Expanding Spacetime Theory

Justifying the EST theory

Three levels of scientific inquiry

There are three levels of scientific inquiry corresponding to deepening levels of understanding.

At the first level the question is: “What?”. What is the nature of a certain phenomena or objects under investigation? How do we recognize and classify them? In the past this was the traditional scientific activity, for example the identification, classification and counting of various species.

At the second level the question becomes “How?” We want to know how certain processes work or how certain species evolved and their relationship to the environment. This is the current level of inquiry in many disciplines where the emphasis is trying to understand the relationship between phenomena rather than just classify and characterize them.

At the deepest level of inquiry the question is: “Why?”. We want to know not just the “hows” of a certain phenomena but why it exists in Nature. Many consider this question to be meta-physical outside the realm of scientific inquiry. But this deeper question has inspired some of the greatest thinkers throughout history. Einstein used to ask himself if the Lord had any options in designing the world or if there are other equally viable possibilities. Although many scientists might not seriously ponder why things are what they are, most are driven by a desire to better understand the world we live in. It is my belief that our inquiry will not end until we will be able to answer the Why question.

The EST theory takes a tiny step in this direction. It is based on a few fundamental principles and if these principles hold true they would explain why the universe looks and behaves the way it does. For example, they would explain what causes the progression of time, how it is implemented by Nature and also give a tentative answer to why time progresses. It also tells us why the quantum mechanical world exists.

Three postulates

The philosophical line of reasoning that leads to the EST theory starts with the proposition that the cosmological scale of material object and dynamic processes is a relative concept and that no absolute scale of things exists in the universe. The scale of material objects (the spatial scale) and the duration of fundamental processes (the temporal scale), for example the period of a spectral line frequency, may only be defined in relation to other objects and processes. This relativity of scale not only makes intuitive sense, since it is difficult to understand why any particular scale should take preference if the universe is all there is, but also is in agreement with theoretical physics, which recognizes scale invariance as a well known example of gauge invariance.

Therefore, I will make universal scale invariance my first postulate:

P1: There is no absolute scale of matter and dynamic processes.

However, in general relativity this gauge invariance seems quite trivial since a different scale may be though of as simply a re-definition of the metrics of spacetime so that different scales merely correspond to different units of measurement. Although this is true if the scale remains constant, the discovery of the cosmological expansion raises the question whether the cosmological scale might change with time. Such an expanding scale would have real physical effects and create a universe with different properties compared to a cosmos with fixed scale. Since general relativity does not distinguish between different scales and since there seem to be no reason why any particular scale should take preference it appears reasonable to assume that if the universe expands by changing the scale both of space and time, different epochs are geometrically and physically equivalent. This reasoning leads to the second postulate:

P2: All spatial and temporal locations are physically equivalent in all respects.

If the scale of both space and time increase we could attempt to model this in GR by a time dependent scale factor, a(t), multiplying all four metrics in the line element. This would model a universe where spacetime expands relative to a fictitious coordinate system with fixed rate of (proper) time as given by the invariant ds. Based on the two postulates above we conclude that the cosmological scale expansion must be exponential with time. In this case different epochs are equivalent because a line element with the scale a(t) is for some constant increment Δt equivalent to one with scale a(t+ Δt). In other words, the line element with scale factor exp(t) is equivalent to the line element with scale factor exp(t+Δt) = constant·exp(t) since spacetimes differing by a constant scale factor are equivalent according to general relativity. Thus, different epochs are physically equivalent. However, this equivalence can only be obtained between spacetimes of differing scales corresponding to some time increment Δt. These two line elements are related via the simple transformation t2= t1+ Δt and therefore strongly equivalent in the sense of Einstein. No continuous variable transformation exists relating different line elements with scale factors exp( t1) and exp(t2). This suggests that the requirement that all epochs are equivalent (covariant) in the sense of Einstein implies that the cosmological expansion must occur in discrete temporal increments. We thus arrive at a third postulate:

P3: The cosmological expansion takes place in discrete temporal increments.

Together these three postulates form the basis for the Expanding Spacetime theory. The third postulate also follows from the impossibility of conceiving a pace of time that accelerates relative to itself. Introducing the expanding cosmological scale as a “fifth dimension” beyond the four dimensions of spacetime in the EST theory circumvents this difficulty.

The search for symmetry is central to modern theories in physics. The word symmetry is here used in a special sense; it denotes invariance under various (group) transformations. For example, the laws of physics are invariant under translations in space and time. An observer in a “galaxy far, far away” in the past or in the future would find the laws that of physics are the same. There also is rotational symmetry; there is no physical difference between different directions in space. But, one symmetry is most fundamental of all - scale invariance. This symmetry preserves everything including the four-dimensional spacetime of general relativity. Since all laws of physics are expressed by general relativity, this symmetry preserves all laws of physics. It preserves the world. We might perhaps call it the mother of all symmetries. Therefore, it should come as no a surprise that the most fundamental property of the universe, the progression of time, is based on this fundamental symmetry.

