not give any clue to the progression of time.

These two aspects of time are closely connected but they are not the same and the coupling between them generates new physical effects. One way of seeing this is to consider the scale expansion to be the primary agent of change ticking away in discrete steps. Although the scale of spacetime increases in a stepwise manner for an inhabitant of the universe the spacetime geometry appears to remain the same because of scale invariance. At each step the universe is reproduced, or updated, at a slightly larger scale. All changes associated with the progression of time including all motion might be implemented in a stepwise fashion. In this way the progression of time updates the four-dimensional spacetime of general relativity at very high frequencies. An observer, who expands together with the universe, experiences this process as continuously changing motion of objects in space. But, in reality everything that exists is made from wave-like modulations in the metrics of spacetime like the waves and ripples on the surface of an ocean. Although the universe globally remains the same the observer sees time going by in the changing wave patterns.

Parmenides and Einstein both concluded that time does not progress. This is actually true if we are referring to the line element of general relativity. Spacetime modeled by general relativity is (possibly) infinite space extending in all directions and time going back to the “beginning” about fourteen billion years ago as measured by the current pace of time. This time is being updated by the progression of time, which increases the length of the second. From the point of view of an observer in the EST universe, time does not progress since the beginning of the universe always lies about fourteen billion years back in time. Thus, if the universe is modeled by a four-dimensional spacetime of general relativity with a constant temporal metric, time does not progress. Instead the expanding scale effects the progression of time.

Standing at the stern of a ship looking back across the ocean we notice the motion of the ship from the water going by. The distance to the horizon is always the same, but the shape of the passing water continually changes. In the same way the distance back to the “beginning” of the universe always remains the same but our environment changes all the time. At each step of time-one a new “slice” of spacetime comes into view and the earlier slices are pushed back in time. General relativity describes a fixed spacetime “arena” that all the time is being incrementally updated by the expanding scale.

This also resolves another difficulty: in relativity space cannot be separated from time. What is “time” to one observer is to other observers a combination of both time and space. Different coordinate representations (i.e. line elements) of the same spacetime in general relativity interpret the time coordinate differently. This makes it difficult to understand the progression of time. We might ask to which observer time progresses. However, the metrics for different coordinate representations of general relativity are related via linear (tensor) transformations, which means that (constant) scale increments influence different coordinate metrics exactly the same. Stepwise scale transformations are covariant and four-dimensional spacetime is gauge invariant with scale as the gauge. The progression of time can then be modeled as a sequence of scale increments, which are the same for all representations. The frequency of these increments could be determined based on the fundamental increment ds, which also is the same for all observers. This explains the progression of time as something that is real and affects everyone in a well-defined way regardless of relative motion or choice of coordinates. It also suggests that Nature might be using two related fundamental invariants rather than one, the increment ds of general relativity plus the invariant scale increment that in the EST theory implements the progression of time.

This also sheds some light on the “geometrodynamical” approach of modeling the dynamic evolution of the universe. The idea here is to consider the metrical topology of the three-dimensional space as a field to be quantized much like the electromagnetic field and from this to derive an equation corresponding the Schrödinger equation with wave function solutions modeling the quantum states of the universe. This leads to the so-called Wheeler-DeWitt equation, the solution of which implies that the Hamiltonian that models the energy of the universe must equal zero at all times. Thus, the solution implies that the energy cannot change with time and since energy and the progression of time are closely related, that time does not progress in the universe. Of course, this does not make much sense. The problem with this line of reasoning is the assumption that we can divide spacetime into space and time and then model the evolution of space as a function of time. This idea obviously flies in the face of general relativity, which considers the spacetime manifold indivisible. Again, we might ask whose time we are dealing with since different observers have different time coordinates. It is easy to see this glaring shortcoming. The geometrodynamical approach might be viewed as a valiant attempt to model the progression of time in general relativity, which actually cannot model it.

