Time within time, or how particles act like bees

Time flows, an instant goes away and is replaced by the next one, in a endless, silent, dull procession (at least, that is what our collective imaginary keeps repeating to us usque ad nauseam).

Pretty boring, right?

Unless... unless you can zoom into one of those instants, and find another time, a hidden time. After all, atoms of matter were thought of as indivisible only a little over one hundred years ago, and, as it turns out, they very very roomy; why should instants of time be any different?

Hidden time. A tantalizing hypothesis, and the basis of a fascinating model of Quantum Mechanics concocted by Pavel Kurakin and George Malinetskii, from the Keldysh Institute of Applied Mathematics and the Russian Academy of Sciences (you can read an informal account here). Kurakin and Malinetskii have developed Cramer's transactional interpretation of QM, and gone a bit further. When a subatomic particle has to move, say from an emitting source to a detector, it sends out probing waves, like scout bees. Each goes its own way, hits the possible targets, and comes back. At the end, a global decision takes place, and the particle moves from one point to the next. This entire set of transactions happens in hidden time. In other words, before the particle has made up her mind, there is no time tick, at least as far as our physical clocks are concerned.

Intriguing, isn't it? A tacit assumption one always makes is that all phenomena occur within the same time scale. But there are other options. Perhaps what for me is a time tick, for you is an entire lifetime, or an eternity...

Yet another chapter in my book on Time.

The timeless universe of Julian Barbour

Bookshops and public libraries are powerful attractors in my life: hardly a day passes by without a fleeting visit to these cornucopias of information and dreams. Friday was no exception: I was at Borders loafing about, and I ended up in the Physics section. My trained eye spotted an interesting title within seconds: The End of Time, by Julian Barbour. I had vaguely heard of the fellow before, through some readings on the interpretation of Quantum Mechanics and on Quantum Gravity. Barbour, I seemed to recall, does not believe in Time. He in not alone, mind you: Melissus, Nagarjuna, Plotinus, McTaggart, and numerous others were also vocal disbelievers. But there is a difference: Dr. Barbour is a theoretical physicist, and physicists (with some notable exception, such as the Loop Quantum Gravity folks) assume space-time as the background where physics happens.

What kind of universe does Barbour envision? His world, which he cleverly christened Platonia, is a world of Nows (by the way, Platonia is also the name of his web site). Each Now is a possible configuration of the entire universe, complete in itself, and static (think of a single photo snapshot). How are Nows concatenated to one another? They aren't. Quite simply, there is notion of similarity describing how far apart two Nows (i.e. two universe's configurations) are. Some photos look similar, others do not. By arranging a list of contiguous Nows, one gets a factitious timeline, a bit like arranging photo grams one gets a movie (notice that you could arrange the deck in more than one manner).

All right, but how come we do experience the flow of time? Here is a clever move by Barbour (as matter of fact, a few others, like Emanuele Severino in Destino della Necessita', had a similar argument, albeit from a different angle). It is called time capsule. A time capsule is a special type of Now, containing some data that appear like traces of other Nows, or fragments of recorded history. Thus, in his view, there is no flow whatsoever, only we (you and I) are inside the same time capsule that suggests the existence of past & future.

Crazy? Not really. After all, what do we know about past and future? Only what our memory and our imagination tell us. No more, no less.

Summing up, Julian Barbour brings us back to the number 3 instead of the Minkowskian 3+1 =4. Space is real, time is not (*). Instead of increasing dimensions, like String theorists do, he reduces them by one. He kills Time.

Allow me to add a coda here, before quitting. I like all of the above, so much so that in my book on Time a section will be dedicated to charting the charming land of Platonia. However, I have a gut feeling that this is a great start, but not the entire story. Perhaps space too is not that real after all. Perhaps we live in a space-time capsule, and the entire vast expanse of this universe is no more than a mad game of mirrors within mirrors. Perhaps the basic ingredients of reality are not Nows, but a multiplicity of Here-And-Nows, hic et nunc. Perhaps....

(*) A note for the math-savvy: I hope my sentence above hasn't mislead anyone into believing that Barbour's universe is R^3. It is not; his kosmos is the so-called configuration space, whose dimension depends on how many entities there are. For instance, if there were only 3 particles, our physical universe would be the manifold whose points are the different configurations of a three-body system. As you can see, it is a pretty roomy house...

PS After coming back home, I chased Barbour all over the net. He appears in a riveting 1/2 hour video, which I truly liked. It is called Killing Time: enjoy.