3 Quarks, 3 Spacial Dimensions, coincidence?

[Fat Rooster]

I was thinking about quarks a while back, and noted that the number of colours is the same as the number of dimensions we perceive. It got me thinking about colour, and questioning whether there are actually 3. Is it possible that quarks have a directional component, and that we need 3 orthogonal quarks in order to create something stable? Like a monkey fist knot, each quark confines the other two in one dimension, and together they are able to form something stable in all 3. Colour would then mean a position on the surface of a sphere, without any points being special. It would be an effect closer to polarisation (continuous) than electrical charge (discrete).

Is anyone aware of any evidence either direction? Would the results of this be distinguishable from colour state superposition? If not, is it a helpful way of thinking about it anyway? When dealing with a single 3 quark hadron, I think the results would be indistinguishable as the axis can just be set to the colours, but how would it affect something like deuterium for 'red' to mean something different in each hadron?

[137beth]

I don't know enough about particle physics to say, but my first hunch is that this is a case of the strong law of small numbers.

[Chronos]

The three generations of quarks might be related to the three generations of leptons. But the number of colors almost certainly isn't, nor is either of those likely to be related to the number of spatial dimensions.

[halfeye]

The three generations of quarks might be related to the three generations of leptons. But the number of colors almost certainly isn't, nor is either of those likely to be related to the number of spatial dimensions.

"Colour" was a daft name and I hate it.

[Radar]

"Colour" was a daft name and I hate it.

Actually it sets up a very good analogy and enables intuitive grasp of the strong interactions, since optically we also percieve three basic colours which cancel each other out when evenly mixed.

Aside from that, we have one gravitational "charge", two electric charges and three colour charges. From the viewpoint of any grand unified field theory it might seem like a more important connection along with the notion that it also lines up those interactions from the weakest to strongest. And yes, I did omit the weak ineractions, which are an oddball among the others. This might also indicate that one should be wary not to devolve into seeing patterns that are not there.

[halfeye]

Actually it sets up a very good analogy and enables intuitive grasp of the strong interactions, since optically we also percieve three basic colours which cancel each other out when evenly mixed.

No!

We as a species have three different colour cones (the colours of the cones shift in the colour blind). Some fish have five. Most mammals have two. Mantis shrimps have eleven. What we as a species have is no basis for doing physics.

In physics there are no colours, there is a continous smooth spectrum of wavelengths and frequencies, with no particular wavelength/frequency any more important/ethical than any other. Higher frequencies/shorter wavelengths are more energetic, but that's all there is to the difference.

The three colours (blue, green, red) mix to black in pigments, mix to white in light beams, but there are also three primary pigment colours (yellow, cyan, magenta) which mix with the light primaries to make white, or subtract from each other as pigments to make the light primaries. Colour is a function of the makeup of the human eye and brain, it's not a universal constant.

[Chen]

No!

We as a species have three different colour cones (the colours of the cones shift in the colour blind). Some fish have five. Most mammals have two. Mantis shrimps have eleven. What we as a species have is no basis for doing physics.

In physics there are no colours, there is a continous smooth spectrum of wavelengths and frequencies, with no particular wavelength/frequency any more important/ethical than any other. Higher frequencies/shorter wavelengths are more energetic, but that's all there is to the difference.

The three colours (blue, green, red) mix to black in pigments, mix to white in light beams, but there are also three primary pigment colours (yellow, cyan, magenta) which mix with the light primaries to make white, or subtract from each other as pigments to make the light primaries. Colour is a function of the makeup of the human eye and brain, it's not a universal constant.

None of this contradicts what Radar said at all. They said that by naming them colors it allowed a more intuitive understanding BASED on the way WE as a species perceive things. As far as nomenclature goes that's one of the best ways to name things.

[halfeye]

None of this contradicts what Radar said at all. They said that by naming them colors it allowed a more intuitive understanding BASED on the way WE as a species perceive things. As far as nomenclature goes that's one of the best ways to name things.

Suppose we augment ourselves to see more colours? or meet aliens? then it's a bloody stupid and inconvient mish-mash.

[Lord Torath]

Suppose we augment ourselves to see more colours? or meet aliens? then it's a bloody stupid and inconvient mish-mash.

You can "What if" any decision into oblivion. It works for now, and for the foreseeable future.

[halfeye]

You can "What if" any decision into oblivion. It works for now, and for the foreseeable future.

There will be tears and the gnashing of teeth because of this foolishness I warn you now.

[gomipile]

There will be tears and the gnashing of teeth because of this foolishness I warn you now.

Well, many of us wish the convention of positive and negative charge and direction of current flow had been chosen in the opposite way that it was historically. However, we continue to get by with a "backwards" system fairly fine.

