I have been watching many science lectures of late; specifically those relating to cosmology, the origins of the universe and quantum mechanics. I do not have a physics or science background, but I like to educate myself about what is considered at the cutting edge of science. Essentially, I want to learn more about the Universe we live in. Sean Carroll is one of the few scientists who apart from being a very smart guy is an immensely engaging presenter.

The mark of true intelligence is not to understand a difficult thing, but to make a difficult thing understandable.

A quick bio:
Sean Carroll is a cosmologist and physics professor specializing in dark energy and general relativity. He is a research professor in the Department of Physics at the California Institute of Technology. Sean Carroll also hosts conversations in his ‘Mindscape’ podcasts with the world’s most interesting thinkers of Science, society, philosophy, culture, arts, and ideas.

There are few videos I find which linger in my psyche long enough; continually prodding me to revisit them until I can sufficiently internalise their full scope and meaning. The above ‘Many-Worlds’ lecture is one such video. To me at least, it seems overwhelmingly relevant; like the Geoffrey West – ‘From Cells to Cities podcast that I felt compelled to write excerpts as a personal development exercise. Some of what is written below is verbatim and some of it is redacted to be more reader-friendly.

Edited: At the time of writing this post I had linked Sean’s presentation above, but it has since been removed from You tube. Despite not having the source material handy, I believe the following excerpts entail the most important parts of the presentation:

The Quantum Mechanics Dilemma

If I were to tell you the position and velocity of every piece of stuff in the universe, the laws of physics can tell you exactly where it will go and where it has been. This is classical Newtonian mechanics.

In the 1920’s Quantum mechanics became a full-fledged theory. Newton’s laws were replaced by the Schrödinger equation for the quantum wave function. The equation tells you how the quantum mechanical wave function evolves with time. The Schrödinger equation is the quantum version of Isaac newton’s second law. It seems parallel to Classical mechanics, however:

The bottom line on Quantum Mechanics: What we observe is much less than what actually exists. Position and velocity are what you observe, but until you measure the particles, their positions don’t actually exist. Only the wave function does. Fundamentally, there is a difference between a thing when you are looking at it and when you are not looking at it. You cannot observe the wave function.

So it’s a particularly different view of reality.
The question you might want to ask is why does reality look normal to us at all. Why don’t I see a probability cloud all over the place? We don’t know.

The Copenhagen Interpretation of Quantum Mechanics

According to the Copenhagen interpretation, the act of observing a system  plays a crucially important central role in the formulation of quantum mechanics.  The wave function collapses and you see the electron in a certain position. The cloud tells you the probability of getting certain outcomes. The question remains; what was the law of physics doing before anyone was measuring things? What do we mean by measurement? Does it have to be a conscious human being? Can a rock, a virus and earthworm do an observation? This is known as the measurement problem in quantum mechanics.

 I think I can safely say nobody understands quantum mechanics. – Richard Feynman

Schrödinger’s Cat:

For explanation of what consists ofthe Schrödinger’s Cat Thought Experiment watch from 18.00 minutes in the ‘Many-Worlds’ video at the top of this page.

The system is in a ‘superposition‘ of all the possible measurement outcomes. Schrödinger took that idea of the superposition of possibilities and amplified until it was macroscopically real.

Entanglement: The state of one part of the universe can be related to the state of another part. As an observer, when you open the box you become entangled with the cat. Before there was a superposition of cat awake and cat asleep. Now there is a superposition of the cat awake and you seeing the cat awake or the cat asleep and you see the cat asleep. So we move into a superposition with the cat. But shouldn’t we include everything such as the whole universe? This is called the ‘environment’.

Process of Decoherence: The ‘environment’ has been interacting with the cat all along. Even before we open the box, the cat becomes entangled with the environment. When we open the box we become entangled with both. This is profound, because once the cat becomes entangled with the environment it can never become disentangled. It’s like mixing cream and coffee together; the increasing of entropy over time. The environment with the awake cat and the environment with the asleep cat will never interact with each other. They have split, they have gone their own ways. They have become two separate worlds and in these two versions ‘you’ can never talk to each other. The decoherence process of entanglement branches the wave function into two copies of the world. Fundamentally, this is pure quantum mechanics. All we did was obey the law of physics. What naturally happens is the wave function of the universe branches into different parts which do not interact with each other and hence they are described as different worlds. This encapsulates the Many-Worlds interpretation of quantum mechanics.

At no point did we put new worlds in. The worlds were already there. In the Copenhagen textbook Schrödinger’s Cat Thought Experiment, we had to erase part of the wave function. So if you saw the cat awake you erase the part where the cat was asleep and vice versa. And ‘you’ are quantum mechanical just like everything else in the Many-Worlds interpretation of quantum mechanics. If an electron can be in a superposition of that place, then a cat can be in a superposition of awake and asleep and you can be in a superposition of seeing the cat awake and seeing the cat asleep. And finally the Universe can be in a superposition of one where you saw the cat awake and one where you saw the cat asleep.

