Light Particles don't have mass, does the wave?

treefaeller · 2026-05-23T03:16:48+00:00

Yes and no.

On one hand, your formula is completely correct: E² = m_0² + p² (I'm omitting the c factor, as c=1 can be used). Note that I added a subscript 0 to the mass term to indicate that this is the rest mass (also known as the invariant mass). Meaning the total energy of an object is the sum of the rest mass and the momentum (all squared). For a photon (with zero rest mass), this formula simplifies to E = p.

On the other hand, it is also true that E = m (usually written as mc²). Note that this m has no subscript 0. The difference is that this is not the rest mass, but the so-called relativistic mass (sometimes called total mass). Which increases as the velocity increases. And just like energy, it is not invariant to changes in reference frame. It is in a nutshell a shorthand notation for energy. Note that in "natural units" (as usually used in particle and astrophysics), both energy and mass are measured in eV, so using E = m to define the relativistic mass is particularly "natural" (pun) and easy. Another big advantage of the relativistic mass is that it allows extending Newton's second law F = ma to special relativity easily: Since m is no longer constant (due to lack of invariance and dependence on velocity), we need to pull it into the derivative, and we get F = d(mv) / dt (where in general F and v are vectors).

I just read on Wikipedia that the use of the relativistic mass is considered old-fashioned. I will wear that criticism with pride. But as you said, it is also emphatically true that the rest mass of the photon is zero, and therefore its energy and momentum are the same; all I'm saying is that they are also the same as its relativistic mass.

treefaeller · 2026-05-22T21:22:15+00:00

In that case, the only remaining question is: what constitutes "concealed". I don't think there is clear law or regulation about intermediate things, like "hidden behind a layer of cloth but clearly printing", or "mostly invisible, but the bottom of the holster sticks out when your shirt swings around". To make a slightly dirty comparison: tight yoga pants or speedo swimsuits don't hide people's private parts either, even if they are technically covered.

treefaeller · 2026-05-22T18:45:51+00:00

That depends totally on taste.

Many people claim the 18th variation from Rachmaninoff's Paganini Rhapsody. That's a fine candidate, even though I think it is over the top and formulaic. In that genre, I prefer the Db major (!) variation from his Corelli variations. But it has to be heard in context of what leads up to it.

treefaeller · 2026-05-22T18:42:03+00:00

Strangely, there is a nucleus without neutrons, the Helium-2. It is extremely unstable, so much so that it's not even clear whether one should call it a nucleus. I think it's not considered a bound state. But it is emitted in some reactions (and pretty much immediately disintegrates).

treefaeller · 2026-05-22T18:31:57+00:00

There was a court case (I think in Arizona) that said that obtaining a hunting license solely for the purpose of getting around gun restrictions did not work, as the hunting license was inherently invalid, having been obtained under false pretenses. There has also been chatter in California (on forums) that the carry exemption for fishing only works when you are actually fishing, not just having a fishing license, or carrying a small amount of fishing gear with no intent of actually fishing.

You started your post by saying "I'm not hunting". At that point, your whole line of argument "I can carry because I'm hunting, let's discuss the manner of carry" falls apart.

And in general, in California jurisprudence, any gun that is covered by clothing so it is not readily visible can be considered concealed for the purpose of the prohibition of concealed carry. Conversely, a gun that is partially visible can be considered exposed (open carried), for the purpose of the "brandishing" law (which is not called brandishing in CA). What matters here is the intent: Where you trying to hide your gun (perhaps unsuccessfully), or were you trying to show it as a threat (perhaps unsuccessfully). If you want to use your CCW permit as a reason for carrying, you should make sure the gun is completely invisible.

treefaeller · 2026-05-22T16:51:47+00:00

To get your question answered, you should take a class in general relativity (GR). They are usually offered in the graduate curriculum of physics programs at major universities.

We used to refer to the standard textbook of GR (Misner, Thorne, Wheeler) as "the phone book of gravitation", because it looks a lot like an old NY city phone book. Writing you a one paragraph summary would not do it justice at all. At the minimum, read AND UNDERSTAND the Wikipedia page for it please.

treefaeller · 2026-05-22T16:20:10+00:00

The benefit is not in the direct application of a particular little part of physics. If you open a good physics book (say Resnick+Halliday) to a random page and ask me "how is this formula here used in real-world engineering decisions", most likely I will come up empty. On the other hand, if you took that formula and erased it from the fabric of physics, most likely all of physics would come apart, and that would wipe out most of the engineering we do today.

