Physics vs formalism

This is something I just have to get off my chest. It’s been bugging me for a while now.

Physics is the endeavour to understand the physical world. Mathematics is a powerful tool employed in this endeavour. It often happens that specific mathematical procedures are developed for specific scenarios found in physics. These developments then often lead to dedicated mathematical methods, even special notations, that we call formalisms.

The idea of a formalism is that it makes life easier for us to investigate physical phenomena belonging to a specific field. An example is quantum mechanics. The basic formalism has been developed almost a hundred years ago. Since then, many people have investigated various sophisticated aspects of this formalism and placed it on a firm foundation. Books are dedicated to it and university courses are designed to teach students all the intricate details.

One can think of it almost like a kitchen appliance with a place to put in some ingredients, a handle to crank, and a slot at the bottom where the finished product will emerge once the process is completed. Beautiful!

So does this mean that we don’t need to understand what we are doing anymore? We simply need to put the initial conditions into the appropriate slot, the appropriate Hamiltonian into its special slot and crank away. The output should then be guaranteed to be the answer that we are looking for.

Well, it is like the old saying: garbage in, garbage out. If you don’t know what you are doing, you may be putting the wrong things in. The result would be a mess from which one cannot learn anything.

Actually, the situation is even more serious than this. For all the effort that has gone into developing the formalism (and I’m not only talking about quantum mechanics), it remains a human construct of what is happening in the real physical world. It inevitably still contains certain prejudices, left over as a legacy of the perspectives of the people that initially came up with it.

Take the example of quantum mechanics again. It is largely based on an operator called the Hamiltonian. As such, it displays a particular prejudice. It is manifestly non-relativistic. Moreover, it assumes that we know the initial state at a given time, for all space. We then use the Hamiltonian approach to evolve the state in time to see what one would get at some later point in time. But what if we know the initial state for all time, but not for all space and we want to know what the state looks like at other regions in space? An example of such a situation is found in the propagation of a quantum state through a random medium.

Those that are dead sold on the standard formal quantum mechanics procedure would try to convince you that the Hamiltonian formalism would still give you the right answer. Perhaps one can use some fancy manipulations of the input state in special cases to get situations where the Hamiltonian approach would work for this problem. However, even in such cases, the process becomes awkward and far from efficient. The result would also be difficult to interpret. But why would you want to do it this way, in the first place? Is it so important that we always use the established formalism?

Perhaps you think we have no choice, but that is not true. We understand enough of the fundamental physics to come up with an efficient mathematical model for the problem, even though the result would not be recognizable as the standard formalism. Did we become so lazy in our thoughts that we don’t want to employ our understanding of the fundamental physics anymore? Or did we lose our understanding of the basics to the point that we cannot do calculations unless we use the established formalism?

What would you rather sacrifice: the precise physical understanding or the established mathematical formalism? If you choose to sacrifice the former rather than the latter, then you are not a physicist, then you are a formalist! In physics, the physical understanding should always be paramount! The formalism is merely a tool with which we strive to increase our understanding. If the formalism is not appropriate for the problem, or does not present us with the most efficient way to do the computation, then by all means cast it aside without a second thought.

Focus on the physics, not on the formalism! There I’ve said it.

Art in research

Does it help to apply some form of creativity in scientific research? Stated differently, does creativity have any role to play in scientific research? I would like to think so.

At first one may think that creativity is only associated with the act of conjuring up things that don’t really exist. A painter paints a land scape scene and applies creativity to render the trees and the clouds in interesting ways. As such, they are different from the trees and cloud in the real scene. In as far as the artist employs creativity, the result become different from reality.

If this is what creativity produces, then it would have no place in scientific research, because in this context, we are not interested in anything that would deviate from reality. But creativity does not only representing that which doesn’t exists. It can also be associated with a much more abstract activity.

When a theoretical researcher tries to come up with a model that describes an aspect for physical reality, he or she needs to create something that has not existed before. It is not initially known whether this model gives the correct description of reality. In that sense, one does not known whether it represents anything that is real. One would know that only after the model has been tested. But before that step can be taken, one needs to create the model. For this first step, the researcher is required to employ creativity.

The act of creating such a model is an act of bring into existence something that has not existed before. The inspiration for this model may be obtained from other similar models or from other models in unrelated fields of study. In the same way, artists get inspiration from the works of other artists. despite the source of inspiration, the resulting model is novel in one way or another. That is where the creativity lies.

So, art and science are not that different after all. Both require the same mental faculties. Perhaps they just call it by different names.

Particle physics impasse

Physics is the study of the physical universe. As a science, it involves a process consisting of two components. The theoretical component strives to construct theoretical models for the physical phenomena that we observe. The experimental component tests these theoretical models and explores the physical world for more information about phenomena.

Progress in physics is enhanced when many physicists using different approaches tackle the same problem. The diversity in the nature of problems need to be confronted by a diversity of perspectives. This diversity is reflected in the literature. The same physical phenomenon is often studied by different approaches, using different mathematical formulations. Some of them may turn out to produce the same results, but some may differ in their predictions. The experimental work can then be used to make a selection among them.

That is all fine and dandy for physics in general, but the situation is a bit more complicated for particle physics. Perhaps, one can see the reason for all these complications as the fact that particle physics is running out of observable energy space.

