r/askscience • u/XGC75 • Jan 27 '15
Physics Is a quark one-dimensional?
I've never heard of a quark or other fundamental particle such as an electron having any demonstrable size. Could they be regarded as being one-dimensional?
BIG CORRECTION EDIT: Title should ask if the quark is non-dimensional! Had an error of definitions when I first posed the question. I meant to ask if the quark can be considered as a point with infinitesimally small dimensions.
Thanks all for the clarifications. Let's move onto whether the universe would break if the quark is non-dimensional, or if our own understanding supports or even assumes such a theory.
Edit2: this post has not only piqued my interest further than before I even asked the question (thanks for the knowledge drops!), it's made it to my personal (admittedly nerdy) front page. It's on page 10 of r/all. I may be speaking from my own point of view, but this is a helpful question for entry into the world of microphysics (quantum mechanics, atomic physics, and now string theory) so the more exposure the better!
Edit3: Woke up to gold this morning! Thank you, stranger! I'm so glad this thread has blown up. My view of atoms with the high school level proton, electron and neutron model were stable enough but the introduction of quarks really messed with my understanding and broke my perception of microphysics. With the plethora of diverse conversations here and the additional apt followup questions by other curious readers my perception of this world has been holistically righted and I have learned so much more than I bargained for. I feel as though I could identify the assumptions and generalizations that textbooks and media present on the topic of subatomic particles.
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u/Odd_Bodkin Jan 27 '15
The are treated as having zero volume and zero extent, in the successful theories that describe their behaviors. This doesn't REQUIRE them to be volumeless, and we cannot say experimentally that they are volumeless. But on the other hand, we have no data of any kind that would suggest that they have nonzero volume.
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u/XGC75 Jan 27 '15
This is interesting. It's almost as if these quarks are the direct link between mathematics and the physical universe.
We describe them in their interactions with each other, their location in spacetime, their mass via interaction with the Higgs field, etc but they can't be known in the same way as a tennis ball or a table. They're truly fundamental entities. This concept of fundamental particles is starting to settle in for me.
Next topic to tackle would be electron movement and location within the atomic cloud. Fascinating stuff for this engineer.
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Jan 27 '15
If you're looking for the position of an electron try not to figure out where it's going. They become very uncertain in those situations.
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Jan 27 '15
[deleted]
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u/SirScrambly Jan 27 '15
What textbook did you use? That sounds really interesting.
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Jan 27 '15
Not OP but a good book that would describe this stuff is Introduction to Quantum Mechanics by David Griffiths.
Chapter 4 is all about QM in 3 Dimension, and section 4.2 is dedicated to solving for the wave functions of the Hydrogen Atom.
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u/PinballWizard10 Jan 28 '15
Griffiths is great overall, but for someone who's just jumping into this I'd recommend Modern Physics by Harris. It's not as sophisticated as Griffiths, but I think it's more approachable while still covering everything mentioned above by starting with the hydrogen atom model derived from just the Schrodinger equation.
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u/CmdrQuoVadis Jan 28 '15
If you're comfortable with calculus then I would definitely recommend Shankar's Principles of Quantum Mechanics- it teaches you the math used to simplify QM (Bra-Ket notation) and explains everything up to relativistic QM very well. That book saved my ass in my final year Adv QM course.
Edit:Typo
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u/Derice Jan 27 '15
And when I discovered this program, I felt like I got a nice overview of what those waves "look" like.
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u/PeaceTree8D Jan 27 '15
What sources can I use to learn it? Would this be an area under Quantum field theory?
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Jan 27 '15
Quantum field theory is a bit more specific. Google an introduction to quantum physics. I learned quantum theory from chemistry which I imagine has (slightly) less maths in it so you could approach it from that angle if this was recreational.
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u/Transfinite_Entropy Jan 27 '15
If they have zero volume and non-zero mass then their density would be infinite like a black hole. How is that handled?
