### How Much Do We Really Know About The Universe?

Stephen Hawking, the British physicist who is the topic of a 2014 biopic, makes a surprising statement in his 1992 book, *Black Holes and Baby Universes*, about the extent to which physics is almost complete. He says: “Although we have not found the exact form of all [the physical laws], we already know enough to determine what happens in all but the most extreme situations.” Hawking adds that he gives it a 50-50 chance that we will find the exact laws in the next twenty years.

We know already that his second statement hasn’t come to pass: 2012 passed and we’re not very close to a complete theory of everything. I’m not trying to pick on Hawking’s predictions, armed with the benefit of hindsight. Rather, what I want to highlight is how little we really do know about the universe, even at the fundamental physical level, and how little we can predict with any certainty, despite Hawking’s statements to the contrary.

We can obviously point to every social science, such as sociology, psychology, or economics, and recognize immediately that predicting the future is a futile task. Experts distinguish themselves by being able to talk intelligently about theory and the future but few are foolish enough to make firm predictions because these experts know that such predictions are impossible given our present state of knowledge, and perhaps impossible in principle.

But the problem of prediction—the sine qua non of science because it allows for testability of theories and thus their possible falsification—goes far beyond the “soft” social sciences. It’s also inherent to physics, the model of firmness in science.

Let me highlight a well-known problem to illustrate my point. Isaac Newton, the British physicist and mathematician who almost singlehandedly developed classical physics, included at the heart of his system the basic equation of what we now call Newtonian gravity. This simple equation shows that gravity declines between two bodies with the inverse square of their distance. So if we’re traveling in a spacecraft away from Earth the farther we go the smaller the gravitational attraction between the spacecraft and the planet, and it drops off pretty quickly but never disappears entirely. Newton’s famous equation, which showed that gravity was a universal force that applied in the realm of falling apples as equally in the realm of planets orbiting a star, only works for two bodies. In my example, it was the spacecraft and our planet.

What happens when we try to solve the equation for three bodies? Well, it gets exponentially more difficult. In fact, Henri Poincaré famously showed in a 1902 paper that the “three-body problem” couldn’t be solved at all. Huh? Why not?

Well, it turns out that even introducing one extra body to the gravitational situation trying to be analyzed introduces such sensitivity to initial conditions that it becomes impossible to make accurate predictions over the long-term. (A nerdy aside: some solutions are possible to this problem and it is now recognized that there are 16 families of solutions; however, these are very limited cases and the general problem is recognized as having no solution, in principle).

Hawking’s point about knowing the physical laws of our universe seems to ignore even this obvious example of the limits to our knowledge. Hawking surely knows about this example because he has, after all, for many decades now occupied the Lucasian chair at Cambridge that Newton himself occupied in the 17^{th} Century.

So was Hawking referring to, rather than our ability to make firm predictions, our ability to instead deduce the relevant equations that govern the universe (even if those equations can’t be solved in many cases)? Even if we interpret his statement in this manner it seems clear that he is also more optimistic than the facts warrant. In fact, it seems far more clear that we know very little about the laws that govern our universe.

General relativity leads to similar problems as we just saw in Newtonian gravity because solving Einstein’s gravity equations, a set of eight inter-linked equations, is fiendishly difficult in real-world situations. This is why Newtonian gravity is usually used in practice rather than general relativity. Many solutions to the relativistic equations have been found but solving the equations for three or more bodies is actually even more difficult than in Newton’s equation. Again, it’s impossible, in principle, to solve the “n-body problem” for general relativity in a general sense: only certain limited solutions are possible.

### The Big Problems In Physics

Lee Smolin discussed in his excellent 2006 book, *The Trouble With Physics*, five major problems that modern physics faces. There are, of course, far more than these problems facing modern physics, but Smolin was highlighting the big ones, which include:

- Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature (“quantum gravity,” “grand unified theory,” or the “theory of everything”).
- Resolve the problems in the foundations of quantum mechanics, either by making sense of the theory as it stands or by inventing a new theory that does make sense.
- Determine whether or not the various particles and forces can be unified in a theory that explains them all as manifestations of a single, fundamental entity.
- Explain how the values of the free constants in the standard model of particle physics are chosen in nature.
- Explain dark matter and dark energy. Or, if they don’t exist, determine how and why gravity is modified on large scales. More generally, explain why the constants of the standard model of cosmology, including the dark energy, have the values they do.

