Expanding Spacetime Theory

The Expanding Spacetime (EST) Theory - A simple explanation to the cosmological puzzles.

A Synopsis.
C. Johan Masreliez

A new cosmological expansion mode is proposed by which all four metrics of spacetime expand. The considerations leading to this theory are presented below and in the sidebar “Justifying the theory” without mathematics. The more advanced reader might prefer to go directly to the sidebar section with technical papers starting with “The Expanding Spacetime theory”.

A fundamental insight

When we think of the universe, we usually have mind something that contains everything there is. There is nothing “outside” the universe because if there were we could naturally include it into the universe we conceive.

In a self-sufficient universe there can be no absolute scale of material objects since scale is a relative concept. If you reflect on this you will realize that the scale of an object always is given in relation to some other object. But, if the size (scale) of an object only may be defined in relation to some other object, why should any particular scale take preference? Einstein's General Relativity (GR) theory does not recognize an absolute scale of things. It tells us that the universe would look the same and behave the same if all objects including elementary particles were twice as large (or small) provided that the scale of time simultaneously changes so that the duration of a second is twice as long (or short). Therefore, the size of material objects only has relative meaning. No absolute predetermined scale can exist in the universe. If it did something “outside” the universe would have to determine the scale, which is a contradiction since the universe by definition contains everything.

This completely relativistic view of the cosmos follows logically from the assumption that the universe is all there is and that nothing can exist “outside” the cosmos that might determine the scale of things. This fundamental insight is not new but has been expressed from time to time throughout the ages by philosophers and may also be found in Eastern religious teachings. The Eastern religions are based on the idea that everything exists and happens in the universe as the result of a tension, or dynamic exchange, between two opposing yet cooperating entities, for example the Yin and Yang of Taoism. In the West, however, where the idea that God created the world has dominated science and philosophy for many millenniums, a totally relativistic universe is not required or even contemplated since an absolute scale of material things is taken as a God given fact.

The Expanding Spacetime

If there is no absolute scale of things we might ask why the scale is what it is, thereby implicitly assuming that the scale of material objects always has and always will remain the same. However, we now know that the universe appears to expand, which makes it natural to consider the possibility that the cosmological expansion might be and expansion of the scale of everything. If both space and time were to expand simultaneously everything would expand in proportion. Locally such an expansion would be very difficult to detect. However, light reaching us from very distant sources would be affected by the cosmological scale expansion during the time for the light to reach us. It is easy to show that this light would become redshifted. In checking other observed features of the universe we find that it agrees with the Expanding Spacetime (EST), i.e. the EST universe looks and behaves exactly like our universe.

We can use Einstein's relativity theory to predict how the EST universe would appear to an inhabitant. By comparing these predictions with astronomical observations we can test the proposition that the scale of the universe actually is expanding. We find that the EST better agrees with observations than the Big Bang theory. Not only does it provide superior agreement with astronomical observations, but the EST theory also resolves several cosmological puzzles in a very natural way. It provides answers to a number of unresolved enigmas the most significant being the nature of the progression of time and the mystery oaf cosmological inertial reference frame. We know that time goes by but up till now there has been no physical explanation for the progression of time. We also know that an inertial reference frame must exist because of an inertial force resisting acceleration. However what creates this cosmological reference frame has been a mystery.

Spacetime Equivalence

The scale-expanding universe is “spacetime equivalent”, by which we mean that all locations in space and time are physically equivalent. This type of equivalence is also known as “conformal” invariance, which means “same shape” invariance. The universe looks and behaves the same on a large scale regardless of location in space or time. The EST universe does not age; it always remains the same. It is eternal. At first you might object to this seemingly strange proposition and argue that the cosmos sooner or later has to run out of energy. This would certainly be true in an expanding universe with a constant progression of time. But in the EST universe time is slowing down and this has the effect of restoring the energy lost by the spatial expansion. Spacetime equivalence is stronger than “The Perfect Cosmological Principle” since the universe is not sustained by spatial expansion and creation of new matter like in Steady State theories. Spacetime equivalence means that all epochs are physically and geometrically the same; the line element of General Relativity always remains the same. Time progresses without changing the universe at large. How this is possible will be explained below.

