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## The Inertial Frame

In 1632, Galileo Galilei first described that in a ship travelling at constant velocity, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary. This is a nice description of an inertial frame.

An inertial frame is one in which Newton’s first law remains true. In other words, in this frame, an object stays either at rest or at a constant velocity unless a force acts on it. A non-inertial frame shall be experienced inside an accelerating rocket. In this frame Newton’s first law will not hold true.

In short, all inertial frames are in a state of constant, straight line motion with zero acceleration. Measurements in one inertial frame can be converted to the measurements in another by a simple transformation.

For example, suppose two cars are moving side by side at the speed of 60 mph in the same direction. The driver of each car will see the other car to be practically still. The speed of a car relative to the other would be the “algebraic difference” of their speeds: 60 – 60 = 0. If the two cars were approaching each other at 60 mph, a driver will see the other car approaching at 120 mph [60 – (–60) = 120].

NOTE: The individual speeds would have to be measured in a common reference frame, such as, earth for the above transformation to be valid.

This simple transformation shall also apply to the relative speed of disturbances moving through a medium. Here the medium stays still while the disturbance moves through it. The speed of the disturbance relative to the medium is determined by the properties of the medium.

For example, suppose a ripple on the surface of water moves at speed, R based on the properties of water. We see two ripples approaching each other, each moving on the surface of water at speed R toward the other. Their relative speed shall be: R – (–R) = 2R. The transformation is the same as in the case of cars in the previous example, because individual speeds are measured in a common reference frame of water.

Sound travels in dry air at 20°C at a speed of 343 meters per second. If two waves of sound are approaching each other, their relative speed shall be 343 x 2 = 686 meters per second. This is because the medium in which these waves are traveling (air) provides a common reference frame. By no means is this relative speed “supersonic”, because this speed is not relative to the medium.

If two beams of light were approaching each other in a medium that provided a common reference frame, similar consideration shall apply. In other words, their relative speed shall be “2c” where c is the speed of light relative to the medium. This shall not violate the limit placed by the medium on the speed of light.

In the 19th century a medium called “luminiferous ether” was postulated for light, but it could not be found in terms of its postulated mechanical properties. The absence of a mechanical medium resulted in the assumption that the relative speed of two light beams approaching each other would also be ‘c’ instead of ‘2c’. This was because no common reference frame existed in the form of a medium. This resulted in a mathematics that led to the ideas of ‘length contraction’ and ‘time dilation’.

Why couldn’t we find any medium for light? Were we looking for the wrong thing?

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## The Ether

In 1873, Maxwell’s effort to determine the relationship between electromagnetic theories and the Newton’s theory of motion resulted in the amazing discovery that light was an electromagnetic phenomenon.

Maxwell wrote in the preface to the first edition of his book A TREATISE ON ELECTRICITY AND MAGNETISM:

“The most important aspect of any phenomenon from a mathematical point of view is that of a measurable quantity… I have therefore thought that a treatise would be useful which should have for its principal object to take up the whole subject in a methodical manner, and which should also indicate how each part of the subject is brought within the reach of methods of verification by actual measurement… before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday’s Experimental Researches in Electricity.

“As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and thus compared with those of the professed mathematicians.

“For instance, Faraday, in his mind’s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance: Faraday saw a medium where they saw nothing but distance: Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids.

“When I had translated what I considered to be Faraday’s ideas into a mathematical form, I found that in general the results of the two methods coincided, so that the same phenomena were accounted for, and the same laws of action deduced by both methods, but that Faraday’s methods resembled those in which we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis.”

It is interesting to note that Maxwell finds Faraday’s “lines of force traversing all space” to be mathematically equivalent to other mathematician’s “centers of force attracting at a distance”. Maxwell notes, “Faraday saw a medium where they [other mathematicians] saw nothing but distance”.

Space is not “nothing” because it has the electromagnetic properties of permittivity and permeability. These properties of space determine the speed of light per Maxwell’s equations. This fact alone should be enough to convince that space is the medium through which light travels.

Why is space not considered to be the medium of light? Why can’t space be that mysterious ether?

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## The Space

According to Maxwell, light travels in space as an electromagnetic wave. This wave has the following properties.

2. ### A changing magnetic field produces an electric field of force

The frequency of the electromagnetic wave is determined by the rate at which the electric and magnetic fields are interchanging back and forth in space as the wave propagates.

Let’s make the following postulate, which is quite reasonable.

“Space, when disturbed, breaks into electric and magnetic fields.”

This is similar to the observation that water, when disturbed breaks into peaks and valleys; or air, when disturbed, breaks into high and low pressure areas.

In case of the ripple in water we see the movement of peaks and valleys, but not that of water. In case of sound we see the movement of high and low pressure areas, but not that of air. We may say that in case of light we see the movement of electric and magnetic fields but not that of space.