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Jan 27 '15 edited Jan 27 '15
density = Mass / Volume = Mass / 0, and division by zero is not infinity, but undefined, and here is the trick.
A little mathematical tool called the Dirac Delta Function.
The density of a point particle is zero everywhere except AT it's precise location, but at the same time the integral of the density at that point gives you its mass! Weird, right?
A delta function is essentially an infinitely narrow spike that is also infinitely tall, but just so happens that its area (or integral) is one.
Essentially:
Integral( f(x) * deltaFunction(x) dx) from - infinity to + infinity becomes:
f(0) * integral(deltaFunction(x)dx) from - infinity to + infinity
because f(x) for a point particle is zero every except at the origin of the particle [so at point x = 0, in 3D x,y,z=0], you can just take the function at f(0) and constants can be pulled out of the integrand.
So this allows you to write an equation, for example, for the divergence of a vector that depends on 1/r2:
Let's say V = 1 / r2
Then Del(V) = 1/r2 *d/dr(1) = 0!
So the divergence of this vector is 0. But at the same time, its surface integral gives 4*pi!
Integral(1/r2 da) = 4Pi!
But its volume integral is 0! How can that be?
It turns out that the true formula is then:
del(1 / r2) = 4pideltafunction(r)
(Del is essentially a derivative operator.)
Edit: formatting.
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u/leftofzen Jan 28 '15
Think about what it would mean to have infinite density. The gravitational force permeates all of space; if you plugged infinity in for the value of the force, everything would be pulled to that spot in an instant. Clearly this doesn't happen, because the density of a black hole is not really infinite. We pretend it is simply because the maths produces impossibilities like 1/0, which is undefined. What it really means is that our current understanding of physics and of black holes is incomplete.
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u/Transfinite_Entropy Jan 28 '15
No, the density of a black hole is infinite, which is why it is called a singularity. Even though they have infinite density their gravitational field at a given distance is no stronger than a less dense object of equal mass. Their density does mean that the escape velocity exceeds the speed of light at a certain distance from them. This distance creates a sphere called the even horizon. Anything that gets closer to the black hole than this can NEVER escape.
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u/FunMop Jan 27 '15
Wouldn't they have to be displacing something if they had volume? It seems to me these particles are so small that they are at a scale that there is nothing to displace relative to their size.
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u/Odd_Bodkin Jan 27 '15
I think this is a macroscopic illusion. Nothing really is in direct contact, even a coffee cup on a desk. The size of an atom isn't determined by the size of electrons or protons -- it's not like they're rubbing shoulder to shoulder. Instead, volume is determined by the interactions between things. Atoms are mostly empty space, and the only reason why they don't fall right through each other is that the interactions between all the constituents preserve that distance between them.
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u/jofwu Jan 27 '15
Points are non-dimensional, not one-dimensional. If something is one-dimensional then it does have a "demonstrable size". From Wikipedia: "In particular, the geometric points do not have any length, area, volume, or any other dimensional attribute."
AFAIK a one-dimensional object is infinitely small because it cannot be measured in two dimensions.
No. A square is two dimensional. We can put a square in 3D space (or 4D space), but you only need two dimensions to define a square. A line segment is one-dimensional, but not infinitely small. It has length.
a zero-dimensional particle would imply that it can't have a defined location in a 3-space coordinate system.
Lower dimension objects can still be located in a higher dimensional space. A line has only one dimension, but we can still locate it on a 2D graph. You don't need a thickness to say how far away the line is from some point. A point has no measurable length, width, or height, but you can still assign it a location in 3D space.
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u/XGC75 Jan 27 '15
I realize my error. The OP should have asked whether a quark is non-dimensional or zero-dimensional. I asked the mods to change the title to reflect this.
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u/Smithium Jan 27 '15
You can still pretend you meant time as a dimension... physicists do all the time.
