Monday, 18 January 2010

Quantum Mechanics and the Fifth Dimension

Its been a long time since I've thought about interpreting Quantum Mechanics. When i was young, I'd often read about how mysterious quantum mechanics is, about Schrödinger's Cat, which i'm sure you've all heard of. And about quantum entanglement, sometimes known as spooky action at distance, a name which captures the mystery but not the effect very well. Quantum mechanics is very mathematical, so it wasn't until I was studying it at my final year at university, that I could understand it well enough, to try to make the connection between the mathematics of quantum mechanics, which works very well at predicting the outcomes of experiment, and some physical mechanism, some process that describes how the universe works. And so back then, I surveyed whats known as the interpretations of quantum mechanics, and plumped for the Many Worlds Interpretion, that the universe actually has many parallel universes, in which random events happenned in all the other fashions that could have happened. Extreme though the idea sounds, I basically haven't changed my view, since I passed my PhD.

They were, and still are, basically four known Interpretions of Quantum Mechanics, or otherwise counting three Interpretions and one experimentially disproven theory that behaved more like Newtons physics, called hidden variables.

In the Copenhagen Interpretation, when an observer measures a system, the system instantly decides which of many possible results it will show the observer, and then remains the same, until somehow disturbed. This is bizarre of course, since measuring could just mean looking at, and it really does seem to matter if there is a eye looking or not. Does is an eye somehow emit a darkenning reverse light backwards in time, that causing the observed system to jump to some definite state. In the Transactional Interpretation, thats exactly what happens. So called advanced waves, travel backwards in time, from some fated, utimately fixed future, fixing a definite state for all obversation along the way. Unfortantely for gamblers and pundits, the Transactional Interpretation, doesn't say what the observed state will actally be, any better than odinary quantum mechanics.

The only other known Interpretation proved mathematically viable, is the Many Worlds Interpretation. In which, every act of storing information, such as looking and recording an experiment, causes the observer (or recorder), to split into different versions, each one recording one of the possible outcomes of the experiment. Each of the recordeds might as well be in different universes for all they can now say about the result that didn't happen in its record. The ordinary math of QM, keeps track of all these parallel outcomes, or parallel universes, and quantum computers, seem to show, that the universe, or multiverse, really does do enough calculation, to know all the other possible outcomes of any experiment. And yes that means, all those what would have happen if the germans won World War II, etc, and all does sub cases like, the german won the war and Hitler was assassinated on what ever perticular day you care to choose.

The Many Worlds Interpetation is great for science fiction authors, because even the very unlikely, and therefore much a thinner volumes of the multiverse, happen somewhere, such as Aliens landing on Earth during World War II. It uses the same mathematics as ordinary quantum mechanics. But although space (and time) are still three dimensionally (plus one for time make 4-d), keeping track of all those possiblities very rapidly needs very large dimensions, of state vector, with one row (or column) describing each possibility.

So I found what In Müllers and Fosters recent paper, fascinated me. They investigated what happens if you try to describe an universe with two distinct dimensions of time. Amazing if you start with a classical (I.E. Newton like math, and not quantum mechanics), universe with three dimensions of space and two dimensions of time, for approprate conditions of the extra dimension of time, produces the maths of Quantum Mechanics and Field Theory almost perfectly. Sci-fi authors have often used the expression sideways in time, to describe parallel universes, but this is the first time as far as I know that mathematics has actually described quantum mechanical parallel universe as sideways in time. For MWI and Sci-fi enthusasts this is great, as is the fact that if the temperature of the extra time dimensional was to cool down, the value of planks constant would vary, possibly leading to regimes in which communication between parallel universes could happen. However for physicists they may a lot more work to do. To get an average value for a quantum variable in the two-times description, you have to integrate over the entire eternity of the spare time dimension, which somehow seems to long, and not local enough, and as the Authors emit, only sometimes mathematically possible. Perphaps descriptions more localised in the spare time dimension are possible. I'd also like to see, if starting with both time dimensions on the same footing, and then switch to polar coordinates would work. Then you'd have one dimension represent the total temporal distance from the big bang singularity, the radial dimension, and one polar time, a circle running from 0 to 2pi, which might better fit the wave nature of matter.

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