You might think I’m about to tell a joke. But no, not me. This is serious physics, folks!
Suppose a particle falls into a hole, and, as in a nightmare (or as in a certain 1970s movie featuring light sabers), the walls of the hole start closing in. The particle will just stay there, awaiting the end. But if the same thing happens to a wavicle, the outcome is very different. Like a magician, the wavicle will escape!
Today I’ll explain why.
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ON July 11, 2024
A central issue in discussions of particle physics’ present and future is known as the hierarchy puzzle. Although I discuss the hierarchy — its confusing nature and the debates that it generates — in my upcoming book, I do so rather briefly, and so, I’ll be putting up some new pages on this website with supplemental information. The same information is relevant for the cosmological constant problem. (Older pages already giving various perspectives on these issues can be found here, here and here.)
I have just posted the first new page, on “zero-point motion” and “zero-point energy.” It begins with a verbal, non-technical description of zero-point motion and zero-point energy. There follows a sketch of the details using pre-university math. Future pages will apply these ideas to quantum fields, addressing notions of “vacuum energy density” and the “cosmological constant”, and then turning to “Higgs feedback” and the core of the hierarchy puzzle.
A quick description of the hierarchy in question: it is a hierarchy of energy scales, or of mass scales. One way it can be described is in terms of particle masses:
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ON February 13, 2024
Atoms are all about a tenth of a billionth of a meter wide (give or take a factor of 2). What determines an atom’s size? This was on the minds of scientists at the turn of the 20th century. The particle called the “electron” had been discovered, but the rest of an atom was a mystery. Today we’ll look at how scientists realized that quantum physics, an idea which was still very new, plays a central role. (They did this using one of their favorite strategies: “dimensional analysis”, which I described in a recent post.)
Since atoms are electrically neutral, the small and negatively charged electrons in an atom had to be accompanied by something with the same amount of positive charge — what we now call “the nucleus”. Among many imagined visions for what atoms might be like was the 1904 model of J.J. Thompson, in which he imagined the electrons are embedded within a positively-charged sphere the size of the whole atom.
But Thompson’s former student Ernest Rutherford gradually disproved this model in 1909-1911, through experiments that showed the nucleus is tens of thousands of times smaller (in radius) than an atom, despite having most of the atom’s mass.
Once you know that electrons and atomic nuclei are both tiny, there’s an obvious question: why is an atom so much larger than either one? Here’s the logical problem”
(These statements about the radiated waves from planets and electrons can be understood with very little work, using — you guessed it — dimensional analysis! Maybe I’ll show you that in the comments if I have time.)
So there’s a fundamental problem here.
Either way, this would lead us to expect
where # is not too, too far from 1. (This is the most naive of all dimensional analysis arguments: two radii in the same physical system shouldn’t be that different.) This is in contradiction to experiment, which tells us that # is about 1/100,000! So it seems dimensional analysis has failed.
Or is it we who have failed? Are we missing something, which, once included, will restore our confidence in dimensional analysis?
We are missing quantum physics, and in particular Planck’s constant h. When we include h into our dimensional analysis, a new possible size appears in our equations, and this sets the size of an atom. Details below.
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ON June 30, 2022
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