As long as the convention allows the math to work out properly for making predictions at the length/energy scale people care about, they probably won't change it.

[Radar]

No!

We as a species have three different colour cones (the colours of the cones shift in the colour blind). Some fish have five. Most mammals have two. Mantis shrimps have eleven. What we as a species have is no basis for doing physics.

Naming convention and doing physics are not the same thing. A rose by any other name... would still have three base "charges". If ever, I would object against the naming of quark types, but I do not hold it against the scientists, since there are too many things to name and you can only have as many good analogies.

[Fat Rooster]

Actually it sets up a very good analogy and enables intuitive grasp of the strong interactions, since optically we also percieve three basic colours which cancel each other out when evenly mixed.

Aside from that, we have one gravitational "charge", two electric charges and three colour charges. From the viewpoint of any grand unified field theory it might seem like a more important connection along with the notion that it also lines up those interactions from the weakest to strongest. And yes, I did omit the weak ineractions, which are an oddball among the others. This might also indicate that one should be wary not to devolve into seeing patterns that are not there.

The charges in electromagnetics are different in that positive charges have different physics than negative ones. We are also able to separate them from atoms, and study them on an individual basis. We know that the electrons in a molecule of hydrogen have the same charge as the electrons in iron because we can remove them and study how they interact with other charged particles. Every electron we have ever studied has the same charge. As far as I know (and correct me if I am wrong), we have never been able to do anything similar with quarks. We have not smashed two protons apart, and compared the colours pairwise to say that "these two are the same colour". We know that each proton requires 3 colours, and the question I'm asking is whether there is any evidence that they are the same 3 colours for every proton. A correlation with the number of dimensions could offer a mechanism for there being as many as there are points on a sphere, while still maintaining the physics we see.


To see how the maths might work, consider a field that applies a force on a test charge at V of
V (x²+y²-2z²)/(V.V)
where x, y and z are the components in the relative axis. The important thing to consider is that if you rotate it to face along all 3 axis, and then sum the fields, they cancel. Despite this field being stupid, as it applies infinite stress, it can operate in a finite energy universe provided it always appears in 3 orthogonal directions. The orthogonality is more important than the actual values of the axis.

[Radar]

The charges in electromagnetics are different in that positive charges have different physics than negative ones.

Pretty much no: they are opposite but otherwise have the same effect as in ++ and -- pairs of the same absolute charge values for each piece react with exactly the same force. There is this small thing with weak interaction that breaks this symmetry ever so slightly, but the point remains.

We are also able to separate them from atoms, and study them on an individual basis. We know that the electrons in a molecule of hydrogen have the same charge as the electrons in iron because we can remove them and study how they interact with other charged particles. Every electron we have ever studied has the same charge. As far as I know (and correct me if I am wrong), we have never been able to do anything similar with quarks. We have not smashed two protons apart, and compared the colours pairwise to say that "these two are the same colour". We know that each proton requires 3 colours, and the question I'm asking is whether there is any evidence that they are the same 3 colours for every proton.

Full separation off colour has never happened, because the strong interaction has its name for a reason. I would have to look into the details of experiments in question, but quite a lot (understatement) of data has been gathered on strong interactions from smashing protons so hard that we do see into their internal structure. The closest we got to see free quarks is the quark-gluon plasma state, which is regularly produced by smashing gold or lead ions hard enough.

To see how the maths might work, consider a field that applies a force on a test charge at V of
V (x²+y²-2z²)/(V.V)
where x, y and z are the components in the relative axis. The important thing to consider is that if you rotate it to face along all 3 axis, and then sum the fields, they cancel. Despite this field being stupid, as it applies infinite stress, it can operate in a finite energy universe provided it always appears in 3 orthogonal directions. The orthogonality is more important than the actual values of the axis.

The thing is, none of the known charges of any kind is directional, so they have nothing to do with spatial dimensions.

There is a thing for which having exactly 3 spatial dimensions is important: stable orbits for gravitational and electrical interactions. As long as we assume locality and conservation laws are basic rules from which others are derived, then the gravitational and electrical force depend on the distance like r^(1-d), where d i the number of spatial dimensions as far as I remember.

[gomipile]

Pretty much no: they are opposite but otherwise have the same effect as in ++ and -- pairs of the same absolute charge values for each piece react with exactly the same force. There is this small thing with weak interaction that breaks this symmetry ever so slightly, but the point remains.

I think Fat Rooster meant that most negative charge is from electrons and most positive charge is from protons, which behave differently from each other. They have different masses, and protons form nuclei, while electrons do not.

