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.

Guiding principles I: substructure

Usually the principles of physics are derived from successful scientific theories. For instance, Lorentz invariance which can be seen as the underlying principle on which special relativity is based, was originally derived from Maxwell’s equations. As we learn more about the universe and how it works, we discover more principles. These principles serve to constrain any new theories that we try to formulate to describe that which we don’t understand yet.

It turns out that the physics principles that we have uncovered so far, don’t seem to constrain theories enough. There are still vastly different ways to formulate new theories. So we need to do something that is very dangerous. We need to guess some additional physics principles that would guide us in the formulation of such new theories. Chances are that any random guess would send us down a random path in theory space with very little chance of being the right thing. An example is string theory, where the random guess was that the fundamental objects are strings. It has kept a vast number of researchers busy for decades without success.

Instead of making a random guess, we can try to see if our existing theories don’t perhaps already give us some additional hints at what such a guiding principle should be. So, I’ll share my thoughts on this for what it is worth. I’ll start with what our current theories tell us about substructure.

The notion of a substructure can already be identified in the work of Huygens, Fresnel, etc. on interference . It revealed that light is a wave. The physical quantity that is observed is the intensity, which is always positive. However, we need to break the intensity apart into amplitudes that can have negative values to allow destructive interference. In this very simple sense, the amplitude (which is often modeled as a complex valued function) serves as a substructure for that which is observed.

Interference

It is not a big leap from interference in classical light to come to the interference in quantum systems. Here the observation is interpreted as a probability, which is also a positive quantity. In quantum mechanics, the notion of a probability is given a substructure in the form of a probability amplitude which can be negative (or complex) to allow interference phenomena.

The concept of a substructure is today perhaps mostly associated with the notion of constituent particles. We know now that the proton is not a fundamental particle, but that it has a substructure consisting of fundamental particles called quarks, bound together via the strong force. Although it is not currently considered to be the case, these quarks may also have some substructure. However, the concept of this substructure may be different from the way it appears in protons.

A new idea that is emerging is the idea that spacetime itself may have a substructure. Ever since the advent of general relativity, we know that spacetime is affective by gravity. In our current formulation of particle physics, spacetime is the backdrop on which all the particle fields perform their dance. But when gravity is added, spacetime joins the dance. It makes the formulation of fundamental theories very complicated. The difference between the particles and spacetime becomes blurred. This leads to the idea that spacetime itself may have a substructure. In this way, it combines the two different ways to look at substructure. On the one hand it may be divided into two parts, perhaps to separate chirality, much in the way intensity separates into an amplitude and its complex conjugate. On the other hand the separation of spacetime may give some substructure to the particle fields, being described in terms of fluctuations in spacetime’s substructure.

Caution is necessary here. Even if these ideas turn out to be valid, they still leave much detail unspecified. It may not be enough to regard the idea of substructure as a physics principle. The importance it to keep to the standard practice in physics: mathematics is merely used to formulate and model the physics universe. It does not tell us something new about the universe unless this is somehow already logically encoded in what we start off with.

Perhaps an example would help to explain what I mean. Einstein formulated general relativity (GR) after he figured out the equivalence principle. So everything that we can learn from GR follows as inevitable logical consequences from this principle. It tells us that the mass-energy distribution curves spacetime, but it does not tell us how this happens. In other words, the mechanism by which mass curves spacetime is not known because it is not a logical consequence of the equivalence principle.

So, the idea is to come up with a general mathematical formalism that is powerful enough to model this kind of scenario without trying to dictate the physics. Remember, quantum field theory is a formalism in terms of which different models for the dynamics in particle physics can be modeled. It does not dictate the dynamics but allow anything to be modeled. Another example is differential geometry which allows the formulation of GR but does not dictate it. Part of the reason why string theory fails is because is a mathematical formulation that also dictates the dynamics. The formulation of a quantum theory for gravity requires a flexible formalism that does not dictate the dynamics.

Vanity and formalism

During my series on Transcending the impasse, I wrote about Vanity in Physics. I also addressed the issue of Physics vs Formalism in a previous post. Neither of these two aspects are conducive to advances in physics. So, when one encounters the confluence of these aspects, things are really turning inimical. Recently, I heard of such a situation.

In an attempt to make advances in fundamental physics, the physics community has turned to mathematics, or at least something that looks like mathematics. It seems to be the believe that some exceptional mathematical formalism will lead us to a unique understanding of the fundamentals of nature.