If we model the cosmological scale expansion by a line element with an exponentially increasing scale factor relative to a fictitious non-expanding coordinate system, how could this be modeled in a coordinate system that expands together with spacetime? For an observer in this expanding spacetime the relationship between the metrics of space and time would always remain the same but there would be additional physical effects due the exponentially accelerating scale. At every instant t= Δt the universe would “look the same” as it did at t=0. One possible way of modeling this mode of expansion is the following iteration:

  1. Spacetime expands from t to t+ Δt by changing the scale factor from exp(t/T) to exp[(t+Δt)/T].
  2. At t+Δt the pace of proper time suddenly slows down by changing the invariant increment ds => ds·exp(Δt/T).
  3. The factor exp(Δt/T) now appears on both sides of the line element and may be eliminated restoring the line element with scale factor exp(t/T) in step 1 above.
  4. The iteration loops back to step 1.

The new and radically different aspect of this cosmological expansion mode is the discrete change of the pace of time in step 2. This takes the EST model beyond GR and established epistemology, which presumes continuous processes. One may well wonder if this radical departure is justified.

The nature of motion

The nature of “motion” has been contemplated for millenniums. How does a moving particle change its position with time? This was an unresolved mystery for the antique Greeks, but since the seventeenth century, with the introduction of differential calculus, we treat motion as a limiting process of infinitely many incremental, diminutive, steps. Since this works excellently when modeling macroscopic motion, the dynamics of moving objects is since the seventeenth century generally treated by solving differential equations assuming a continuous progression of time.

Although with take the validity of continuous motion for granted, upon deeper reflection this idea seems rather strange. In fact, it is difficult if not impossible to think of motion as a continuous process. We always tend to visualize motion as a sequence of small displacements. The difficulty with continuous motion is that it implies that an infinite number of steps must occur in a very short time. The ancient Greeks recognized this puzzle as one of Zeno’s paradoxes. More recently the same problem has reappeared in the context of quantum theory since it appears that the nature of the quantum world is discrete rather than continuous.

The very natural idea of moving by a sequence of consecutive steps might actually be the way Nature implements motion. Continuous motion might never occur in Nature. It is not unlikely that the notion of a continuous physical process is a human idea supported by a mathematical representation, differential calculus, without corresponding physical reality. The nature of the progression of time might very well be discrete, and the modeling of dynamic processes by differential equations might fail in the quantum world.

In addition to this philosophical argument I offer the following comments:

To begin with, the EST model, which is based on a discrete progression of time, better agrees with astronomical observations than the Big Bang model and it resolves several cosmological puzzles. It also predicts a new phenomenon, Cosmic Drag, which explains the spiral form of galaxies and recently might have been verified by direct observations in the solar system.

Second, philosophically there is nothing wrong with the assumption that the scale of the universe might change with time and that all epochs are equivalent. Everyone will easily grasp this cosmological expansion mode. However, such a continuous scale expansion process cannot be modeled (covariantly) by GR and has therefore not been seriously considered in the past. But, we ought to be able to model a cosmological scale that expands with time. The fact that we cannot do this indicates a weakness in available mathematical models rather than a constraint to be imposed on the way the universe works. In short, the fact that we cannot model it does not mean that it cannot be.

Third, quantum mechanics and GR, the two dominant theories of the twentieth century, are incompatible, which shows that something important is missing in our understanding. Either one, or perhaps both, of these theories are incomplete. I believe that GR is incomplete in that it cannot model the quantum world since it excludes the possibility of a discrete evolution of time. It appears that GR could be generalized by including discrete gauge transformations that do not change the energy-momentum tensor. I also believe that our understanding of the quantum world is incomplete, since we have not been able to give a physical explanation to the wave functions.

Fourth, quantum mechanical representation of fields leads to infinities in the calculations. Some of these problems may be handled by ugly ad hoc “normalization” techniques but others remain. We know that this deficiency in the theory must be due to lacking insight into the nature of matter and spacetime. Again, something really important is missing. If the problem were superficial it would have been resolved long ago. Since it still remains it indicates that a problem must exist at some deep level. I believe that the problem lies in the modeling of spacetime as a continuous manifold and motion as a continuous process.

These shortcomings of modern physics clearly show that our current understanding is inadequate and that we must find a way out of the constraints imposed by accepted epistemology. Such a step necessarily must take us outside known science and may therefore initially be considered “unscientific”. Unfortunately, this also means that any attempt made in this direction initially will be rejected by the main body of a scientific establishment who typically defines “science” as being comprised of the already known.

But, soon a new generation will break the constraints of traditional epistemology finding solutions to many currently unresolved problems.

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