In the EST universe evolution is not three-dimensional but four-dimensional with the expanding scale ticking off the progression of time as a fifth dimension. This permits us covariantly to model the evolution of the four-dimensional spacetime as a function of the scale regardless of reference frame. With scale expansion it is no longer surprising that the net energy of the universe always is and always will remain equal to zero. On a large scale the geometrical structure of the four-dimensional spacetime never changes, it remains the same regardless of epoch. In this sense the universe does change with time, it does not age. This explains why the Hamiltonian always remains equal to zero.

The universe has succeeded with a beautifully elegant trick. It is eternally evolving yet forever remaining the same.

There is an interesting commentary on the nature of the Big Bang expansion at:

Zeno's paradox and quantum mechanics.

The Greek scientist-philosopher Zeno challenged the continuity of space and time with his famous paradox:

An arrow flying toward its target must pass the midpoint after traveling half the distance. Then it has to pass the midpoint of the remaining part where a quarter of the distance remains. After this, it passes the then remaining midpoint where one eight of the distance is left and so on. It has to pass an infinite number of midpoint locations before hitting the target and do this in a very short time. According to the ancient Greeks this is impossible. (However, we now know that the sum of an infinite geometric series of ever shortening time intervals is finite.)

In the EST theory the question of the divisibility of time returns in a different form. If the pace of time accelerates so that each second is a fraction longer than the previous second, how can this situation be expressed by the four-dimensional spacetime? In short, how can we model time that accelerates relative to itself? This question is resolved by implementing the slowing progression of time as part of a scale expansion of both space and time. To an observer that expands with spacetime it would on the average appear that the pace of time does not change since all references also change. If the velocity of light is constant, all measured distances remain the same measured by timing a light beam. This suggests that the scale expansion would be unobservable. However, since we are dealing with a temporal acceleration, there are inertial effects. This is not surprising. Consider light beamed from an accelerating spaceship back to its launch pad. Since the spaceship accelerates and is gaining speed the light becomes progressively more and more redshifted over time. Thus, acceleration in space causes a redshift that increases with time and distance. The expanding scale in the EST theory implies time acceleration, which has a similar effect in that it is redshifting light from distant galaxies.

But, we are still left with the question how time can expand relative to itself. This problem might be resolved if time were to progress in discrete two-step cycles. In the first step of the cycle the spatial scale expands slightly, which at least in principle might be noticed as a slight increase of all spatial distances. In the second step the pace of (proper) time slows down, which would have the effect of restoring all measured distances. In the second step an observer “jumps into” the new, expanded, scale. To an observer participating in this stepwise expansion if would appear as if the scale of everything oscillates yet remains the same on the average.

Using general relativity it is fairly straightforward to show that an oscillating scale would explain the quantum world. Thus, the discrete scale expansion mode gives raise to the discrete nature of quantum mechanics. This provides the missing link between general relativity and quantum mechanics and explains the nature of the wave function. With this interpretation the solutions to the Schrödinger equation are not abstract mathematical functions expressing probabilities but are modulations of the metrics of spacetime. If the metrics oscillate the wave function solutions to the Schrödinger equation become low amplitude, low frequency modulations of very high frequency “carrier” oscillations in the metrics of spacetime that carry the rest mass energy of particles. A particle consisting of a spatially confined oscillation of the metrics of spacetime at the Compton frequency will by special relativity generate the de Broglie matter wave as a relativistic effect when it moves. The geodesic of general relativity is identical to the de Broglie/Bohm momentum relation and this can be used to show that the wave functions also might be interpreted as probability functions. Thus, if the scale of spacetime oscillates, the commonly accepted probabilistic interpretation of the quantum mechanical wave function is a secondary property resulting from the oscillating spacetime metrics.

Einstein's doubt on the completeness of general relativity.

