“Electromagnetic theory gave a first crucial insight 150 years ago. The Scottish physicist James Clerk Maxwell showed that when electric and magnetic fields change in time, they interact to produce a travelling electromagnetic wave. Maxwell calculated the speed of the wave from his equations and found it to be exactly the known speed of light. This strongly suggested that light was an electromagnetic wave – as was soon definitively confirmed.”
“Until quantum theory came along, electromagnetism was the complete theory of light. It remains tremendously important and useful, but it raises a question. To calculate the speed of light in a vacuum, Maxwell used empirically measured values for two constants that define the electric and magnetic properties of empty space. Call them, respectively, Ɛ0 and μ0. The thing is, in a vacuum, it’s not clear that these numbers should mean anything. After all, electricity and magnetism actually arise from the behaviour of charged elementary particles such as electrons. But if we’re talking about empty space, there shouldn’t be any particles in there, should there? This is where quantum physics enters. In the advanced version called quantum field theory, a vacuum is never really empty. It is the ‘vacuum state’, the lowest energy of a quantum system. It is an arena in which quantum fluctuations produce evanescent energies and elementary particles.”
“What’s a quantum fluctuation? Heisenberg’s Uncertainty Principle states that there is always some indefiniteness associated with physical measurements. According to classical physics, we can know exactly the position and momentum of, for example, a billiard ball at rest. But this is precisely what the Uncertainty Principle denies. According to Heisenberg, we can’t accurately know both at the same time. It’s as if the ball quivered or jittered slightly relative to the fixed values we think it has. These fluctuations are too small to make much difference at the human scale; but in a quantum vacuum, they produce tiny bursts of energy or (equivalently) matter, in the form of elementary particles that rapidly pop in and out of existence.”
“These short-lived phenomena might seem to be a ghostly form of reality. But they do have measurable effects, including electromagnetic ones. That’s because these fleeting excitations of the quantum vacuum appear as pairs of particles and antiparticles with equal and opposite electric charge, such as electrons and positrons. An electric field applied to the vacuum distorts these pairs to produce an electric response, and a magnetic field affects them to create a magnetic response. This behaviour gives us a way to calculate, not just measure, the electromagnetic properties of the quantum vacuum and, from them, to derive the value of c.”
“So, let’s assume that these constants really are constant. Are they fundamental? Are some more fundamental than others? What do we even mean by ‘fundamental’ in this context? One way to approach the issue would be to ask what is the smallest set of constants from which the others can be derived. Sets of two to 10 constants have been proposed, but one useful choice has been just three: h, c and G, collectively representing relativity and quantum theory.”
“In 1899, Max Planck, who founded quantum physics, examined the relations among h, c and G and the three basic aspects or dimensions of physical reality: space, time,and mass. Every measured physical quantity is defined by its numerical value and its dimensions. We don’t quote c simply as 300,000, but as 300,000 kilometres per second, or 186,000 miles per second, or 0.984 feet per nanosecond. The numbers and units are vastly different, but the dimensions are the same: length divided by time. In the same way, G and h have, respectively, dimensions of [length2)] and [mass x length-35 metres, 2.2 x 10-44 seconds. Among their admirable properties, these Planck units give insights into quantum gravity and the early Universe.”
“But some constants involve no dimensions at all. These are so-called dimensionless constants – pure numbers, such as the ratio of the proton mass to the electron mass. That is simply the number 1836.2 (which is thought to be a little peculiar because we do not know why it is so large). According to the physicist Michael Duff of Imperial College London, only the dimensionless constants are really ‘fundamental’, because they are independent of any system of measurement. Dimensional constants, on the other hand, ‘are merely human constructs whose number and values differ from one choice of units to the next’.”
“Perhaps the most intriguing of the dimensionless constants is the fine-structure constant α. It was first determined in 1916, when quantum theory was combined with relativity to account for details or ‘fine structure’ in the atomic spectrum of hydrogen. In the theory, α is the speed of the electron orbiting the hydrogen nucleus divided by c. It has the value 0.0072973525698, or almost exactly 1/137.”
“Today, within quantum electrodynamics (the theory of how light and matter interact), α defines the strength of the electromagnetic force on an electron. This gives it a huge role. Along with gravity and the strong and weak nuclear forces, electromagnetism defines how the Universe works. But no one has yet explained the value 1/137, a number with no obvious antecedents or meaningful links. The Nobel Prize-winning physicist Richard Feynman wrote that α has been ‘a mystery ever since it was discovered… a magic number that comes to us with no understanding by man. You might say the “hand of God” wrote that number, and “we don’t know how He pushed his pencil”.’”
“Whether it was the ‘hand of God’ or some truly fundamental physical process that formed the constants, it is their apparent arbitrariness that drives physicists mad. Why these numbers? Couldn’t they have been different? One way to deal with this disquieting sense of contingency is to confront it head-on. This path leads us to the anthropic principle, the philosophical idea that what we observe in the Universe must be compatible with the fact that we humans are here to observe it. A slightly different value for α would change the Universe; for instance by making it impossible for stellar processes to produce carbon, meaning that our own carbon-based life would not exist. In short, the reason we see the values that we see is that, if they were very different, we wouldn’t be around to see them. QED. Such considerations have been used to limit α to between 1/170 and 1/80, since anything outside that range would rule out our own existence.”
“These possibilities are entertaining to think about – and they might well be real in adjacent universes. But there’s something very intriguing about how tightly constructed the laws of our own Universe appear to be. Leuchs points out that linking c to the quantum vacuum would show, remarkably, that quantum fluctuations are ‘subtly embedded’ in classical electromagnetism, even though electromagnetic theory preceded the discovery of the quantum realm by 35 years. The linkage would also be a shining example of how quantum effects influence the whole Universe.”
“Presumably the different parts of the multiverse would have to connect to one another in specific ways that follow their own laws – and presumably it would in turn be possible to imagine different ways for those universes to relate. Why should the multiverse work like this, and not that? Perhaps it isn’t possible for the intellect to overcome a sense of the arbitrariness of things. We are close here to the old philosophical riddle, of why there is something rather than nothing. That’s a mystery into which perhaps no light can penetrate.”