# A quick primer on the basic forces in physics

There was an interesting question posed by Marcus Ranum about the nature of the WIMPs (Weakly Interacting Massive Particles) that are being looked for as the constituents of dark matter, and which are proving to be so elusive. He wondered why their presence could not be detected via gravity since it was to explain the gravitational effects of galaxies that they were postulated in the first place. I thought the question merited a quick primer for those interested in understanding it in a little more depth.

Part of the confusion surrounding this issue is that the term ‘weak’ refers to both the strength of a force as well as being the name given to one of the four basic forces. All the elementary particles that we know of interact with each other via one or more of the four basic forces: strong nuclear, electromagnetic, weak nuclear, and gravity, listed in descending order to strength. Each of those forces is believed to be generated by the elementary particles exchanging other elementary particles known as ‘gauge bosons’. The strength of the force depends on the strength with which each gauge boson interacts with the elementary particle.

For the strong nuclear force, these gauge bosons are called gluons and are massless. So, for example, quarks exchange gluons and the force thus generated is very strong and increases rapidly with distance between the quarks which is why individual quarks have not been isolated. Quarks seem to be permanently trapped inside larger particles. The proton, for example, contains three quarks, the pion has two quarks, and so on.

For the electromagnetic force, the gauge bosons consist of photons that are also massless. Electrically charged particles exchange photons and this generates the electromagnetic force and while this is strong, the force decreases with distance between charged particles and that is why we are able to overcome the attraction of opposite charges within an atom and get isolated single charges such as electrons and protons.

For the weak nuclear force, we have three gauge bosons: W+, W, and Z0, that have quite large masses on the elementary particle scale, close to 100 times the mass of a proton. The weak interaction is involved whenever we have neutrinos.

For gravity, the gauge boson is the graviton, which is also believed to be massless though we have not as yet directly detected it because the interaction is so extremely weak that it is only when one of the interacting masses is massively large (like planets, starts, black holes, galaxies, etc.) that the cumulative strength becomes detectable.

So to summarize, gluons couple strongly to particles, photons less so, weak interactions even less so, and gravitons couple so weakly that they have not been directly detected as yet.

The problem with dark matter, as ahcuah pointed out, is that we don’t know what it is made of and so we can only speculate as to what its interactions with familiar matter may be. (Recall that when we say we ‘detect’ a particle in an experiment, what we are saying is that we observed the particle interacting with some particle in the detector. In the LUX experiment, they were looking for the recoil of Xenon atoms as a result of interacting with a WIMP.) We know that because dark matter is believed to be all around us in huge amounts and yet we do not feel it, it cannot be a strong or electromagnetic interaction. We know it has mass so the gravitational interaction plays a role but that does not help us in detecting it because of the extreme weakness of that force. Because it had to have been produced in the Big Bang, we believe it must interact via a force other than gravity so we hope that it interacts via some kind of weak interaction, either of the kind we already know or of a new kind. That is why people are looking for WIMPs.

As is the case in science, we start with what we know and then move beyond. In the early days, it was suggested that WIMPs may consist of weakly interacting particles that we are already familiar with, such as neutrinos, so that the particle and the interaction would be known ones. But that seems to have been ruled out and WIMPs, if they exist, are now believed to a form of matter that is not part of the current known elementary particle spectrum. Various theories that predict different properties have been proposed and what the recent negative results suggest is that some of the ones seen as most promising are becoming less plausible contenders.

1. Pierce R. Butler says

… quarks exchange gluons and the force thus generated is very strong and increases rapidly with distance between the quarks …

So the bond between quarks in remote galaxies is exponentially stronger than that between those in my leftmost eyelash? Pls define “bond” in this context (even if it requires stirring martinis).

… individual quarks have not been isolated. … The proton, for example, contains three quarks, the pion has two quarks, and so on.

And what on? That sequence leads to what you just implied doesn’t exist.

