In the early 1800s, Marquis de Laplace thought that because science was doing such a good job explaining everything, that it would be possible to predict everything if only scientists knew the total make up of the universe at one moment in time. He thought this could extend even to predicting human behavior. This idea remained influential for decades, though it was unpopular among those who believed God’s freedom to act should be uninhibited.
Laplace was optimistic about a unified theory of everything more than a century ahead of Hawking. But he faced opposition from religious groups, who disliked how this idea affected their notion of an omnipotent god. This opposition seems to have been ineffective, as Hawking states the idea remained popular, showing the enthusiasm spread. People wanted to know exactly how the world worked, and couldn’t be put off the idea, once offered.
Later, Lord Rayleigh and Sir James Jeans suggested hot bodies, like stars, radiate energy at infinite rates; this would mean the total energy emitted would be infinite, however, which is not considered possible. Max Planck then suggested that light, and all waves, would be emitted in certain amounts, called quanta. Higher frequencies of light would be emitted in higher-energy quanta. This would make the energy released, and the energy the star lost, finite.
Work continued on unfinished business in the scientific arena. Planck’s discovery of quantum theory did a lot to help scientists understand how stars and other objects emit energy, as well as how to apply that energy in the lab. Slowly, scientists were eliminating infinities from humanity’s understanding of the universe.
Werner Heisenberg used this theory to create his uncertainty principle. To measure a particle’s position and velocity, one must shine light on it to see where it is. The higher the frequency of the light in the quantum, the more accurately you can see the particle, because the wavelengths of the light will be shorter. But that means more energy will be applied to the particle, therefore changing its position or velocity. So, the more accurately one wishes to measure a particle’s position or velocity, the more uncertainty created. This is a fundamental principle of the world.
Scientists can see particles by shining light with high-frequency wavelengths on the particles, because if the particle is smaller than the gap between each wave crest, it cannot be directly detected. As Planck’s quantum theory of light tells us, high-frequency quanta (or packets) of light have more energy. That means the more accurately one wants to see the particle, the more energy that is then applied to that particle, and the more that energy will push the particle off its original course. Essentially, scientists cannot definitively position particles in space-time.
This was the end of Laplace’s idea of determinism. There was still place for God in this model, but it did not help mere mortals to understand how he might work. Instead, it was better to leave out of the theory that which humans cannot see.
If scientists cannot accurately locate particles, there is no way they can definitively know the make up of the entire universe, meaning Laplace’s hopes of being able to predict even human behavior were dead. But, this uncertainty left lots of room for God’s autonomy, which Hawking notes to show how religion tends to occupy the unknown or unknowable aspects of the universe.
Heisenberg, Erwin Schrodinger, and Paul Dirac in the 1920s created quantum mechanics based on the uncertainty principle. This theory does not predict definite outcomes, but potential outcomes. It works on the basis of probability, with no definite outcome for each individual observation, therefore introducing randomness into science. Einstein objected to this approach despite the fact his Nobel Prize was partly awarded for his contributions to the theory. He said, “God doesn’t play dice.” Yet quantum mechanics works very well with observations and it underlies all of modern science, including electronic chips. The only areas of science that not yet been integrated into this theory are gravity and the larger structure of the universe.
Science, once again, was turned on its head. Scientists could no longer confidently place particles in space-time, let alone accurately predict their movements. This was something Einstein could not accept, it seems on religious grounds based on the quote Hawking provides. Nevertheless, science works on objective assessment of observations, Hawking emphasizes, in continuing to discuss the theory that expanded and developed whether Einstein backed it or not.
Planck suggested that light, although a wave, could act as a particle, being emitted only in certain quanta. Heisenberg’s uncertainty principle made particles seem more like waves, with their movement spread out according to probability. There is therefore a duality between waves and particles in this new theory. This means scientist must consider the interference of these waves, where the peak and a trough of two waves meet, canceling each other out. This same effect creates the colors in bubbles, as waves overlap and strengthen or cancel each other out.
Even the distinction between particles and waves became blurred in this new age of science, something that scientists seemed to absorb on the basis that it agreed with observations. This necessitated a new approach, again. Hawking provides an everyday example here to help the reader, who, like the scientists of the time, now must wrap their head around another new perspective.
If particles can be like waves, this canceling out happens with them also. If one passes light through two slits in a paper divide onto a wall behind, the light will generally travel different distances from the light source, and through the slits, to reach the wall. Therefore, the wavelengths of these beams of light will overlap rather than arrive “in phase with each other,” canceling out where a wave’s trough hits a peak, or strengthening each other where a peak combines with another peak. This creates a fringed pattern of light on the wall, as the light has not hit in a uniform manner. This happens with particles in the same way. But when passing just one particle through one slit at a time, the pattern still shows, as though it had passed through both slits at the same time and interfered with itself.
When a wave crest meets another wave crest, they combine into a larger crest. When crest meets a trough, they cancel each other out into nothing. So, as light waves bounce around on their way to the wall, they are not all traveling in unison with each other, creating lines of light on the wall that represent this interference that happens as different waves meet. The same effect happens with particles, as crests support crests and cancel out with troughs on their passage through the divide, toward the wall. The really remarkable thing is this happens when passing just one particle through the divide! The question therefore is how does the one particle cancel itself out, as it ought to only take one path, rather than interfere with other particles.
This has helped scientists to understand the atom. At first atoms were seen as mini solar systems, with a nucleus orbited by other miniscule particles, but many wondered why it did not all collapse. Niels Bohr suggested in 1913 that electrons could only orbit at specific distances, which would balance it all out. According to quantum mechanics, the electrons would move as waves, and therefore would only form orbits where the wavelengths were whole numbers. If the wavelengths needed to complete an orbit was not a whole number, then the wavelength would cancel itself out when the electron’s trough met a peak on its way around.
Using the same logic, Bohr discerned that an electron’s wavelength would eventually cancel itself out on its orbit around the nucleus of an atom if its wave crests didn’t match up each time round. Otherwise, a crest would eventually meet a trough and cancel out. As such, electrons would fit into the orbits where their wavelengths would be consistent with each orbit, holding the atom’s structure together.
Richard Feynman created the sum over histories theory to explain this. A particle is said to travel from A to B by every possible path. By adding up all the wavelengths for all the paths, and finding which cancel each other out, one can find the probability of traveling from A to B. This provides the math to predict particle movement, though in practice it is too difficult for calculating the movement of anything more than a simple atom.
Bohr’s work allowed Feynman to take the next step and find a mathematical way to assess all of this unpredictability and find the most likely paths electrons would take even in molecules, which are a group of atoms. As Hawking notes, however, in reality the math is too hard to do, meaning scientists are left accepting the unpredictability of the universe’s smallest particles.
Einstein’s general theory of relativity is considered a classical theory because it does not include quantum mechanics. This does not lead to inconsistency, though, as gravitational forces are so weak compared to other forces. But gravity would be much stronger in black holes or at the big bang, and as such needs to be integrated into quantum mechanics. Just as the idea of atoms collapsing was wrong, so too might be ideas of singularities. Scientists need to unify these two theories and already know some properties such a theory would have, as well as the areas in which it would have the greatest significance.
As Hawking mentioned previously, the unification of physics depends on integrating the general theory of relativity and quantum mechanics, which might not be as mutually exclusive as they appear at first glance. He holds out hope because achieving unification would answer some of the most perplexing mysteries scientists have grappled with, mysteries they cannot even see and which, potentially, might be proven not to exist at all.