The Many Memories of Quantum Mechanics

Quantum mechanics (QM) is the physics of the small stuff of the universe - the smaller the better. (General relativity applies to the big stuff - the bigger the better.)

There are three mathematical formulations of QM. They are formulations, not separate theories, because they are exactly equivalent mathematically. One, due to Schrödinger, is based upon space-time, wave patterns, and makes the universe look continuous. Like, really continuous. Schrödinger functions have no boundary - each one fills all of possible space if you wait long enough. A second, Heisenberg, is based upon observable energy movement, quantum jumps, and makes the universe look like particles. In this view, all particles but one are made of other particles - the universe is the ultimate particle. The third, Everett, is based upon information, and makes the universe look sensible - like we think we are.

In the world of theoretical physics, if you want to be right, to be an authority, use Schrödinger and Heisenberg. But, if you want to get things right, to understand them, try Everett. But, never forget that they are all mathematics, not physics based on observables.

When some physicists are between ideas, they argue about the 'meaning' of QM. All too often, it sounds like democracy being your right to say what you think without thinking. Some of the non-thoughts out there about the Everett formulation are really, well, out of this world. It's usually referred to by denigrating physicists and would-be mystics alike as the 'many worlds' theory. As I've mentioned, it isn't a theory. It's exactly the same thing as the Schrödinger and Heisenberg formulations. Any criticism of one is a criticism of them all. But the Everett formulation is indeed about many worlds, as long as you clarify what a QM world is.

The world of a quantum particle is, I submit, everything that has happened to that particle that can affect its future interactions with other particles. "Many histories" is a better way of describing the concept. But, only things that can affect future interactions are part of QM history. Most of what has 'happened to a particle' can no longer affect its future, because each particle only has a small number of memory locations (quantum degrees of freedom) with which to 'remember' things. The far past is not an observable, or, past states are decorrelated. So, "many memories" is the way I prefer to think of a QM world.

Superposition of States

The easiest idea in the Everett formulation to jump on at first glance is that each time a particle interacts with another particle, 'new worlds' are created, each containing a different possible result of that interaction. So, the number of worlds seems to increase without limit and that is nonsense.

It would be nonsense. But, it isn't what happens, in this world anyway. Here is a human analogy of a quantum jump and of multiple worlds.

Suppose that your significant other is visiting the next town and, on the radio, you hear that half that town has been blown up by a gas leak. By the time you hear the news, your other is only in one state. One way or another, the explosion is complete. But, you sure aren't in one state! Half of you is worried that your bed won't be warm tonight, the other half is worried that the breakfast argument will be continued at dinner. You phone your nurturing parent for some solace, and promptly create a pair of worlds at the other end of the telephone line...

Finally, you get that phone call, from your s.o. or from the police. One way or another, you make your quantum jump and one of your states (worlds) dissolves from reality. Gradually, your family and friends follow suit as they talk to you. Of course, years later, you can still run into someone who asks "Did your ? ?" But, once everyone who interacted with any of you when you were in two pieces (in superposed states) has heard the news, or has passed on to that other world, your world is back to being one again with regard to that particular matter.

That's what happens to quantum particles. Quantum worlds fade from existence as fast as new ones are created. The amount of information in a closed universe is constant. (I'm personally not sure if a universe with black holes in it is closed.) Schrödinger's cat is in one state - it's us, our knowledge, outside the cat's closed box that's in two states. But you'd never guess that from Schrödinger's formulation. You have to follow the information.

An 'observer' can be as small as a single radioactive nucleus - things our size and complexity are not required. In fact, any two even partially-correlated quanta can 'observe' another single quantum. In the limit, quantum mechanics is a continuous function.

Correlation of States

There is another aspect of QM that Everett's formulation makes too obvious to avoid - there is no one reality. Every quantum world differs from every other. Existence is relative. How can this be? Is our universe not consistent?

Again, a human analogy is useful.

When you go to a party, you usually meet people you've never met before, whose worlds you have never known. Some of those worlds can be quite something, too! In physics language, there is little correlation between your states. By the end of the evening (interaction), you have some shared party experiences - your states are more correlated than they were before. If you never meet again, the shared memories fade, and your worlds slowly return to almost their previous separateness (they decorrelate). You'll never be the same again, but you're still the same you.