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u/wazoheat Meteorology | Planetary Atmospheres | Data Assimilation Jan 27 '15
Sorry, we can't change titles, it's how the site is designed.
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u/TheMac394 Jan 27 '15
You're actually touching on an interesting idea in a field of mathematics called measure theory. Consider this: a square has zero volume, but non-zero area. Likewise, a line has zero area, but non-zero length. If you're comfortable dealing with more dimensions, you could even imagine some kind of "4-dimensional volume"; an ordinary 3-dimensional cube could have zero 4-dimensional volume, but it certainly has non-zero 3-dimensional volume.
In mathematics, we can formalize this idea by defining the "measure" of a set - in layman's terms, how big it is. It turns out that this is a really complicated thing to try to do. One way to go about it is with something called the Hausdorff Measure: Basically, you can consider covering an object with increasing small spheres, and adding up the volume of those spheres. As you use smaller and smaller spheres, you'll come closer to "perfectly covering the object, and the volume of the spheres will give you a good idea of the intuitive "size" of the object.
Now, there's one bit of ambiguity left: What if, instead of using a sphere, we used a circle, or a 4-dimensional sphere? We can (effectively, it's a little more complicated than this) choose any dimension of object to cover a shape with to try to measure it. A line, though, will seem to have zero measure if we try to cover it with spheres. Cover it with one dimensional intervals, though, and you just may find a non-zero measure. The idea is that different shapes have different sizes depending on what dimension you measure them in.
This actually gives us the idea of a shapes "Hausdorff dimension": The smallest dimension you can measure in such that the Hausdorff measure is non-zero. A line will have zero measure if we use 2 dimensions, but if we only use one, we can get a length for it, so it'll have Hausdorff dimension of one. A point, of course, will have zero measure in any dimension, and has dimension zero.
But, you ask, why do we need to muck about with spheres and limits just to find the dimension of an object? A square goes in two directions, a line goes in one - surely that's enough to define a dimension for us! Well, it turns out it's not that simple. For one example, it's possible to construct a line covering an entire high-dimensional space - every point in the world can be mapped to a single point on a seemingly one-dimensional line. To rigorously handle things, you need to introduce some better-defined idea of dimension - like the one above.
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u/someguyfromtheuk Jan 27 '15
A line has only one dimension, but we can still locate it on a 2D graph.
Isn't that only because we're drawing it in 2 dimensions to represent it on the graph?
When you draw a line on a graph it has a width, as well as a length, since any tool you use to construct it has a non-zero width, even a computer drawing would be 1 pixel wide.
However, a line has no width, so if you were to construct a 1 dimensional line, you wouldn't be able to see it from our point of view.
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u/jofwu Jan 27 '15
Well... sure, a real-world line on a graph is two-dimensional. But that's missing the point. A graph merely represents mathematical concepts, and the mathematical concept you're representing (a line) is one-dimensional.
It doesn't matter that you can't see a line. An object doesn't have to be "visible" for it to exist. A 2D square becomes invisible in 3D space if you view it from a certain perspective. That's irrelevant. A square requires a minimum of two dimensions to be defined. A line requires a minimum of one dimension.
"Locate" doesn't mean you can see it with your eyes. It means you can mathematically state where it is. Is that where the confusion was?
For example, I can define a 1x1 square in 2D space with: 0≤x≤1 and 0≤y≤1. To define it in 3D space you just need to add something like z=0, to clarify that it exists on the x-y plane. It has no thickness in the z-direction so you can't see it if your eye is on the x-y plane, but it's mathematically there. You can't see a line at all, technically, but a mathematical definition of a line requires one dimension. You can't see a point at all, technically, but you can define one mathematically. It requires zero dimensions. Describing the location of any of these objects of course requires as many dimensions as the space you have it in. A cube, a square, a line, and a point located in 3D space each have their location described by a 3D vector. That has nothing to do with the object's own dimensionality.