Obviously, based on what I’ve written before, this approach is not ideal. However, we need to understand that the challenges in fundamental physics is different from those in other fields of physics. For the latter, there are always some well-established underlying theory in terms of which the new phenomena are studied. The underlying theory usually comes with a thoroughly developed formalism. The new phenomena may require a refinement in formalism, but one can always check that any improvements or additions are consistent with the underlying theory.

With fundamental physics, the situation is different. There is no underlying theory. So, the whole thing needs to be invented from scratch. How does one do that?

Albert Einstein

We can take a leave out of the book of previous examples from the history of physics. A good example is the development of general relativity. Today there are well established formalisms for general relativity. (Note the use of the plural. It will become important later.) How did Einstein know what formalism to use for the development of general relativity? He realized that spacetime is curved and therefore need a formalism that can handle curved spacetime metrics. How did he know that spacetime is curved? He figured it out with the aid of some simple heuristic arguments. These arguments led him to conceive of a fundamental principle that would guide him in the development of the theory.

That is a success story. Now compare it with what is going on today. There are different formalisms being developed. The “fundamental principle” is simply to get a formalism that can handle curved spacetime in the context of a quantum field theory so that the curvature of spacetime can somehow be represented be the exchange of particles. As such, it goes back to the old notions existing before general relativity that regarded gravity as a force. According to our understanding of general relativity, gravity is not a force. But let’s leave that for now.

There does not seem to be any new physics principles that guide the development of these new formalisms. Here I exclude all those so called “postulates” that have been presented for quantum mechanics, because those postulates are of a mathematical nature. They may provide a basis for quantum mechanics as a mathematical formalism but not for the physics associated with quantum phenomena.

So, if there is no fundamental principle driving the current effort to develop new formalisms for fundamental physics, then what is driving it? What motivates people to spend all the effort in this formidable exercise?

Recent revelations gave me a clue. There was some name-calling going on among some of the most prominent researcher in the field. The proponents of one formalism would denounce some other formalism. It is as if we are watching a game show to see which formalism would “win” at the end of the day. However, the fact that there are different approaches should be seen as a good thing. It provides the diversity that improves the chances for success. More than one of these approaches may turn out to be successful. Here again an example from the history of science can be provided. The formalisms of Heisenberg and Schroedinger both turned out to be correct descriptions for quantum physics. Moreover, there are more than one formalism in terms of which general relativity can be expressed.

So what then is really the reason for this name-calling among proponents of the different approaches to develop formalisms for fundamental physics? It seems to be that deviant new motivation for doing physics: vanity! It is not about gaining a new understanding. That is secondary. It is all about being the one that comes up with the successful theory and then reaping in all the fame and glory.

The problem with vanity is that it does not directly address the goal. Vanity is a reward that can be acquired without achieving the goal. Therefore, it is not the optimal motivation for uncovering an understanding of fundamental physics. I see this as one of the main reasons for the lack of progress in fundamental physics.

How far away is that star?

On a clear night, far away from the city lights, one can look up and enjoy the beauty of the starry sky. This display must have enticed people for as long as people existed and I’m sure the question has often come up: how far away are those stars?

Well, there is an interesting tale of discovery related to the progression of measuring sticks that give the ability to determine the distances to astronomical objects. Part of this tale is how Edwin Hubble discovered that the universe is expanding.

The realization that we live in an expanding universe complicates the answer to the question of how far away astronomical objects are. Apart from the fact that the distances change, there is also the issue of what distance we observe at a given point in time. If I use the apparent brightness of a star with a known absolute brightness, then one may think (at least I would have) that the implied distance is between us (the earth) and the location of the star at the time the light was emitted. This is not the case.

Diagram of light from a star or galaxy propagating to be observed on earth

The above diagram tries to explain what happens. The black dots represent a star or galaxy (the source of the light) at different locations in an expanding universe. The blue dot is the earth which is kept it at a fixed location in the expanding universe. The red circles represent the expanding sphere of light after being emitted by the source at some point in the past. Assuming that the universe expands uniformly, we see the source would always remain at the center of the expanding sphere. Moreover, since the observed apparent brightness is given by the total emitted power divided by the total surface area of the sphere, the associated distance is the distance from the earth to the current location of the source. This is called the proper distance to the source.

Amazing, we are able to know the distance to an object at its current location even if we cannot see that object now. Who knew?