The Vertical Fundamental

There is the classical world; beneath that is the quantum world; and perhaps, beneath that is the quantum gravitational world. This is the vertical fundamental. Consider the following three statements; the first about a ball in the classical world, the second about an electron in the quantum world, and the third about ‘whatever it is’, in the quantum gravitational world.

• The position of a ball in space is the same thing as the ball itself.

• The wave function of the electron is the same thing as the electron itself.

• The ‘whatever it is’ in the quantum gravitational world is indistinguishable from the ‘quantum space-time’ in which it is supposed to dwell.

Let us consider these assertions one by one. The first of these is clearly false. The ball as a material object lives in space, and it is not the space itself. By the time we get to the second statement, we are already beginning to think how intimately the wave function is related to the electron. It is not quite the electron, because it lives in the Hilbert space, whereas the electron is in physical space. The wave function is complex, whereas the electron is a real material object, and the squared modulus of the wave function gives the probability of finding the electron at this or that position in space. Already we are in troubled waters! To explain the outcome of the double slit interference experiment, we must accept that the electron behaves like a wave, but we cannot add the so-called probability waves. At every space-time point we must add the two complex wave functions corresponding to the passage of the electron from the two slits. And then take the square of the sum, to explain interference. So, is the electron the same thing as the wave function or not?! It seems real, it seems complex. Mystery! How can a complex wave travel through space-time? It makes no sense.

When we examine quantum theory more closely, we realise there are other prob­lematic issues with the theory, and when we resolve those issues, it helps us also resolve the above mystery. The first is that classical time is alien to quantum theory, and there ought to exist an equivalent reformulation of quantum theory which does not refer to classical time [6-8]. The search for such a reformulation points us to an underlying space-time which is non-commutative [9]. The second issue is that quantum EPR correlations suggest a violation of locality and some kind of influence outside the light cone, which to some people suggests the need for a radical rethink of the space-time structure in special relativity [10]. We have argued that the non- commutative space-time which we were led to, is the one in which the electron and its associated wave function live, and in this scenario there is no longer the discom­forting acausal quantum influence during an EPR measurement [11], nor trouble in understanding double slit interference. And what use there is then, any longer, to distinguish the electron from its wave function? So, with some conviction, we revise the second statement above, as follows

• The wave function of the electron is the same thing as the electron itself, when viewed from the non-commutative space-time in which the electron lives.

Classical space-time is only an approximation to the underlying non-commutative space-time, emerging from a coarse-graining. All material objects dwell in this non- commutative space-time, but in such a space-time, there is no concept of classical position, nor of classical time, nor of classical events. Everything is everywhere all the time! [12]. What is the use then, of distinguishing space-time from material objects? They must be one and the same thing. We have been led this far, by trying to resolve the puzzles and mysteries of quantum theory, starting from the weirdness of the double slit experiment with electrons.

And if there is no distinction between space-time and matter, could we even talk of substance, or of the ultimate constituents of matter? To talk of constituents, we must have the space-time in which the constituents live. And that we no longer have. All that we will have is a set of beautiful equations. No atoms, no electrons, no people, no here nor there, Whatever there ever was, has now become same as the mathematics which describes it. The law has become the thing; the thing has become the law. We do not have to any longer ask where does mathematics live, because the where has become mathematics. Platonism meets Nominalism. If we read in a bottom up manner the three assertions stated at the beginning of this section, we see how laws apparently become distinct from things, as we emerge into the classical world.

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