mass

The Standard Model More Deeply: Masses, Lifetimes and Forces

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Today’s post is for readers with a little science/math background:

Last week, I explained, without technicalities, how the various elementary forces of nature can be inferred from the pattern of lifetimes of the known particles.  I did this using an image, repeated below, that organized the particles by their masses and lifetimes.  I’ll add more non-technical posts on the Standard Model in the coming days. But today’s post is a tad more technical, using dimensional analysis (a physicist’s secret weapon) (which I demonstrated here, here and here) to explain key features of the image: the red line, the blue line, and the particles at the upper left, as well as why there is a high-energy and a low-energy version of the weak nuclear force.

Figure 1:  An assortment of the known particles particles clustered into classes according to the “force” that causes them to decay. See this recent post for details.

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E = m c-Squared: The Simple Dimensions of a Discovery

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In my last post I introduced you to dimensional analysis, an essential trick for theoretical physicists, and showed you how you could address and sometimes solve interesting and important problems with it while hardly doing any work. Today we’ll look at it differently, to see its historical role in Einstein’s relativity.

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The Murky NY Times Op Ed on Dark Matter

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Appropriate for General Readership [Apologies: due to a computer glitch, the figure in the original version of this post was not the most up-to-date, and had typos, now fixed.] On Tuesday, the New York Times Editorial page ran an Op-Ed about dark matter… and although it could have been worse, it could certainly have been … Read more

A Short Break

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Personal and professional activities require me to take a short break from posting.  But I hope, whether you’re a novice with no knowledge of physics, or you’re a current, former, or soon-to-be scientist or engineer, or you’re somewhere between, that you can find plenty of articles of interest to you on this site.  A couple … Read more

Mass-ive Source of Confusion

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One of the challenges for a person trying to explain physics to the non-expert — and for non-experts themselves — is that scientific language and concepts are often frustratingly confusing. Often two words are used for the same thing, sometimes words are used that are fundamentally misleading, and often a single word is used for two very different but related concepts. You’d think we’d clear this stuff up, but no one has organized a committee dedicated to streamlining and refining our terminology.

A deeply unfortunate case, the subject of today’s post, is the word “mass”. Mass was confusing before Einstein, and then Einstein came along and (accidentally) left the word mass with two different definitions… both of which you’ll see in first-year university textbooks. (Indeed, this confusion even extended to physicists more broadly, causing the famous particle physicist Lev Okun to make this issue into a cause celebre…) And it all has to do with how you interpret E = mc² — the only equation everybody knows — which relates the energy stored in an object to the mass of the object times the square of the universal speed limit c, also known as “the speed of light”.

Here are the two possible interpretations of this equation. Modern particle physicists (including me) only use the first interpretation. The purpose of this post is to alert you to this fact, and to point you to an article where I explain more carefully why we do it this way.

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Article on Atomic Nuclei

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Posts have been notably absent, due mainly to travel with very limited internet; apologies for the related lack of replies to comments, which I hope to correct later this week. Meanwhile I’ve been working on a couple of articles related to the nuclei of atoms, part of my Structure of Matter series, which serves to … Read more

Higgs Symposium: A More Careful Summary

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My rather hasty, breathless and inconsistent summaries (#1, #2 and #3) of last week’s talks at the excellent Higgs Symposium (held at the University of Edinburgh, as part of the new Higgs Center for Theoretical Physics) clearly had their limitations.  So I thought it might be useful to give a more organized overview, with more … Read more

The Constancy of the Heavens — Verified Anew

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This is a post about constancy and inconstancy, one of my favorite topics.  And about how alcohol can make you smarter.

There are many quantities that we call “constants of nature”.  Of course, anything we call a “constant” is merely something that, empirically, appears to be constant, to the extent we can measure it.  Everything we know comes from observation and experiment, and our knowledge is always limited by how good our measurements are.

We have pretty good evidence that a number of basic physical quantities are pretty much constant.  A lot of evidence comes from the constancy of the colors of light waves (i.e. the frequencies of waves of electromagnetic radiation) that are emitted by different types of atoms, which appear to be very much the same from day to day and year to year and even across billions of years (neat trick! will describe that another time), and from here to the next country and on to the moon and to the sun and across our galaxy to distant galaxies.  For example, if the electron mass changed very much over time and place, or if the strength of the electromagnetic force varied, then atoms, and the precise colors they emit, would also change.  Since we haven’t ever detected such an effect, it makes sense to think of the electron mass and the electromagnetic force’s strength as constants of nature.

But they’re not necessarily exactly constant.  One can always imagine they vary slowly enough across time or place that we wouldn’t have noticed it yet, with our current experimental technology.  So it makes sense to look at very distant places and measure whatever we can to seek signs that maybe, just maybe, some of the constants actually vary after all.

[I wrote a paper in 2001 with Paul Langacker and Gino Segre about this subject (Calmet and Fritzsch had a similar one).  This followed the observational claims of this paper (now thought false) suggesting the strength of electromagnetism varies across the universe and/or with time.  A lot of what follows in this post is based on what I learned writing that old paper.]

Suppose they did vary?  Well, the discovery of any variation whatsoever, in any quantity, would be a bombshell, and it would open up a door to an entirely new area of scientific research.  Once one quantity were known to vary, it would be much more plausible that others vary too.  For instance, if the electron mass varies, why not the W particle’s mass, which affects the strength of the weak nuclear force, and thereby radioactivity rates and the properties of supernovas?  If the electromagnetic force strength varies, why not that of the strong nuclear force?  There would be interest in understanding whether the variation is over space, over time, or both.  Is it continuous and slow, or does it occur in jumps?  One can imagine dozens of new experiments that would be proposed to study these questions — and the answers might reveal relations among the laws and “constants” of nature that we are currently completely unaware of, as well as giving us new insights into the history of the universe.

So it would be a very big deal.  [Though I should note it would also be puzzling: even small variations in these constants would naively lead to large variations in the “dark energy” (i.e. cosmological “constant”) of the universe, which would potentially make the universe very inhomogeneous.  However, we don’t understand dark energy, so this expectation might be too naive.] Since there’s no story about it on the front page of the New York Times, you can already guess that no variation’s been found.  But a nice new measurement’s been done.

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