**Al and the Casino**

Al doesn’t know why he still plays this game. Before picking up the dice, he’s hesitant how to bet. Not due to any anxiety; he couldn’t be calmer. It’s the realization of his thorough indifference to ‘craps’ that makes him pause to reassess.

*“Why bother playing, when there’s no way of telling what’s going to happen next?”*

He wished the cinema had never closed. Yet, when it got replaced by this casino, he still kept coming. It’s the only entertainment around.

He loved the cinema. There it *was* possible to guess what was going to happen next. As he queued at the ticket booth, it was always comforting to know that the film was ‘in the can’ long before he sat down. It was there waiting for him to discover it.

Most people chose to discover it by letting it wash over them, one frame at a time. But not Al. He’d try to guess. Then he felt like the whole thing had some worth, like he was learning something. He’d sit there night after night trying to see patterns on the screen.

He’d guess what the protagonist would do next. Who committed the murder. How to escape from the room. He got lots wrong at first. But, after a while, he got pretty good at it. Any successful guess made during one film would be taken with him to the next. He’d learn from his mistakes. Now, tell him the director and the writer, show him the first 5 minutes, and he’d often predict the rest of the plot.

His friends would tell him he should just relax and enjoy the film. They thought he was missing the point, over-analyzing things.

But, he was aware that the more he guessed and thought about it, the more he’d see in the film. Much more than just the plot. He’d look out for the angle of the shots, the transitions, the soundtrack, all the details. He’d enjoy it *more* that everyone else. He’d see things that other people couldn’t see because they weren’t looking for them. For Al, playing the game made for a richer viewing experience.

This all depended on the films following rules. And, as far as he knew, they did. The cinematic conventions would of course change depending on the latest technology, fashions and current events. So the rules might be temporary rules, but rules nevertheless. He had to make that assumption to play the game.

It sounded strange when he thought about it, but what Al loved most of all was when he was wrong. Those were the best films. He had to reassess what he thought. Change his guesses to fit the new events. He’d *learn* something from those films. That’s why people like twists, he supposed.

Back in the casino, here with the dice, any guesses would be a waste of time. Sure, you could guess, but it wouldn’t help you next time. Guess correctly or incorrectly, the odds will still be the same for the next roll. You’d learn nothing. Lottery players don’t learn anything when they get the numbers wrong (except that they should stop playing lotteries).

“Place your bets,” he heard the dealer say as he carried his chips away from the table.

**Albert and the Quantum Physics**

When Quantum physics developed in at the start of the 20th century, Albert Einstein (or ‘Al’) stuck around to play for a while. But eventually he picked up his chips and walked away.

His life’s work – special and general relativity – depended upon some basic assumptions about how the world works. What physicists had done with quantum physics suggested that these assumptions were wrong.

It is popular to quote Einstein as saying, *‘God does not play dice with the universe.’* However, this is a famous misquote. What he in fact said was:

‘Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the “old one.” I, at any rate, am convinced that

Hedoes not throw dice.’

Letter to Max Born (4 December 1926); The Born-Einstein Letters (translated by Irene Born) (Walker and Company, New York, 1971)

Einstein was subtle with his words, but not malicious. To understand what he abhorred about quantum physics, you must understand his philosophy of science. And in doing so, you will understand one of the things that is strange about quantum physics.

**The Meaning of ‘Random’**

Einstein wouldn’t quite agree with Al about the dice game in the story above. To see why, let’s look at the odds.

If we assume that there is an equal chance of each number being rolled by one die, we can calculate the odds of getting a total on two dice. To figure it out for any particular number, a mathematician might encourage you to draw a table such as this:

First Die/ Second Die |
1 |
2 |
3 |
4 |
5 |
6 |

1 |
2 | 3 | 4 | 5 | 6 | 7 |

2 |
3 | 4 | 5 | 6 | 7 | 8 |

3 |
4 | 5 | 6 | 7 | 8 | 9 |

4 |
5 | 6 | 7 | 8 | 9 | 10 |

5 |
6 | 7 | 8 | 9 | 10 | 11 |

6 |
7 | 8 | 9 | 10 | 11 | 12 |

It has all the possible totals from the numbers on two dice. There are 36 possibilities and 6 of these add up seven. So, the odds of rolling a seven from two dice are 6/36, or 1/6.

