The Boundary of Space


Reference: Subject: Logic

Here is a summary of some thoughts from Einstein’s essay “Relativity and the Problem of Space“.

  1. Newtonian physics treats space, time and matter to be independent of each other. This brings into question the physical reality of space. Newtonian physics does not offer answer to this question.

  2. The basic concept of space comes from the dimensions suggested by objects. Space is not considered by philosophers to have a physical reality of its own.

  3. We ascribe physical reality to those things that we can experience directly, and extend that reality through consistency of logical association among observations. The scientific thought evolves this way.

  4. Descartes is logical in arguing that space and bodies should be continuous; but the details of logical associations need to be worked out.

  5. Geometrical concepts, such as, straight line, point, surface, do not directly deal with space. Primitive experience of space comes from placing material objects in “empty space”; but it is difficult to think of unbounded space devoid of matter.

  6. The axiomatic structure of three-dimensional Euclidean geometry derives from the way bodies can be packed into space. There is an underlying assumption of bounded space, though it may not be so obvious.

Einstein had combined space and time by assuming a constant wavelength to period ratio (c) of electromagnetic disturbance, but he was still struggling with the problem of matter being looked upon as absolute. He knew that matter could somehow be combined with space.

How does space relate to matter? What is happening at the boundary of space with matter? Is space extension of matter? Euclidean geometry assumes space to be bounded. How is space bounded? What is the relationship of space with its “bounds”? If space has bounds then what is bounding those bounds? This leads to an infinite regression. One may then ask, “Is space itself a bound?”

The Disturbance Theory defines space as the limiting condition of electromagnetic disturbance as its frequency goes to zero. This is an assumption of the same nature as Einstein’s assumption that speed of light is constant.

Thus space acts as the lower bound of electromagnetic disturbance.

At the upper bound of electromagnetic disturbance we have frequency increasing toward infinity. We calculate the disturbance level of gamma rays to be greater than 65. NOTE: The disturbance level is log2 of frequency associated with disturbance.

Calculations show that the disturbance level of electron is 66.7, and the disturbance level of proton and neutron is 77.6. It appears that the electromagnetic disturbance exists as a field in which high frequency regions (in gamma range) start to converge into electrons, which then further condense into protons and neutrons. This conjecture is logically consistent and it is worth investigating further.

Thus matter seems to act as the upper bound of electromagnetic disturbance.

The Disturbance Theory reverses how we view the problem of space. The problem is not what bounds space, but what is it that space bounds. What space is bounding is not matter but disturbance. And it is disturbance that converges and condenses as matter.

The interface between matter and space consists of electromagnetic disturbance.

So, space does not have existence independent of matter. Its existence depends on disturbance and its convergence and condensation into matter. This explains the continuity that Descartes was looking for.


NOTES (Oct 7, 2022):

  1. The “disturbance” of Disturbance theory is now recognized as the most general reference to SUBSTANCE. Substance is anything substantial enough to be sensed.
  2. The “frequency” of disturbance is now recognized as the consistency (thickness, solidity) of substance.
  3. Space is the limiting condition of substance as consistency goes to zero.
  4. Matter is the limiting condition of substance as consistency goes to infinity.
  5. From space to matter we have a spectrum of condensing substance.
  6. As the substance condenses its extent (space) shrinks and duration (time) increases.
  7. Lesser condensed substance forms the background of greater condensed substance.


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  • vinaire  On December 12, 2015 at 9:38 PM

    Einstein says, “In order to arrive at the idea of an objective world, an additional constructive concept still is necessary: the event is localised not only in time, but also in space.”


    It seems that one can arrive at the idea of an objective world only when one takes a viewpoint that is attached to the whole universe and not to individual parts.



  • vinaire  On December 13, 2015 at 5:43 AM

    Einstein says, “The concept of space as something existing objectively and independent of things belongs to pre-scientific thought, but not so the idea of the existence of an infinite number of spaces in motion relatively to each other.”


    I have to disagree with Einstein here. Space does exist objectively as the boundary of objects. It does not exist as independent of objects.

    The idea of “the existence of an infinite number of spaces in motion relatively to each other” can be understood only in terms of infinite number of viewpoints in motion relatively to each other. These viewpoints shall be narrow and attached to objects that are moving.

    Einstein is diving here into subjectivity, which is a dangerous thing for a scientist to do.



  • vinaire  On December 13, 2015 at 6:11 AM

    Sense experience is acquiring ideas and images directly from hard-wired interpretation of electrical impulses arriving at the brain. These hard-wired interpretations are based on genetically programmed associations in one’s DNA. These associations continually modify themselves to become logically consistent.

    “Calling to mind” is reconstructing ideas and images from earlier hard-wired interpretations. These would be relatively soft interpretations.

    There may be additional harmonics of this cycle.



  • Chris Thompson  On December 14, 2015 at 2:27 AM

    In this context, there is no need for space to be bounded. Many weirder ideas and theories would dissolve in unbounded space. From the simplest idea of “Big Bang,” this more naturally inflates into an undisturbed field of what? . The matter and energy of “our universe” could be local, even if that locality were a hundred trillion light years across.


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