Guiding principle: quantum gravity

One of the aims of fundamental physics is to obtain a theory that can combine gravity with quantum physics. As I mentioned before, theory space is vast. A successful venture into theory space needs a reliable guiding principle. Without any experimental result pointing out the direction we need to take, the selection of such a guiding principle for the formulation of a quantum theory of gravity is difficult.

Some people believe that quantum gravity is the domain of the Planck scale where quantum and gravitational effects coincide. It requires extremely high (experimentally unattainable) energy densities. It also assumes that such high energy densities allow things like black holes and worm holes to pop in and out of existence. That is however an unscientific notion. Things don’t just pop in and out of existence, least of them black holes, regardless of the energy density.

Moreover, there are no such things as worm holes. I don’t care that Einstein thought they may exist. The idea represents one of those cases where the mathematics is over extended to produce a spurious solution that, although allowed mathematically, has no physical meaning. So they cannot pop in and out of existence anyway.

Hence, it is unlikely that there is anything interesting happening at the energy scale represented by the Planck scale, or more accurately called the hypothetical Planck scale. Therefore, I would not recommend any statements about what happens at this hypothetical Planck scale as a reliable guiding principle for quantum gravity.

As a more reliable guiding principle, we need to address the question, what happens to the gravitational field produced by a quantum state? What I mean by a quantum state is a state of matter in which quantum effects are manifest. An example of such a quantum effect is entanglement. So the question in this case is, does the gravitation field become entangled with the quantum state, or is the gravitational field uniquely produced by some combination of the elements in the superposition that represents the entangled state?

We can address the question with our current theory of general relativity. In Einstein’s field equation for general relativity, the curvature tensor of spacetime is equated to the stress-energy tensor of the matter distribution. In the context of quantum theory, the latter becomes an observable – an operator that can be traced with the quantum state to produce the observed stress-energy tensor of the quantum state. Obviously, the observed stress-energy tensor does not represent the entanglement anymore. Therefore, the curvature of spacetime produced by such an entangled state is affected by a combination of the elements in the superposition and does not become entangled with the state.

What does this say about the guiding principle for quantum gravity? What it seems to say is that there is no need for quantum gravity. The spacetime that we live in is a background in which the intricacies of quantum physics play out without becoming involved. The only effect that the quantum state of matter has on the gravitational field is through a unique stress-energy distribution for the entire state.

This conclusion is based on the assumption that Einstein’s field equation is valid on the small scale of quantum physics. It has been tested at larger scale and so far no deviations have been found. Without any observed deviations, there is not strong motivation for expecting that it would not be valid at the scales of quantum physics.

However, there is one aspect that Einstein’s field equation does not explain. It shows the connection between the curvature of spacetime and the distribution of matter, but it does not explain how mass-energy curves spacetime. It does not give a mechanism for this process. Such a mechanism may be hiding in the quantum description of matter. If such a mechanism can be uncovered, it would lead to a more comprehensive theory that would “explain” the Einstein’s field equation.

The search for this mechanism may be somewhat different from a search for a theory of quantum gravity. However, it can be seen as a more focussed attempt at formulating a theory of quantum gravity. To find this mechanism, we can perhaps focus of fermions. I think there are still some mysteries associated with fermions that need to be uncovered. Perhaps that can lead us to an understand of the mechanism for the way that mass-energy curves spacetime.

The way forward

It is a new year. Time to look ahead, having completed a project toward the end of last year. Well, it still has some things I can look at, but I did make a bit of a breakthrough (if removing an error that resolved an annoying divergence can be called a “breakthrough”). Now, it is natural to look further ahead and ask oneself where one is heading.

In my case, I still hope to develop a formalism that is powerful enough to formulate fundamental theories that incorporate the dynamics of the standard model with gravity. But wait, isn’t that what they are trying to do with string theory and all those other theories?

No, there is a difference. The idea is not to build the speculative aspects of a new theory into the formalism itself. It seems to me that all the currently popular attempts to formulate theories of fundamental physics incorporate speculative ideas into the mathematics of the formalism itself. If they fail, the whole thing fails and there is nothing to salvage.

The only physics that should be built into the formalism is physics that has been established as scientific knowledge. That is the situation with quantum field theory. It has special relativity built into it, because that has been confirmed experimentally. Thus it allows speculative new theories to be formulated.