Few know that Einstein was well aware that general relativity cannot be a complete description of the world. In the following passage (1959, “Reply to Criticism”, in Schilpp (editor) Albert Einstein Philosopher and Scientist) Einstein's expressed his life-long doubt regarding the interpretation of general relativity, in particular the crucial connection between elements of the theory and physical reality:

For the construction of the present theory of relativity the following is essential:

  1. Physical things are described by continuous functions, field-variables of four coordinates. As long as the topological connection is preserved, these latter can be freely chosen.
  2. The field variables are tensor components, among the tensors is a symmetrical tensor gik for the description of the gravitational field.
  3. There are physical objects, which (in the macroscopic field) measure the invariant ds.

If 1 and 2 are accepted, 3 is plausible, but not necessary. The construction of a mathematical theory rests exclusively upon 1 and 2. A complete theory of physics as a totality, in accordance with 1 and 2 does not yet exist. If it did exist, there would be no room for the supposition 3. For the objects used as tools for measurement do not lead an independent existence alongside of the objects implicated by the field equations.
- Albert Einstein

One must admire Einstein's honesty and integrity. Not many would willingly point out a weakness in their own masterpiece. But, for Einstein Science was more important than personal ego.

In the last sentence he points out that for a theory to be complete its connection with the material world must implicitly be defined by the theory. General relativity theory can be developed from the first two conditions, but to connect it to reality the invariance ds has to be introduced empirically in terms of some physically measurable quantity. Einstein was keenly aware that the four-dimensional spacetime of general relativity does not specify the relationship between the increment ds and absolute measurable quantities and therefore that general relativity might be an incomplete description of the world. For example, how can we know whether a certain coordinate system believed to be “at rest” is not falling in a uniform gravitational field (or is “accelerated in time” as in the EST theory)? This observation reflects his recurring uneasiness when faced with the physical definition of the fundamental increment ds. General relativity does not specify ds; it is a relative concept that must be re-defined from application to application. Einstein's sensitivity to the question of calibrating the spacetime metrics is also evidenced by his objection to Schwarzschild's exterior solution. He questioned the assumption that spacetime is Minkowskian infinitely removed from matter, arguing that without matter or energy the metrics are undefined rather than determined with some specific values.

The fact that general relativity does not uniquely specify the increment ds might be illustrated by considering the line element:

ds2 = C gij dxidxj

This line element yields identical equations regardless of the constant C; i. e. general relativity implicitly does not define the lengths of “rigid measuring rods” and cannot be used to define any absolute scale of particles and material objects. Thus, general relativity is underdetermined, leaving open at least one fundamental degree of freedom, the scale factor C, which in the EST theory models the progression of time.

It is noteworthy that the reason for Einstein's uneasiness with assigning any meaning to the metrics of spacetime in the absence of matter and energy disappears in the EST universe, which in the absence of matter and radiation still contains spacetime energy in the form of a non-zero energy-momentum tensor. This energy-momentum tensor defines (the group of equivalent) metrics and conversely the metrics define the energy-momentum tensor evaluated in the cosmological reference frame. This cosmological reference frame of the EST theory is induced by cosmic drag implied by the geodesic of freely moving bodies. Although the EST reference frame coincides with Mach's stellar reference frame they are not equivalent since the EST frame is generated by cosmic drag via a feedback mechanism. On the other hand, Mach's reference frame is defined by the presumed stationary positions of distant stars and galaxies in the universe. However, this reasoning is circular in the absence of any physical mechanism decreasing relative motion.

The question of a cosmic reference frame has been heatedly debated over centuries; its possible resolution provides strong philosophical support for the EST theory. However, since relative velocities of all inertially moving bodies decrease over time, the price paid for the existence of a cosmic reference frame is the invalidation of Newton's first law of motion. After all, Aristotle might have been right in believing that the (relative) velocities of freely moving bodies decrease over time.

Newton's first law and the question of a cosmological rest frame.

