ER=EPR : an idea in search of a theory, and Einstein's small-print

After experiments confirmed that quantum non-locality is for real, it has often been said that Einstein has been proven wrong.

However, what Einstein said was more precise than is made out to be. Namely, if reality is non-local, then either quantum mechanics is incomplete, or special relativity (and its description of spacetime structure) is approximate. This second part is entirely overlooked when talking of the `spooky action at a distance'.

Most mainstream physicists took the experimental confirmation of non-locality as matter of fact, with nothing more to be done about it. Clearly Einstein knew better: there is a quantum influence outside the light-cone which special relativity does not allow, and this means quantum systems travel through spacetime in ways which are not consistent with assuming that spacetime is 4D and has a causal light-cone structure. This needs to be explained with new physics. One cannot get away simply by saying that since such non-local influences do not permit information to be transferred faster than light, all is well between quantum mechanics and special relativity, no tension, and nothing more is to be done. This is a misreading of Einstein - physicist Roger Penrose and philosopher Tim Maudlin , amongst others, have repeatedly emphasised the need for an overhaul of how we see spacetime, given that nature is non-local.

Some years ago mainstream physicists Susskind and Maldacena vouched for Einstein, and suggested that quantum systems have an extra channel available to them for travel through spacetime (the Einstein-Rosen bridge of general relativity, the wormhole) which classical systems do not have access to. Quantum processes are only apparently non-local : the wormhole allows essentially instantaneous but causal travel.

This is a good idea in search of a theory: for the ER=EPR idea to be convincing, there has to be a theory of quantum gravity which is such that: classical spacetime is emergent but only classical systems live in 4D spacetime with its causal light-cone structure. Quantum systems live in a space (perhaps higher dimensional) which is in a sense a combination of 4D spacetime and a wormhole like feature. Through these extra dimensions, travel time is of the order of L/c, and with L of the order of 10^{-13} cm this is about 10^{-23} s, even if Alice and Bob are billions of light years apart.

The octonionic theory was not developed to explain quantum non-locality, but manages to explain it, as a byproduct of its inevitable structure. The O-theory was developed to seek a reformulation of quantum theory which does not depend on classical time. In this theory, right from the word go, quantum systems do not live in 4D spacetime, even at low energies. They live in a higher dimensional space, which contains 4d spacetime as a subset, and where the extra dimensions are complex. The absolute magnitude of the scale of these extra dimensions is microscopic, but not Planck length. It is of the order of the short range of the electroweak and strong interactions. These extra dimensions, accessible only to quantum systems, play the role of the wormhole of Susskind and Maldacena. But the wormhole like feature has not been invoked in an ad hoc manner; it is a part of the theory, and indicates the modification of the spacetime of special relativity that Einstein hinted at.

None of this is inconsistent with quantum theory as we know it. Quantum dynamics can be written on octonionic space, or to an excellent approximation, on classical 4D spacetime. When we do the latter, without realising that this is only an approximation to the former, we are confronted with the non-locality puzzle (to which we then seek ad hoc solutions), and confronted with so many free parameters in the standard model of particle physics. We seem to be solving quantum problems one at a time: non-locality, BH information loss, origin of matter-antimatter asymmetry, etc. with the solution to one problem having no bearing on the solution to another problem. However we need to realise that there are so many difficulties at the interface of quantum theory, relativity, standard model, and cosmology, that at this juncture we need to address the core foundational problems of quantum theory and spacetime, and come up with a theory from which gravitation, and quantum theory, are emergent. The rest then is likely to take care of itself.

When the dynamical variables do no commute, the underlying coordinate geometry must also be non-commutative.

The Einstein hole argument shows that for the points of spacetime to be distinguishable from each other, the spacetime has to be overlaid by a metric. The metric at a point then acts as a flag, a marker so to say, labelling the point.

In quantum theory as currently formulated, there is assumed to exist a background spacetime and a universe dominated by classical bodies and fields. This permits a metric which serves as marker.

However, when there are no classical objects around, the metric undergoes quantum fluctuations [because it is being produced by quantum sources] and hence can no longer serve as a marker. The distinguishability of spacetime points is lost.

We see that in conventional quantisation, we necessarily keep the universe dominantly classical, and quantise a negligible fraction of it. What should we do if we want to quantise everything that is classical, in one go?

Consider Newtonian mechanics, or special relativity as a starting point. Raise every dynamical degree of freedom (configuration variables and their corresponding canonical momenta) to the status of matrices. Do not impose Heisenberg quantum commutation relations [q,p]=i\hbar by hand (they will emerge). Replace the four dimensional spacetime coordinate geometry by a non-commuting coordinate system. The Einstein hole argument no longer applies.

We have a matrix-valued polynomial Lagrangian. It's trace defines the trace Lagrangian to be used in the action principle. Use a new absolute time to describe evolution. The Lagrangian dynamics so defined is a pre-quantum theory, from which quantum theory emerges. In a sense this pre-quantum theory can be called true quantisation, a no-holds barred purist quantisation wherein all classical elements are removed. What we call quantum theory is a stop-gap, a half-way home, which serves very well phenomenologically, but leaves a lot unexplained as well.

The non-commutative geometry dictates what we mean by elementary particles, and what properties they have. It also dictates what form the Lagrangian takes. In Newton's mechanics the simplest description of the universe is as a collection of colliding point particles, and the Lagrangian for each one of them is simply it's kinetic energy. So we raise the position variable of each point particle to a (Grassmann number valued) matrix, and define its velocity as the time rate of change of its matrix-valued position vector in the non-commutative space. Then we can define the kinetic energy as the trace Lagrangian - in place of the mass of the particle there is a length scale, which is the only parameter associated with the particle. The universe consists of such colliding matrix-particles.

Because the entries in the matrices are Grassmann numbers, there is a natural place for bosonic and fermionic degrees of freedom, and for particles and forces. And there seems to be a possibility that we can derive our observed universe from the above pre-quantum, pre-spacetime dynamics, because the observed symmetries possibly coincide with those of the underlying non-commutative geometry.