Confusion over what Einstein’s Theories of Relativity actually revealed about the true nature of space and time created a major storm of controversy in the early part of the 20th century and continues, though more quietly, to this day. Most people think that Relativity has been “proven” by science and that only cranks would continue to think there is something to debate.
What is not known, by the general public, is that later in life Einstein himself began to reflect on what he had accomplished and expressed some doubt that he had, in fact, been correct about some interpretations of his theories ideas concerning the true nature of time and space.
The Original Sin
Einstein’s original sin, centered on his use of the discovery of the speed of light and the fact that it seemed to be constant no matter which reference frame it traveled in. This means that no matter how fast a light source travelled, the maximum speed light that was emitted from that source had a fixed upper limit. There are other interpretations that could be imagined about the nature of light, space and time from that discovery, but it was Einstein’s interpretation that world came to accept as the true one. Let us see why.
The following excerpt from is from JimCanales’ book, The Physicist and the Philosopher: Einstein, Bergson, and the Debate That Changed Our Understanding of Time (which I have previously posted about here). The source material she draws on comes from Einstein’s Autobiographical Notes. If one is not familiar with Relativity Theory this might be difficult to follow, but I will explain it as best as I can. (I highly recommend reading Ms. Canales’ book to understand the debate in a fuller way.)
Einstein’s sin, as he described it, had been to define an “ideal clock” as both a physical thing (an actual clock) and an ideal entity (based on the speed of light defined as constant). Einstein would never be able to free himself entirely from critics who accused him of being unable to justify his reasons for considering a “light clock” as an “ideal clock.” For this very reason, “an ideal clock” appeared to be different from “all other things.” Einstein could not forget that this led to an “inconsistency.” But if he had not defined a “clock” in this dual way, his work would have either had to “forego a physical interpretation,” with the disastrous result of “reducing physics to geometry,” or perhaps worse, it would have remained a mere technical treatise about coordinated clocks. To avoid this danger, Einstein chose to embark on this inconsistency and tread a “clock” both ideally and concretely. His “sin” was “justified,” he continued, because he had accepted the “obligation…of eliminating it at a later stage.” But even by the end of his life, he was still unable to find a solution.The Physicist & The Philosopher: Einstein, Bergson, And The Debate That Changed Our Understanding Of Time; Canales p345
To be fair to Einstein, at the time he proposed his theories in 1905, the atom had still not been discovered. Maxwell’s equations were only about 20 years old. The famous Michelson–Morley experiment concerning the constancy of the speed of light was a surprise to everyone and still being debated.
Einstein was trying to determine how this new information about light could change our perceptions of the universe. In the early years after his presentation of Relativity, Einstein admitted to being unsure what his theory said about the reality of time and space. Did time really slow down and distances shorten when traveling close to the speed of light or was it only the appearance of change?
It should be remembered that Einstein was working in a patent office in 1905, anti-Semitism was on the rise, and his personal life was something of a mess. He was under a lot of pressure and so he needed to come up with something amazing to establish his reputation. For a time, he seemed convinced that his theory reflected a new understanding about the nature of time and space. If it did not, as he said, it would simply be “reducing physics to geometry” and nothing more. It is not hard to see that he wanted to believe it was more.
What was Einstein’s “inconsistency” exactly?
In Einstein’s time there was a growing concern that a standard for such things as length or time could not be found in nature. Metrologists could simply set a standard by declaring one, but it would be completely arbitrary. The hope was to find standards that would remain consistent and be established anywhere. Finding a standard in nature would solve this problem, the practical importance of this problem related to the new fields of communication (signaling) and the settling of border disputes between nations.
How important were debates about standards of time to relativity? The issues at stake were very different from previous debates about the standardization of weights and measures – scientists were not simply debating the use of a particular standard, such as a yard or meter. Einstein’s solution to the scientific problems of his era involved considering that both time and length units dilated under certain circumstances. It did not matter how these units were expressed because the units themselves were changing. Scientists and philosophers were well aware that they could adopt a different system to define time and length units in ways that would compensate for these dilation effects. Or they could accept Einstein’s brilliant offer. For the most part, they did.The Physicist & The Philosopher: Einstein, Bergson, And The Debate That Changed Our Understanding Of Time; Canales p112
If you have studied physical science or mathematics, then the problems raised by using the same natural phenomena to establish more than one standard will be obvious. But, one does not need advanced courses in either field to see why this is a solution that would be difficult to verify.