According to Newton's first law of motion, perhaps originally proposed by Galileo, a freely moving body without external forces will continue to move forever at constant velocity in a straight line. Although modified by general relativity, by which the motion might be affected by the curvature of spacetime (the geodesic), this principle has been a cornerstone of the theory of motion for over three centuries. But, on a cosmological scale it seems that Newton's first law should be questioned since observations suggests that not all relative velocities are equally likely. Rather, observations show that the relative velocities between galaxies are quite low, less than one percent of the speed of light. This is an unexplainable surprise since computer simulations show that if galaxy clusters were formed by gravitational contraction in the expanding Big Bang universe, relative velocities would be much greater than what they actually are. Also, there is no explanation to the loss of angular momentum, which must take place during the formation of spiral galaxies from contracting gas accumulations.

These mysteries are explained by the EST theory, which predicts a new force of Nature - cosmic drag. Cosmic drag gradually slows down relative motions of freely moving bodies and reduces relative angular momenta. It explains the low relative galaxy velocities and their loss of angular momentum. In addition, it explains the hitherto unexplainable spiral form of galaxies and why newer stars are found in the outer regions of galaxies while older stars typically are found closer to the center. Cosmic drag also predicts that the planets in our solar system slowly spiral toward the Sun with increasing angular velocity. This angular acceleration has recently been detected by direct observation of the planetary motions as reported at the meeting of the International Astronomic Union, 2000 (Kolesnik, 2000). Cosmic drag also defines a cosmological reference frame toward which all motion converges. The existence of such a reference frame explains how the phenomenon of inertia is possible, something that could not be explained by Isaac Newton and forced him to postulate the existence of an absolute reference frame.

Dark Matter, the Cosmological Constant and the accelerating universe.

The now popular Inflation version of the Big Bang theory implies that spacetime must be flat, which in turns means that the mass density on the average should equal the so called Critical Density originally derived by Einstein. However, the actual mass density estimated from observations merely is a small fraction of the Critical Density. It appears that a lot of energy “is missing”. This is the mysterious Dark Energy.

In the EST universe there are two canceling energy densities, a cosmological constant generated by the spatial expansion and a cosmological pressure generated by the temporal expansion. The part of this combined energy that in the Big Bang universe would correspond to actual mass density (the T00 component) exactly matches the Critical Density. In this way the EST theory implicitly includes both Dark Energy and a cosmological constant.

Recently there has been some talk about an accelerating cosmological expansion. Two groups have made observations of supernovae Ia explosions and based on these observations they have concluded that the cosmological expansion seems to accelerate. However, there is another possibility. If the redshift effect were to be tired light, as implied buy the EST theory, the supernova observations would agree perfectly with the predictions. The cosmological acceleration simply disappears. It is only in the Big Bang model that these observations are interpreted as acceleration.

Here we have another example how a questionable cosmological model leads to strange interpretations that are explained by inventing new mysterious properties of the universe.

A long list of unexplainable implications of the Big Bang theory have accumulated over the years, for example:

Thus, many contra-indications to the Big Bang scenario have accumulated over more than half a century since the theory began to gain popularity. However, researchers typically concentrate on one particular aspect at a time, for example the recent supernova Ia observations, trying to find some explanation for their particular set of observations while discarding several conflicting interpretations suggested by other observational programs. As a result we now have a view of a world occupied by strange things, for example, Quantum Creation, Baby universes, Inflationary expansion, Dark Matter, Dark Energy, invisible Galactic Halos, smaller but more numerous galaxies in the past, and now most recently, Cosmological Acceleration. But, this is not new in the history of humanity. Unexplainable phenomena always have been explained by mythical figures, like gods, elves and trolls. Today we don't believe in elves and trolls. Instead we believe in equally strange entities disguised by modern physics. The reason for these human inventions is the same - we don't yet understand the universe and can only explain the world based on what we know, while inventing whatever we need to fill the knowledge gap.

The importance of group theory in modern physics.