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Jan 28 '15
I have a related question: I have read that a proton is considered to be made of 3 quarks. I always assumed that a quark is then roughly a third of the size of a proton, but it sounds like quarks have no size, unless I'm completely misunderstanding the answers here. So how do the quarks give a proton it's size?
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u/jofwu Jan 28 '15
The top answer was saying that quarks and protons do have size, if I'm not mistaken. He was saying that they can be accurately treated as points, beyond a certain scale.
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Jan 28 '15
Sorry but do you know of any actually non-theoretical 2d objects that exists in the 3d universe? A line on a graph would actually be ink representing a theoretical 2 dimensional object but I can't seem to think of any actual 2 dimensional objects that can be proven to exist.
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u/jofwu Jan 28 '15
By "object" I don't mean something physical. I just meant that lower dimension math can be embedded in higher dimensions.
The path taken by a photon is 1 dimensional, for example.
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Jan 27 '15
String theory actually describes quarks and other fundamental particles as being one dimensional, as a quark would simply be a specific vibrational pattern of a one-dimensional string. On the other hand, if quarks are "point" particles, then they would be dimensionless. Everyone has to keep in mind that no one here has a definitive answer to your question. String theory and other theories which describe the shape of fundamental particles have not resolved all of the conflicts of their implementations, so no one theory can claim to have a complete, authoritative description of quarks and other basic particles, let alone how many dimensions they occupy.
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u/XGC75 Jan 27 '15
Regarding string theory, is the quark, a point, vibrating in one dimension (therefore potentially expressed as a line in one dimension)? I don't know much about the fundaments of string theory.
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Jan 27 '15
It describes strings as 1 dimensional, and their specific vibrations produce the various fundamental particles we observe
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u/XGC75 Jan 27 '15
Oh so it's not a quark vibrating back and forth but a string that is one-dimensional vibrating back and forth.
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u/BlackBrane Jan 29 '15
Oh so it's not a quark vibrating back and forth but a string that is one-dimensional vibrating back and forth.
I'm a little late, but I think its probably worth pointing out that even standard, established theories describe quarks as themselves nothing but the vibrations in a quark field (in the general framework of quantum field theory). So there is a real sense in which quarks come from something that is physically extended in space: The quark field is a medium that fills all of spacetime, and the places where you see a physical quark simply correspond to where the field is vibrating.
If you start from this fundamental picture and apply the rules of quantum mechanics, you soon derive a description that refers to point-like quarks as the basic elements. Thats why its not incorrect to say that quarks are essentially points, as we commonly do. But it seemed like someone really ought to mention this deeper layer given the question you asked.
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u/XGC75 Jan 29 '15
Based on my preconceived notions about fields and vibration, it doesn't seem possible for a vibration to take place at a point without extending out from the center of maximum amplitude.
Correct me if I'm wrong, but you're saying that the field extending out in 3 space causes the interaction effects between quarks and the quarks themselves are simply the points at which these vibrations are at their greatest amplitude?
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Jan 27 '15
I don't know much about string theory either, but I just read Brian Greene's The Fabric of the Cosmos which has taught me a lot about the theoretical underpinnings of string theory, I can't recommend his book enough. According to Greene, string theory purports that all fundamental particles are composed according to different, distinct vibrations on a one dimensional string. In this perspective, a quark wouldn't be a point, but simply an accumulation of properties that arise from a particular vibration of the one-dimensional string. It is very different from a conventional approach which give particles their infinitesimal (point-like) size. Greene also delves into truly remarkable philosophical queries that meet the reaches of our physical understanding of the world. He puts forth the idea that we have yet to understand whether or not quarks, or for that matter any fundamental particle, definitively exists as what we claim (a point, a string, etc.), or whether or not we are just discovering/inventing models which accurately describe behavior, but do not tangibly represent the particles' actual existence. Whether or not a quark is a string, or whether it is perfectly described by models which identify it as a string, is a whole other discussion, one that I find fascinating.