A new physical property - time acceleration

What we call energy is closely related to the progression of time. Obviously, without the progression of time there would be no motion and without motion no energy. If you are familiar with special relativity you recognize that temporal “motion”, i.e. the progression of time, is related to the energy as the temporal component of the momentum vector. All energy is ultimately motion and motion depends on the progression of time. If the pace of time were to slow down, all moving objects would appear to pick up speed relatively and their energies seemingly to increase. Thus, a slowing progression of time releases energy throughout the universe. This energy source is eternal since the pace of time can keep slowing down forever by a tiny fraction every year. The induced energy keeps the universe in perpetual motion.

The often referred to age of the universe that is estimated at 14 billion years is the age of the universe measured with the current pace of time. It does not indicate how old (or rather how aged) stars and galaxies really are. Time went faster in the past relative our present pace of time, which means that objects and structures could be aged more than 14 billion years. The aging time has no beginning in the EST. Adding an infinite number of time intervals each interval slightly shorter (by a fraction) than the preceding interval forms a geometric series with a finite sum. Paradoxically the age of the universe is both finite and infinite depending on the measure of time. Based on the present pace of time the age is finite but galaxies can in principle still be infinitely aged. This resolves one of the most difficult problems with the Big Bang theory since we know that certain stars in the Milky Way and that galaxy clusters and filaments are much older than the time since the Big Bang creation.

The EST expansion mode

The EST theory is based on a fundamental symmetry; the universe is “scale equivalent”, i.e. there is no a priori predetermined scale for the spacetime metrics. Observers living in hypothetical universes of different scales would find them identical in all aspects. This also means that the pace of atomic time (the temporal metric) is proportional to the spatial metric regardless of scale. This conclusion, which is based on scale equivalence, also means that atomic time differs from proper time as given by “ds” in the EST line element (except at t=0). People familiar with GR usually objects to this idea since in GR the increment “ds”; is the “proper time” on a geodesic, which is invariant under variable transformations. This idea is central to GR.

However, the EST model is different in that the various epochs are not related via continuous variable transformations and thus GR is not sufficient for modeling the EST. Since continuous variable transformations guarantee equivalence and since all epochs ought to be equivalent it is at first sight disappointing that no continuous variable transformation exists between epochs. But, it is just this feature that explains the progression of time! The failure of GR to model exponential scale expansion where all epochs are equivalent motivated some investigators in the past, for example Weyl and Dirac, to modify general relativity to include this capability using Weyl's geometry. However, if we simply accept that it is impossible to use any continuous variable transformation and instead consider the possibility of discrete variable transformations corresponding to a discrete progression of time we find that all epochs could be strongly equivalent as desired.

The EST expansion mode might then be modeled by the cycle:

  1. A continuous scale expansion going from the scale exp(t/T) to exp((t+Δt)/T).
  2. At t+Δt the factor exp(Δt/T)is eliminated (“thrown away”) since spacetimes of different scales are equivalent. This corresponds to a discrete reduction of the pace of time that changes the proper time increment ds to ds·exp(Δt/T). As a result the pace of atomic time slows down just enough to compensate for the spatial expansion.
  3. The original EST line element reappears with scale exp(t/T). Retuning to step 1 above activates the iteration.

This cycle permits the universe to expand forever without changing the line element, i.e. the spacetime geometry or physics. Of course, the question remains why there is cosmological scale expansion. I don't know the answer to this question. However, if there were no scale expansion there would be any energy in the universe and we would not be here to ask the question. The main purpose here is to investigate whether the EST theory's predictions agree with the observations.

Modeling the progression of time in GR has always been enigmatic since GR deals with spacetime geometry, which is a static concept. Einstein thought that the progression of time merely is an illusion since nothing in GR gives any clue to the progression of time. Although we are used to think of the progression of time as being associated with the motion in four-dimensional spacetime along the time axis, there is nothing in general relativity that tells us what might cause this motion. On the other hand, in the EST model progression of time enters via the discrete scale expansion, which maps the spacetime geometry forward in time in a stepwise manner.

