Many worlds or only one?

English: Position and momentum of a particle p...
English: Position and momentum of a particle presented in the phase space. (Photo credit: Wikipedia)

Scientists often use the concept of a “phase space“, which is basically a representation of all the possible states that a system may be in. For the trajectory of a thrown stone for instance, the phase space would be a four-dimensional space, comprising the three dimensions of space, which define where the stone is, and one of time, which defines when the stone is in a particular position.

The trajectory of the stone is a line in this 4-d space, as the location and time information about the stone is known exactly. However, the stone is not a point and maybe be spinning at the same time that the whole object is flying through the air. This means that the trajectory would actually be a complex four-dimensional worm in phase space.

An animated GIF of a tesseract
An animated GIF of a tesseract (Photo credit: Wikipedia)

What if we were to introduce a probability factor into the experiment? Maybe we would set up the projectile to be triggered by an atomic decay or something similar. We would get a different worm depending on how long the atom takes to decay.

Clearly, if we want to show the all of the possible versions of the worm, the worm now becomes a sort of 4 dimensional sheet. Well, more like a 4-d duvet really, as the stone is not a point object.

Bedding comforter or duvet. Français : Couette...
Bedding comforter or duvet. Français : Couette (literie). Deutsch: Daunendecke, umgangssprachlich Federbett. (Photo credit: Wikipedia)

Within the 4-d duvet, each worm represents a case where the atom has decayed, and each of these cases has a probability associated with it. The probability can be expressed as the probability that the atom has decayed by that time or not, and can run from one to zero.

Actually the probability starts from zero and approaches one but doesn’t quite reach it. In practise in a group of atoms some will decay quickly and others will take longer. If there are a finite number of them, then the chances of any one lasting a long, long time are quite small, and all of the atoms are likely to decay in a moderately short time, a few multiples of the half-life anyway. However there will be a finite but microscopic in the extreme possibility, that an atom will survive for as long as you may consider.

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We can add another dimension to the phase space, one of probability. This gives us a five dimensional phase space, and the duvet becomes five dimensional. However, an atom decays at a certain time, and there is a single five dimensional worm in the phase space going forward. The space is no longer a phase space though, as a phase space, by definition, describes all possible states of the rock/launcher/atomic trigger, and doesn’t change.

According to the Copenhagen interpretation of quantum physics the state of a quantum system is described by a set of probabilities. When a measurement of the system is made the state becomes certain, and it is said that the waveform described by the probability function has “collapsed”.

Copenhagen (Photo credit: Wikipedia)

The famous thought experiment of Schrodinger’s Cat is a description of the difficulties of such a case. The cat is enclosed in a box equipped with a mechanism which will release a poison and kill the cat if triggered by the decay of an atom. At some time after the experiment starts the atom may or may not have decayed so the quantum states “decayed” and “not decayed” are superimposed, and therefore so are the states “dead” and “not dead” of the cat.

How do we know if the stone has been fired yet? Well, we go and look to see, and we either see the stone in its launcher or we don’t. Quantum physics says that the stone exists in a superposition of states – launcher and not launched. The question this raises is, if this is so, how does looking at the stone “collapse” the superposition when we look?

Three wavefunction solutions to the Time-Depen...
Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the particle at a certain position. The top two rows are the lowest two energy eigenstates, and the bottom is the superposition state \psi_N = (\psi_0+\psi_1)/\sqrt{2} , which is not an energy eigenstate. The right column illustrates why energy eigenstates are also called “stationary states”. (Photo credit: Wikipedia)

That quantum superposition is real is indicated by any number of experiments, even though many physicists working in the field (including Schrodinger himself) have expressed discomfort at the idea.

In quantum physics the evolution of everything is defined by the Universal Wave Function. This can be used to predict the future of any quantum physical system (and all physical systems are fundamentally quantum physical systems). Unfortunately for easy understanding, interpretation leads to the superposition problem mentioned above.

Many people have tried to resolve this issue, and the best success has been achieved by the exponents of the Many Worlds Interpretation (MWI), as described by Everett and championed by Bryce DeWitt and David Deutsch. The view of the MWI exponents is that the Universal Wave Function is fundamental and expresses a true picture of all reality. All of it, that is. Not just a physical system and its observer.