In modern physics, particularly in string theory, mathematical group invariance plays a central role. A mathematical group is a number of entities (members of the group) that are related via particular transformations. If a member of the group is subjected to transformation it will change but always in such a way so that it still remains within the group. Thus, the group transformations or operations define the group. An example is the operation “translation in space”. In this case the group is very large and consists of all material objects and physical processes. What remains invariant for this group is all laws of physics, i. e. the laws of physics do not change with spatial location. Another example is the group defined by rotations in space. The laws of physics remain the same independent of the direction is space. A third is invariance to translation in time. The laws of physics do not change with time. These examples may seem trivial because they are so self evident, but it can be shown that translation invariance corresponds to preservation of momentum, rotational invariance to the preservation of angular momentum and time invariance to the preservation of energy. These are three fundamental laws of physics. This preservation, or invariance, of some physical quantity or feature under the group transformation that defines the group is often referred to as “group symmetry”. For example, the translation group is symmetric relative to translation in space. In general, if an observable property is preserved there must be some underlying symmetry that causes it.

Group symmetries are closely related to the laws of physics, in fact the modern view is that most laws of physics might be explained in terms of group symmetries. Thus, group symmetries describe regularities that define rules or properties, which become the “laws” of physics. The most important symmetry of all might be the symmetry that exists between spacetimes of different scale. This symmetry preserves the geometry of spacetime, which according to general relativity includes all forms of energy and all laws of physics. Everything that exists, i.e. the whole world, is covered by this universal group. The corresponding transformation, changing the scale, leaves the universe invariant. It should come as no surprise that Nature might make use of this fundamental symmetry to implement the progression of time as proposed by the EST theory.

With each discrete step of the progression of time, spacetime is mapped onto itself in a slightly different configuration. What we perceive as motion could have its ultimate cause in the changing scale of spacetime, which causes changes to take place within the group that constitutes the universe. If this were an eternal process we would expect that all locations in time and space would be symmetric (equivalent). The fundamental importance of group theory now becomes clear. Any change with time taking place via physical processes must necessarily be implemented via group transformation. If this were not the case some transformation would exist that sooner or later would cause a member of the universe to leave the group. This member would simply cease to exist or a new entity outside the group would be created. However, this would imply asymmetry in time. The universe would be physically different after this event. Therefore if the universe is symmetric in time and all epochs equivalent all physical processes must be implemented via group transformations that do not change the basic constituents of the universe. Thus, all change we see when time progresses must be the result of permutation of already existing entities. The progression of time “stirs the pot” without changing its content. This suggests that the nature of matter and of spacetime might be discrete and that discrete fundamental “atoms of spacetime” exists that are subject to never ending permutations.

This line of reasoning also argues against the existence of black holes. Black holes are irreversible processes that change the universe. They are impossible in an eternal universe without the creation of new matter somewhere else. In the EST theory black holes cannot exist since the energy-momentum tensor for vacuum differs from zero. Schwarzschild's external black hole solution only exists if the energy-momentum tensor for vacuum disappears.

The constraints of established epistemology.

Epistemology of science could perhaps be defined as being the documented description of the physical world in scientific terms. It is important to recognize that this description necessarily must use language and conceptions gradually developed during generations. This includes preconceived ideas and observational facts interpreted and presented in a form acceptable to the contemporary science community. New developments typically are first presented in scientific articles and later published in books. By this process a consensus is developed and maintained regarding how the world is to be perceived and described.

One of the most widely used means of describing physical processes is by differential equations, which form the basis for both general relativity and quantum mechanics. Today this mathematical tool is of primary importance. It is interesting to see how things have changed since the days of Newton, who together with Leibniz discovered differential calculus. Newton never used this powerful new tool in his Principia, probably because it was not generally known at the time and therefore not acceptable to his contemporary scientific community. Although Newton must have used calculus to derive many of his results, he presented most of his findings by the ingenious use of classical geometry. Undoubtedly science would not have developed very much without the mathematical machinery independently developed by mathematicians over many centuries.

