Integers and the Physics

Someone very rightly said: “God made the integers, every other number is that the work of man. Now after more than a century, no mathematician would deny the importance and utility of the developments that Kronecker railed against. Yet I think that a lot of harbors some sympathy for his statement. The integers hold a special place within the heart of mathematicians.

Many of the foremost famous unsolved conjectures relate to the properties of the primes. More importantly, the integers are where we start mathematics:
they are how we count.

In this article, I might wish to view Kronecker’s quote through the lens of theoretical physics. Tested against our greatest theories of Nature, I will be able to argue that the statement is wrong.

Experimentally, falsifiably, wrong. It is not obvious that the integers have anywhere in physics. The counting that's evident in mathematics isn't very easy within the world. I was taught in college that
there are 9 planets within our solar system. Now there are 8. or even 13. As this instance shows, the matter of finding the integers in Nature lies not within the counting, but rather within the defining. The Kuiper belt contains objects ranging in size from a few thousand kilometers to a couple of microns. you'll only decide which objects are
planets and which are merely lumps of rock if you use a reasonably arbitrary definition of what it means to be a planet.

To seek out the integers in physics, we'd like Nature to provide us with objects which are naturally discrete.

Fortunately, such objects exist.

While the definition of a planet could also be arbitrary, the definition of an atom, or a fundamental particle, is not. Historically, the first place that the integers appeared was within the table of elements. The integers
labeling atoms which, we now know, count the number of protons − are honest.

Regardless of what developments occur in physics, I'm sure that we'll never observe a stable element with √500 protons that sits between titanium and vanadium.

The integers in physics are here to remain.

Comments

Time Management: Pomodoro Technique

Are you facing challenges in managing your time properly? If you often waste time on unproductive tasks and finally at the end of the day feel you have wasted your day. Pomodoro Technique may be a good solution to all your problems. Today I am going to discuss here, a very useful technique to improve your productivity and better time management. The credit for this technique goes to Francesco Cirillo. He utilized a tomato-shaped sandglass to manage his time effectively. He called it the Pomodoro technique (which is an Italian word for “tomato”). The idea behind the Pomodoro Technique is to break down all of your tasks into 25-minute time blocks. Between two session , keep a five-minute break. And after completing four Pomodoros sessions taking an extended break usually 15-20 min. There are six steps in the original technique: Decide on the task to be done. Set the Pomodoro timer (traditio...

Puzzle- 100 Prisoners and a Light Bulb

Every once in a while, I hear puzzles about 100 prisoners and a meticulous, demanding warden. All of these puzzles share a common characteristic, a set of prisoners must work together to devise a clever scheme to thwart the warden. I hear these puzzles often enough that each time they reappear, I view them with an increased level of understanding corresponding to the stage of my mathematics education. Any problem may have a solution, but, sometimes, that solution may not be the most efficient one possible. For example, suppose you want to find something in your room but don’t remember where you put it. You can either search the room by yourself. Or you can call your (many) friends to help you. From a correctness standpoint, both solutions are correct. You’ll find what you’re looking for eventually. But from an algorithmic standpoint, the second solution where you search in parallel with your friends is better because it has a shorter runtime. The same holds for solutions to the 1...

IIT Delhi Launches IITPAL Portal

The Indian Institute of Technology (IIT) Delhi launched an interactive IIT- PAL website —iitpal.iitd.ac.in — to give free videotape lectures to class 11 and 12 scholars who are preparing for competitive examinations similar as JEE, NEET, IAT and others. www.iitpal.com This action of the Ministry of Education (MoE) had started with an end to make their understanding of the wisdom subjects (Physics, Chemistry, Maths and Biology) better and to help tone- studying scholars do well in competitive examinations like JEE, NEET, IAT and others. Now, to bring all coffers together, IIT-D has launched a website. The website —iitpal.iitd.ac.in — will act as a single platform where scholars across India can pierce videotape lectures that are telecast on the Ministry of Education’s Swayam Prabha Channels, interact live with IIT Professors and ask them questions. “ This website will be helpful to scholars especially from regions where they may not have access to specialist prec...

IITPAL

Search This Blog