But that’s just the result of the specialisation of science. We don’t have “physicists” or even “psychologists” anymore – everyone is working on their own increasingly narrow fields. That’s unavoidable, as the amount of accumulated knowledge builds, but it also means we have fewer and fewer “big” thinkers. It still doesn’t change the fact that you can’t talk about physics without math, and you can’t talk about math without philosophy.
See research by Ray Cummings and his cousin e.e.
That depends somewhat on the nature of the observation (and, indeed, the observer). 
Might be time for a double-slit experiment.
:golf clap:
Me too. Great minds and all that. Can I at least post the Swift original that August de Morgan adapted?
Underwhelming, yes, but not nonexistent. I would argue that things like “Copenhagen interpretation” and “many-worlds theory” are very philosophical, given the lack of physical evidence for them. Moreover, I think the instigation behind such theories is frequently the complaint that “Quantum physics screws with causality, and we can’t have that, can we?”, which is certainly more in the philosophical realm than the experimental.
I’m not sure what you mean by “talk about math”, but one thing I do know is that most mathematicians have 0 (or < 0) interest in philosophy. I once went to a series of talks that purported to be about philosophy of mathematics and quickly realized that they didn’t know shit about mathematics or–more importantly since this is what they were claiming to know–how mathematicians work. I know one counter-example to this, but he has actually published papers in mathematics so he actually knows what doing mathematics is like. At any rate, nearly all mathematicians just get on with the job and ignore the philosophy, if any, behind it. And we nearly all believe that we are talking about something other than formal axioms.
Hari Seldon writes:
> And we nearly all believe that we are talking about something other than formal
> axioms.
That’s a philosophically interesting statement in itself. What are mathematicians doing if not arguing from axioms?
Philosophy is applied aesthetics.
Aesthetics is applied psychology.
Psychology is applied neurology.
Neurology is applied biology.
It’s subatomic particles all the way down.
electron-like particles [electron, muon, tau] (3)
neutrinos (3)
quarks (6)*
Z, W, photon, gluon (4)
Higgs (1)
= 17 fundamental particles that we know about. These are included in our mathematical description of nature as “point-like” particles meaning they have no size, and there is currently no experimental evidence of any size or substructure to these particles. If experimental evidence of size or substructure is found, that would be very exciting and would require some deep changes to the Standard Model of particle physics.
Everything else is composed of the above. If it’s a particle you’ve heard of it, it’s probably made of quarks. Protons and neutrons are the most well-known “hadrons” (a term for things made of quarks), with each being made of three particular quarks tied together in the lowest energy configuration possible. This is analogous to, say, a hydrogen atom being made of a proton and an electron. For hydrogen, the force holding the proton and electron together is electrical. For protons and neutrons, the force holding the constituent quarks together is a different fundamental force of nature, the appropriately (if uncreatively) named strong force.
There is a very long list of known hadrons, with new discoveries still being made. To see an overwhelming list, click down into the “mesons” and “baryons” tabs of this table.
For the fundamental particles themselves, we have so far been able to describe all observations of them and their interactions using the successful Standard Model, which is a mathematical framework for describing, well, particles and their interactions. Within the Standard Model, the different sorts of fundamental particles can have rather different characteristics and roles, but they are all plugged in as “quantum fields”.
A “field” without the word “quantum” attached, as has been mentioned, is a mathematical function that has a value at all points in some space. An example of a field might be the temperature everywhere on earth. If you specify latitude, longitude, and altitude, there is a temperature at that point. This ensemble of temperature values for all of space might be represented by a symbol T, in which case we might call T the “temperature field”.
A quantum field is the same, but different. The value of the field at each point in space is related to the probability that the particle is at that point, but in order to handle other properties of the particle and to deal with things like particles coming into existence or dying off through interactions and decays, the mathematical toolkit carries additional quantum mechanical nuts and bolts.