It must be emphasized that the EST line element and GR does not properly model the universe since GR does not handle a discrete progression of time. GR is “blind” to the discrete reduction of the pace of time in step 2 of the expansion cycle since discrete scale transformation does not change the GR equations or the energy-momentum tensor. We should view the EST expansion as a sequence of consecutive very short time intervals where the metrics expand and GR is valid, each interval followed by a discrete reduction in the pace of time. To an observer expanding with the universe it appears as if the metrics oscillate at very high frequencies (the quantum vacuum fluctuations). I have been able to demonstrate that the world of quantum mechanics directly follows from GR if the metrics in the Minkowski line element oscillate, see the paper “A link between General Relativity and Quantum Mechanics” at this web site. As you see the EST theory pushes the envelope of accepted epistemology by extending GR from continuous manifold to a discrete scale expansion via scale equivalence. Invariance under continuous variable transformation is extended to invariance under discrete scale expansion and a continuous pace of time is replaced by a discrete progression of time. This opens up a whole new area of research.

A new world-view

The EST theory offers a completely new view of our world that at first may seem strange because it is so unfamiliar. However, when you get used to it, it will become very natural to you. Imagine how people initially must have felt when Copernicus told them that the Earth was not fixed after all but was orbiting the Sun. The EST theory tells us that the pace of times not fixed but is slowly changing while space is expanding. With this assumption the mysterious creation of the universe simply disappears and is replaced by eternal existence. Although you might feel that an eternal universe is rather strangest certainly is not stranger than the creation of everything from nothing in the Big Bang.

Cosmic Drag

In assessing any new theory like the EST the main practical questions should be:

  1. Does the new theory provide better agreement with observations?
  2. Are there any new predictions that might confirm it?

For the EST theory the answer to both these questions is “yes”. The EST theory's agreement with observations is superior to that of the Big Bang theory and its predictions may be tested directly by observing the motions of stars in a galaxy, the planets in the solar system and signals from space probes.

The EST theory may be “falsified”, i.e. it can be proven wrong, since it predicts a completely new effect - cosmic velocity drag. This is an observable effect. If we cannot confirm it, the theory must be wrong.

According to the EST theory the relative velocities or rotations of all freely moving objects and systems will diminish with a time, decreasing with a time constant equal to the “Hubble time”- the age of the Big Bang universe. Thus the EST theory predicts that the relative velocity between two freely moving objects will decrease by fifty percent in approximately eight billion years.

In addition, objects orbiting a central mass accumulation, for example the planets orbiting the Sun, will move in shallow spiral trajectories rather than in circles or ellipses. These spiral trajectories also explain the shape of spiral galaxies. Stars in the galaxy are freely falling toward the galaxy center following spiral paths. The shape of spiral galaxies is very easy to understand in the EST theory but is a mystery in standard physics that cannot be explained. Simulations based on standard physics show that spiral arms will not form and that the galaxy disc is much thicker than what we observe. On the other hand, according to the EST theory the stars are freely falling toward the center of the galaxy and gravitation pulls them together into arms with narrow cross sections.

According to the EST theory the Earth approaches the Sun by about twenty-five meters per year. Cosmic drag also causes the Earth to accelerate in its orbit by about three arc-seconds of a degree (3/3600 of degree) per century squared. This very tiny angular acceleration has been detected but has in the past been attributed to a slowing rotation of the Earth rather than an accelerating motion of the Earth around the Sun.

If cosmic drag can be verified by observations it will implicitly confirm the EST theory. Using modern technology it is fairly easy to design tests that either will refute or confirm the theory. But since the effect is so small and since people have not been looking for it in the past, cosmic drag has until now gone undetected or not been recognized for what it is. Although discrepancies due to cosmic drag has been noticed, they usually are attributed to a number other possible causes. However, now when we know what to look for we can design tests that will confirm cosmic drag by direct observation. The only thing needed is the will to implement these tests.