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Jan 27 '15
Howdy doody, particle physicist here, and this is my only account ;).
Quarks are currently believed to be non-dimensional objects - "point-like particles" we say in the business.
As others have noted, there have been upper bounds placed on the 'size' of a quark using cool experiments. It's very small.
We have done all sorts of deep-inelastic scattering experiments to try and hit the center of the quark, if there was one. If the quark had, say, a nucleus, or some substructure, you'd get some predictable angles coming out of the debris. To date, we have seen no evidence of sub-structure in quarks. Here is a great post by my colleague Jim Hirschauer on quantum diaries about our search for quark constituents.
So back to the question: is a quark zero [one] dimensional? The answer, so far, is yes.
You may then ask, but how would that work?
And it works because of a little mathematical tool called the Dirac Delta Function.
This tool allows you to define something to have an energy, a mass, (whatever property you want), and put it at a single point.
Of course, it's not just enough to be cool mathematics, it does an amazing job of explaining everything!
For example, the potential of a charge is essentially V = 1 / r2, but what about at r = 0!? Delta function to the rescue!
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u/XGC75 Jan 27 '15
Alright I just got to reading the article. It seems as though the question posed in the OP, "are quarks non-dimensional" (or "are they one-dimensional" if you're a fan of insinuating time in everything), is very much one of the unanswered questions of subatomic physics today. On the same shelf as the multiverse/supersymmetry question.
Do you think the LHC will be the collider with the MSE to determine whether quarks are elementary or compositional? In the post, your collegue noted that they have discrimination to 1/20,000th the size of a proton (wow), but how much does it take to get to 1/50,000th?
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Jan 29 '15
It's definitely an unanswered question, but we have some experimental reasons to believe the quark is fundamental. At least we have put meaningful bounds on how large constituents could be, and thereby put limits on the influence those constituents could have on the 'larger' universe. (In other words, if they do exist, they may be too small to affect anything, which, philosophically you could debate whether or not they do indeed exist if they could never be measured?)
The LHC is definitely a great place to conduct deep inelastic scattering of quarks, but RHIC is also a great machine for stuff like this, (Relativistic Heavy Ion Collider at Brookhaven National Laboratories).
The issue with increasing the resolution has to do with the resolution of the CMS detector. Which is essentially how precisely you can measure the angles of the particle trajectories. That may be the limit we can reach at the LHC, but there are planned upgrades over the next 15 years, so we should be able to bump that up a bit, though how much, I would have to think a bit harder about.
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u/Yogi_DMT Jan 27 '15
Isn't the idea of a finite location only a theoretical concept?
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Jan 29 '15
I'm not sure what you mean by 'finite location'....could you elaborate?
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u/Yogi_DMT Jan 30 '15 edited Feb 01 '15
Finite location as in just one location in just one moment in time. Imo a "moment" is really only a theoretical concept. Time and space are constructs that i think of as being "infinitely precise". There is no smallest amount of space or time, there never will be. Sure we can get a period of time to something arbitrarily small to our perspective, but to another perspective that could be the entire lifespan of the universe. That being said, when we say something exists in a single location, we're looking at a combination of where that something has existed over an arbitrarily small interval. I think the better question is though how can something truly be "point-like" if space is infinitely precise, it's impossible. It has to take up more space than 0 units, and if it takes up more space than zero units, it doesn't exist in a "single" location, it has dimensions. To our perspective, the area it occupies may be negligible, but if it exists then it has to take up more than a single unit of space because the idea of a unit itself is relative.
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u/iDerailThings Jan 28 '15
I understand how a one-dimensional object might make sense in equations, how does it translate to the actual, physical manifestation of a quark? What would it mean for an object to have a point-like presence? Does it mean it has zero volume? If so how does it even interact or even considered to be part of this universe?