None of this says what a fundamental particle is. It just says what we describe it as mathematically (and, thus, linguistically). This description, though, works exquisitely well*** at predicting experimental data.
- or 18, depending on how you want to label things
** glossing over some important mysteries
*** see (**)
[QUOTE=Hari Seldon]
I once went to a series of talks that purported to be about philosophy of mathematics and quickly realized that they didn’t know shit about mathematics or–more importantly since this is what they were claiming to know–how mathematicians work. […] At any rate, nearly all mathematicians just get on with the job and ignore the philosophy, if any, behind it.
[/QUOTE]
That’s certainly been my experience too. (I’m a mathematician in real life.) In all of the math classes I’ve taken and actual mathing that I’ve done, the contribution of philosophy has been nil. I took a couple of classes and attended a few talks on the philosophy of quantum mechanics and of math, and my reaction was the same as yours: the philosophers there didn’t understand the subjects they were talking about or how mathematicians and physicists work. (And this was at a top-tier university whose philosophy department was rather good.) At this point, we have far better tools available than philosophy to solve questions of math and physics; and it’s only after ditching philosophy in favor of, well, math and physics that those areas have been successful and productive. That includes not just answering specific, narrow questions, but the “big questions” of “big thinkers” as well: what energy is and why it’s conserved, why the electric charge of a quark is a rational multiple of the charge of an electron, why electric charge is quantized at all, etc. It’s fine to say that philosophers are considering whatever deeper philosophical questions of quantum mechanics there are; but at some point, I expect answers.
[QUOTE=Hari Seldon]
And we nearly all believe that we are talking about something other than formal axioms.
[/QUOTE]
It may not be clear to people who aren’t mathematicians that math papers, lectures, etc. are not formal (in the technical sense) proofs. They’re impeccably rigorous and sound, but it’s not like a paper on, say, 4-manifold topology has anything to do with set theory or philosophy.
But we’re getting away from the original topic of what subatomic particles are made of.
Pasta, are all hadrons composed of exactly three quarks?
As there are six kinds, does that mean there are 6^3 different hadrons? (216?)
Some are made of three quarks, some are made of three antiquarks, and some are made of a quark plus an antiquark. (I glossed over antiparticles in my previous post. Almost all of the fundamental particles have “antiparticle” counterparts, increasing the number of known fundamental particles.)
These particular combinations are allowed because they respect the rules enforced by the strong force. You couldn’t have, for instance, two quarks plus one antiquark.
The three-quark (or three-antiquark) combinations are called baryons. The quark-plus-antiquark combinations are called mesons.
Given the above, I will read your question as “Are there 6^3 different baryons?” No, for few reasons. First, are you familiar with atomic excitation, whereby an atom can be its lowest energy state or it can be “excited”, perhaps by hitting it with light and putting the system into a higher energy configuration with possibly different angular momentum as well?
Well, these systems of quarks do the same thing, although it isn’t usually light that puts them into excited states. A proton is made of two “up” quarks and one “down” quark (“up” and “down” being the names of two of the quarks*). This quark content can be written “uud”. A Delta is a different uud baryon, but the system is in a higher energy state and has an extra quantum of angular momentum. It’s a different particle with a different mass and a different future (for instance, the Delta decays very quickly to other hadrons) even though it’s built from the same three quarks. Since there are many energetically possible bound states of uud, there end up being many possible uud particles. About 30 are known just with uud. Similarly large numbers are known for udd, uuu, and ddd. It adds up quickly when the other quarks are brought into the mix.
On the flip side, the “top” quark is too short lived to form hadrons. When a top quark is produced, it decays very quickly to a different quark + other stuff, and that different quark will bind up with other quarks into a hadron. But no hadron containing a top quark has ever been observed, and none is expected.
- quark names: up, down, charm, strange, top, bottom
At the risk of introducing or furthering a hijack, I think this is perhaps the greatest misunderstanding between science and philosophy (or, most often, misconception scientists have of philosophy): that you can somehow supplant the wishy-washy nebulous doings of philosophers with the sounder, more successful practices of scientists. But that’s just (what philosophers would call) a category error: science and philosophy simply aren’t after the same kind of knowledge.
