Terry Longhurst, FIAP is celebrating the centenary of Einstein’s seminal paper on Special Relativity by taking the opportunity to develop his distinctive ideas about Einstein’s theories from, as he says, an analyst’s standpoint. Here’s the second instalment, in which Terry looks at the weaknesses in the Special Theory and how they were addressed in the General Theory of Relativity.

Einstein’s original theory was breathtaking in its scope, but was also flawed. Firstly, Hendrik Lorentz had proposed that the change in the physical dimensions of a material object were caused by a drag effect with respect to the ether. However, having discarded the ether as a material entity, Einstein could not explain why the dimensions of material objects varied, let alone spatial and temporal relationships. He used Lorentz’s equation simply because his principle of relativity did not work without it. Ouch.

Secondly, Lorentz proposed his equation because without it the known behaviour of light was inconsistent with the existence of a material space. However, when Einstein used it to describe the way that events would differ from different frames of reference he made an assumption which, as far as I am aware, he never realised is an assumption. It is that the observed motion of material objects and that of light are extremes of a contiguous range of behaviours. This does not have to be so. It could be that the behaviour of light is simply different from that of material objects.

Thirdly, and most telling at the time, the theory was self-contradictory. The ‘twin paradox’ exposes the contradiction. This has been related so often that I hope that only the briefest reprise is needed:

Imagine two twins, one of whom travels in a space ship to a nearby sun. The other remains on the Earth. We’ll call them Trevor and Eric for ‘Traveller’ and ‘Earthbound’. According to the principle of relativity, time would pass more slowly for Trevor when viewed from the Earth. So when he returned, he would be younger than would the stay-at-home Eric. However, according to the concept of relativity, all motion is relative. So for Trevor, less time would appear to pass for Eric. When he returned, Eric would therefore be younger than he would be.

This is known as a ‘reductio ad absurdum’, whereby a proposition is proved to be false because it leads to mutually exclusive conclusions. It showed that Einstein’s concept of relativity and his principle of relativity were incompatible, i.e. that both could not be correct.

Einstein’s General Theory. Albert Einstein knew that his original theory was in tatters, so in 1916 he published his General Theory. If his original theory was breathtaking, the General Theory was mind numbing. He invented a new field of mathematics, Tensor Calculus. This was, and is, an awe inspiring mathematical edifice. A tour de force. The intellectual equal of Ludwig Van Beethoven’s Fifth symphony and Alessandro Botticelli’s Birth of Venus. It places him amongst the greats.

Einstein presented the General Theory as being a logical extension of his original theory. He based it on his principle of relativity, and maintained that space did not exist, but introduced the gravitational field as a material medium. He also added Hermann Minkowski’s concept of a four-dimensional space-time continuum, in which travel through time is just as possible as travel through space. Overall, Einstein produced a view of the universe in which gravitational forces shape and distort time and space. It was, and remains, a heady mixture.

The introduction of gravity as a material medium resolved the twin paradox. All motion was now relative to the gravitational field, so the twin paradox could not arise. But maintaining that space did not exist was pure sophistry. The gravitational field was a material medium, in which all motion takes place, and which defines the absolute state of rest. If that is not a material space, then I don’t know what is.

And Minkowski’s four dimensional space-time continuum is a mathematical abstraction. It does not really exist. It can’t. Why not? Because it treats time as a dimension in the same context as the three spatial dimensions. What’s wrong with that? Well, actually, quite a lot.

Firstly, it allows the possibility of time travel. This immediately gives rise to paradoxes equal to the ‘twin paradox’ that showed the flaw in Einstein’s original ideas. For example, if I travel to the past and change events such that my parents never meet, I would not be born. But if I were not born, I would not be able to travel to the past, so my parents would meet…and so on. This is fundamentally incompatible with causality.

Secondly, the whole of matter does not coexist at one place, but the gravitational force on any body is the sum of the gravitational forces exerted on it by every other body in the universe. This is mind boggling, but true. And very, very important. So I’ll repeat it, just in case you did not grasp its significance first time. The gravitational force on any body is the sum of the gravitational forces exerted on it by every other body in the universe. So all of matter, wherever in the universe, coexists and interacts.

However, if everything in the universe coexisted at all time in the same sense as it coexists throughout the universe, then the sum total of the gravitational attraction would cause the universe to collapse.

Next month, Terry asks whether the General Theory is consistent with the known behaviour of light and draws some interesting conclusions. You can contact Terry at tlonghurst@iap.org.uk.

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