Sorry -- when I can’t follow the physics, I chew on the English…

2. says

What happens is that if you try to separate two quarks (say, in a pion) the force (and therefore energy involved) rapidly gets so large that that energy gets converted into two new quarks which then combine with the quarks you are trying to separate, one per. But then you don’t have any free quarks, just 2 pions (or other bosons).

3. Brian English says

The truth is they’re called wimps because they’re weak. The acronym is to save face. It’s a nothing particle, no mass, it’s pathetic. Can’t even detect it! Now, if we had a Trump-Boson, that would be yuge! Very detectable, all the smart people know how detectable it is. Big hands too, you’d need a wall!

I find the concept of massless particle paradoxical. I think of a photon hitting the retina, or a detector and having enough mass to impart some minute force. But that’s obviously wrong. And the weak-nuclear particles having so much mass they weigh more than a proton. Do they have more mass than a neutrino? It’s amazing, and I’m not doubting it, just how counter intuitive it seems. I need to learn more about this stuff to have a better grasp. (Assuming I’m able to grasp it).

4. says

You don’t need mass to impart force, just momentum (after all, force is the rate of change of momentum). The relativistic formula (using c=1) relates energy, momentum, and mass: E^2 -- p^2 = m^2.

5. Mano Singham says

Pierce @#1,

All the strongly interacting particles are made up of combinations of quarks. There are six kinds of quarks. The rule is that each quark is assigned what is called a baryon number +1/3 and its anti-quark has the number -1/3. Each strongly interacting elementary particle has to have quarks so that the sum of the baryon numbers add up to an integer. So a proton has three quarks with baryon number 1. So does a neutron. A pion has a quark and an anti-quark with baryon number 0. You can have particles with other combinations of quarks and anti-quarks (that was my “and so on”) as long as the total baryon number is an integer.

To follow up on ahcuah @#2, as an analogy, think of a length of elastic. It has two ends. Think of the ends as the quarks. As you pull on the ends and the ends get further apart, the force between them gets larger. At some point the elastic breaks. Now you have two pieces of elastic, each still with two ends. That is analogous to how you end up with two pions when you pull the two quarks in a pion (technically a quark and an anti-quark) apart.

Something similar happens when you try to knock out one of the three quarks in a proton using (say) a high energy photon. As the quark gets pulled out, the restoring force trying to pull it back in gets larger. At some point it gets large enough that the bond snaps, creating a new quark and an anti-quark. The new quark goes back and joins the other two quarks so that you get a proton or a neutron with baryon number +1, while the new anti-quark joins up with the expelled quark to form a pion with baryon number 0. So the net result is that you started with a proton and ended up with a proton (or neutron) plus a pion but still no free quark.

As Rob explains it in #6, as long as the combinations of quarks in a particle take a certain form, the force exerted by that combination on other combinations does not increase with distance but instead is a very short range force. The rules for what combinations have this feature are a little more complicated than adding baryon numbers, but it involves assigning quarks a property known as ‘color’ that can have three values red, green, and blue (kind of the way electric charges have two ‘colors’, + and -). As long as the net color adds up to zero (i.e., it is ‘colorless’ which can be done by red+green+blue, red+anti-red, and so on), the particle as a whole exhibits only the short range force. This is why two protons have just short range strong forces between them and can be separated quite easily. Each of them have three quarks such that the total color of each is zero.

6. Rob Grigjanis says

Pierce @1:

So the bond between quarks in remote galaxies is exponentially stronger than that between those in my leftmost eyelash?

Not when they’re in their “confined” states. Quarks interact with each other primarily* via the strong interaction. The strong analogue to electric charge is called color (an arbitrary naming having nothing to do with colors), and there are three colors, with three associated anticolors. Three quarks of different colors form a “colorless” combination (a baryon), as do a pair of any color plus its anticolor (a meson). When the early universe had cooled sufficiently, the quarks basically condensed into these confined combos. In both cases (baryon and meson), the net color charge of these combos is zero, so they have no long range attraction to other quarks. There is however a residual short range force, which is the nuclear force binding nucleons (the baryons known as protons and neutrons) together.