But, to a 19^{th} century theoretical physicist, all this talk of probability would be of no interest. Einstein was interested in how the universe worked, not any particular details. In his own words:

I want to know how God created this world. I’m not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts, the rest are details.

E. Salaman, “A Talk with Einstein,” The Listener 54 (1955): 370-371

Don’t get excited if you are a theist, for Einstein God *is* the equations, nothing more. He would often frame his opinions with these pantheist ideas. What Einstein meant by ‘[God’s] thoughts’ were the general laws of the universe that described the happenings of all time and space.

This is an assumption. We have to assume that the universe operates under rules, else we would be unable to make any predictions about it. And we must assume that these rules are *universal* – they apply to all time and space – else how would we know what we were able to investigate? For example, how did Aristotle know that the heavens were made of different stuff to the Earth? Well, he clearly didn’t because he was wrong. It was an arbitrary partition of the world, decided by our small perspective and biases. The assumption that the universe follows universal rules is the best stance the human mind has against ignorance.

Approaching scientific thinking in this manner was exceptionally successful in the 19th century. At one point during the Enlightenment (after Newton’s laws were applied to the solar system, but before chaotic systems were discovered) it was conjectured that it would be possible to know *everything* about the universe. *If* you could do two things. [Yet, both of these are far beyond the capabilities of the human condition.] First, get all the laws correct. Second, know the exact positions and motions of all the particles in the universe at any one instant (called the ‘initial conditions’). Apply the laws to that instant and you could predict any moment before or after it.

Al was doing this with the movies. Knowledge of the writer and director were the laws, and the first 5 minutes were the initial conditions. 19th century physicists applied this to smaller scales too. Take any small, closed-off, section of the universe. It was thought that if you knew the correct laws, and the initial conditions, you’d be able to predict what would happen in that small space.

So, let’s apply that idea to the dice. If you knew enough about the situation, you would say one of two things about the dice you are about to roll. Either they would come up seven, or they won’t. It either happens or does not happen – there is no sense in saying that the event has a ‘good’ or ‘poor’ chance of happening.

The outcome depends *only* on what the rules of the universe are, and the initial conditions. Specifically for the dice, mechanics and gravity are the laws. And the position, mass and velocity of the dice and crap table are the initial conditions.

In our story, Al was wrong about the dice – it was possible to predict what would happen next. But, if that is so, what do we mean when we say that “the throw of a dice is random”?

*For a 19th century physicist, the word “random” says nothing about the universe, but only about our ignorance of it.*

**‘Randomness’ in Quantum Physics**

The discovery of nuclear radiation at the turn of the 20th century was the first step towards changing the old assumptions.

It was quickly figured out that when a radioactive source decays, it chucks out a particle and the the source chances into something else. For example, a beta emitter will chuck out an electron and one of the neutrons in the source atom will change to proton.

The obvious question for a physicist to ask when confronted with a new event is to ask: what are the rules to determine when this happens? While they didn’t know the answer, they found they could use statistical ideas to figure out what a large number of radioactive atoms would do.

It is similar to rolling dice. If you guess the roll of one die, you’ll likely be wrong, fives times out of six. But if you rolled 600 die, you could predict that 100 will come up six and you’d perhaps be 5 or so out. So you’d have a percentage error of around 5%. If you rolled 6 million dice and said 1 million would come up 6, your percentage error would be even less.

With the radioactive materials, there are a lot more dice. 1 gram of Uranium has 10^{20} atoms (one with twenty zeros). So physicists got really good a predicting how many electrons would be chucked out of a radioactive materials at any given time.

You might have been a physics student and rolled some dice to model a radioactive source. You start with 100 dice where each die represent a radioactive atom. You roll them all at once and take out the one that come up six. You say these have ‘decayed’ and removed them from the pile, as they are no longer ‘radioactive’. Make a note of how many, then roll the remaining dice. Repeat until there are none left.

The pattern of decay for the dice looks very much like the decay pattern of an actual source of radioactive material, both of which can be modeled by an equation.

Great. But what does each individual radioactive atom actually do? What’s the equation that tells you exactly when a radioactive atom will decay?

No one knows.

I’m not just saying I don’t know – *no one knows*. The best we can do is give a probability of when it will happen. As far as we know the process of radioactive decay is an *intrinsically* random process.