We are, unfortunately, far from solving any of these problems. Smolin’s book discusses in depth the problems with string theory, which attempts to resolve the first question by reconciling quantum theory and general relativity under a single framework. That these very large problems remain unsolved weighs heavily against Hawking’s optimism.

Marcelo Gleiser, a physicist at Dartmouth University in Vermont, supports my point in his 2014 book, *Island of Knowledge**: The Limits of Science and the Search for Meaning*, stating in the prologue to his book:

From our past successes we are confident that, in time, part of what is currently hidden will be incorporated into the scientific narrative, unknowns that will become knowns. But as I will argue in this book, other parts will remain hidden, unknowables that are unavoidable, even if what is unknowable in one age may not be in the next one. We strive toward knowledge, always more knowledge, but must understand that we are, and will remain, surrounded by mystery.

Taking an even deeper look at the nature of knowledge in our modern world, Nancy Cartwright examines in her 1999 book, *The Dappled World**: A Study of the Boundaries of Science*, how little we know about the universe. The dappled world she refers to is the patchwork of physical laws and theories that work pretty well in some limited situations. But her point is that there are vast gaps in our understanding that remain and our ability to predict outcomes is terrible in all but the most simple of situations.

### Are There Even Bigger Problems Remaining In Physics?

A major problem that Smolin alludes to but doesn’t include in his top five list is this: there is another important integration and reconciliation of different physical theories that has yet to happen. Going one step beyond reconciling quantum mechanics and general relativity, we need to reconcile thermodynamics with these two other pillars of modern physics. The nature of time is at the heart of this reconciliation. The problem is that most modern physical theories include a reversible concept of time. This means that the equations can be used to look backwards or forwards in time and there’s no basic difference between these two temporal directions. This is a problem because when we look at the world around us, near or far, we see irreversible processes everywhere, including the stubborn fact that eggs don’t unbreak themselves spontaneously, cream doesn’t unmix itself from your coffee when you stir the spoon the other way, and stars don’t unform gradually as gas drifts away slowly. All of these processes are irreversible despite the fact that our equations are often reversible.

By recognizing that irreversible processes are common in nature we should also recognize that time itself is fundamentally asymmetrical and irreversible. This notion of time allows us to make progress with the big problem of reconciling the concept of irreversible time in thermodynamics with the concepts of time in quantum mechanics and general relativity.

The Belgian-Russian physicist Ilya Prigogine made this point in a series of books and articles over a long career that ended with his death in 2003. He won the 1977 Nobel Prize in chemistry for his work on non-equilibrium thermodynamics, which is all about irreversible processes. Prigogine has this to say on the nature of time in his most readable book, *The End of Certainty: Time, Chaos, and the New Laws of Nature* (p. 19):

[A]ccording to the fundamental laws of physics, there should be no irreversible processes. We therefore see that we have inherited two conflicting views of nature from the nineteenth century: the time-reversible view based on the laws of dynamics and the evolutionary view based on entropy. How can these conflicting views be reconciled? After so many yeas, this problem is still with us.

Prigogine’s many decades of work is all directed at resolving this problem and his solution is to call for a comprehensive re-working of modern physical theories to incorporate an irreversible/asymmetrical concept of time. In other words, modern physics has yet to incorporate the concept of evolutionary time and an evolving universe. This is a big job, to be sure, but it has to be done if we are going to make real progress on the Theory of Everything that Hawking and many others wish to see happen.

### Evolving Time, Evolving Views

Things change and maybe Hawking now agrees with me anyway. He stated in a 2004 talk: “Up to now, most people have implicitly assumed that there is an ultimate theory that we will eventually discover. Indeed, I myself have suggested we might find it quite soon. However, [new developments in quantum gravity have] made me wonder if this is true. Maybe it is not possible to formulate the theory of the universe in a finite number of statements.” Hawking is here recognizing that perhaps his dream of a simple equation or set of equations that can explain and predict the entire universe is an impossible dream.

He adds at the end of this interesting talk:

Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I’m now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery.

Hear hear, and kudos to Mr. Hawking for allowing his views to change and acknowledging that process of evolutionary change.

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