I have a horrible feeling I explained this badly 🙁

*They can also interact via the electromagnetic and weak interactions.

7. Brian English says

You don’t need mass to impart force, just momentum (after all, force is the rate of change of momentum). The relativistic formula (using c=1) relates energy, momentum, and mass: E^2 – p^2 = m^2.

I assume this was in response to my ignorance. OK, p = mv (mass times velocity). This is classical I guess, and not quantum, but relativity is classical too. And your formula E^2 -- p^2 = m^2 (does that mean E = sqrt(m^2 -- p^2) = mC^2 or E^2 = m^2*c^4?). So mass is involved. I guess if mass = 0 then E^2 = p^2 and E = sqrt(p) = +/- p = +/-mv. and E = 0 (m=0 so mC^2=0), and a massless particle has no energy. 🙂
Probably not, I’m sure they’re different Es and ps and ms…..

8. Rob Grigjanis says

Mano, I didn’t see your response until after I posted.

9. Rob Grigjanis says

Brian @7:

relativity is classical too

No. p=mv is nonrelativistic. As ahcuah said, the correct relativistic relation is p=sqrt(E² -- m²) (with units such that c=1). For massive particles, this reduces to p=mv for v much less than c. For massless particles, it is p=E.

10. says

Brian @7. Continuing with what Rob said, you also need to know that the word “classical” is ambiguous. When it comes to relativity, “classical” means Newtonian. When it comes to quantum mechanics, “classical” refers to (somewhat imprecisely) not having wave/particle duality.

Adding back in the c’s, E^2 = p^2c^2 -- m^2c^4, true for all particles. For particles at rest, p=0, and thus E=mc^2. For a massless photon (or other massless particle), m=0, so E=pc.

11. says

Darnit, screwed up the signs. E^2 -- p^2c^2 = m^2c^4.

12. Brian English says

Cool. Thanks, I quickly checking the appendix of the a Kindle book on quantum mechanics that explains some of this, and missed the bit that is Newtonian (elementary classical) mechanics, not relativistic (classical) mechanics. Elementary classical versus classical. My bad. 🙂

13. Brian English says

So, out of interest, and not jest. If E = pc. What is the formula for p? p = E/C? (OK, a little in jest ;)) Or is it not something derived from first principles, but something measured?

14. Mano Singham says

Brian @#7,

The relativistic relationship between energy E, mass m, and momentum p is as ahcuah said in #4.

If you don’t set the speed of light c=1 as he did, then the expression is E2-(pc) 2=m2c4. The expression p=mv for momentum is a non-relativistic approximation that holds when v is much smaller than c.

When you have a massless particle, then m=0. The relativistic expression then reduces to E=pc and hence the momentum p=E/c. You cannot use p=mv for massless particles because all massless particles travel with speed c and hence the condition for using p=mv no longer holds.

(There was a flurry of responses while I was composing my reply to Brian so please excuse the redundancies.)

15. Brian English says

Mano @14

The relativistic expression then reduces to E=pc and hence the momentum p=E/c. You cannot use p=mv for massless particles because all massless particles travel with speed c and hence the condition for using p=mv no longer holds.

That makes perfect sense.

So, we have a photon traveling along at c (or is it C?), no mass to slow it down or whatever mass does. C is constant, so can be ignored or set to 1 as above, p varies proportionally to E. Cool. A photon has momentum because it has energy. When it ‘strikes’ something, it imparts momentum or some impetus, which we detect. I guess in classical (I’m sure I’m now in deep and still digging) we think of photons as particles only, that seems to make sense.

16. Mano Singham says

Brian @#15,

This distinction between particles and waves should not to be taken too far because of the wave-particle dualistic nature of quantum mechanics that asserts that every particle exhibits either characteristic depending on the experimental conditions probing it. Rather than think of particles in terms of whether they are classical or quantum, it is perhaps better to think of particles as ‘localized’ in that they occupy a fairly limited range of space. This is in contrast to waves that extend over a large region of space.

