Quantum Information as Everything

Issue #65

A while back I wrote a book titled “Decoding Reality” in which I claimed that information (and not energy or matter) should be considered the most fundamental entity in our universe. This view is natural for me because the axioms of quantum physics already have a strong information-theoretic flavour. One axiom is about the states of physical systems, which are vectors in quantum physics, or, as Schrödinger called them, “catalogues of information”. Another axiom says that the dynamics of quantum systems is such that the relative information between two states (signifying the degree of similarity between them) can never change in time. In other words, quantum physics preserves information. Third, and the final axiom, says that things that we can observe should be represented in quantum physics by “catalogues of catalogues of information” (which are, speaking somewhat loosely, multiple states considered together at the same time).

Photo by Julian Rösner on Unsplash

I have been inspired by a number of other physicists promoting similar ideas, but none more so than John Wheeler and Carl von Weizsäcker. The American John Wheeler coined the phrase “it from bit” to capture this information-centred approach to reality. One question, of course, is to explain exactly how “its arise from bits”. The other question is where the underlying bits come from in the first place. I think the person who did more than others in the direction of answering these two questions was the German Carl von Weizsäcker. He actually, and independently from Wheeler, also advocated that information is key to reality.

I was therefore recently very excited to have been made aware of an old and creative paper by Weizsäcker, Scheibe and Sussmann entitled “Complementarity and Logic III: Multiple Quantization”. It turns out that this paper has never been translated into English (the original was in German), but these days the abundance of AI tools allows us to have things like this translated in a matter of seconds. Needless to say, the paper was not available to me while writing “Decoding Reality” (otherwise I would have definitely covered it in there).

In any case, Weizsäcker, who was a PhD student of Heisenberg, had the idea that everything arises from quantum bits of information (and not classical ones as Wheeler had advocated). These qubits also represent logical binary choices, but the quantum ones, and Weizsäcker called them Urs. An Ur really is just a qubit, which means that it has two basis states, a zero and a one, and all superpositions of the two are also allowed (unlike in the case of a classical bit, which does not admit superpositions).

As my readers will almost certainly remember, I have frequently argued against introducing a classical reality into our description of the world. Given that we already know the microscopic domain to be quantum, it is difficult to make this fact consistent with a macroscopic classical picture. This is why I also side with Weizsäcker, namely supporting the view that information has to be quantum. A hybrid system in which classical information interacts with quantum information is simply inconsistent because the interaction between the two can never be made to comply with other known principles (such as, for instance, the principle of information conservation).

In the aforementioned paper, Weizsäcker and his colleagues then proceed to make a number of amazing claims. First of all, a qubit has four real numbers attached to it (two complex amplitudes). The fact that this number is the same as the dimensionality of spacetime (3 spatial dimensions +1 temporal one) could not be an accident as far as they are concerned. In fact, one can derive the momentum of a (massless) particle by multiplying another vector with 4 components by the qubit 4-vector. This momentum, when multiplied by itself, equals zero, which encapsulates the fact that the energy of a massless particle is just its momentum times the speed of light.

From this simple construction, the authors proceed to argue that the wave equation for photons (the Klein-Gordon equation) follows directly and it simply tells us that, unless the energy of the particle equals to the momentum times the speed of light, the wavefunction of the particle has to vanish (since otherwise the massless particle could travel at speeds different to the speed of light!). This is the level that Weizsäcker and his colleagues call the second quantisation (the first quantisation being the Urs themselves).

To get to quantum field theory, you need to quantise again (third time, according to Weizsäcker’s methodology), which is just the usual quantisation of the wavefunction to upgrade it into a q-number (normally called the second quantisation by everybody else). And, of course, a question automatically comes up as to whether we need to quantise beyond this, the fourth time or more (which is still an open question! – and I’ve written about it in my latest book “Portals to A New Reality”). By increasing the number of Urs, massive particles can be taken care of, too.

And, now, something I’ve always found fascinating (I was aware of this before I read Weizsäcker’s paper, but I now realise that this is where it is first mentioned in the literature). I’ll quote straight from it: “Special relativity, so far as it is a mathematical theory of space and time, is already a quantum theory of a deeper underlying simple alternative. The Lorentz group is an (unfaithful) real representation of the group of complex linear transformations of the quantum-mechanical state space of that alternative”. In other words, special relativity is a consequence of qubits too! (The Lorentz group is a mathematical description of transformations that allow us to move between observers travelling at different speeds, a key technique in special relativity.)

But, if special relativity is a consequence of quantum logic, what about general relativity? General relativity is our best theory of gravity, so could gravity also be a consequence of quantum information? I think so myself, but I’d better leave the reasons behind this to another blog post.

Till then, take care of yourselves,

Vlatko