Here's Michio Kaku, writing in 1994, on the overall ugliness of the Standard Model. Has the situation improved or deteriorated since then? "...perhaps most important, it is very ugly because it crudely splices three very different interactions together. Personally, 1 think that the Standard Model can be compared to crossing three entirely dissimilar types of animals, such as a mule, an elephant, and a whale. In fact, it is so ugly and contrived that even its creators are a bit embarrassed. They are the first to apologize for its shortcomings and admit that it cannot be the final theory. This ugliness is obvious when we write down the details of the quarks and leptons. To describe how ugly the theory is, let us list the various particles and forces within the Standard Model: 1. Thirty-six quarks, coming in six "flavors" and three "colors," and their antimatter counterparts to describe the str ong interactions 2. Eight Yang-Mills fields to describe the gluons, which bind the quarks 3. Four Yang-Mills fields to describe the weak and electromagnetic forces 4. Six types of leptons to describe the weak interactions (including the electron, muon, tau lepton, and their respective neutrino counterparts) 5. A large number of mysterious "Higgs" particles necessary to fudge the masses and the constants describing the particles 6. At least 19 arbitrary constants that describe the masses of the particles and the strengths of the various interactions. These 19 constants must be put in by hand; they are not determined by the theory in any way Worse, this long list of particles can be broken down into three "families" of quarks and leptons, which are practically indistinguishable from one another. In fact, these three families of particles appear to be exact copies of one another, giving a threefold redundancy in the number of supposedly "elementary" particles (It is disturbing to realise that we now have vastly more "elementary"particles than the total number of subatomic particles that were discovered by the 1940s. It makes one wonder how elementary these elementary particles really are.) The ugliness of the Standard Model can be contrasted to the simplicity of Einstein's equations, in which everything was deduced from first principles. To understand the aesthetic contrast between the Standard Model and Einstein's theory of general relativity, we must realize that when physicists speak of "beauty" in their theories, they really mean that their theory possesses at least two essential features: 1. A unifying symmetry 2. The ability to explain vast amounts of experimental data with the most economical mathematical expressions The Standard Model fails on both counts. Its symmetry, as we have seen, is actually formed by splicing three smaller symmetries, one for each of the three forces. Second, the theory is unwieldy and awkward in form. It is certainly not economical by any means. For example, Einstein's equations, written out in their entirety, are only about an inch long and wouldn't even fill up one line of this book. From this one line of equations, we can go beyond Newton's laws and derive the warping of space, the Big Bang, and other astronomically important phenomena. However, just to write down the Standard Model in its entirety would require two-thirds of this page and would look like a blizzard of complex symbols."
i think it has worsened, but only slightly. for example, he says that we have to put in 19 arbitrary parameters, but today that number is 25, since we now know that the 3 neutrinos have mass and also they have parameters that tell you how their mass and flavour eigenstates are related. so this makes the equation of motion longer, and with more arbitrary parameters. since everything else in the theory already had masses and mixing angles, though, it didn't bother us so much to add them for the neutrinos as well.
i want to add that while i mostly agree with Kaku, i do want to point out some nice features. Bundles and bundle connections, which are the mathematical framework behind the standard model, have proven to be one of the most important objects in mathematics in this century, and are regarded as rather geometrical and beautiful. the standard model is just a gauge theory. problem is, it has a funny gauge group SU(3)xSU(2)xU(1), and too many matter fields. the 3 generations, the mass hierarchies, the mixing angles, these things all take what started off as a beautiful simple theory and just keep loading it up with crap. compare it with the other modern physical theory, GR, which has almost no room at all to add stuff. your equation is 8πκG<sub>μν</sub>=T<sub>μν</sub>. there is only one thing you can add to this, and that's the cosmological constant. of course, you also have to have some matter theories to find out what the stress tensor is on the right hand side of that equation. but that is viewed as external to the theory of relativity.
Thanks for your replies, lethe. Kaku was arguing in favour of string theory, which might be conceptually simpler in some ways but seems mathematically monstrous. Perhaps the subatomic world really is as untidy as the Standard Model tells us.
but think about it another way... the one inch vs 2/3 page descriptions you stated are for people who already know the theory and know what tensors are and howt o proof the field eq'ns But to someone who doesn't know either which would you think is easier to learn? If you were to actually give the field eq'ns for someone to learn i'd think the description would take more than 1 inch. considering my 200pg txt is 90$ CDN. Now that you bring up the topic of string theory. Can you stick one string inside another creating a rubber band effect and then pull the string to some large tension...would taht string not break?
well, actually, for various reasons, we think that the Standard Model cannot be the whole story. for starters, it ignores gravity, and at some energy scale, gravity cannot be ignored. but even if there were no gravity, the Standard Model would still have holes, and we do need some more powerful theory to fix those holes.
any particle physicist will tell that the standard model is far from complete, it does however provide some explanatory power, so it is kept around. as far as particle physics is concerned, we are still missing a huge part of the story. hopefully some of thse new high energy accelerators coming on line in the next few years will reveal something to point us in a direction of which theory could be the right one. many people think that if the higgs boson does exist it will be found at these new energy levels. if this is true, well there will be nobel prizes to be won.
I like your mathematics: At this moments, the particles are: 3 families with 2 quarks in each with 3 colors each = 18. 3 families with 2 leptons in each = 6. 4 elctroweak gauge bosons = 4 8 gluons = 8. 1 higgs = 1. 18 + 6 + 4 + 8 + 1 = 200. you are right.
Most of the particles in the list you gave are composite particles, not eleementary particles. If you add composite objects, why don't you add Hydrogen, Oxygen, Water, Carbon monoxide, Carbon dioxide, my motorcycle, my computer etc, then you will have not 200 composite objects but billions of billions. WOW, we have billions and billions of composite objects. well, surely the standard model is wrong, such are all quantum field theories. Long live aether theory
perhaps there is a link between all the elementary particles that we haven't found yet. Like maybe the fundamentals are the FCPs
Where did you hear that? Gluons are gauge bosons. They are the carrier of the color interractions. Like most of the particles that you have listed, they have not been tracked in a bubble chamber. I have listed the 4 gauge bosons of the electroweak interraction. The photon is one of them. In my computer monitor and your computer monitor, the accelerating potentials in the CRT are different. At my monitor, there are electrons, what are the particles in your monitor? I remind you that they do not have the same energy. Photons with different energies are still photons. They solve the same field equations with different initial conditions.
You can slow photons down, even "stop" them temporarily. Thus you can accelerate them after that. They just can't go past the speed of light in a vacuum, which is the case for electrons as well.
Please show me your proof that from the aether theory the electron and the neutrino are the same particles. So you argue that electrons at some energy and neutrinos with the same energy are the same particles, even though they have different momentum? Do you also argue that they have the same electric charge?
this thread is going to hell in a hand basket neutrino and the electron are the same particle? that is a big stretch. there are some things we know that are really important. one is, charge is conserved! lepton number is as well. if you look what comes out of some of collisions, you will easily realize how electrons and neutrinos cannot be the same particle!
