Tag Archives: energy

A Little Math; A Lot of Physics

One of my current goals is to explain how the Higgs field works to anyone who’s learned a bit of physics at the beginning-university or advanced pre-university level. As a step toward the goal, I am creating a set of pages that explain how fields work, why quantum mechanics implies that sufficiently simple fields have particles, and which aspect of a field’s behavior determines the masses of its particles.  You will find that knowing a little physics and a little math is helpful.

[I’m afraid that most of you who never had a beginning physics class at all will have to be patient. It’s an even greater challenge for me to explain the Higgs field to someone who’s allergic to math, or hasn’t had much math yet; I’m hoping my current efforts will help me see how surmount that challenge.  But meanwhile you might like to read my Higgs FAQ and my popular article on Why the Higgs Particle Matters.]

The first step is to remember how a ball on a spring works — one of the first things one learns in any physics class — and then learn a little bit about how quantum mechanics changes the answer — one of the first things one learns in a quantum mechanics class.  This is where the concept of a “quantum” first makes its appearance in physics.  Those articles are now ready for you to look at.  The next step [waves, both without and with quantum mechanics] will follow over the coming week.

Note: I’ve included, for the first time on this website, some animated gifs among the figures.  These should animate when you click on them.  I know they need improvement; over the next day I’ll be trying to make them faster to load and run.  Please be patient and let them load; but do let me know if you can’t make them work at all, and if so, what browser and hardware you’re using.  Update: they should be much faster now.

The Stability and Instability of the Neutron

One of the strange but crucial features of our world is that every type of atom except hydrogen contains neutrons in its nucleus, even though neutrons, on their own, decay (to a proton, electron and anti-neutrino) within about 15 minutes on average.  At first glance this seems puzzling.  At second glance too.  How can stable matter be made from unstable ingredients?

The reason this is possible has everything to do with Einstein’s special relativity, and the way mass and energy are intertwined there.  A crucial role is played by the energy that is most important for binding things together, which I’ve called “interaction energy”.

I’ve now written an article explaining why neutrons inside of nuclei can be stable, giving the example of the deuteron (one proton bound to one neutron) which is the nucleus of “heavy hydrogen”, or “deuterium”.  If you understand this example, you’ll basically understand the point for other nuclei as well.

[For those of you in the New York City area: I’ll be joined by the wonderfully talented singer-songwriter-pianist Andrea Wittgens in giving a physics/music joint performance/presentation at the storied Cornelia Street Cafe, Sunday May 13th at 6 p.m., as part of their Entertaining Science series.  It’s entitled Rhapsody for Piano and Universe, and intended for the general public.  The place is pretty small, so get reservations in advance.]

The Energy to Bind Them All

I have written a lot about energy, but I’ve put off introducing the most important type of energy again and again.  It’s the most important, because it is this type of energy that is responsible for all the structure in the universe, from galaxy clusters down to protons and everything in between.  It is the most challenging to write about because it is not particularly intuitive.   All the types of energy we intuitively understand, such as the energy of motion, are positive, but this type of energy, crucially, can be negative.  On this website I’ll call it “interaction energy” (not the technical term, but my own, chosen to avoid misconceptions that might otherwise arise) because it is associated with the interactions among fields — including their little ripples that we call “particles”.  If you’ve taken physics you’ve heard of “potential” energy; what you learned within that concept is a subset of what is included under interaction energy.

I’ve been wanting to address this for a while, because many of you have asked penetrating and central questions about the basic structure of matter, such as:

  • Why is the neutron stable inside of atomic nuclei, given that on its own it is unstable?
  • Why is the proton arguably heavier than the quarks and gluons that make it up?

And there are other equally important questions that no readers have yet stumbled upon but that I ought to address.  Before I can answer any of those questions, however, I have to first describe interaction energy and the role that it plays in structure.

So — without further ado, here’s the article.  This was an especially hard article to write and it may well be confusing in places — so I very much welcome your feedback, in order that I can try to make it clearer, if necessary, in later versions.

Relativity for the Energetic Masses

Ok, folks: yesterday’s first installment of my mass and energy article, discussing energy and momentum, has been extended with a second installment.  Mass has made its appearance now, along with Einstein’s famous relations between energy, momentum, mass and speed, which are described and analyzed using… triangles.  Yes, if you can remember what Pythagoras had to say about triangles, you can understand quite a lot about what Einstein was saying about relativity when he proposed his striking revision of Newtonian thinking.  And I also address some obvious puzzles that bother everyone the first time they hear about this stuff…

The new material from today starts with the section marked “Mass … “.

Mass and Energy Article Taking Shape

Quick update today; just wanted you to know that some qualitative discussion of energy and momentum appears in this new article, to which I will add a discussion of mass over the next day or two.  The article also has a bit more about Emmy Noether, the mathematician whom I wrote about yesterday.