Wisdom is the path to knowledge

As a physicist, I cherish the freedom that comes with the endeavor to uncover new knowledge about our physical world. However, it irks me when people include things in physics that do not qualify.

Physics is a science. As a science, it follows the scientific method. What this means is that, while one can use any conceivable method to come up with ideas for explaining the physical world, only those ideas that work survive to become scientific knowledge. How do we know that it works? We go and look! That means we make observations and perform experiments.

That is the scientific method. It has been like that for more than a few centuries. And it is still the way it is today. All this talk about compromising on the basics of the scientific method is annoying. If we start to compromise, then eventually we’ll end up compromising on our understanding of the physical world. The scientific method works the way it works because that is the only way we can know that our ideas work.

Some people want to go further and put restrictions on how one should come up with these ideas or what kind of ideas should be allowed to have any potential to become scientific knowledge even before it has been tested. There is the idea of falsifiability, as proposed by Karl Popper. It may be a useful idea, but sometimes it is difficult to say in advance whether an idea would be falsifiable. So, I don’t think one should be too exclusive. However, sometimes it is quite obvious that an idea can never be tested.

For example, the interior of a black hole cannot be observed in a way that will give us scientific knowledge about what is going on inside a black hole. Nobody that has entered a black hole can come back with the experimental or observational evidence to tell us that the theory works. So, any theory about the inside of a black hole can never constitute scientific knowledge.

Now there is this issue of the interpretations of quantum mechanics. In a broader sense, it is included under the current studies of the foundations of quantum mechanics. A particular problem that is much talked about within this field, is the so-called measurement problem. The question is: are these scientific topics? Will it ever be possible to test interpretations of quantum mechanics experimentally? Will we be able to study the foundations of quantum mechanics experimentally? Some aspects of it perhaps? What about the measurement problem? Are these topics to be included in physics, or is it perhaps better to just include them under philosophy?

Does philosophy ever lead to knowledge? No, probably not. However, it helps one to find the path to knowledge. If philosophy is considered to embody wisdom (it is the love of wisdom after all), then wisdom must be the path to knowledge. Part of this wisdom is also to know which paths do not lead to knowledge.

It then follows that one should probably not even include the studies of foundations of quantum mechanics under philosophy, because it is not about discovering which paths will lead to knowledge. It tries to achieve knowledge itself, even if it does not always follow the scientific method. Well, we argued that such an approach cannot lead to scientific knowledge. I guess a philosophical viewpoint would then tell us that this is not the path to knowledge after all.

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.