*It is an assumption of quantum mechanics that some physical processes are random by their nature, regardless of how much you know about it.*

Even if you knew exactly the position, velocity, mass and all the other physical properties of the radioactive atom. Even if you knew all the equations for the electroweak interaction (check out the link if you like mathematical intimidation). Even if you knew all of this, you still wouldn’t be able to predict when one radioactive atom would decay.

**Einstein’s Problem**

This is what Einstein was suspicious about. It was now assumed, not that the universe followed rules, but pseudo-rules. Part random and part determined. [The technical term is ‘stochastic’.] The new assumptions amounted to saying that there are limits to what is possible to know about the universe. For Einstein, this was a step backwards, to a time where people like Aristotle made arbritary assumptions, partitioning the cosmos into the areas we can understand and areas we cannot. In Aristotle’s time, it was the heavens that we could never know. For quantum physicists, it was predicting radioactive decay.

Very quickly, physicists found that many other processes yielded to this assumption, and achieved extraordinary results. As more and more of quantum mechanics was being developed with intrinsic probabilities, Einstein worked to spot inconsistencies in the theory.

To recover the assumption that universe follows rules, Einstein wanted to show that the quantum mechanics was in some way incomplete. The goal was to suggest that everything that quantum mechanics can do could be done with a physics following the old assumptions (now being called ‘classical physics’). He wanted to show that the ignorance implicit in the equations of quantum mechanics need not be accepted so readily.

Every attempt failed, and Einstein switched study to other things. He dedicated most of the rest of his life to a finding synthesis between his theory of gravity and electromagnetism, one which operated under the old assumption that the universe follows rules. He work was never completed.

**Recovery?**

Might the new assumption of intrinsic probability one day be shown to be in error? Is it possible that we might one day find a set of universal rules that describe everything that quantum mechanics has, yet doesn’t require any intrinsically random variables?

In 1964 (nine years after Einstein’s death) physicist John Stewart Bell published an astounding piece of logic called Bell’s Theorem. In it, he claimed that any theory based on classical assumption is *incapable* of predicting the phenomena quantum mechanics predicts, all of which has been repeatedly observed in experiments. In other words, intrinsic probabilities appear to be a *necessary* assumption for our theories from now on.

Feynman put it like this in his undergraduate Caltec Lectures on Physics:

One might still like to ask: “How does it work? What is the machinery behind the law?” No one can “explain” any more than we have just “explained.” No one will give you any deeper representation of the situation. We have no ideas about a more basic mechanics, from which these results can be deduced.

We would like to emphasize a very important difference between classical and quantum mechanics. We have been talking about the probability that an electron will arrive in a given circumstance. We have implied that in our experimental arrangement (or even in the best possible one) it would be impossible to predict exactly what would happen. We can only predict the odds! This would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. Yes! Physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible, that the only thing that can be predicted is the probability of different events. It must be recognized that this is a retrenchment in our earlier ideal of understanding nature. It may be a backward step, but no one has seen a way to avoid it.

Feynman, Richard. “Feynman Lecutres on Physics Vol. 1″ (1963) Chapter 37: Quantum Behavior p. 10

And still no one has found a way around the puzzle. At present, we still assume the universe is, in some parts, intrinsically random.

*Education, Philosophy, Physics, Science*

swanzsteve

2013/04/09

Might quantum behaviour be chaotic rather than random? Is it possible to tell the difference?

Bearing in mind the number of neutrinos flying around and who knows what other, as yet, unknown stuff.

jamesthenabignumber

2013/04/10

Good question!

The trouble with the classical concept of ‘chaos’ is that we assume it is possible to know the initial conditions to some extent, even if the level of accuracy is poor. Indeed, it is this poor accuracy that is the supposed cause of faulty predictions later on, since we assume the classical laws are approximately true and in other circumstances make very good predictions.

Now, if we suppose that quantum behavior is due to a chaotic system, the we should be able to measure some initial conditions that give rise to the seemingly random behavior. However, nobody has ever been able to do this.

I don’t really have a full perspective on this question yet, so I will have to think a little more about it a little more, but I think this is the main trouble.

I found this interesting to read, and hopefully you will too:

http://facultyweb.berry.edu/ttimberlake/qchaos/qchaos.html