Cosmic Adventure Episode 2.04 Where did these equations come from?

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WHERE DID ALL THESE EQUATIONS COME FROM?

Cosmic Adventure Episode 2.05


The Origin of Relativity

It goes without saying that Einstein’s theory of relativity is one of the most revolutionary ideas ever produced by a human mind.

But it is quite marvellous to think that this latest idea had its origin in the oldest fairy tale in ancient Greek mythology. It all started with the god aether.

Aether?


Aether

The term ‘aether’ stemmed from a Greek root meaning ‘pure, fresh air’, ‘upper air’ or ‘clear sky’. Somehow in modern time, it had become the mysterious substance that pervaded the entire universe.

Aether the first-born of the elemental gods. Painting By

Evelyn Pickering De Morgan, Night and Sleep, 1878.


Light –An Electromagnetic Wave

In the nineteenth century, aether exploded into prominence when James Clerk Maxwell discovered that light is an electromagnetic wave.

As a wave, light needs a medium for its propagation - just like sound waves which need air as their transmission medium.

Maxwell thought that aether was the medium for light.


Light Speed Constancy

Secondly, the existence ofastationary aether medium would provide a natural explanation to the constancy of light velocity without further assumptions.

Electromagnetic waves


The Absolute Frame in Classical Mechanics

Thirdly, before Maxwell, the renowned physicist Isaac Newton also had aether to be the seat of his absolute reference system in space.


Medium for Gravitation

Fourthly, aether might also be the medium through which the force of gravitation was transmitted.

Gravitation


Foundation of classical Science

In short, aether is the very foundation of classical science. Without the existence of the aether, all the development of physics up to the nineteenth century would have been non-solid.


The Detection of the Aether

In the mid nineteenth century, physicists were working hard to find evidences to establish the existence of the aether.

In the late nineteenth century, many ingenious experiments had been carried out in an attempt to detect the existence of the mysterious medium.

However, the aether had been so elusive that all the experimental results had turned out to be negative.


Light through Aether

Maxwell had a bright idea.

By using common sense, Maxwell thought that aether to light is just like air to sound. Just as the speed of sound is relative to the air, so the speed of light must be relative to the aether.

It is hard to measure aether, but it should be possible and much easier to measure the motion of light through the aether.

Hard to detect aether

Easier to detect wave


In his article on the aether in the ninth edition of the Encyclopaedia Britannica, Maxwell put forth his idea:

“If it were possible to determine the velocity of light by observing the time it takes to travel between one station and another on the earth’s surface, we might, by comparing the observed velocities in opposite directions, determine the velocity of the aether with respect to these terrestrial stations.”


Speed of Earth

However, in ordinary life, the ratio of 𝑣 to 𝑐 is so small that it is close to zero. What about the earth? The earth is moving at a mean velocity of29.78 or about 30 kilometres per second in its orbital motion around the sun. This figure is a good percentage of that of light.

𝑐 + 𝑣𝑐 − 𝑣

𝑣 = 30 kilometrse persecond


Addition of Velocity

The idea was simple:

When a man speeds towards a light source, light will come to him faster; When he receded, it would took light a bit longer to reach him.*

𝐴𝑝𝑝𝑟𝑜𝑎𝑐ℎ𝑖𝑛𝑔 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦= 𝑐 + 𝑣

𝑅𝑒𝑐𝑒𝑑𝑖𝑛𝑔 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦= 𝑐 − 𝑣

*(Today, we know that this way of adding light velocities classically is wrong. But the practice was prevalent at those times.) This is the first fault in the theory.


Relative Aether Wind

This means that the undetectable aether wind would be whistling through the earth at a velocity of 30 kilometres per second just like still air whistling pass a speeding car.

The air is not actually moving. It is the feeling of moving wind that is created by the movement of the car.

Wind created by speed of car

Relative wind speed created


Adding Speeds of Light

In real numerical values:

The speed of light (c) is 300,000 km/s and the speed of the Earth (v) orbiting the Sun is 30km/s.

When light rays head upstream against the Earth movement the speed is:

𝑐𝑎𝑝𝑝𝑟𝑜𝑎𝑐ℎ𝑖𝑛𝑔 = 𝑐 + 𝑣 = 300,000 𝑘𝑚/𝑠 30 𝑘𝑚/𝑠

When the light rays head down stream in the same direction is:

𝑐𝑟𝑒𝑐𝑒𝑑𝑖𝑛𝑔 = 𝑐 − 𝑣 = 300,000 𝑘𝑚/𝑠 − 30 𝑘𝑚/𝑠


1878 Publication

In his 1878 Encyclopaedia Britannica

article Maxwell further suggested an

experiment to determine the velocity

of the earth through the aether

using light in the following way:

“Split a ray of light, and send the two

resulting rays at right angles to each

other. Let one travel at right angles

to the motion of the earth through

the aether while the other travels in

the direction of the motion of the

earth through the aether. . . .In

com

ing

ligh

t

Horizontal lightVer

tica

l lig

ht

Splitting

Earth’s motion

Aether wind created


Reflecting & Rejoining

Maxwell Continued:

. . . Reflect the two rays back after each has travelled exactly the same distance to join up again and let them interfere.”

This must mean, if you could measure the speed of light accurately enough, you could also measure the speed of light travelling upwind. When compared the sum of the two measurements it should be twice the wind speed.”

Horizontal light

Ver

tica

l lig

ht

Rejoining&

Interfering


MICHELSON’ RIVER ANALOGY

To be continued on: Episode 2.06

Cosmic Adventure Episode 2.04 Where did these equations come from?

Science

Transcript of Cosmic Adventure Episode 2.04 Where did these equations come from?