OK, so I am finally done with moving my stuff, and so, from now on, should be able to find at least some time for ‘net activities, including browsing and blogging (not to mention also picking up writing my position paper on QM from where I left it).
Alright, so let me resume my blogging right away by touching on a very foundational aspect of physics (and also of maths).
Before you can even think of building a theory of physics, you must first adopt, implicitly or explicitly, a viewpoint concerning what kind of physical objects are assumed to exist in the physical universe.
For instance, Newtonian mechanics assumes that the physical universe is made from massive and charge-less solid bodies that experience and exert the inter-body forces of gravity and those arising out of their direct contact. In contrast, the later development of the Maxwellian electrodynamics assumes that there are two types of objects: massive and charged solid bodies, and the electromagnetic and gravitational fields which they set-up and with which they interact. Last year, I had written a post spelling out the different kinds of physical objects that are assumed to exist in the Newtonian mechanics, in the classical electrodynamics, etc.; see here [^].
In this post, I want to highlight yet another consideration which enters physics at the most fundamental level. Let me illustrate the issue involved via a simple example.
Consider a 2D universe. The following series of diagrams depicts this universe as it exists at different instants of time, from through . Each diagram in the series represents the entire universe.
Assume that the changes in time actually occur continuously; it’s just that while drawing diagrams, we can depict the universe only at isolated (or “discrete”) instants of time.
Now, consider this seemingly very simple question:
What precisely does the above series of diagrams depict, physically speaking?
Can you provide a brief description (say, running into 2–3 lines) as to what is happening here, physics-wise?
At this point, you may perhaps be thinking that the answer is obvious. The answer is so obvious, you could be thinking, that it is very stupid of me to even think of raising such a question.
“Why, of course, what that series of pictures depicts is this: there are two blocks/objects/entities which are initially moving towards each other. Eventually they come so close to each other that they even touch each other. They thus undergo a collision, and as a result, they begin to move apart. … Plain and simple.”
You could be thinking along some lines like that.
But let me warn you, that precisely is your potential pitfall—i.e., thinking that the question is so simple, and the answer so obvious. Actually, as it turns out, there is no unique answer to that question.
That’s why, no matter how dumb the above question may look to you, let me ask you once again to take a moment to think afresh about it. And then, whatever be your answer, write it down. In your answer, try to be as brief and as precise as possible.
I will continue with this issue in my next post, to be written and posted after a few days. I am deliberately taking a break here because I do want you to give it a shot—writing down a precise answer. Unless you actually try out this exercise for yourself, you won’t come to appreciate either of the following two, separate points:
- how difficult it can be to write very precise answers to what appear to be the simplest of questions, and
- how unwittingly and subtly some unwarranted assumptions can so easily creep in, in a physical description—and therefore, in mathematics.
You won’t come to appreciate how deceptive this question really is unless you actually give it a try. And it is to ensure this part that I have to take a break here.