The inclusion of special relativity may also be the reason why quantum field theory cannot model gravity, which goes beyond special relativity. The obvious thing is then to modify the part that involves the special relativity and to replace it with general relativity. Well that has been tried and did not work.

I think the reason why the obvious extension of quantum field theory to incorporate gravity did not work is because it does not incorporate the formulation of states. Gravity depends on the nature of states. Therefore, my idea is to replace the path integral formulation with a functional phase space. Such a functional phase space formulation allows the definition of arbitrary complicated states. Such a functional phase space formulation is an idea that has been bounced around in the literature, but I have not seen a complete formulation that can handle gravity.

“Post-empirical science”

The informed reader will know that the title represents an oxymoron. Without its empirical character science would not be science. It is very much what defines the cultural activity that we call “science” to be what it is.

Why then this glaring contradictory notion? It has popped up in the literature related to a recent “publicity stunt” where a simulation of a wormhole in a toy model was blown out of all proportions by being deemed to have created an actual wormhole. The simulation was done on a puny quantum computer incorporating merely 9 qubits.

Although this story has been hyped by various sources (and I am not going to give any links because I don’t want to mislead more people), many people have strongly criticized the story, including John Horgan, Scott Aaronson, Ethan Siegel, and Peter Woit. I can go on to try and clarify, but these posts are doing a much better job than I can.

Of course it is nonsense. A simulation is a numerical calculation of the physical process under study. It is not the real thing. And it does not matter whether the simulation is done with a classical digital computer or with a quantum computer. It is still just a simulation. Moreover, the amount of information that one can extract from 9 qubits is 9 bits, which is barely enough to specify one single ASCII character in a text document. So, no wormholes were created.

Perhaps the result they obtained from their simulation agreed well with what they expected to see, but that does not mean that it qualifies as being an experiment. Simulations and experiments are different things. Usually simulations are used when the direct calculations are too difficult. However, there is almost no limit on what one can simulate. It does not have to be something that can actually exist. If I have a set of equations that describe some weird imagined process that cannot exist in our universe, I can still program those equations into a computer and simulate it. For this reason, the results of a simulation can never take the place of an actual experiment.

What does this have to do with the notion of post-empirical stuff? Well, the problem lies in fundamental physics where it becomes progressively more difficult to perform experiments to learn about how things work. As a result, people are trying to motive that we start to learn about these things without having to do the experiments. That would have been great if it could work. Unfortunately, it has been tried before and found not to work. That was what the philosophers did before the advent of the scientific method. The nonsense they came up with still bounces around in the cultures of the world.

No! the day we cannot perform experiments to learn how this universe works is the day we stop learning more about our universe. A lot of people may go on coming up with stuff, but for sure, that stuff is worth nothing if it cannot be shown to work that way in our universe.

Unfortunately, there is already a lot of this going on, as this hyped wormhole nonsense demonstrates. It is related to several such non-scientific ideas that people work on and call physics, even though they don’t have much or any hope ever to show that it actually works that way through a scientific process.

The annoying thing is that there are prominent people in the physics community that are driving the hype. They’ve been doing this with other similar stories. Apparently, the reason for this hype is to induce funding agencies to give them more funding. Well, I think that if funding agencies can be led by their noses so easily, then the situation is more hopeless than I thought. These prominent people are not prominent for having done any solid scientific work. There are also other ways to become prominent. Well, I’ve ranted enough about people being prominent for the wrong reasons and don’t want to do it again.

Confinement and particles

The idea that fundamental fields are just that, fields and not particles, runs into a problem at some point. If I pick up a tennis ball and bounces it a few times then I am basically handling a particle. So, somewhere between the tiny scales of fundamental physics and the larger scales of everyday life, particles need to appear.

If the fundamental fields are just fields interacting at points, then any combinations of such field would still be fields, even though they may be interacting with one another. No, particles! Then there would also not be atoms consisting of nuclei and electron bound to them in different orbitals.

So, at some point, or some scale, a transition needs to happen where particles are created. How would that happen? It seems that if there are no fundamental particles, the universe would be condemned to exist as a soup of fields at all scales.

Then it occurred to me that there is a process that may be able to introduce particles. Confinement to the rescue! The highly nonlinear dynamics of the strong force, which is modeled by quantum chromodynamics (QCD) is believed to introduce a special scale (the QCD scale) where the force becomes so strong that it confines itself to regions with a restricted volume. The size of this volume is believed to determine the size of protons and neutrons.

