The light that Einstein sees

I read another New Scientist article today. The article was written by Brian Greene. While it didn’t give me a lot of new information, it made an interesting point about what it means (and when is it particularly effective) to take our mathematics seriously.  He talked about Einstein’s insight regarding the speed of light.  It was in the late 1800s, he explains, when Maxwell’s equations gave it the value of 300,000 kilometers per second (close to experimental measurements).  But the equations didn’t say anything about the standard of rest that gave this speed meaning.  Greene reminds us of the postulated invisible medium for transmitting light (the ether) which he calls a makeshift resolution to the problem. He then goes on to highlight a particular aspect of Einstein’s insight.

It was Einstein who in the early 20th century argued that scientists needed to take Maxwell’s equations more seriously. If Maxwell’s equations did not refer to a standard of rest, then there was no need for a standard of rest. Light’s speed, Einstein forcefully declared, is 300,000 kilometers per second relative to anything. The details are of historical interest, but I’m describing this episode for a larger point: everyone had access to Maxwell’s mathematics, but it took the genius of Einstein to embrace it fully. His assumption of light’s absolute speed allowed him to break through first to the special theory of relativity – overturning centuries of thought regarding space, time, matter and energy – and eventually to the general theory of relativity, the theory of gravity that is still the basis for our working model of the cosmos. (emphases added)

This is a detail about Einstein’s thinking that I hadn’t understood in quite that way.  It’s a provocative idea. Mathematical necessity overrides the expectations created by our physical intuition.  If the equation doesn’t depend on a standard of rest, than neither does the speed of light.  Mathematics, here, is acting much like a human sense, a mode of perception.

After reading this, my own thoughts went down a number of different paths, which I can’t recall well enough to repeat here.  But the precedence that mathematics has taken in physical theories, eventually led me to look at discussions centered around whether reality was fundamentally made of material or meaning.  One of the schools of thought that reflects this question finds information to be more fundamental to reality than material.  Paul Davies and Niels Henrik Gregersen compiled a collection of essays that address this issue in the book Information and the Nature of Reality. In his introduction, Davies describes Einstein’s theory of special relativity and general relativity as the first blow to our confidence in the idea of ‘matter.’

By stating the principle of an equivalence of mass and energy, the field character of matter came into focus, and philosophers of science began to discuss to what extent relativity theory implied a ‘de-materialization’ of the concept of matter.

Later, of course, quantum physics not only amplified this question, but also raised other yet unanswered questions about the significance of the observer.  Again from Davies:

A wave function is an encapsulation of all that is known about a quantum system. When an observation is made, and that encapsulated knowledge changes, so does the wave function, and hence the subsequent quantum evolution of the system. Moreover, informational structures also play an undeniable causal role in material constellations, as we see in, for example, the physical phenomenon of resonance, or in biological systems such as DNA sequences.

In an interview for the radio show To The Best of Our Knowledge Davies said this about the view of reality that quantum theory may be expressing:

…when we human beings, make observation of the world, we are interrogating nature, we are getting yes/no answers in the most primitive way. Every scientific experiment consists of doing exactly that. Come back to the simple example I gave where it is obviously true that the electron bounds to the left or the right. You get a yes/no answer. In the world of Quantum Physics, we get into another subtlety here. Which is the possibility of the super position. Now, you toss a coin it is heads or tails. But in Quantum Physics, if you toss a quantum coin, and this might be like the spin of particle or something, you can have a little of heads and another tails. Or a little bit of tails, but a lot of heads. You can have any mixture of the two.  In other words, an atom can be in the head and tails state, or in both states, at once. So in this sense the theory can take us to a God’s eye view, not a human view. Whenever human beings make observations, they get definite yes/no answers. But, if we could look to the world through these God-like eyes, and see the superposition, we would see that there is more than just yes and no or one and zero.

Certainly this opens the door to theological discussions, which the book does include. But just as interesting is the more fundamental question:  What is the mode of perception that mathematics provides?  Our visual systems structure the data that floods the retina.  To what does mathematics give structure?

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