Of course, yes, the charge itself behaves the same way when reversed. Positrons and antiprotons behave the same as their matter counterparts except for a sign reversal in situations where only their electromagnetic interactions matter.

[Fat Rooster]

Pretty much no: they are opposite but otherwise have the same effect as in ++ and -- pairs of the same absolute charge values for each piece react with exactly the same force. There is this small thing with weak interaction that breaks this symmetry ever so slightly, but the point remains.

Gompile has it correct. Electrical charge is tied to other quantum numbers in a way that colour is not.

Full separation off colour has never happened, because the strong interaction has its name for a reason. I would have to look into the details of experiments in question, but quite a lot (understatement) of data has been gathered on strong interactions from smashing protons so hard that we do see into their internal structure. The closest we got to see free quarks is the quark-gluon plasma state, which is regularly produced by smashing gold or lead ions hard enough.

Quark gluon plasmas are locally colourless, and I believe that the theory requires superposition of colour to match reality. The question then translates to whether the basis vectors for colour (whether they correspond to space or not) are arbitrary, or whether there are special ones that crop up more (like positive and negative electrical charges).

The thing is, none of the known charges of any kind is directional, so they have nothing to do with spatial dimensions.

The directionality would be extremely well hidden. While the fields generated would be directional, the existence of any net field would be forbidden, and hence undetectable. What would be detectable would be that any attempt to separate particles which are tied to the fields would require absurd amounts of energy (because it would create a net field) in a way that is not directional. ie, a/the strong force.

There is a thing for which having exactly 3 spatial dimensions is important: stable orbits for gravitational and electrical interactions. As long as we assume locality and conservation laws are basic rules from which others are derived, then the gravitational and electrical force depend on the distance like r^(1-d), where d i the number of spatial dimensions as far as I remember.

I think conservation of momentum and energy give you stable orbits for any conservative field in any number of dimensions, at least for the 2 body problem (where we can always project down to 2 anyway). The 3 body problem is unstable even in 3 dimensions.

[Chronos]

You can't really say that electromagnetism has two charges but chromodynamics has three. By that standard, you'd have to say that there are six colors, red, green, blue, antired, antigreen, and antiblue, since antiquarks have anticolor (this is what allows the mesons to be colorless).

[halfeye]

You can't really say that electromagnetism has two charges but chromodynamics has three. By that standard, you'd have to say that there are six colors, red, green, blue, antired, antigreen, and antiblue, since antiquarks have anticolor (this is what allows the mesons to be colorless).

See, that's already losing the dynamic of the analogy. In human vision there are red-cyan, blue-yellow and green-magenta. The thing is that cyan is blue+green, yellow is red+green and magenta is red+blue. Anti-red is presumably not blue+green (cyan), so the analogy has already utterly broken down, and that's before we get into the extended spectrum with infra-red, ultra-violent, radio, gammas and x-rays.

[Radar]

You can't really say that electromagnetism has two charges but chromodynamics has three. By that standard, you'd have to say that there are six colors, red, green, blue, antired, antigreen, and antiblue, since antiquarks have anticolor (this is what allows the mesons to be colorless).

If anyone here knows this topic better, then please correct me, but as far as I know, regular quarks can only be red, green or blue. Antiquarks can be anti-red, anti-green and anti-blue. The analogy still works, since for example anti-red behaves like a combination of green and blue. In essence quarks are RGB and antiquarks are CMY. No analogy is perfect, but at least we get some traction out of chromodynamic naming convention. It is way better to use that then invent some completly new words, since it only makes things less understandable.

edit:

Gompile has it correct. Electrical charge is tied to other quantum numbers in a way that colour is not.

True, there is more freedom with colours. This is also probably the reason why strong interactions are so short-ranged, since gluons have to carry colour charge.

Also: any directionality would violate conservation of angular momentum and this we should have observed already - especially if it is a fundamental feature of one of the basic interactions.

[maruahm]

Particle physics isn't my specialty, I'm on the QFT side. But I'm just going through the Wiki page for quarks right now and I see no indication that the quarks are in any fundamental way bound by the dimensions of space. So yes, it seems like coincidence.

[Chronos]

I don't actually have any problem with using color words to name the kinds of quark charges. We had to call them something, after all, and the alternative would be either to use something for which the analogy was even worse, or to make up new names. I'm just saying that "1 kind for gravity, 2 kinds for E&M, 3 kinds for chromodynamics" is inaccurate, since it uses a different standard of counting for E&M and chromodynamics.

[halfeye]

I don't actually have any problem with using color words to name the kinds of quark charges. We had to call them something, after all, and the alternative would be either to use something for which the analogy was even worse, or to make up new names.

In which way would making up new names be bad? Supposedly English passed the million words mark several years ago, and we're not even close to running out. Reusing old words brings all of their baggage with them, which leads to expectations, which will often be mistaken.