17. Brian English says

Mano @16. Thanks. It’s strange. a photon is localized in some sense, but when you shine a beam of photons you get an interference pattern, like its ensemble is a wave. But that’s probably wrong too. Thanks for the answers, the problem is I know a few factoids, but have forgotten or never knew how it all fits together.

18. Rob Grigjanis says

Brian @15: Actually, the idea that electromagnetic fields carry momentum precedes the notion of photons as particles. We’ve known EM fields carry energy since the late 19th century. Add Einstein’s 1905 E=mc² paper and stir, and it follows that it must also carry momentum. See here.

P.S. It’s c.

19. sonofrojblake says

This is all great, except the stuff about the weak force.

The weak interaction is involved whenever we have neutrinos

What does that even mean? I’m not criticising as such -- I’ve never really seen a good explanation of the weak force. Apparently (Wikipedia) it’s “responsible for radioactive decay”, but again -- what does that mean? The other three forces are understandable as the things which hold together nuclei (strong force), magnets (electromagnetic force) and solar systems (gravity), but I don’t even have a conceptual model for what the weak nuclear force does. It doesn’t even seem to be a “force” in the sense the other are. Any clues?

20. Rob Grigjanis says

sonofrojblake @19: The huge difference between the weak force and the others is that the mediators of the force (the W+, W–, and Z0 bosons) have a large mass, about 100 times that of a proton. This means they tend to decay very rapidly, with a lifetime on the order of 10^-25 seconds. Photons, on the other hand, can sail merrily through space forever or until they hit something. So rather than hold stuff together, they mostly act as mediators for other particles’ decays. Like the muon for example.

21. Rob Grigjanis says

“So rather than hold stuff together, they [the W and Z bosons, I mean]…”

22. sonofrojblake says

I’m still struggling with a conceptual model for what they actually DO, here. (That said, I’ve never entirely understood the idea that the attraction between two magnets is down to an exchange of photons. Really?) I think the problem is largely linguistic -- “act as a mediator” has a number of possible meanings I’m familiar with, none of which I can attach to radioactive decay. Thanks, though, for the understandable notion that because the mediator is massive, and hence decays quickly, they’re not able to… er… project force as we commonly understand it. I would say this is the area of physics I am most annoyed/disappointed that I don’t “get”. I appreciate that my knowledge of other areas is probably pop-sci nonsense largely unrelated to the reality and hard sums of the proper subject, but here I don’t even have the illusion of a clue.

23. Friendly says

I’m still struggling with a conceptual model for what they actually DO, here.

IANAP (I am not a physicist), but as I understand it, unlike the other three interactions, the weak interaction produces no “bound states”; in other words, it doesn’t attract anything to anything else. Rather, it causes quarks to change their “flavor,” allowing particles to decay into other particles with less energy. In so doing, it can break CP symmetry, which causes certain decays to be non-reversible and might thus contribute to either or both of (a) the preponderance of matter over antimatter in the universe and (b) the directionality in which we perceive time.

24. Rob Grigjanis says

sonofrojblake @22: Yeah, the whole language of “photon exchange”, “act as a mediator”, etc can be a bit challenging. It’s hard to avoid when you’re talking about things which really have no classical analogue. Maybe a better way to think of it, or a way to make things even more obscure 😉

Space is permeated by a bunch of fields corresponding to each kind of particle. A particular particle (electron, photon, muon, etc) is an excitation of its corresponding field, like a wave in water.

But the fields can also interact with each other. So as a muon (an excitation of the muon field) travels through space, it is disturbing the electromagnetic field and the weak field. These disturbances are often referred to as virtual particles, which I think can be misleading, but it’ll do for now.

The em disturbances (virtual photons) don’t change the identity of the muon, but they can hit other charged particles, resulting in a deflection of both muon and other particle.