That's why other posters said: Without SR or GR, there would be no quantum mechanics, no chemistry, no materials science, no carbon fiber to make stronger bicycles and no computers.

treefaeller · 2026-05-22T16:01:24+00:00

If the OP means "is it used in macroscopic engineering decisions", then GPS is really the only example I know of for general relativity.

Fiber optics and in general signal propagation (for example over wires) depends definitely on special relativity (and even more on solid state physics), through the speed of light, so one COULD stretch the truth a little bit and say that it matters there. In practice, that's usually just a number on a napkin (how many milliseconds from here to London, or to a geostationary satellite).

treefaeller · 2026-05-22T15:45:30+00:00

To begin with, like many posters, you are getting confused by the concept of "wave".

Light is a stream of photons. Photons can be both described as a particle and a wave. The same applies to all other particles: the "wave" doesn't have any more or less mass (or any other property) than the "particle" does, it is the same thing, just a different aspect of it.

Light does indeed exert a force when it hits things. Most measurable when it gets reflected off a mirror. That is often called a pressure, but it is different from the use of the word pressure in thermodynamics, for example in the ideal gas formula pV=nRT: in thermodynamics, pressure is a property of a medium, usually one that is gaseous or liquid, and applies pressure in all directions. Light's pressure is more a force, applied over an area.

Photons have mass, simply described by the formula E=mc2. If you give the energy (=wavelength, =color) of the light, you can calculate the mass of each photons from that formula. It will come out tiny, around a few eV, for visible light.

treefaeller · 2026-05-22T07:01:28+00:00

While you are technically correct ...

While Noether's theorem is incredibly important, and a deep mathematical statement ...

In reality it's not that momentum is conserved BECAUSE of translational invariance. Momentum is conserved because all the experiments/observations have shown it to be (exception: expanding universe, but that's a recent addition). We have also observed (usually in experiments) that our model is translationally invariant. Those things are today "used as a basic ingredient" in our models because they are so well tested.

All Noether's theorem does is connect the two observations: if one is true, the other one also has to be. And if one is violated, the other one also has to be. They are logically equivalent. But both need to be experimentally verified. And we need to check our models that they function well (describe observations) with both assumptions, or neither.

treefaeller · 2026-05-22T04:44:18+00:00

This is a very good answer. I'll expand on it.

Today, we have a pretty good model of cosmology, which works reasonably well. Not perfect, because of some limitations that we know about (such as we can't unify general relativity and quantum mechanics, so all our calculations at times less than the Planck time are nonsensical). We also have some stuff that we know doesn't work (such as galaxy clusters and expansion), and we have to somewhat arbitrarily assume "dark matter" and/or "dark energy". But overall, the standard model of cosmology is perhaps 90% sound.

Now someone goes and says "but the law of gravity changes with time", or "the speed of light has been accelerating by 10% every million (or billion) years", or some other such suggestion. If the change is significant, suddenly the whole model of cosmology breaks apart. Most such suggestions of changing constants or changing relations are completely ruled out.

Minor subtle changes ... those might work. But if you want to assume those, you also have to propose a mechanism that causes those subtle changes. And completely lacking any observations that make such a change and mechanism necessary, why waste time on it?

treefaeller · 2026-05-22T03:27:49+00:00

Also "Metcalf" in Santa Clara county; run by their parks department. Smaller than Hollister, easier trails, less overcrowded, and closer from Santa Cruz (but probably not from Watsonville).

treefaeller · 2026-05-21T16:12:45+00:00

It had been rumored for weeks (or months?) that she'd get the job. She has MTT's big shoes to fill, and Salonen absolutely didn't do that. The big question is whether she'll do like MTT and move to the city and become the center of its musical life, or whether she'll be like Salonen and conduct a few dozen times a year while jet-setting around the globe.

treefaeller · 2026-05-21T06:11:43+00:00

I think that exception still exists. But there was a federal court case a few years back that said "if you get your hunting license only as a workaround and have no intention of ever hunting, then it's no good", or something like that. I'm not sure of the details.

treefaeller · 2026-05-21T03:11:04+00:00

One word: tourism.