‘It’s not that ‘Many-Worlds’ is a theory of extra worlds, it’s that once you do quantum mechanics all the different worlds are already there. You can’t get to them, you can’t see them.

Hugh Everett, a graduate student of the 1950s examined in his PHD thesis what quantum mechanics is really trying to tell us. He argued there is no classical realm. There is no separate realm of people making observations of quantum systems because essentially you and I are made of atoms which are made of elementary particles which in-turn obey the rules of quantum mechanics. What this implies is that there are all these separate copies of reality. Every time a nucleus decays (or it doesn’t decay) it branches the wave function of the universe; every time particles scatter off each other and become entangled in their environment that also branches the wave function of the universe. There are many branches of the wave function that might come into existence. The space of all possible wave functions is called Hilbert’s space. It’s very very big.

The entirety of the assumptions that go into the Many-Worlds theory is: there are wave functions and we obey the Schrödinger equation. That’s it. Everything else is a consequence, a prediction, an implication of those assumptions. Are those assumptions testable? Yes of course. Whenever we do a quantum mechanics experiment we are testing the Many-Worlds theory. Despite what has been done up to this point, it still isn’t a fully-developed theory.

In Everett’s version ‘Many-Worlds’ there is nothing random about the world. The Schrödinger equation always applies and simply says what will happen next. It is completely deterministic. The problem is when you do experiments you see probabilities. When you have in front of you a nucleus which you know is going to decay we have no way of predicting with certainty when that decay will happen. The best we can do is ‘probability’.

There is something fundamentally stochastic and random about how nature works.

So there is a challenge to ‘Many-Worlds’. We know what the future wave function is going to be, but how do you get the probabilities out of a theory which has no probabilities in it?

Self locating uncertainty: You know the wave function of the universe, but not where you are within it. Among other things; you branch, and I branch. There are two copies of me, two future-selves and neither one of them know which branch they are on. There will necessarily be a short period of time when the branching has already happened. This process of decoherence in which the cat and its quantum system interacts with the environment is incredibly fast like 10 to the minus 20 seconds. Decoherence has happened much before your conscious-mind can process the outcome of that particular experiment.

So which branch are you on? The answer is it is the wave function squared. If the amplitude of the wave function of the cat being asleep was the square root of 30% then you should give yourself a 30% chance on being on the branch of wave function where the cat was asleep and vice versa.

Entanglement and Quantum fields

Atoms are not empty space. Atoms are mostly wave function. Electrons are either spinning clockwise or counterclockwise. Two electrons because of entanglement can be in a state of either; both spinning clockwise or both spinning counterclockwise. There is no possibility of one spinning counter and the other clockwise. But what will I observe when I look at a particle?  There would be a 50% probability that it is either spinning clockwise or counter. All I know is the other ‘entangled’ electron is spinning the same way. As Einstein demonstrated, the amount of entanglement between two particles doesn’t depend on how far away the 2 particles are.

These days our best theories are not about ‘particles’ per se rather of ‘fields’, like the electric field, the magnetic field, and the gravitational field. And essentially what a particle is; is a ‘vibration’ in the field. There are many different fields in this room. And if it’s vibrating softly we don’t see anything and if it’s vibrating enough you see a particle. Fields which are nearby are highly entangled and those which are far way not so-entangled.

What we have are different quantum mechanical degrees of freedom that are entangled or not. When the degrees of freedom are highly entangled we define that to be nearby and when they are disentangled we define that to be far away. You get an emergent notion of geometry of distances and time out of the quantum mechanical properties of entanglement. This theory seems to work. Entanglement defines both the geometry of space, and the energy within it. This is a new exciting perspective of the problem of quantum gravity. ‘Nature’ of course doesn’t start with a classical theory and therafter quantized, rather, nature is quantum from the start.

We shouldn’t be starting with the classical theory of relativity and then applying rules to turn it into a quantum theory.  Maybe we should be starting with quantum mechanics.

Perhaps we shouldn’t be quantising gravity but finding gravity within quantum mechanics. What we find; and it seems reasonable; is that this emergent geometry that we define from quantum entanglement obeys the above equation (see above image). It obeys Einstein’s equation for general relativity. On the left hand side is the expression how much curvature there is in space-time and on the right an expression of how much ‘stuff’ there is in the Universe. How much energy, heat, and momentum etc. So Einstein’s version of the gravitational field between two bodies depends on how far away they are – Newton’s law of Gravity. This rule governs how the curvature of space time responds to energy and momentum and we are able to see that rule emerge from a theory that doesn’t even have space-time in it. It is solely quantum entanglement.

By taking quantum mechanics seriously; by thinking deeply about what it means to be in a quantum state; how it evolves; branching, decoherence and asking questions about the classical world in that theory you not only get an answer that explains cats and electrons, but maybe the universe itself.

Related Links:
1. Sean Carroll – Mindscape podcast Episode 28: Roger Penrose on Spacetime, Consciousness, and the Universe.