When we build a building out of bricks, properties of these little things determine possible buildings. For example, there are absolutely no brick-only high-scrapers, cause bricks have a relatively low limit on pressure they can withstand, and bonds between bricks cannot possibly handle forces that develop in a tall building. For a small house, bricks' properties are enough, and a designer doesn't have to think about bricks' material, and can think about them in a simple way, with details abstracted away. This abstraction works for small all-brick houses, but breaks, or leaks, in a design of high-scrapers. The lesson here is that underlying real foundation is important. Is this lesson relevant to Quantum Mechanics (QM)? You see, QM was formed in the beginning of 20-th century as a set of mathematical postulates, that are to be used, when describing experiments with tiny things. This is a set of mathematical abstractions over reality, and it seems to leak, as seen at least in the following issues: a) observer-effect in QM, making observer a little special, b) story with the cat (referred as EPR paradox), c) difficulty in saying if particles are particles or waves. Whatever QM postulates abstract, that is leaking back. As a result, there are lots of different interpretations of QM mathematics, each suggesting what is real or not. Unfortunately, all these interpretations start with concepts already present in QM, and always produce exactly the same final calculations. Hence, they are not even called theories, but, rather, interpretations of QM theory. Can we, in 2012, do better? History is a good guide. In 1905, Einstein put result of Michelson-Morley experiment as a postulate for his theory of Special Relativity (SR). Experiment, i.e. something that is real, is used as a postulate, from which other things are derived. More so, one may use different mathematics, like Minkowski suggested, cause a choice of mathematical language is not stipulated within initial postulates. More so, given SR, Albert comes up with a guess about reality called Equivalence Principle, which, when dressed in pseudo-Riemannian mathematical language, gives, with an additional guess of an actual form of equation, a theory of General Relativity (GR). What can we take as reality-inspired postulates to form theory about matter (necessarily quantum), in 2012? Let's see. Lots has been done experimentally since 1920's. The pinnacle of this development is Standard Model (SM), with Higgs being the latest and possibly the last target. What can we take from this body of evidence as a physical essence for a postulate? SM is a bunch of Quantum Field Theories (QFT). QFTs describe different "particle fields" and interactions among them. Fields are mathematical functions over some space, which forces us to talk about space, not just matter. Marrying SM and GR hasn't worked out within current use of mathematical tools like fields. This then brings us to a question that may be fields' abstraction is also leaking, and we have to take from SM experimentally seen stuff, but without fields layer. Can it be done?  When Feynman came up with his diagrams to give some sense to mathematical entities in QFTs, he was severely criticized. No one was supposed to visualize and think in terms of little particles, as particles were also waves. Well, Feynman's approach worked to produce calculations for Quantum Electrodynamics (QED). And then it worked for other QFTs, to the point that today all QFTs in SM are using Feynman diagrams. Each vertex on any diagram represents an interaction term, at which all incoming particles are annihilated, and outgoing particles are created. Think of it, each particle participates in exactly two events: one is its creation, another is its annihilation.  Can these Feynman pictures be a mere trick, used to construct perturbative solutions to theories till some day, when someone will show us exact solutions. This has been a thought for a very long time. But get this, after QED, same diagram approach was used for experimentally verified QCD, and for Higgs mechanism (that describes how effective particles acquire mass). These successes of thinking in terms of fundamental particles, and apparent lack of exact, non-perturbative theories, after many years of search, is a hint to us, that these fundamental particles is what actually exist. So, on the basis of the above educating arguments, let's guess the following postulate (postulate #1 in the paper): Existence Postulate: There exist particles that are annihilated and created at interaction events. What sort of interaction events may or may not happen, what states of particles are required for interaction, and in what states particles are created, all of these aspects are dictated by a type of particles. Does this postulate subtract something from experimental evidence? No. All that folks at CERN have are these fundamental particles created and annihilated at interaction events. Does this postulate add anything not seen, like extra dimensions or other universes? No. Postulate is just about what we see in experiments. The other fact from experience is that we cannot say deterministically where and which interaction shall happen, and what will results be (postulate #2 in the paper): Postulate about Probabilistic Nature of Particle Events: Particle events are probabilistic. It is impossible to answer with certainty all following questions simultaneously: a) which event will occur, b) when and where relative to other events the said event will occur, and c) what will be the state of incoming and outgoing particles. Since every quantum system is an effective thing, consisting of specific fundamental events, we immediately get a postulate about probabilistic nature of quantum systems' interactions (postulate #3 in the paper). Extension of this postulate from two to many systems, where one is not interacting, leads to interaction confinement postulate (postulate #4 in the paper). We used results of a double-slit experiment to assemble confinement postulate. These two last postulates were initially formed in an older paper, but they are not really fundamental in the light of QFTs. Yet, this older paper shows how it is easy to construct common QM Hilbert spaces, unitary evolution and even Schrödinger equation, on the basis of the postulates. Please, refer to said papers as formulas look much better there in a latex form, than in html. Note that provided here postulates are a physical essence of QM math, which we can construct. And it might be other math, if it works. Math language here is not fixed by postulates. Are we done? Nope, as we haven't said anything about spacetime. And we have at least two options here. The first option is to explicitly postulate existence of a spacetime, in which fundamental particle events occur. With this, and with QM math we get ourselves to present day state of affairs, minus need of QM interpretation. This way we do not fix differences between GR and QM. And this option gives us no possibility to drawing conclusions independently from known QM and GR theories. The second thing is to do something else. What, though? In a recent piece, Giovanni Amelino-Camelia makes a good point that only those points of spacetime are relevant, where particle events occur. We have never detected empty spacetime points. We can only say that given events have a certain separation between each other. This separation is just a relation between these events, this simple, no strings attached. Upon reading Giovanni's paper I wrote my own with: Spacetime Postulate: Particle interaction events define spacetime points. See the paper for more details about space and time. It is an area for further investigation, and it shows that our prime postulates both provide foundation to form QM mathematics, and give further direction to form spacetime theory, all along the lines, like the guy said: "First we guess it. Then we compute the consequences of the guess. And then we compare results to experiment." |