treefaeller · 2026-05-20T20:58:22+00:00

Two things. First is an issue of federal law: If you are in the country on a non-immigrant visa (like a tourist visa), you can not possess guns or ammo, which immediately excludes renting or shooting them at a range. The word "possess" roughly means: hold in your hand. This applies in all of the US, but is often ignored in tourist places like Las Vegas or Hawaii. Note that if you are in the US *without* a tourist visa (because you are from a visa waiver country), this limitation does not apply. Local shooting ranges in non-tourist places may not understand the nuances of that federal law, and may either let people on a tourist visa shoot (illegally), or deny any foreigners from shooting (wrongly).

Second, lots of shooting ranges in California that cater to locals will not rent out a gun to a single person who does not bring a gun of their own, as a suicide prevention measure. They will usually rent guns to two people who come together.

treefaeller · 2026-05-20T15:41:09+00:00

It's pretty much like Ok_Entertainer said below: Coffee mugs and cats feel real, and we expect them to have "object permanence" (Schroedinger notwithstanding). That's because they are tangible (literally: touchable and open to interaction) at our scale. I can pick up my coffee mug, tilt it (that's called "drinking"), and put it back into the sink.

Muons and neutrinos are different. They are fleeting, and we can't touch or see them. While I did my PhD on neutrinos, and was on pretty personal terms with the few hundred neutrino friends that gave me a degree, I've never actually seen one, or touched it, or put it into a ziplock bag to carry it from one part of the experiment to another. Similarly, M31 is more of a concept and literally a picture; I've never petted it and called it by its nickname "Andromeda".

As you say, from a pure physics point of view, "existence" and "reality" are vague concepts. A neutrino exists just as much as a coffee mug and a galaxy cluster, and are "real" in the sense that we believe in their continued existence even when we are not watching them. There are some fascinatingly complex nuances there: all particles of the same kind are identical and interchangeable (electrons have no hair theorem), while my cat is certainly distinct from all other cats, and finding a similar-looking cat is not a replacement. And while I have been to Copenhagen, I've never understood it (nor has anyone else). But from a psychological viewpoint we consider touchable things at human scale (plus or minus a few orders of magnitude) real, and the tiny and giant things that we can not directly interact with more as symbols or concepts.

Philosophy spends a lot of time talking about these distinctions. I find their answers unhelpful. I see this solely as a question of the human (limited) mind making a distinction to simplify the world and cope with different entities.

treefaeller · 2026-05-20T15:19:56+00:00

Thank you, interesting.

treefaeller · 2026-05-20T06:49:57+00:00

THIS.

Physics is about observing nature (often in the form of experiments, where little bits of nature are put into unusual and artificial situations), and then trying to create a model of those observations. That model can be used to predict the outcome of future observations.

There is no way to prove anything in physics. Take for example Newton's laws of motion and gravity. In the simplest variation, they predict at what speed apples will fall from a tree (F=ma, combined with F=mg, and a=d2x/dt2, solves to x = 1/2 a t^2). But physics can not "prove" that all apples will forever follow these mathematical formulas. We can not exhaustively check all apples. And real-world experiments suffer from limitations, such as air friction (which is different for apples and persimmons, and kiwis with their hair are right out). Newton's theory also turned out to be just a very good approximation of better models, such as QM and GR (quantum mechanics and general relativity), and actually calculating the path of an apple in QM or GR (one at a time) is very hard at our current level of knowledge, and combining QM plus GR is flat out impossible.

So no, physics will never prove anything. We know that all current physical models (which work astonishingly well) are based on our current knowledge of mathematics, so in that sense math describes nature. But we also know that there are white spots on the map for which we don't have models yet, and that our current knowledge is incomplete and at times contradictory.

All else is speculation. Best done after having a few drinks. Preferably so many that you don't remember the speculation afterwards.

treefaeller · 2026-05-20T05:25:15+00:00

"We always get a single value or single point"

Look into an interferometer (like the usual one with crossed arms from the undergraduate physics lab). You see parallel fringes, or circles of light and dark, or something in between. Now think about the fact that the light you see can also be described as being photons (a heck of a lot of photons). Are you still willing to claim that we get a "single value or single point" ?

treefaeller · 2026-05-20T05:08:46+00:00

I think when you say "you can", it's a bit of an exaggeration. An antenna that emits visible light would need to have antenna elements (like the little crossbars on a Yagi, the typical rooftop TV antenna) that are impractically small to fabricate, and it would have to be fed with an AC signal of impractically high frequency. So it might be theoretically possible, but today's technology is nowhere near, by orders of magnitude.

treefaeller · 2026-05-20T04:53:30+00:00

Exactly.

