Reference: Disturbance Theory
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 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.
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 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 inertial frame, similar consideration shall apply. In other words, their relative speed shall be “2c” where c is the speed of light. 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. The absence of a medium resulted in the assumption that the relative speed of two light beams approaching each other would also be ‘c’ instead of ‘2c’. This resulted in a mathematics that led to the strange ideas of ‘length contraction’ and ‘time dilation’.
Why couldn’t we find any medium for light? Were we looking for the wrong thing?
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 the mysterious ether be space itself?
The answer to this question seems to be tied with the mystery of inertia. Neither space nor light seem to exhibit the property of inertia. Therefore, we cannot apply the considerations of the inertial frame to space and light.
Let’s make the following postulate. It is a reasonable postulate.
“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, 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 itself.
How does this compare with the 19th century consideration of “luminiferous ether”?
The “luminiferous ether” was assumed to be rigid to electromagnetic wave of light. If light were a disturbance in space, we can see this disturbance to propagate when changing electric field generates a magnetic field, and a changing magnetic field generates an electric field. The problem of ether being rigid to electromagnetic wave of light is thus resolved.
The “luminiferous ether” was also assumed to be completely permeable to matter. Is this true? Doesn’t matter encounter resistance when pushed through space? What is inertia?
By light, we don’t just mean the visible light. It refers to the whole electromagnetic spectrum from low frequency radio waves to very high frequency gamma rays. We may understand the nature of this spectrum better by looking at the structure of atom.
Gamma rays are produced in the disintegration of the nucleus of an atom. This nucleus is surrounded by electrons. Beyond these electrons is electromagnetic field, and beyond that field is space. From space to the nucleus of an atom we seem to have the whole electromagnetic spectrum.
The electromagnetic spectrum represents an increasingly disturbed space. The nucleus of an atom then represents a highly disturbed state of space that appears as mass.
We can now see that the movement of mass through space shall require undisturbed space to suddenly go to a highly disturbed space. This would create a resistance. This resistance may explain the mystery of inertia. The higher is the mass, the greater would be this resistance, and the greater is inertia.
Space is not completely permeable to matter. The resistance of space to matter is observed as inertia.
There is an illusion of space being permeable to matter because we see matter gliding through space. But matter is “gliding through space” only when it is either still or moving at a constant velocity relative to other matter. The fact is matter “gliding through space” is not moving through space. It is moving through space only when it is accelerating.
Matter may be conceived to be moving at the velocity of light relative to a light wave; but if matter is not accelerating, it is actually standing still relative to space.
The Space Reference Frame
When we look at space as the medium of light we no longer need the relativistic math developed by Einstein. We can apply the classical inertial frame to understand that two light beams approaching each other shall have the relative velocity of ‘2c’; and this shall not violate the limit on ‘c’ as the universal constant.
The universal constant ‘c’ may be seen as the ratio of the wavelength of light to its period. This connects space to time in the domain of electromagnetic field. This is true even in the domain of matter, but it not so obvious because wavelength and period of “disturbed space” are both infinitesimal in that domain. Thus space and time appear to be absolute and independent in the domain of matter but that is not really the case.
The inertial frame of Galileo and Newton represents a special case of a more general inertial frame where space and time are related by the universal constant ‘c’.
The inertial frame of Galileo and Newton identifies matter as the basis of the observer. It may be referred to as the Material Reference Frame (MRF). The more general inertial frame identifies space as the basis of the observer. We may refer to it as the Space Reference Frame (SRF).
The general inertial frame (SRF) is consistent with all of physics. It also provides a much more elegant explanation for INERTIA.