However, there is a hidden danger here that generally is not appreciated by the people of science. Mathematics and the language used for communicating science implicitly tend to limit the scope of our understanding by constraining us to describe the world by methods that perhaps might be inadequate. For example, the widespread use of differential equations tends to limit us to considering only continuous coordinates. This clearly is a problem since we now know that Nature in the quantum domain is not continuous but discrete. The circumstance that the Schrödinger equation is continuous but still seems to describe the quantum world might be explained if it models resonating spacetime in response to the presence of a particle. However, it does not describe the motion of an individual particle, which very well could be discrete. This explains how a continuous differential equation can model quantum energy states and wave functions, but fails when modeling the detailed motion of particles.

Similarly, general relativity is limited to continuous four-dimensional manifolds and cannot model the discrete nature of the real world. This is the reason for why general relativity and quantum mechanics are incompatible. The discrete world of the quantum domain simply cannot be described by general relativity. Einstein's belief in the continuous spacetime manifold of general relativity might have been the main reason to why he did not discover the connection between general relativity theory and quantum mechanics. By constraining ourselves to continuous differential equations we are shutting the door to a deeper understanding.

How can we overcome this dilemma? Even if we found a new description we would be in the same position as Newton was. We would not be able to use this new tool to describe the world because it has not yet been added to the scientific tool chest and vocabulary. One way of breaking out of this evil circle would be the discovery of some new fundamental and powerful principle of Nature that forces us not only to recognize the limitation of current epistemology but also shows us how to develop a new approach. Of course, at first such a new insight will be rather traumatic, in particular to people who are used to see the world through the spectacles of traditional science. They would resist any new idea that threatens to shake their hard won foundation of knowledge. Unfortunately, the people most likely to resist any dramatically new development are to be found in the teaching profession. They do not want to hear that what they have been teaching over many years, and perhaps also published in books, might be wrong after all. Since many journal editors are in the teaching profession, new revolutionary ideas have a difficult time getting recognition.

In the context of the EST theory, the realization that the universe is scale equivalent and might evolve by expanding its scale, with the implication that the expansion is discrete, is a new fundamental insight that invalidates the use of general relativity when modeling the universe but explains quantum mechanics. This would be a revolutionary development, which the present scientific community might refuse to seriously consider. As one reviewer of my paper on quantum theory puts it, the EST theory is “too far out“ and is to be discarded without any real attempt to understand it.
In a nutshell the problem is this: It is easy to explain the EST theory to a layperson, who immediately understands what is meant by a scale expansion. In fact, to most laypersons the EST theory makes better sense than the Big Bang theory. However, the learned specialist encounters difficulties when trying to reconcile the theory with what he knows. A scientist might discard the theory as being unscientific simply because it cannot be modeled by known science. This is an acute dilemma since cosmological scale expansion intuitively makes sense and cannot be ruled out by known science. However, it cannot be modeled by general relativity. But, the fact that four-dimensional scale expansion cannot be modeled by general relativity does not mean that it is impossible. There must be some other way to model it and when we find an acceptable way of doing this it will erase the gap between quantum mechanics and general relativity leading to a new revised worldview.

The challenge to scientific innovation.

If the EST theory explains so many things why hasn't it been acknowledged by the scientific community? The answer might be that the theory still is very new and perhaps considered “unscientific” since it is based on a new idea, time acceleration, which is difficult to confirm and to model by known science. I don't think anyone really could reject the possibility that the universe might be scale invariant so that no particular scale takes preference, and also that the cosmological scale could change with time. However, there is no provision for modeling such a situation in general relativity. General relativity is based on geometry, which implicitly is a static concept. The line element of general relativity describes a four-dimensional geometry giving no clue to what might cause the progression of time. If the progression of time is related to a changing cosmological scale it is by symmetry natural to assume that all epochs are equivalent. This means that the cosmological expansion must occur in discrete steps in which space expands and the pace of time slows down. This immediately invalidates general relativity.

