You know that scientists are a little crazy when they have to jump off of rooftops to learn that space and time can stretch like a trampoline. Or that we often contemplate the silliest notions, like that of cats that can be dead and alive at the same time only when they are in a box. And if that wasn’t enough, PETA is probably pissed off at Schrödinger for animal cruelty. Maybe.
Our view of the universe over the last century has changed so dramatically that it really takes your intuitions about reality to the trash heap. Richard Feynman, one of the founders of quantum field theory, commented on how weird the world appears to us in a lecture: “The thing that’s exciting about this is that in nature is strange as it can be, in this sense: that the rules that are gonna be obeyed… are so screwy, you can’t believe them!”
He also said that no one, including himself, understood quantum mechanics. Sounds promising, I know. So, what have we actually learned, and what makes it so peculiar to us human beings?
For starters, whenever you walk into physics class starting at 8:30am in the morning and arrive just in time, you might say to yourself, anyone who comes in after me is late. There you’ve already made a false assumption about the world. We all believe that time ticks according to our awesome Rolex watch and so our time must be correct. Albert Einstein destroyed much more than just this notion. Not only can clocks run at different rates due to gravity and motion warping time and space, but in fact, your wristwatch is deceiving you… time doesn’t really flow at all.
Who knew Parmenides was such a good theoretical physicist? Einstein also remarked that if you can’t explain something simply, you don’t really understand it. So, let’s breakdown things about physics so that we can all agree on how bad we are at judging reality. For starters, it is surprisingly easy to fool the human brain. It is actually quite the mystery of evolution as to what caused our brains to grow in size so rapidly, and over such a short and recent period of time. Yet they still have their shortcomings. For example, consider the following image:
Move your eyes across this field of blue dots and you may discover they are moving like a water wave. That is, if you were crazy. Because they aren’t moving at all. You silly goose. Believe it or not, it is simply the awkward shading and coloring scheme of the circles in this picture that proceeds to illicit your brain into thinking that motion is taking place. You should see from this trivially simple example that our minds are not so impervious to being deceived by nature as we might foolishly believe.
In comes quantum mechanics. As it turns out, the quantum theory gets a bad rap due to mystics who will invoke it in some kind of new age spiritualism nonsense. Don’t be fooled: you will never be able to transcend your body using wave functions. However, you might be able to walk through a wall, if you try enough go times. Go ahead, we’ll wait…
Basically, quantum mechanics tells us that nature does not like to be told what to do. In any given experiment, only the likelihoods of various outcomes can be determined. We don’t really know what goes on in particle interactions, but what we do know is that in the quantum world, there is very little that we can currently measure that we can predict with certainty. For the mathematically inclined reader (if you and math broke up in high school and never got back together during a high school musical, skip to the next paragraph), the state vector of a quantum system |𝛹⟩ determines the probabilities for various outcomes in experiments to occur. It solves the famous Schrödinger equation Ĥ|𝛹⟩=i∂|𝛹⟩/∂t where Ĥ is an operator representing the system’s energy called the Hamiltonian. Once Schrödinger’s equation is solved, |𝛹⟩ may be expressed as a linear combination the eigenvectors |n⟩ of Ĥ. This looks like |𝛹⟩ =∑|n⟩⟨n|𝛹⟩. If we set |𝛹⟩=|m⟩, meaning we place the system initially in a pure energy state, then we are guaranteed to always measure E(m), the associated eigenvalue for |m⟩, when we measure the energy. But if we instead decided to measure a different observable quantity Â, then we would have to express the pure energy state |m⟩ as a linear combination of the eigenvectors |a(n)⟩ of Â. This would instead give us |m⟩=∑|a(n)⟩⟨a(n)|m⟩. Now the probability amplitude to measure Â and obtain the associated eigenvalue A(k) is 𝒜(𝓉)=⟨a(k)|n⟩=∑⟨a(k)|a(n)⟩⟨a(n)|m⟩=⟨a(k)|m⟩, which can be nonzero in general, no matter which A(k) we look for in the experiment.
It seems that in the quantum realm, when we treat objects as if they can be in two places at once, they act as if they do just that. They can even appear to be influenced by us in such a way that they “decide” how to behave before we measure them. Wrap your head around that. Throw your intuition about nature out the window. It won’t help you here.