Dr. Yuri Kolesnik at the Russian Academy of Sciences has recently collected observations of the inner planets taken during the last 250 years. He has analyzed these observations in relation to the modern extragalactic reference frame and applied modern correction factors. His results suggest planetary acceleration as predicted by the EST theory with excellent agreement with the theory if the Hubble time is about fourteen billion years. These results were presented at the year 2000 International Astronomical Union's meeting.

The EST connection with quantum theory

One very interesting and totally unexpected implication of the EST theory is a possible connection between cosmology and quantum theory via Einstein's General Relativity theory. Einstein was almost alone in his steadfast critique of quantum mechanics believing that the theory of quantum mechanics is incomplete in that something important is missing. Quantum Mechanics (QM) consists of a number of mathematical rules by which we can predict the outcome of interactions between atomic and sub-atomic particles. The theory is like a magical black box with inputs and outputs. You put in a question, pull the math crank, and out comes the answer. Although the answers given by QM usually are right nobody really knows why. Many have tried to figure out what's going on inside the magical box but still there is no good explanation. Others have given up on trying to find an explanation and some even think that an ontological explanation for QM never will be found.

Einstein would have been pleased to learn that not only was he right in his assertion that QM is incomplete but ironically the explanation to the quantum mechanical world might be found in the equations of his own GR theory.

According the EST theory the scale of the universe expands. However, in order to obtain spacetime equivalence GR demands that the pace of time decreases in discrete increments. This is a purely mathematical requirement that formally preserves spacetime equivalence. Intuitively one may understand why the progression of time must be discrete. How can you even conceive continuous acceleration of time relative to itself?

To an observer (you or me) in the expanding universe it will appear that this discrete, stepwise, expansion causes the scale of spacetime to vibrate at very high frequencies. In modeling such high frequency scale oscillations in GR we find that the basic relations of quantum theory directly fall out of the GR equations! It appears that QM might result from oscillating spacetime metrics caused by the cosmological expansion! This explains why the strange quantum world exists at all. It is caused by the cosmological expansion. The vibrating metrics of spacetime influences the motion of particles and is the ultimate cause of QM. The cosmological expansion permeates everything at all levels sustaining the elementary particles and the bubbling spacetime froth that is the quantum world.

According the Special Relativity a moving region of spacetime with oscillating scale will generate a modulation of the metrics just like the de Broglie matter waves. It thus appears that the quantum mechanical wave function is a nothing but modulation of the spacetime metrics. A particle is guided by the resulting spacetime curvature; it moves on a geodesic (the de Broglie/Bohm guiding function) just like the planets are guided by the curving spacetime surrounding the Sun.

Summing up

The EST theory provides straightforward explanations to many up till now unsolvable mysteries. It is based on the fundamental insight that no absolute scale can exist in the universe. The new theory describes a universe that looks and behaves just like the cosmos we observe. The cosmic drag effect predicted by the theory is a new physical phenomenon that soon may be confirmed by direct observations in the solar system. The scale expansion implies that time progresses in discrete increments. This expansion mode might create high frequency oscillations in the metrics of spacetime, which when modeled in General Relativity describe the quantum world. In this way the cosmological expansion becomes the dominant force in the universe that effects everything from the very large cosmological scale down to the quantum scale of atoms. The expansion causes time to progress and is the eternal cosmological energy source. Thus, the cosmological expansion is much more than just an interesting feature of the universe. The scale expansion lies at the very core of our existence. It permeates everything and everybody; it is the progression of time and is the eternal life force.

Learning more about the EST theory

If you found all this interesting you may download my book “The Expanding Spacetime theory”. The book develops the detailed arguments that lead me to the EST theory and compares it to the Big Bang theory. It clearly demonstrates that the EST theory gives a superior description of our universe. You may find my paper published in Astrophysics and Space Science on the sidebar “The Expanding Spacetime theory”:

Masreliez C.J., The Expanding Spacetime Theory,Astroph. & Space Science, 266, Issue 3, p. 399-447 (1999)

Astronomical observations in support of the EST theory are reported in:

Kolesnik, Y.B., Analysis of the secular variations of longitudes of the Sun, Mercury and Venus from optical observations, IAU Proceedings2000.

You may also find this paper on the sidebar together with several more.

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