“Even after Enistein’s theory of relativity was expanded significantly, criticisms pertaining to its relation to light-based standards continued to linger to the century’s end. In the 1970s, the Harvard Physicist Leon Brillouin described the problems in determining the constancy of the speed of lilght given that time and length were both defined using light waves: “The unit of length is based on the spectral line of krypton-86… and the unit of time is based on the frequency of a spectral line of cesium….Hence the same physical phenomenon, a spectral line, is used for two different definitions: length and time.” Under this system any change in the velocity of light could go undetected because the changes would cancel out when length was divided by time: “It should be stated, once and for all, whether a spectral line should be used to define a frequency or a wavelength, but not both!” he wrote with complete exasperation. Since length and time were both defined through light waves, scientists were left with no other standard with which they measure the velocity of the waves themselves.
Brillouin protested that “with the legal definitions of length and time it seems rather difficult to check experimentally” some of the claims of relativity.The Physicist & The Philosopher: Einstein, Bergson, And The Debate That Changed Our Understanding Of Time; Canales pp112-113
The very act of describing the velocity of light as a constant rather than a variable changed the structure of the equations. Instead of space and time being described by Euclidean Geometry, we now view space and time with a different geometry, Non-Euclidean Geometry. This is where the idea that space is curved comes from – we have curved space by our equations, but we have not, in fact, proved that space is curved.
The entire premise of Einstein’s Theory of Relativity rests with the assumption that the speed of light has a constant upper limit and is known not to change in any time frame. In Einstein’s autobiographical notes Canales finds this stunning confession:
The physicist also confessed that he remained uncomfortable with how his theory depended so centrally on a particular number, the value of the speed of light. This fundamental constant seemed arbitrary and too directly tied to contemporary telecommunications. He stressed how the seeming arbitrariness of the number c for the speed of light could be eliminated. If the unit of seconds from the equations were replaced by “the time in which light travels 1 cm” it could be made to equal one. It’s disconcerting “numerical value” could be embellished by metrological institutes, which were less visible to the public and could be asked to shift units in order to end up with the nice number one. This, he believed, could be a step in the right direction, but it was hardly sufficient.”The Physicist & The Philosopher: Einstein, Bergson, And The Debate That Changed Our Understanding Of Time; Canales p345
There is a bit more here than meets the eye because Ms. Canals are limited to explanations without using mathematics to explain what Einstein is saying. Why does Einstein suggest that manipulating the units to make c=1? It is because he has defined time as a dimension like space, but time and space are measured in different units. That’s the inconsistency. And it causes all kinds of problems when solving equations.
The “suggestion” to make c = 1, is more than a suggestion today. Here is an excerpt from Dr. Richard Feynman’s lectures that he gave in the 60s:
Let us get rid of the c; that is an absurdity if we are going to have a wonderful space with x’s and y’s that can be interchanged. One of the confusions that could be caused by someone with no experience would be to measure widths, say, by the angle subtended at the eye, and measure depth in a different way, like the strain on the muscles needed to focus them, so that the depths would be measured in feet and the widths in meters. Then one would get an enormously complicated mess of equations in making transformations… and would not be able to see the clarity and simplicity of the thing for a very simple technical reason, that the same thing is being measured in two different units.Feynman Lectures on Physics – Space-Time
When my professor in college, a decade later, explained this bit of sleight of hand to the class, he said that we should understand this manipulation was not “legitimate.” It was done for simplicity – to make the math easier. We were equating time and space by giving them the same set of units, but we were to always keep in mind that at some end stage of our thinking we would have to decouple them again.