Proton model (with fundamental particles), from Desy

So, although the fundamental fields are just fields with no particles, the mechanism of confinement may be responsible for adding particles in our universe. As a result, the constituents of the nucleus of the atom are particles in the true sense of the word. The nuclei can now act as the sources of the potentials that bind the electrons to form atoms.

If confinement is the reason why we have real particles in this universe, then the process of confinement is very important. The funny thing is that it is not yet a solved problem in theoretical physics. In fact, there is an outstanding Millennium Problem of the Clay Mathematics Institute about the mass gap in Yang-Mills theories, which is related to the problem of confinement. Perhaps it is something that theoreticians in fundamental physics can focus on.

Seriously, it is not that complicated

It was more than a 100 year ago that Max Planck introduced the notion of the quantization of radiation from a black body. The full-blown formulation of quantum mechanics is almost a hundred years old (the 5th Solvay conference more or less represents that achievement). Over the years since then, many ideas have been introduced about quantum physics in the struggle to understand it. Once new ideas have been introduced, nobody can ever remove them again regardless of how misleading they may be. Nevertheless, among these ideas, we can find enough information to form a picture representing an adequate understanding of quantum physics.

It would be very arrogant to claim that this understanding is unassailable or even complete. (I still have some issues with fermions.) Therefore, I simply call it my current understanding. It is a minimalist understanding in that it discards the unnecessary conceptual baggage (thus following Occam’s razor). Yet, it provides an ontology (although not one that guarantees everybody’s satisfaction).

I’ve written about many aspects of this understanding. So, where possible, I’ll thus link to those discussions. Where additional discussions may be necessary, I’ll postpone those discussions for later. Here then follows a breakdown of my current understanding of quantum physics.

Firstly, fundamental particles are not particles in the traditional sense. They are not “dimensionless points traveling on world lines.” Instead, they are better represented by wave functions or fields (or partites). Interactions among these fundamental fields (using the term “fields” instead of “particles” to avoid confusion) are dimensionless events in spacetime.

As a consequence, there is no particle-wave duality. Fields propagate as waves and produce the interference as, for example, seen in the double-slit experiment. Whenever these fundamental fields are observed as discrete entities, it is not a particle in the traditional sense that is being observed, but rather the localized interaction of the field with the device that is used for the observation.

Secondly, interactions are the key that leads to the quantum nature of the physical world. What Max Planck discovered was that interactions among fundamental fields are quantized. These fields exchange energy and momentum in quantized lumps. This concept was also reiterated in Einstein’s understanding of the photo-electric effect. Many of the idiosyncratic concepts of quantum physics follow as consequences of the principle of quantized interactions.

The Heisenberg Uncertainty Principle is not a fundamental principle. It is a consequence of the quantization relations associated with interactions. These relations convert conjugate variables into Fourier variables, which already represent the uncertainty principle. As a result, the conjugate variables inherit their uncertainty relationship from Fourier theory. It becomes more prevalent in quantum physics, due to the restrictions that the quantization of interactions imposes on the information that can be obtained from the observation of a single “particle.”

Planck’s constant only plays a physical role at interactions. Once these interactions are done, the presence of Planck’s constant the expressions of the fields have no significance. It can be removed through simple field redefinitions that have no effect on the physical representations of these fields. As a result, the significance that is attached to Planck’s constant in scenarios that are not related to interactions are generally misleading if not completely wrong.

Thirdly, another key concept is the principle of superposition. The interactions among fundamental fields are combined as a superposition of all possibilities. In other words, they are integrated over all points in spacetime and produce all possible allowed outcomes. As a consequence, after the interactions, the resulting fields can exist in a linear combination of correlated combinations. This situation leads to the concept of entanglement.

Since a single “particle” only allows a single observation, the different measurement results that can be obtained from the different elements in a superposition are associated with probabilities that must add up to one. The coefficients of the superposition therefore form a complex set of probability amplitudes. The conservation of probability therefore naturally leads to a unitary evolution of the state of the single particle in terms of such a superposition. This unitarity naturally generalizes to systems of multiple particles. It naturally leads to a kind of many-worlds interpretation.

It seems to me that all aspects of quantum physics (with the exception of fermions) follow from these three “principles.” At least, apart from the question of fermions, I am not aware of anything that is missing.