## Einstein’s Unfinished Work

I asked on Quora the following question, which led to an interesting exchange.

If two sound waves passed each other in opposite directions, would they be traveling at relatively twice the speed of sound for that medium?

Mathematically, this answer to this question should not change whether we talk about sound waves or light waves for the following reason.

The speed of a wave depends entirely on the property of the medium. As long as the properties of the medium do not change, the speed of the wave remains the same. This fact is observable for sound as well as for light. There was no question about the medium for sound as it is obviously understood to be material. However, in late 19th century, question arose about the medium of light because it could not be identified with any material.

But that question was settled when no material-based ether was found and electromagnetism (light) was established as a physical reality in its own right. Electromagnetic field demonstrably became a substance that was more basic than matter.

We may postulate space as electromagnetic field of zero frequency. This space breaks into electric and magnetic fields the moment it is disturbed. Thus it has definite physical properties in terms of permittivity and permeability. This makes space a physical medium. Light then travels as a disturbance in a physical medium.

Mathematically, light is a disturbance in a physical medium just like sound.

To repeat, the speed of a wave depends entirely on the property of the medium. Speed may be expressed as the ratio of “wave length to period”. This ratio shall then be constant regardless of the frequency of the wave. When we use uniform vibratory motion of frequency as the frame of reference we automatically satisfy the requirement of the principle of relativity.

We see space as rigid to account for the motion of matter in an”inertial” frame of reference. But space cannot be rigid when we consider the electromagnetic wave propagating through it. Therefore, for light we need  a “non-inertial” frame of reference that sees space as flexible.

The principle of relativity is not violated when we consider uniform translatory motion of material objects in an inertial frame of reference, and uniform vibratory motion of frequency waves in a non-inertial frame of reference.

Einstein’s Special Theory of Relativity was intended to solve the erroneous view of Newtonian mechanics that space and time were absolute and independent. This view came under question when electromagnetic phenomenon was discovered. Einstein actually solved this problem by simply postulating that light travels at a constant speed, thus setting up a dependence between space and time.

#### Einstein’s postulate of constant “speed of light” implies that it must depend on certain physical properties. This confirms the view of space as a physical medium.

Space is rigid for matter but flexible for light. We cannot, therefore, use the same rigid frame of reference to compare the translatory motion of rigid objects with the vibratory motion of light. This means that,

Lorentz transformation, which assumes space to be rigid, cannot be used to determine transformation between space and time.

We need to determine the relationship between the inertial frame of reference applied to mass, and the non-inertial frame of reference applied to frequency.

This seems to be the work left unfinished by Einstein.

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