What do I mean by that? Progress in particle physics is (to some extent at least) indicated by understanding the fundamental mechanisms of nature at progressively higher energy scales. Today, we understand these fundamental mechanisms to a fairly good degree up to the electroweak scale (at about 200 GeV). It is described by the Standard Model, which was established during the 1970’s. So, for the past 4 decades, particle physicists tried to extend the understand beyond that scale. Various theoretical ideas were proposed, prominent among these were the idea of supersymmetry. Then a big experiment, the Large Hadron Collider (LHC) was constructed to test these ideas above the electroweak scale. It discovered the Higgs boson, which was the last extent particle predicted by the standard model. But no supersymmetry. In fact, none of the other ideas panned out at all. So there is a serious back-to-the-drawing-board situation going on in particle physics.

The problem is, the LHC did not discover anything else that could give a hint at what is going on up there, or did it? There will be another run to accumulate more data. The data still needs to be analyzed. Perhaps something can still emerge. Who knows? However, even if some new particle is lurking within the data, it becomes difficult to see. Such particles tend to be more unstable at those higher energies, leading to very broad peaks. To make things worse, there is so much more background noise. This makes it difficult, even unlikely, that such particles can be identified at these higher energies. At some point, no experiment would be able to observe such particles anymore.

The interesting things about the situation is the backlash that one reads about in the media. The particle physicists are arguing among themselves about the reason for the current situation and what the way forward should be. There are those that say that the proposed models were all a bunch of harebrained ideas that were then hyped and that we should not build any new colliders until we have done some proper theoretical work first.

See, the problem with building new colliders is the cost involved. It is not like other fields of physics where the local funding organization can support several experimental groups. These colliders require several countries to pitch in to cover the cost. (OK, particle physics is not the only field with such big ticket experiments.)

The combined effect of the unlikeness to observe new particles at higher energies and the cost involved to build new colliders at higher energies, creates an impasse in particle physics. Although they may come up with marvelous new theories for the mechanisms above the electroweak scale, it may be impossible to see whether these theories are correct. Perhaps the last energy scale below which we will be able to understand the fundamental mechanisms in a scientific manner, will turn out to be the electroweak scale.

Glad I did not stay in particle 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?

Fabulous trip

During the last two weeks, I did not post anything. That is because I was traveling. First, there was the conference that I attended. After that, because I have some friend living in the same city, I took a few days visiting them. What a memorable time I had.

It is so green. What a contrast to the grays and browns that I experience here at home. So where is this wonderful place? Ottawa, Canada!

Parliament Hill in Ottawa

In the Byward Market, I bought some apples. One can buy a variety of fresh vegetables and fruit. The area has a variety of different restaurants and shops.

Byward Market Ottawa

I also visited the University of Ottawa and the National Research Council during my trip. These visits gave me the opportunity to discuss research collaboration opportunities with some people in my field of research.

It is not often that I travel these days. Basically, I don’t enjoy traveling . But for some reason, trips to Canada are always great. I just love that country.

Mandalas

Art and religion has many regions of overlap. It is an organic interaction that leads to much richness in cultures. One can just think of all the Byzantine art as an example.

Among the forms of art associated with Eastern religions, one finds the mandala. It is an abstract pattern, usually circular in design and often has some symmetries. Its meaning is some way associated with the universe, however, there’s more to it. Part of the whole significance is the actual creation process of a mandala. A person would tend to start from the centre and work his way outward. In this way, it represents how the individual is being connected with the universe. At least, that is what I understood from what I read about it.

These days one often encounter mandalas in various non-religious contexts. It may even be regarded as a theme in abstract design. One can for instance notice them in adult colouring books.

It is fun to makes one’s own design for a mandala and to let the creative juices flow. The one above I made using POV-Ray. One can play with the colours. Here I decided to make it look like a metal wire construction. The reflection at the bottom did not come out so nicely.

Politically jaded

Yes, when it comes to politics, I don’t count myself among the most enthusiastic. This is perhaps surprising in view of the fact that I live in one of the most politically turbulent countries in the world. Well, that is also precisely to reason. Being inundated with politics over the media on a constant basis, one eventually becomes jaded.

So, why am I writing about this? It is in response to a recent blog post. Sorry Son, I missed it when you posted it and now it is a bit late to leave a comment. So, let my make an exception and say what I think about these things.

My advise? Turn off your radio when the news comes on. If one cannot do anything about all those terrible things, then what is the point of knowing about them? All that happens is that one becomes upset, depressed, anxious, and have all sorts of such negative emotions. It affects one’s health and still the situation remains the same.

The funny thing is that one tends to have a vague idea about what is going on anyway. One may not know the details, but I’ve learned over the years that the truth about the detail is often different from what one is being told.

How are we to treat our fellow human in this country? Here I’m going to be very Biblical about it: Love your neighbour as you love yourself. What if he is your enemy and hides hatred behind his smile? Love you enemies as well, do not repay hatred with hatred.

Yes, despited the fact that the government is screwing up severely, they still remain in power. Evidently, we don’t really have a democracy. After being in power for a quarter of a century, the majority of people still live in poverty. I have a theory about that. Since these poor destitute people form the power base for the current government, it is not in the government’s interest to uplift them. So, perhaps it is a secret policy of the government to maintain a large ignorant poor destitute population to ensure that these destitute people will again vote them into power at the next election in the false hope that it will improve there condition. It is also in my view why education is such a disaster in this country.

I cannot do anything about that, at least not in the short term. All I can do is to contribute my little part to make the world a better place in as far as I have an influence. I set a good example; educate those that I am in contact with; spread love and ignore the hated. OK, I also maintain a blog and have even written a book, but if that makes a big difference then I don’t see it.

In the very long term, perhaps several generations from now, things will get better. Whether my culture will still exist in this country, I don’t know. Probably not. On the other hand, perhaps civilization would have fallen all around world by that time.

Who knows?