Everett’s view, as described in his thesis, is that an observer, as well as the object that he is observing is a subsystem of the system described by the Universal Wave Function. The wave function of these two subsystems does not describe a single state for each of these subsystems, but the states of the two subsystems are superposed, or in Everett’s term, correlated.

en:Many-worlds interpretation
en:Many-worlds interpretation (Photo credit: Wikipedia)

When a particle is observed it may appear to be in state A 70% of the time (correlated with a state A for the observer). Similarly it may appear to be in state B 30% of the time (correlated with a state B for the observer). This led Everett to postulate a ‘split’ of the universe into a state A and a state B.  (The term ‘split’ appears to come from DeWitt’s interpretation of Everett’s work).

The probabilities don’t seem to have a function in this model, and this is odd. The probability that the cat is dead when you open the depends on how long you wait until you open the box. If you wait a long time the cat will more likely be dead than if you opened it earlier.

English: Diagram of Schrodinger's cat theory. ...
English: Diagram of Schrodinger’s cat theory. Roughly based on Image:Schroedingerscat3.jpg (Photo credit: Wikipedia)

This means that the world splits when the cat is put in the box, as from any moment it can be alive or dead, but you do not find out which branch you are in until you open the box sometime later.

I’m ambivalent about the MWI. On the one hand it is a good explanation of what happens when a measurement is made or the cat’s box is opened, and it does away with the need for a waveform collapse, which Everett argued against in his paper. However it is profligate in terms of world creation.

English: Schrödinger's Cat, many worlds interp...
English: Schrödinger’s Cat, many worlds interpretation, with universe branching (Photo credit: Wikipedia)

Another issue is that the split is decidedly binary. The cat is alive in this world and dead in that one. However most other physical processes are, at the macro level anyway, continuous. When a scientist takes a measurement he writes down, for example, 2.5, but this is only inaccurate value as it is impossible to measure something exactly and it may be wrong by up to 0.05 on either side of 2.5 (given the one decimal point value shown).

Consequently, I’d prefer an interpretation where there is no split, but instead a continuum of possibilities as part of a single world. Maybe the single path that we tread through life is an illusion and across the Universe, by virtue of the Universal Wave Function, we experience all possibilities, though to us it feels like we are only experiencing the one.

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Where are all the heroes and heroines?

[I’m posting this early as I will not be able to post tomorrow or Monday as per my schedule]

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The Cricket World Cup continues and now we have only the final match left. New Zealand versus Australia. The success of the New Zealand team and the reaction to their semi final win led me to think about heroes.

The saying goes that every one likes a winner, and since the New Zealand team has exceeded many peoples’ expectations, the local media are ecstatic. Most ordinary New Zealanders who would not normally be interested in cricket have been tuning their radios and TV to the match commentary or streaming the matches from the Internet.  Indeed it would be fair to say that the whole country is behind the team.

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Interestingly, the New Zealand commentators, who covered the semi final and who were jumping for joy when New Zealand won, were almost as quick to sympathise with the losing South African team. This empathy was probably because it was an amazing game with a breath taking finale, played all the way through in good spirit, and the South African team who so nearly won it called truly be called gallant in defeat.

The match could have gone either way up until the very end, and I think this helped the New Zealand team and the New Zealand public to commiserate with the South Africans. It so nearly was the New Zealand team on the losing end of the match. It was an amazing end, with grown men hugging and grown men crying.

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Being a small country New Zealand doesn’t often have sporting heroes or heroines, but it does happen. New Zealand players have gone to Australia the UK, Japan, France and even the US to play their sport, be it soccer, basketball, rugby union or rugby league. New Zealand doesn’t have the funds to pay professional sports persons that these other countries do.

Somehow or other this doesn’t seem to affect the quality of the sports stars in the local sporting arenas. In fact returning players often find it a little difficult to get back into the top level teams on their return from an overseas period of their career.

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In New Zealand the public has a curious attitude to top sports persons. If a New Zealander were to meet one of his or her sports idols, he or she would probably as likely offer to buy him or her a drink as ask him or her for an autograph.

