- Theory of relativity
- Fairly Simple Math Could Bridge Quantum Mechanics and General Relativity
- Why can't Einstein and Quantum Mechanics get along?
- Instant Expert: General relativity
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Although this question is extremely difficult to answer, the question itself is as simple as deciphering a pop star's lyric. Before we begin solving the unsolvable universe, let's break down the components. First let's tackle quantum mechanics.
Theory of relativity
And it's a good place to start, because it's the study of something extremely small -- matter and radiation at the atomic and subatomic levels. It was really only when scientists began understanding atoms that regular old physics needed a bit of an amendment. Because as scientists looked at atoms, they didn't behave as the rest of the universe did. For instance, electrons didn't orbit the nucleus like a planet orbiting the sun -- if so, they would've careened into the nucleus [source: Stedl ].
It became clear that classical physics didn't cut it on an atomic scale.
Fairly Simple Math Could Bridge Quantum Mechanics and General Relativity
So quantum mechanics arose out of a necessity to understand how very small phenomena acted differently than the Big Things in science. What we discovered was that something like a photon could act as a particle which carries mass and energy and a wave which carries only energy. Not always, but…. First of all, the prevailing quantum theory, quantum field theory, is fully relativistic from the onset.
When I say fully relativistic, I mean special relativity.
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Sure, things get interesting in the general case, we have to fully embrace the field concept and give up on the notion of particles altogether but the theory works. Well… Einstein tells us that matter is the source of gravity, through the stress-energy tensor. But in a quantum theory, this stress-energy tensor consists not of numbers but of so-called noncommuting operators. Does this mean that the gravitational field must also be described by a quantum theory? Well, maybe… but nobody succeeded with that. We do not have a viable quantum theory of gravity.
Electricity, for instance, sends photons between charged particles, the strong force uses gluons, and the weak force uses the W and Z bosons. Because of quantum uncertainty, there is no way to figure out which slit a particular electron travels through: An electron literally travels through both slits at once. This, in and of itself, is kind of nuts, but in the context of gravity, it gets even stranger. If the electron goes through one slit it presumably creates a very slightly different gravitational field than if it goes through the other.
It gets even stranger when you realize that according to Wheeler's delayed choice experiment it's possible to set up the experiment so that after you've already run the experiment, you can retroactively observe the system and force the electron to travel through one slit or another though you can't choose which.
Crazy, no? Put another way, the world of gravity is supposed to be entirely deterministic, but quantum mechanics is anything but.
There's an even deeper issue: unlike with, say, electricity which only affects charged particles, gravity seems to affect everything. All forms of mass and energy respond to gravity and create gravitational fields, and unlike with electricity, there aren't negative masses to cancel out the positive ones. We can imagine a quantum theory of gravity, at least in principle. Like with the other forces, there would be a mediator particle, proactively called the graviton , which would carry the signal. We could even imagine probing smaller and smaller scales, and seeing more and more virtual gravitons being sent between particles.
Why can't Einstein and Quantum Mechanics get along?
The problem is that on smaller scales, there are higher and higher energies. The nucleus of an atom requires much more of a punch to break apart than peeling an electron off the outside, for instance. On the smallest scales, the swarm of insanely high energy virtual gravitons would produce an incredible energy density, and that's where we really run into problems. Gravity is supposed to see all forms of energy, but here we are generating an infinite amount of highly energetic particles which in turn generates a huge gravitational field.
Maybe you see the difficulty.
Instant Expert: General relativity
At the end of the day, every calculation involves a whole bunch of infinities flying around. I am required by long tradition to point out that we have no freakin' clue how physics is supposed to work on scales smaller than the Planck Length. On those scales, quantum mechanics says that miniscule black holes can pop into and out of existence through sheer randomness, suggesting spacetime itself gets pockmarked if you look at it too closely.
We try to avoid these collisions of theories through a process known as "Renormalization" thrown in as fan service for the experts. Renormalization is simply a fancy way of saying that we only do the calculation down to a certain scale and then stop.
It gets rid of the infinities in most theories, and allows us to carry on with our lives. Since most forces only involve taking differences between two energies, it doesn't really matter if you add or subtract a constant to all of your numbers even, ostensibly, if the constant you're adding is infinity. The differences work out fine. Not everyone is so sanguine with this.
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The great Richard Feynman noted :. The shell game that we play.
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But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. Those objections aside, things get even worse when we talk about gravity.