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Reference: A Logical Approach to Theoretical Physics

Here is my view on the reality of space-time.

• The Euclidean space is an idealization of dimensions of matter.
• Space is not necessarily discrete like dimensions of matter.
• Space is not necessarily rigid like dimensions of matter.
• In reality, space is neither discrete nor rigid.

Here the word “discrete” is used in the sense opposite to “continuous” meaning “apart or detached from others; separate; distinct”. We can talk about dimensions in discrete terms, but we cannot do so with space. Space is a continuous whole.

Here the word “rigid” is used in the sense opposite to “flexible” meaning “firmly fixed or set”. We can talk about units for the dimensions of matter to be fixed, but not so for space.

• A Euclidean point is an idealization of a location in space.
• A location in space is not necessarily dimensionless.
• A location is continuous with the space around it.
• A location is approximated by a discrete point only when there is matter.

It is matter that fixes locations in space by virtue of being rigid. When there is no matter, we cannot fix or pinpoint locations in space.

• Calculus approaches continuity from the direction of discreteness.
• Calculus talks about gradually shrinking infinitesimals in that process.
• We need mathematics that approaches discreteness from the direction of continuity.
• Such mathematics will approach discreteness as frequency.

Calculus uses a matter-centric viewpoint that approximates continuity in terms of shrinking infinitesimals. When there is no matter as in the case of electromagnetic fields we cannot use rigid infinitesimals for reference. We may need to use lessening frequency to approach continuity. Here discreteness seems to be provided by frequency.

• Mathematics considers a discrete point to be a primitive notion.
• In reality, it is the continuous space, which is a primitive notion.
• The rigidity of space is a function of disturbance in it.
• Infinite frequency of disturbance generates total rigidity in space.

We cannot use dimensionless Euclidean point as primitive notion because it is not seen as expanding into a continuous space. But we can use continuous space as primitive notion because we can see it as shrinking to generate a dense point that approaches discreteness. It is this “density” that can be associated with rigidity.

• Discreteness starts to form as space is disturbed.
• This discreteness increases with frequency.
• At a certain threshold  frequency, rotational fields start to form within the electromagnetic fields.
• The first stable form of such rotational field is the electron.

It is postulated that electromagnetic field is the disturbed space. As this disturbance increases as frequency, pockets of rotational electronic fields appear in the wider electromagnetic field.

• As these rotational fields grow the high frequencies at their center starts to collapse to form a hard nucleus.
• The next stable form of this rotational field appears to be the hydrogen atom.
• Mass is naturally created in the nucleus as the frequency of disturbance increases the most at the center.
• The mysterious factor here is the role of “frequency”.

Mass is naturally created in the nucleus as the frequency of disturbance increases. The task now is to understand the nature of this disturbance.

The theory of special relativity talks about contraction of space and dilation of time at speeds approaching the speed of light. Such conclusions are subjective because the “observer” in that theory is limited in its observation by the speed of light.

Objectivity exists to the degree observer uses the whole universe as its reference. This means using all physical and mental senses. The moment one uses part of the universe as its reference one’s viewpoint descends into subjectivity. Thus mathematics employed by Einstein’s theory of Special Relativity is subjective.

Objectivity is the consistency among inputs from all physical and mental senses. To the degree this consistency is missing, observation is incomplete and subjective.

Reference: From my response on Quora

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Reference: A Logical Approach to Theoretical Physics

This research may be summarized as follows,

(1) From void to the core of the black hole, there is a spectrum of substance of increasing density.

(2) Substance has intrinsic motion. That motion is zero when the density is infinite as for the core of the black hole; and that motion is infinite when the density is zero as for the void.

(3) The intrinsic motion is inversely proportional to the density throughout the spectrum of substance.

This relationship is as basic as the Newton’s laws of motion.

Reference: A Logical Approach to Theoretical Physics

From Wikipedia,

“Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism.”

The null results from Michelson-Morley’s experiment in 1887 led to the belief that the speed of light is the same in all inertial frames. For example, light is observed to have the same speed, c = 3 x 10⁸ meters/second, relative to the earth and also to the sun, even when earth is moving at a speed 3 x 10⁴ meters/second relative to the sun.

But, Earth and Sun, together as a system on a larger scale, are moving at the same velocity with respect to light. The anomaly, therefore, is local and not universal. Logically, it means that space and time characteristics, which determine the speed of light, maintain a constant relationship on a universal basis, while their individual characteristics may vary locally.

We know that the space and time characteristics are intrinsic to substance. As summarized in The Universal Frame of Reference, space is tied to the extents of substance, and time is tied to the duration of substance. Therefore, space and time are tied to the density of substance. As density changes, the space-time characteristics change accordingly, but in a constant relationship.

Mathematically, this constant space-time relationship leads to the Lorentz transformation (see Special Relativity explained at Khan Academy).

Lorentz transformation, however, transforms space and time coordinates from one local frame to another, considering that the speed of light is the same in both frames of references. The mathematics provides the following relationships.

When c is infinite, βc reduces to v, β reduces to 0, and γ reduces to 1. Lorentz transformation reduces to Galilean transformation. This means that Galilean transformation is valid in the universal frame of reference, and our task is to scale the motion in the local frame of reference to motion in the universal frame of reference. This is done by β. The resulting change in γ is the correction factor that needs to be applied to the Galilean transformation.

If v = 3 x 10⁴ m/s is the velocity of the Earth relative to the Sun, we are scaling it down by the speed of light, c = 3 x 10⁸ m/s in the universal frame of reference by β = v/c = 10^-4. For this value of β, we may calculate γ = 1 + 5 x 10^-9.

This means that a local velocity of v = 3 x 10⁴ m/s provides a small correction factor of 5 x 10^-9 to the Galilean transformation.

It is to be understood that a velocity differential in free space equates to a density differential (see The Universal Frame of Reference). Therefore, we may interpret the above numbers to mean that an increase in velocity of v = 3 x 10⁴ m/s may equate to decrease in density by a factor of 5 x 10^-9.

It should be noted that Lorentz transformation provides a very general correction for the material domain, and it may not account for finer details, such as, the Earth’s velocity is not linear relative to the Sun. In the material domain v is much smaller than c because the inertia (density), in general, is very high.

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