The weak disturbances (virtual W bosons) momentarily change the muon to a muon neutrino. Having done so, there’s a probability that the virtual W then decays to an electron and an electron antineutrino. So instead of a deflection, we have three new particles (muon neutrino, electron, electron antineutrino) and no muon. That’s muon decay.

Hope I didn’t just create more confusion!

25. Rob Grigjanis says

Friendly @23:

the weak interaction produces no “bound states”

Yeah, that comes down to the masses of the W and Z bosons. They decay so quickly that their “range” as a force is only about 10^-18 m, which is 1/1000 the radius of a proton.

26. sonofrojblake says

That started to make sense, then I realised I’d never heard of the muon field. More books! (Thanks, I definitely think that helped.)

27. Rob Grigjanis says

sonofrojblake @26: You can think of muons as supersized electrons, having about 200 times the mass.

28. Pierce R. Butler says

ahcuah @ # 2: … the force (and therefore energy involved) rapidly gets so large that that energy gets converted into two new quarks …

Mano Singham @ # 5: … you started with a proton and ended up with a proton (or neutron) plus a pion …

Rob Grigjanis @ # 6: Not when they’re in their “confined” states.

Thanks for all of y’alls’ patience with a physics illiterate! Here’s yr reward: more stupid questions…

So (a bit of) the energy used to split the particle turns into another particle? And the Laws of Conversation of Everything remain undisturbed? We end up with a little bit more matter (I s’poze stellar fusion simultaneously reduces the matter-fraction by orders of magnitude more at any given second)?

Rob G @ # 6: Three quarks of different colors form a “colorless” combination…

Is this the root of the “color” metaphor, as with R, G, & B lights combining to make a “white” beam?

29. Rob Grigjanis says

Pierce @28:

Is this the root of the “color” metaphor…

I always assumed so. The naming of things has never been physicists’ strong suit, so to speak. As Feynman said;

The idiot physicists, unable to come up with any wonderful Greek words anymore, call this type of polarization by the unfortunate name of ‘color,’ which has nothing to do with color in the normal sense.

30. Pierce R. Butler says

Rob Grigjanis @ # 29: The naming of things has never been physicists’ strong suit…

I thought Gell-Mann did pretty good by pulling “quarks” out of James Joyce.

“Color” and “Charm” I can excuse on grounds of sleep deficiency, but “Spin”, to those of us living on supra-microscopic scales, is just wrong.

31. Rob Grigjanis says

Pierce @30:

“Color” and “Charm” I can excuse on grounds of sleep deficiency…

I don’t excuse “charm”. After the up and down quarks, the next to come along was called “strange”. A stupid name, and the stupidity continued with “charm”. For a while, the next (maybe last) two were called “beauty” and “truth”, but some sense was restored and they are now called “bottom” and “top”.

…but “Spin”, to those of us living on supra-microscopic scales, is just wrong.

I disagree on this. It’s the intrinsic angular momentum of a particle. Can you come up with a better name?

32. Pierce R. Butler says

Rob Grigjanis @ # 31: It’s the intrinsic angular momentum …

So two of the properties of quarks do have relevant & meaningful names? Thanks for setting me straight!

Maybe “bottom” & “top” should be renamed after the lead characters in 50 Shades of Grey

33. John Morales says

I dunno about poor naming… I see it as whimsical.

Friendly above mentioned flavour, and then there’s quantum chromodynamics.

(And when I was in school, a term of reference was the particle zoo. Nice to see progress made!)

34. Rob Grigjanis says

John @33:

and then there’s quantum chromodynamics

That just follows from ‘color’; it’s the theory of color charge (i.e. strong) interactions. I’m all for a bit of whimsy, and for me (if not Feynman) ‘color’ and ‘flavor’ are OK, as long as the American spellings are used. ‘strange’ and ‘charm’ are just mimsical.

35. Rob Grigjanis says

And we can’t speak of whimsy, quarks, and particle zoos without mentioning Gell-Mann’s Eightfold Way.

36. John Morales says

Rob, 🙂