3: What does paradox teach?
Imagine me in the same sitting position as Feynman in the header image and telling you this story!
This is the third and final article in the series. The titles of the three articles in this series are:
- Is Obvious True?
- How deep are our assumptions?
- What does a paradox teach?
In this, I answer these questions by giving a brief account of all the blabber in my previous two articles and its conclusion.
In our so-called day to day life, elders, teachers and whoever thinks they are wise enough advise us one pretty common thing: ‘Use your common sense’. But is it really wise to do that? What is common sense actually?
Common sense is a set of knowledge which is assumed as right or observed as a right by a large group of society since it is a common set among many, we call it common sense. Some varied definitions of it are, it is the basic understanding of the surroundings we develop sub-consciously through our day to day experiences, which isn’t really sorted out consciously.
How can we trust our instincts or common-sense or something I like to refer to as sub-conscious knowledge? It didn’t enter your mind consciously. One thing we can do is to verify through a logical approach. We can use math to verify if it is possible to do that. For example, I have done some such verifications in some other articles which you will find here, one such article is here, where I tried to find a pattern of heads and tails that wins the most number of games.
In that article, we will see that the result is somewhat counter-intuitive. It is against common sense, something which was obvious. As I quoted earlier, ‘Nothing is more deceptive than an obvious fact’. (Answered my first question)
I try to use math wherever possible to check out whether my conclusion is right or wrong since math is the most logical language I know as of now. Similarly, I was studying something obvious to most of the educated ones, the process of energy absorption and emission. It was so obvious that we never questioned whether energy is conserved in such processes.
I took it for granted until one day I somehow wanted to write it down in math to verify and get some fun writing math. That’s when I saw the paradox, energy is not conserved. I met with a paradox.
What to do when we meet a contradiction or a paradox? We are there because some of our assumptions might be wrong or that no such result is possible. In the case of this paradox, either the assumptions I took in writing it’s math are wrong or it’s possible that absorption and emission aren’t real processes. But we know in our day to day life, absorption of light is real. It is real because that’s how we are seeing things with our eyes, that’s how mirrors work.
So it was clear that my assumptions are wrong. My assumptions were :
- Mass of atom is taken to be same in every frame
- The energy gap from the ground state to excited is taken to be same in every frame
- Relativistic effects on relative velocities are not taken into account
- Absorbed photon energy is only used in jumping from the lower quantum level to higher i.e. the photon energy is either same or higher than the energy gap
When your assumptions are wrong, you get a chance to correct them. That’s what I did. I corrected all the four assumptions and re-did all the math to check for the conservation.
Guess what I got it wrong again. I met with the same paradox. When there is a paradox, I had two things to check for: assumptions or the result. I checked for both and turns out the paradox still exist. What does it mean?
It means we reached the stage where we ask ourselves: How deep are our assumptions? (my second question).
Are my noted assumptions the end of the line or are they derived from some other assumptions? Well, yes! But the paradox second time also could mean there is something wrong with correcting assumptions. But I was careful enough to use only experimentally verified theory, ‘relativity’ to do those corrections. So no problems.
The yes part in the above paragraph means that at least one of my assumptions are not basic and are derived. After some thought, I did find out that to be true. Some of my assumptions are derived from Bohr’s model of the atom, where it says energy gap between two levels is proportional to the Mass of the nuclei system and dependant on the quantum numbers and nothing else.
I did get to resolve the paradox as I found the part where the mistake is. The paradox must be resolved since the process of absorption and emission is real, which makes Bohr’s theory inaccurate.
If the paradox is between an experimentally verified result and some presumable perfectly logical theory, then the theory must be the wrong one. (Answer to the third question)
Take away lessons can be many but I will end this article by quoting Feynman: ‘Science is a way of trying not to fool yourself. The principle is that you must not fool yourself, and you are the easiest person to fool.’
If anyone wants to read the whole (complicated) report in a single PDF, you can find it here.