In the EST theory I model the discrete expansion by piecing together consecutive intervals in general relativity during which spacetime expands interrupted by brief intervals where the pace of (proper) time slows down. Using this model I have derived the various features of the EST model including the tired light redshift and the new cosmic drag phenomenon. The future will tell if my approach is right. So far it seems that this EST model better agrees with observations and it explains many cosmological phenomena. However, since the modeling approach I use yet is unproved it is met by suspicion by the specialists. This cautionary stand is nothing new but is implicit in the scientific process of accumulating knowledge. The main thing to keep in mind is that there must be some way of modeling an expanding cosmological scale with a slowing progression of time.

There are two main directions of scientific activity that both are equally important. I will call them “scouting” and “occupation”. Scouting is usually done by individuals searching for new properties of Nature beyond the realm of the currently known. The new areas that occasionally are discovered by the scouts are eventually, after gaining acceptance, developed and cultivated by the occupation forces of mainstream of science, which handle the orderly merging of new information with known epistemology, in this process creating what we usually mean by Science. People involved with this latter effort typically have radically different personalities than the scouts. They are good at organizing and defining the domain of known science. Occasionally these personality traits are found in the same person, like in Isaac Newton or Albert Einstein, and then the result could be spectacular. The scientific community represents various degrees of attitudes between these basic personalities.

The scouts and the occupants are sometimes cooperating sometimes pulling in different directions. The occupants typically see and evaluate everything from the viewpoint of what is known. They are the experts of book knowledge, the defenders of “good science” concerned with preserving the “right” teaching and defending it from the dark forces of pseudo-science, mysticism and unfounded speculation. Typically these are the editors of prestigious scientific publications who are very concerned not to publish anything that might be considered unscientific. The more prestigious the publication, the more reluctant they are to publish revolutionary new findings. Therefore, new great advances in science usually first appear in more obscure presentations for example in posters shown at scientific meetings, in less known journals, and more recently on the Internet. The further a new idea deviates from the accepted epistemology, the longer it takes for it to reach the mainstream awareness. There are many examples of this. Copernicus' theory, which was published in the same year as his death, was not generally accepted until about seventy-five years after his death. The initial flights of the Wright brothers were completely ignored by the scientific community since its leading spokesmen had stated that heavier than air flight is physically impossible. Newspapers refused to report on the early flights although a passenger train passing the field where the test flights took place now and then stopped on its tracks to let the passengers see for themselves. It was only after presidential intervention that the Wright brothers finally obtained scientific recognition.

Unfortunately, people concerned with keeping science pure and “scientific” often make up their minds in advance on what is to be considered acceptable and what is not. To many of them science consists of the known epistemology presented in an accepted language and everything beyond known science is considered “unscientific”. Of course, this greatly simplifies the task of a journal editor who only has to check if known science and the right language is used in an article submitted for publication. But, unfortunately this could also prevent new and important ideas from being published. Although this indicates a shortcoming in the way new developments in science are communicated it should be made clear that the scientific review process prevents the publication of much nonsense. A reviewer typically is a person who by others is considered to be an expert and also considers her - or himself an expert. It is very tempting for such a person to reject any radically new idea that implicitly challenges the expertise of the reviewer, particularly if this challenge comes from someone unknown. If the innovation is too great, the blinding light outside the cave of known epistemology will become uncomfortable compared to the familiar dim surroundings inside the cave. The review process is a double-edged sword that in clearing the field of science from unwelcome weeds occasionally cuts down its most beautiful flowers.

It is my conviction that there is so much more to this world than what we presently know and can explain by contemporary science. Known science is like a spotlight that merely lights up a very small part of the huge unexplored cave that is our world. Outside this illuminated area dwells the vast unknown and the answers to many questions.

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