“If we are ever unsure or “frightened” that after we have this system with c=1 we shall never be able to get our equations right again, the answer is quite the opposite. It is much easier to remember them without the c’s in them, and it is always easy to put the c’s back, by looking after the dimensions.”Feynman Lectures on Physics – Space-Time
I understood what the professor was saying, at least I thought I did. We were doing something “unnatural.” But, when I asked my fellow classmates about it, some of them thought that the equations were not only a mathematical model, they were really expressing something about the reality of space and time.
We had studied classical physics for two years before this subject was introduced and we had been told that the mathematical models and equations we used must reflect what we observed about the real universe. If we did not do this, we would find we were missing some crucial understanding of reality and our experimental results would not match the theoretical ones. But, we were now entering a new world where experimental data was harder to come by due to the high speeds and atomistic world we were studying. Were we really being told now to stop worrying about experimental data, to imagine nature FROM the mathematical model, and then accept the mathematical game we were playing as reality?
This was only the beginning of the switch in approaching the study of the physical universe I encountered in college. From then on, I often felt, during my final semesters at college, as if I was Alice wandering through the Looking Glass.
Through the Looking-Glass, and What Alice Found There
Alice again enters a fantastical world, this time by climbing through a mirror into the world that she can see beyond it. There she finds that, just like a reflection, everything is reversed, including logic (e.g. running helps you remain stationary, walking away from something brings you towards it, chessmen are alive, nursery rhyme characters exist, etc.).Wikipedia
Einstein used a set of equations called the Lorentz Transformation Equations to develop his theories. These equations are used to describe the relationship between two observers in separate inertial frames of reference. These reference frames were defined combining 3 dimensions of space against a fourth dimension of time. Using this mixture as a coordinate system could be legitimate to make the math easier, but saying it is reality is an example of a logical fallacy known as Circular Reasoning. This fallacy occurs when your conclusion is drawn from your assumptions.
This fallacy can be observed in Feynman’s Lectures below: [The reference to Eqs. 17.1 and 17.3 refer to a graph of space-time and equations – which you can see for yourself by following the link below]:
Now in Eqs. 17.1 and 17.3 nature is telling us that time and space are equivalent; time becomes space; they should be measured in the same units. What distance is a “second”? … It is 3×108 meters, the distance that light would go in one second. In other words, if we were to measure all distances and times in the same units, seconds, then our unit of distance would be 3×108 meters, and the equations would be simpler.Feynman Lectures on Physics – Space-Time
Is time and distance made of the same stuff? I cannot be sure if Dr. Feynman believed this, but then physicists are notorious for not being precise with their language. He appears to say the equations are NATURE. But, the equations were set up to express both time and space as types of DIMENSIONS. The idea that time and space could be expressed in the same way – and that they could be expressed with interchangeable measurements – was baked into the original setup of the equations.
Whatever they do believe, physics professors have a lot of ground to cover and often want students to move beyond the “philosophy” of the problems. If one can embrace the new mathematics as it is presented to them, life would be smoother. “No one understands it,” is often heard as an explanation. It reminds me of the old charge against Catholic priests about their stock answer of “It’s a mystery” when asked a question they cannot answer. At least the priests were philosophically correct, even if they were unwilling or unable to teach the reason why a thing is a mystery. Physics professors are asking students to accept not only bad philosophy, but also bad science.
So, what is to be done? I believe that, in time, Relativity will be taught in a fashion similar to the teaching of the Bohr model of the atom. The Bohr Atom is useful to explain some aspects of molecular interactions. It is still taught in introductory classes in physics and chemistry, though it is made clear that we no longer believe that it is a true picture of the atom. In the same fashion, the teaching of Relativity needs to be revised as it will take a new approach to the study of light to resolve the more troubling aspects of Relativity theory.
Einstein had hoped all problems would resolve themselves at some point in the years after he presented his theories. But at the end of his life, the problems had been swept under the rug and very few people were aware that they had ever existed.
Einstein was a brilliant man who offered an innovative solution at a difficult time in science. But, all is not well in the land of Modern Physics and it begins here with Einstein’s original sin.