[Radar]

I think conservation of momentum and energy give you stable orbits for any conservative field in any number of dimensions, at least for the 2 body problem (where we can always project down to 2 anyway). The 3 body problem is unstable even in 3 dimensions.

I forgot to answer that earlier: conservation of momentum and energy is not enough. What you look at for a two body problem is energy and angular momentum. So the conserved quantities of concern are (for number of dimensions d greater then 2):

E=m V^2/2 - m M G/R^(d-2)
L=m VxR = mR^2 w

with "x" representing vector product and "w" as angular velocity. Also assuming M is much greater mass then m and effectively stationatry It is easier to see the situation, when you look at an effective force in such a system

F= L^2/(m R^3)-m M G/(R^(d-1))

For d=3 it creates a stable system - any small changes in R with the same L push you back and there is a single clear point, where both forces cancel out.

For d=4 both parts of the force change in the same manner with respect to radius, so circular orbits are possible, but even smallest changes make the orbiting object float away or tumble into the center of mass. For higher number of dimensions things are even worse.

While one would have stable orbits in d=2, there would be another problem present - the potential energy would have a logarythmic dependence on the distance, so you could never fully escape gravitational pull even excerted by a small pebble. I am not sure if the whole universe could be stable in such a case.

[maruahm]

In which way would making up new names be bad? Supposedly English passed the million words mark several years ago, and we're not even close to running out. Reusing old words brings all of their baggage with them, which leads to expectations, which will often be mistaken.

Things in academia are often named out of expediency, and nomenclature is rarely semantically optimal. As an academic, my very first concern is that whatever I write in my research article is immediately understood by my peers. This way I won't have to waste space reintroducing, say, the heat equation if I insist that the more correct title is "uniform constant diffusion operator".

It'd take a herculean coordinated effort to agree to change the names of quarks. Outside a few contexts, e.g. Cristoffel symbols in differential geometry and general relativity which had a congress of mathematicians and physicists agree on notation back in the mid-20th-century, you don't really see that coordination. At best, nomenclature evolves over time to pick up general trends. And that's the best you can usually hope for.

[Fat Rooster]

I forgot to answer that earlier: conservation of momentum and energy is not enough. What you look at for a two body problem is energy and angular momentum. So the conserved quantities of concern are (for number of dimensions d greater then 2):

E=m V^2/2 - m M G/R^(d-2)
L=m VxR = mR^2 w

with "x" representing vector product and "w" as angular velocity. Also assuming M is much greater mass then m and effectively stationatry It is easier to see the situation, when you look at an effective force in such a system

F= L^2/(m R^3)-m M G/(R^(d-1))

For d=3 it creates a stable system - any small changes in R with the same L push you back and there is a single clear point, where both forces cancel out.

For d=4 both parts of the force change in the same manner with respect to radius, so circular orbits are possible, but even smallest changes make the orbiting object float away or tumble into the center of mass. For higher number of dimensions things are even worse.

While one would have stable orbits in d=2, there would be another problem present - the potential energy would have a logarythmic dependence on the distance, so you could never fully escape gravitational pull even excerted by a small pebble. I am not sure if the whole universe could be stable in such a case.

Ah, right. See what you mean. I had thought that required an exponential potential gradient, rather than anything superquadratic. Oops, thanks for taking the time.

With monodirectional forces, such a system would not make sense, but if an opposite 'charge' existed, it could be stable. Equal quantities of each charge could make the first power cancel at long distances, with separations causing fields that drop off quadratically. Any charge imbalance would be forbidden by finite energy considerations, and any separation would result in large forces to avoid dipole moments. It looks a lot like how the strong force works anyway.

One of the reasons for asking this is that I realised I could produce a toy model of something that had infinite energy fields but finite total energy, only requiring 3 isomorphic 'charges' (and hence looking like the strong force), by using the 3 axis of space. It didn't make much sense for those three axis to be special though, as it would work for any 3 orthogonal vectors. Hence asking if the colours are special, or simply 'orthogonal' and defined relative to each other locally. I don't expect to learn much from my toys, but sometimes they raise interesting questions.

[georgie_leech]

I don't actually have any problem with using color words to name the kinds of quark charges. We had to call them something, after all, and the alternative would be either to use something for which the analogy was even worse, or to make up new names. I'm just saying that "1 kind for gravity, 2 kinds for E&M, 3 kinds for chromodynamics" is inaccurate, since it uses a different standard of counting for E&M and chromodynamics.

Ooh, ooh, we could use 1!, 2!, and 3! though, and then it looks way more pattern-y. I've seen philosobabble built on less.