New Zealanders expect sports stars to be approachable, and in many cases they are. Because it is a small country, a sizeable number of the fans will have gone to school with them, or lived next door to them, or perhaps worked with them when they were starting out, before they became professional sports persons.

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New Zealanders tends to excel in what could be called minor sports. This is probably partially because in the larger countries, the ones in which the sport arose or where it has become very popular the best athletes are attracted to the major sports. When a New Zealander or New Zealand team do succeed in major sports it is front page news ‘back home’.

Even when it is a minor sport (such as Greco-Rona wrestling or lawn bowls) if a New Zealander does well they become well known, at least in New Zealand. New Zealanders realise this full well and wryly comment that something is “world famous in New Zealand“.

English: L & P bottle model in Paeroa, showing...
English: L & P bottle model in Paeroa, showing the label design as used from the 1970s to the 1990s Deutsch: L&P Modellflasche in Paeroa mit dem Label, dass von 1970gern bis 1990gern verwendet wurde. (Photo credit: Wikipedia)

So we have the likes of Stephen Adams doing well in American basketball, and the average New Zealand man in the street knows that he plays for Oklahoma City Thunder, and the average New Zealand sports buff could probably tell you what his scores were.

Heroes and heroines have been around since people started to form towns and cities and to write down their histories. Back in the times that the Greeks and Romans held sway in Europe, it is likely that total population of the Earth would have been measured in millions rather than the billions that live on the Earth today. Towns and cities of the time would probably have appear small to modern eyes – Rome is believed to have peaked at around one million people at its peak in the second century of the Common Era.

Roman Infantry Edit
Roman Infantry Edit (Photo credit: Wikipedia)

Since the populations were so small compared to today it is likely that the heroes and heroines of the time were known personally to a large part of the population. Since the population was so small the six degrees of separation of the modern world are likely to be reduced to three or four. Admittedly the lines of communication would likely be way slower in the ancient world but Julius Caesar was likely be a friend of a friend of a friend of every person in the world at that time.

English: Map of the Roman Republic in 40 BC af...
English: Map of the Roman Republic in 40 BC after the recent conquests of Julius Caesar. (Photo credit: Wikipedia)

Given the small population of the time, heroic events would be quickly well known and the heroes and heroines would become household names. Since this would happen mostly by word of mouth, the Chinese Whispers effect would be strong. Intentional and unintentional misunderstandings would mount up and would inflate the story, so that instead of the hero overcoming three others, one at a time, he instead reputedly takes on a dozen all at once.

When you read of Julius Caesar and his legions, I at least get the image of vast armies, but a legion was between 5,000 and 1,500 men. Caesar conquered Gaul with only a few legions, say 10,000 men probably which doesn’t seem very many, but there was little real opposition in numerical terms.

The initials SPQR stood for Senātus Populusque...
The initials SPQR stood for Senātus Populusque Rōmānus (“The Senate and the People of Rome”). They were emblazoned on the banners of Roman legions. (Photo credit: Wikipedia)

It’s not as if there were a strong national structure to oppose him, as the tribal structure common in those days might extend to a city or two, or a region and Julius Caesar was able to exploit regional rivalries to take control of the region. He of course had to contend with heroes popping up, like Vercingetorix who unified the previous divided Gauls.

Heroes and heroines have only one fate – they win at first (which makes them heroes or heroines), but eventually they lose and then they usually die. Vercingetorix eventually lost to Julius Caesar at the battle of Alesia, and Julius Caesar cemented his hold over Gaul.

English: Monument of Vercingétorix in Alesia (...
English: Monument of Vercingétorix in Alesia (Alise-Sainte-Reine) Deutsch: Denkmal des Vercingétorix in Alesia (Alise-Sainte-Reine) (Photo credit: Wikipedia)

Even Julius Caesar, eventually, lost both his empire and his life, at the hands of his former friends, who briefly became heroes themselves, before quickly losing their lives too.

While modern day sporting heroes and heroines don’t actually die, they eventually suffer defeat and become radio or TV commentators, which may be a worse fate. So I hope that the New Zealand cricket team wins the Cricket World Cup tomorrow, but if they can’t manage it, they have put on an amazing show in getting this far.

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