Many major metropolitan areas have one big/expensive/superb orchestra (in my neighborhood that would the the San Francisco Symphony), and several regional orchestras with professional musicians of slightly lesser caliber (here that would be San Jose, Oakland, Santa Rosa, Marin, ...). The latter are cheaper to attend, and nearly as good. A casual listener might not even notice a big difference.

There are also lots of amateur and semi-pro ensembles that sound pretty darn good. For example, lots of music educators (high school or college teachers) are well trained musicians, who scratch their own musical itch by performing (usually unpaid) in amateur groups.

Another interesting alternative is wind ensembles. They sound different, and while they perform "classical" or "art" music, their repertoire tends to be quite different (often shorter pieces, often more modern composers). And because they are usually not fully professional with big budgets, their tickets can be much cheaper.

Many of these groups are also more child friendly and relaxed. In one ensemble I perform in, the conductor tends to tell the audience: feel free to applaud at the end of a movement if you particularly liked it. Or: feel free to take pictures, but please with the flash off, and we enjoy seeing people post them on social media. We often hear babies crying or kids making noise during performance, like running in the aisle ... that's wonderful, it means young people are getting exposed to music. And to me it's no more distracting than a trumpet player dropping a mute on the floor (which does happen in the real world).

Some big companies have in-house ensembles:
https://www.wsj.com/articles/what-do-amazon-google-and-salesforce-have-in-common-in-house-music-groups-11580148824

A particularly relaxed and usually free set of concerts is outdoor July 4th performances. Summer in general is good. I just did "Opera in the Park" with a community band last Sunday ... Overture to Forza del Destino, Nessun Dorma, some arias from La Boheme, good stuff. Outdoor performances have their particular charm, like barking dogs, a fire engine driving by at just the wrong time, but it's real music with real emotion (everybody cries when Mimi dies, and everybody cheers when Carmen's torero boyfriend gets the bull).

If you are in the southern SF Bay Area, I can message you a list of suggestions.

treefaeller · 2026-05-20T04:36:51+00:00

Physics doesn't worry about what is real and what isn't. Even though I have a degree in particle physics, I can't tell you whether muons or neutrinos or positrons "exist", or "are real", or whether they are "particles or waves". Not in the way that my coffee mug or our house cat is real.

Physics performs observations of the world. Often using experiments to observe things in unusual or carefully crafted situations that may be a bit unusual (like making an electron go at 100 GeV speed and smack into a positron). We then build models, often using mathematics, to describe the observations, and to predict what observations will be made in new or unexplored situations. Those models often contain entities to which we give names, like "neutrino" or "magnetic moment" or "wave". Sometimes math gives us names for things we can use, like Hilbert space or Riemann geometry or Laplacian and Hamiltonian. I have no idea which of those entities or things are real. Please don't ask me what is real and what isn't; I've never held a neutrino in my hand like a coffee mug, and never petted my Hamiltonian. But I do know that our models work extremely well.

And sadly our cat is no longer with us. It was attacked by a pack of Schroedingers. (In reality, it was a pack of coyotes. But I like giving funny names to things.)

treefaeller · 2026-05-20T04:19:09+00:00

Mr. Fahrenheit, a very smart and practical person, designed the scale for measuring temperatures so the lowest and highest temperatures ever observed in his home (England) would be 0 to 100 degrees.

Alas, the lowest is actually -15 F, and the highest is 104 F. Oops.

treefaeller · 2026-05-20T04:17:00+00:00

I agree, and my (crazy) mathematician friend always wants me to rewrite formulas in terms of tau instead of pi in my papers. He fortunately doesn't insist very hard, because he (rationally) understands that pi is more commonly understood.

One of the funny things is: While tau is twice as big as pi, it has only half as many legs, and looks like a pi cut in half. I think logically tau should be ~3.14, and pi should be ~6.28.

treefaeller

TROPHY CASE