That's what happens in the quantum world too. However, QM seems to take the concept to its limit - every quantum world seems to be correlated with every other world precisely to the degree necessary to keep the universe consistent, and no more. The many worlds of QM are very precise entities in their own way - the most precise of any physical theory we know.

The Arrow of Time

Another aspect of the universe that Everett's formulation can help to understand is time direction. Time has two distinct attributes. Cyclic time is like a pendulum. It's reversible, related to Planck's constant, and is obvious from Schrödinger's equations. But, time also has a direction to it, and that's not obvious from Schrödinger or Heisenberg at all. In fact, many physicists whose student days predate Everett still consider the arrow of time to be a flaw of our understanding. It is, however, self-evident in the Everett formulation - quantum worlds abruptly appear, then gradually fade from existence, a clearly time direction dependent phenomenon analogous to the appearance and spread of ripples on a pond after a point disturbance. Forget the 'eternal dance' nonsense - things do happen to individual quanta in QM.

Entangled States

For some, it is an article of faith that there must be things that can never be understood. Having listened as a postgrad student at Cambridge to the clarity of Paul Dirac, and having ended up as a Maxwell's daemon with respect to a single electron of a single atom, I disagree. I believe that QM will ultimately prove to be as simple and as understandable as is possible for a theory that permits the self-organization of sentient creatures such as us. In few areas is this view more useful than when considering what happens when one quantum splits into two.

Only half a century ago, the greatest minds we then had mostly considered that everything I did in my last years at NRC was impossible. Impossible even in principle. When one of Canada's foremost physicists visited my lab and saw what I saw, he exclaimed, "I never thought I would live to see this!" (Mind you, another who earlier looked at the complex of lasers I needed to get working together on my lab table, enquired if I had a death wish!) And yet, what I ultimately was able to observe was as simple as possible: one quantum, via a Poisson series that was perfectly random excepting only one degree of freedom - the time scale. A quantum exists between observations - I've followed one for 12 hours, others have for almost a year.

So, when one quantum splits into two, follow what's observable. Knowledge of the split constitutes an observation; that's the only way we know the two quanta are entangled, and both remain local to this first observation throughout. That first observation is why we can know that when one quantum is set, the other will follow suit. Alternatively, if we don't have any knowledge of ('observe') the split, we have no way of knowing that the two quanta are entangled. In this situation, when one is set, there is no way local to the second quantum to know that it is correlated to the first; we can only compare their states after the two observations are brought to a single reference frame. Not only that, but such an observation pair would have to be repeatable in order for us to gain confidence that a source of correlation existed.

In physics, observables, EPR is a local experiment - we just don't understand what the math is telling us yet. Just as we didn't understand for half a century what the math was telling us about single quanta. (I explore one possible approach here.)


Planck length is roughly 10-35m. We believe this to be the minimum characteristic length that space can have. The size of our universe is roughly 1026m (depending on how you measure it).

In between these, there seem to be two islands of minimal complexity: the size of a proton plus an electron (atoms): 10-8m, which is determined by QM, and the size of typical stars: 109m, which is determined by general relativity. Our size, 2 m, is the geometric mean of these last two. If our world is complex to only a few parts in 108, we can exist between these two islands.

In fact, we see much more complexity than this. QM at heart is spherical functions - all that matters is distance from the quantum. It seems that three-dimensional space is necessary for our existence. For example, knots can only exist in 3 dimensions. It seems that one aspect of relativity, that the same laws of physics apply anywhere in our universe, is also an essential postulate of local physics. QM may in fact be a supremely simple spherical function, and all the complexity required to produce life may be due to the properties of a 4-dimensional local space. Spin has something to do with that 4th dimension; let's wait for the mathematicians to understand it in their language, then maybe all of us will.

Consider the complex bonding options of carbon, with only 7 electrons, or the asymmetrical shape of a water molecule H2O with only 13. Both, especially water, are fundamental to life as we know it. The interaction of any spherical function with the 4-dimensional space that includes relativity may be sufficient to permit the necessary complexity for sentience without QM having to provide any of it directly.

John Sankey (1990)
other notes on physics