A Hidden Giant Placed a Beacon

No absolute space, and then no absolute time.

[Image: a frame from the presentation discussed.]

Note the central terms of “1 divided by c squared”.

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The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, only a kind of union of the two will preserve an independent reality.

Hermann Minkowski 1908-08-21

A Presentation

Cambridge University have held symposia on Physics in honor of the late Stephen Hawking. I commend to you the video below, a presentation by Brian Cox at one such event. It is in the style of his public outreach for science. His audience are physicists and other interested academics. He does not employ language which assumes a deep understanding of physics. He considers a range of interesting topics in a manner which is widely accessible.

Cox begins with life and its likelihood or lack thereof. More specifically, he considers complex life which is able to ponder the universe, which is a far higher bar. Interesting though that topic is, and well worth listening to, it is the central part of Cox's presentation which caught my attention.

Although I make effort to highlight important scientific contributions by women, there shall be none of them here. The topic weaves the work of three men. Most readers will have heard of two of them, though only those who have studied physics or engineering at university will likely have heard of the third. I consider this a travesty.

Cox's narrative leads to Einstein's General Theory of Relativity, a topic which can seem opaque to non-scientists. One of Cox's great skills is the ability to distill the core of a scientific theory and make it accessible to a lay audience. The questions that Cox is encouraging us to ask, are what realizations lead Einstein to formulate, first Special Relativity and then General Relativity? In both cases there were implications of existing, tested theories which the scientific community either chose not to consider, or had yet to realise.

No Absolute Space

Imagine a person on a train which is moving past a station. On the train a ping pong ball is dropped and bounces twice on the table. For an observer on the train, the places where the ping pong ball impacts are the same, on the table. For an observer on the platform the train has moved between the two impacts and thus the impacts occur in different places.

An implication of Sir Isaac Newton's laws of motion is that there is no way to discover if one is stationary or moving at a constant speed in a constant direction. In either state there is no change in momentum, no force is applied. Given no other physics acting, no measurement can distinguish between these seemingly different states.

This implies that they are different equally valid frames of reference. Thus, there is no "correct" frame of reference for describing what was happening to the ping pong ball on the train. On the train, one would describe the ball as impacting in the same location on the table, and the train station moving past outside. On the platform, the station is stationary, the train is moving and the impacts of the ball occur in different locations. Both are correct.

This implies that there is no "absolute space". The technical term is an absolute standard of rest, or inertial reference frame. This worried Newton, for it didn't accord with his view of God. He refused to accept that there was no absolute space, even though it was implied by his own laws.

Newton declared that he was standing on the shoulders of giants, which is true. His major work, Principia, synthesized work done by other mathematicians. He needed this work to formulate differential calculus which is the mathematical structure required to express his laws. (I once sat down with my son to discuss calculus.)

Einstein does not declare himself standing on giants but does offer praise to the 19th Century Scottish physicist who formulated the equations describing the interaction between magnetic and electric fields (shown in the introductory graphic).

His praise could not be higher:

So bold was the leap, that his genius [was] forced upon the conceptions of his fellow workers.

No Absolute Time

Hidden in the Scottish physicist’s equations, Einstein recognized, was the destruction of absolute time.

The key to that realisation, a hint as to why the speed of light is such an important thing, are the terms involving c^2 (c squared) in the equations. The way in which Cox describes this is that it doesn't matter how fast you are moving or not, but when measuring changes in electric or magnetic fields we must all get the same result. This implies that c (the speed of light) is constant in any reference frame. This is the basis for Special Relativity.

Cox goes on to present the "light clock", Einstein’s thought experiment which implies that a moving clock must run slower than a stationary clock. This is true. Indeed, our GPS satellites would degrade in accuracy over time if they did not factor this difference in the speed of the flow of time.

From Newton we have no absolute space. From James Clerk Maxwell, the Scottish physicist, we have no absolute time. It took the genius of Einstein to see these implications of known, successfully verified theories, and bind them into the most accurate description we have of "gravity", the structure and behaviour of space-time.

It is worth noting that the predictions of General Relativity have been tested again and again and again for over a hundred years and the theory stands. Recently, the LIGO experiment even confirmed gravitational waves, which is already leading to an entirely new branch of astronomy.

James Clerk Maxwell

Please remember the name of James Clerk Maxwell. His equations describing electro-magnetic fields are based on decades of observational work by other luminaries such as Ampere and Faraday. We see here the beautiful struggle and cooperation between experimental and theoretical physicists.

Maxwell synthesized the experimental work and left a beacon in his equations which signaled the destruction of absolute time. It took another genius, Einstein, to see it.

Sources

Professor Brian Cox Our Place in the Universe, Prof. Brian Cox addresses Hawking 75 Symposium at Cambridge University (2017-07-02), Science Den, uploaded 2021-08-29