Science really is after statements of the kind ‘the fine structure constant is (roughly) 1/137’, or, one some conceptions, after statements describing the empirical content of such a sentence; philosophy, on the other hand, is far better understood as being concerned with analysis and clarification of such statements: what does it mean to say ‘the fine structure constant is (roughly) 1/137’? Philosophy could not have discovered the value of the fine structure constant; that is, to the extent you want to consider science as separated from philosophy—there’s obviously a good historical case to be made that they at least share the same roots—and I’m not saying that they are separated in the sense of ‘non-overlapping magisteria’, or something like that.
Science, without philosophy, really only gives you a black box called a ‘theory’: you put in some input, and out comes an experimental procedure, alongside a prediction of what you will observe upon following it. If this prediction is correct, we move on to the next; if it turns out to be false, we try to come up with a better black box. What it is, however, that enables the black box to make these predictions is left wholly opaque; to the extent that one then speculates about a picture of reality that might obtain and in which the predictive capability of the black box would find an explanation, one is engaged in philosophy.
Wow, that’s weirder than I would have thought.
Is the number of particles limited? Other than by the amount of energy involved?
What’s it all for, what do all those particles DO?
Strictly speaking, there are hypothesized particles called “pentaquarks”, consisting of four quarks and one antiquark (or vice-versa), though none have yet been observed. And one can also consider a bound state of multiple hadrons (such as an atomic nucleus) to also be a hadron (the Large Hadron Collider is called that not because it’s a large collider, but because it collides large hadrons, such as gold nuclei).
And I would consider 17 to be a reasonable count for the number of subatomic particles, since the properties of the antiparticles are directly determined by the properties of the particles, and likewise for the different colors of quarks. Plus, if one’s going to start calling a red up quark a fundamentally different particle than a green up quark, one might as well say that a spin-up quark is a different particle than a spin-down quark, and that way madness lies.
Oh, and I would also include the graviton on the list of particles that we know of, for at least some values of “that we know of”. We’ll probably never detect individual gravitons, we still haven’t even detected streams of many gravitons (though we’re close), and what little theory we have on them tells us very little, but we’re pretty sure at least that they exist in some form or another.
And also the growing tetraquark evidence linked to above.
The color counting rears its head sometimes since, unlike spin, it doesn’t factor out of questions that involve both leptons and quarks. For instance, when estimating certain branching fractions on the back of an envelope, you have to count quarks three times relative to leptons.
“Pretty sure” seems a bit strong, but YMMV.
The number is limited in that if you try to make something sufficiently esoteric and high mass it would want to decay to simpler, lower mass things so quickly that it never actually forms in the first place. Instead, the lower mass things would get made. The number of hadrons known stems primarily (nearly exclusively) from experimental data, as the mathematics of the strong force make it computationally very hard to make predictions about what groupings should be stable, what mass they should have, what lifetime they should have, etc. These calculations have caught up with the data for the most part, but they haven’t blown past it.
What are you for? (asks the Lambda(2100) baryon…)
All these hadrons are just the consequences of the building blocks. LEGO blocks are simple, but if some blocks are stuck together when you take them out of the bucket, the new combined entities just are.
So, you gotta kinda roll with the complexity. In the same way that, say, the element thulium is there just because 100 neutrons and 69 protons happen to be stable when they join up, so too are all these combinations of quarks and antiquarks just there. But also in the same way that without thulium the world would be a little different, so too with these particles.
(Some have seemingly direct roles in places, like Delta particles causing an upper limit on cosmic ray protons reaching earth or affecting the opacity of materials to certain energy gamma rays. But it would be a little cheating to say “What if the Delta weren’t there?” because that’s equivalent to saying “What if the details of strong force were different?”, in which case nuclear structure and beyond would also change dramatically.)