The above postulate provides a seamless continuity from space to electromagnetic fields. How does this compare with the 19th century consideration of “luminiferous ether”?

The “luminiferous ether” was required to be elastic enough to allow light to travel. This requirement is met when we consider light to be a disturbance in space, we can see this disturbance to propagate when changing electric and magnetic fields generate each other. The problem of ether being “rigid” to electromagnetic fields is thus resolved.

But it was perceived that “luminiferous ether” was  permeable to matter, because matter could move freely through it. This “fact” was actually seen as contradictory to ether being elastic. This created confusion. Is this confusion resolved when we see space as the medium of light?

The truth seems to be that matter cannot move freely through space.  Matter encounters resistance when pushed through space. This resistance is INERTIA.

Newton defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:

“The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.”

Maxwell states in “A Treatise On Electricity & Magnetism, Vol1, Art. 5

“If, as in the astronomical system, the unit of mass is defined with respect to its attractive power, the dimensions of [M] are [L3T -2].”

These dimensions of mass may be looked upon as “(area) x (acceleration)”, which agrees with Newton’s description of inertia as “innate force of matter.”

The context of light as an electromagnetic wave may be expanded from low frequency radio waves to very high frequency gamma rays of the electromagnetic spectrum. Gamma rays are produced in the disintegration of the nucleus of an atom. The de Broglie frequency of the  nucleus places it well inside the gamma range. The electrons surrounding the nucleus have frequencies at the beginning gamma range. Beyond these electrons we may visualize the lower parts of the electromagnetic spectrum. Beyond that spectrum is space.

From space to the nucleus of an atom we seem to have the whole frequency range of the electromagnetic spectrum.

Space seems to represent the lower end of the electromagnetic spectrum as frequency reduces towards zero. Mass seems to represent the upper end of the electromagnetic spectrum as frequency increases towards infinity. The increasing frequency throughout the spectrum seems to represent an increasingly disturbed state of space. The nucleus of an atom then represents a highly disturbed state of space, which appears as mass.

When we visualize mass as “a region of high frequency”, It is like intense disturbance moving through undisturbed space, there shall be a high frequency gradient at the boundaries of this “region”. As mass moves through space, the undisturbed space in the path of mass must cross this high gradient of frequency. It must go from undisturbed to a highly disturbed and back to undisturbed space after the mass has passed. Obviously, there would be resistance. The greater is the mass, the higher would be this resistance. This is inertia.

There is an illusion of space being permeable to matter because we see matter gliding through space. But in those moments, matter is moving at a constant velocity.  That motion is relative to other matter and not relative to space. Motion relative to space is accompanied by acceleration.

It is very possible that light propagates as a disturbance through space. Space imparts elasticity to electromagnetic fields, which then appears as inertia.

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## Space as a Reference Frame

When we look at space as the medium of light we find it consistent with the following excerpt from Wikipedia,

In classical physics, light is described as a type of electromagnetic wave. The classical behaviour of the electromagnetic field is described by Maxwell’s equations, which predict that the speed c with which electromagnetic waves (such as light) propagate through the vacuum is related to the electric constant ε0 and the magnetic constant μ0 by the equation

Thus, from classical physics point of view, when two beams of light approach each other, their relative velocity can be ‘2c’, and this would not violate the limit on ‘c’ as postulated by Einstein. We may also define ‘c’ as the “wavelength to period” throughout the electromagnetic spectrum that includes mass at its upper end.

For matter both wavelength and period are infinitesimal. Therefore, space and time are experienced as absolute and independent in the reference frame of matter in which we live. Thus,

In a more fundamental way, ‘c’ is the ratio of Space to Time.

The inertial frame of Galileo and Newton uses matter as its basis. It may be referred to as the Material Reference Frame (MRF). The more general inertial frame identifies space as the basis. We may refer to it as the Space Reference Frame (SRF).

The inertial frames of Galileo and Newton are based on the reference frame of matter. Matter represents a special case of a more general reference frame of space.

The SRF (space reference frame) provides consistency throughout the classical physics in a fundamental way. It offers a very simple and elegant explanation for INERTIA.

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## The Ultimate Basis

This bottom line in my view is — If light is made up of moving particles (like bullets from a gun), then no “medium” is required. We just have discrete particles. But if light is moving as a disturbance among particles then there is a medium, which is seen as a continuum.

So, the question becomes,

“Is light consist of moving particles, or is it a continuum of disturbance?”

In other words,

“Is light connected throughout, or does that connection gets broken intermittently?”

And ultimately…

“Is reality fundamentally continuous or discrete?”

We can see discreteness emerging from continuity, but not the other way around.

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