Leaving the small scale stuff behind, we enter the realm of relativity, which governs the galactic scales of the universe. Einstein’s daydream of what it would be like to ride a beam of light forced him to conclude, based on physics that was known during the early 20th century, that time and space are woven together like the threads of your clothing. They simply can not be separated. Furthermore, he was able to show that gravity was the result of matter and energy warping and curving this space-time fabric (time to skip ahead again, you brave souls). Given a four-dimensional Lorentzian manifold (ℳ,𝔤), equipped with a metric tensor 𝔤, the Einstein field equations relate the trace-reversed Ricci curvature G of ℳ to its source through G=8𝜋𝛵, where 𝛵 is the stress-energy tensor of the source. Then the trajectories particles are determined by the geodesic equation δν(τ)/δτ=0, where ν is the tangent vector to the manifold parametrized by the affine parameter τ. Notice that, just like space, time plays no privileged role in the manifold or in the field equations. The difference between time and space only manifests itself in the metric signature of ℳ, which for any four-dimensional Lorentzian manifold is (-,+,+,+) up to a sign. In fact, plenty of solutions are known which allow time to flow in reverse, such as Kurt Gödel’s spherically symmetric rotating dust solution.
So in Einstein’s world, time is to be viewed no differently than space. Yet how does this imply that we have all been cunningly fooled by the universe and that the flow of time is an illusion? Well, many have argued that relativity alone is enough to conclude this, but there is yet one more idea we could invoke. We currently do not understand how gravity, as Einstein viewed it, integrates with the picture of the world given to us by quantum mechanics. However, along with the plethora of suggestions that have been presented over the years, one such method has been investigated by such great thinkers as Bryce DeWitt, James Hartle, and Stephen Hawking. The equation governing this toy model of quantum gravity is so simple that even the poor folks who have nightmares about algebra and calculus do not have to run away this time.
It is called the Wheeler-deWitt equation:
No, really, that’s all there is to it.
Of course, we’ve left out some complicated details, but the important message is what this equation is telling us. Earlier, when we were discussing quantum mechanics, we were dealing with Schrödinger’s equation. The right hand side was not zero; it depended on how quickly the system evolved in time. Physically, this meant that the Ĥ term generated the flow of time evolution for the system. But in the Wheeler-deWitt equation, Ĥ doesn’t generate anything at all- it’s what mathematicians call the “Hamiltonian constraint.” In other words, one concludes mathematically that time isn’t even a part of the ultimate theory of quantum gravity. As Hawking put it, the big bang is sort of like the beginning of a meter stick. It makes no sense to ask what was before time began, just as it makes no sense for an ant on a ruler to wonder how the ruler doesn’t go farther back than the zero-inch mark. This feature of reality, should it be true, would be known as timelessness.
This could all be trashed one day if we discover the so called Theory of Everything and it conflicts with the Wheeler-deWitt equation, or even relativity. Yet for now, our best understanding of the universe does not even privilege a direction to time, much less a flow of time. It is truly stunning to realize not only what we have learned about our world, but that it is more peculiar than science fiction. How is it that our physical intuitions about what should be true is so many orders of magnitude removed from what is true?
We began considering ourselves as the center of the universe. Why wouldn’t we? No other animal could build the Hubble space telescope or the large hadron collider, even though those achievements were only realized far after this myth was dispelled. Our brains appear as extremely massive on any scale you’d like to pick, even though it’s generally difficult to measure intelligence accurately. But we unfortunately have a dangerous tendency to resist that which is unfamiliar to us. Galileo was condemned to prison for believing the earth revolved around the sun, simply because the catholic church had made geocentrism dogma. Michael Servetus, the physician who discovered pulmonary circulation, was burned alive by the Inquisition in Switzerland. Even Albert Einstein’s theory of relativity was burned and banned by the Nazis for being “Jewish Science.”
We evolved to survive. Not to do mathematics, or write poetry, or wonder about the world. Why are we so afraid of the dark? It likely aided our survival back when we didn’t have secure housing and had to worry about Scar creeping on us during bedtime. But even in our own homes, we fear ghosts in the hallways and the boogeyman in our closets. The amazing fact is, it would probably give you a heart attack if your eyes were to be opened for the first time. We can only see about .0035% of the light around us; that means there are somewhere around 200 thousand colors invisible to us. Around half a trillion solar neutrinos just now (every second) passed through your eyes’ exposed surfaces, completely undetected by your corneas. And we haven’t even mentioned the octillion (a billion billion billion, or 10 to the 27th power) air molecules in your room, all of which couldn’t care less that your lamp is turned off.
Our human intuition about the world could really use, as Red liked to say, a swift kick in the ass.