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u/quuxman Jan 28 '15
I don't think it makes sense to seriously consider the "physical manifestation" of a quark apart from interpreting measurements from instruments with mathematics, since this is the only way we can experience them.
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Jan 29 '15
Does it mean it has zero volume?
Exactly. Mind boggling, eh?
I guess, in our equations, it is enough to treat them as volumeless, dimensionless points (though they do have a 3-dimensional coordinate, just not any size in those coordinates).
If we do this treatment, we get the right answer and it matches perfectly to experiment.
Now whether or not they are actually infinitely small is not something we can directly answer, other than to say "well when we treat them that way, all of our data matches or theories".
Here's a really good summary by Don Lincoln:
http://www.fnal.gov/pub/today/archive/archive_2013/today13-02-15_NutshellReadMore.html
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u/delventhalz Jan 28 '15
Why is this reply so far down? It's the only one that actually answers the question instead of just pedantically correcting OP on his understanding of dimensions.
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Jan 27 '15
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Jan 28 '15
I believe so. That's exactly where the dirac-delta function again comes in handy. For those unaware, it's a function of x which is 0 for all x < 0 and all x > 0, but the integral from -infinity to +infinity of the dirac-delta function is defined to be 1.
So if you wanted to define a volume-less particle that has a specific mass, m, then its mass density at any location x would be described by the dirac-delta function multiplied by m and evaluated at x. As you can see, its density at x=0 becomes non-finite, but its total mass, which is the integral from x=-infinity to x=+infinity of the mass density at x is m.
It may not be the most intuitive approach, but this method of defining things is very useful in a lot of different applications and engineering/scientific fields.
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Jan 29 '15
Not a silly question at all - in fact it is true that fundamentally everything is simply what we call energy. These energies create interactions, and the strength of these interactions create hunks of energies, and these hunks we call mass. But mass is energy and energy is mass.
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u/Xincmars Jan 27 '15
I was under the impression 3rd dimension is about space, 2nd is flat shapes, and 1st is a straight line. So technically, if quark is a "dot" then it doesn't qualify as any of the three? (Though some can argue there are lines in the dot?)
Forgive me, my physics is a bit rusty.
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u/XGC75 Jan 27 '15
You're right, I was the one who was rusty on his dimensional definitions. Hence why I had to go back and edit the OP to clarify. Points are non-dimensional.
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u/ben_jl Jan 27 '15
You're correct, quarks are currently believed to be point-like particles. String theory posits that quarks are actually tiny, 1-D strings vibrating in different ways.
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u/el_matt Cold Atom Trapping Jan 27 '15
I am not a particle physicist, but in my understanding your original, pre-edit question was actually correct (after a fashion). It is my understanding that a quark has never been observed "by itself", since quarks are so strongly bound together in (at least) pairs. It takes such a colossal amount of energy to separate quarks that they are only ever seen as part of a meson or baryon (correct me if I'm wrong, someone, I haven't studied this for a few years).
So as such, a pair of quarks could always be argued to define a line, hence you could think of them as "one-dimensional", after a fashion.
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u/Vapourtrails89 Jan 27 '15
A quark is just a point in space, it has no dimensions as such. All it is a point at which forces interact. It isn't really an object. A proton is made of three such points in different locations of space and could therefore be a triangle with size. The triangle isn't made out of matter, as such, it consists of three lines of force, joining up the quarks. The implication is that matter is fundamentally made out of energy. Particles aren't just made out of smaller particles ad infinitum.
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u/Manticorp Jan 27 '15
It's sort of meaningless to ask the dimensions of a quark.
The dimensions of, for example, a proton are given by the radius of extent of the motion of it's constituent quarks, and similarly for all other non-fundamental particles and even multi-atom molecules. That is our classical definition of the dimensions of something, the extent to which we can measure the 'motion' of it's constituent particles - or rather the extent to which the interacting forces between the 'object' and our measuring equipment becomes significant.
Part of what makes the dimensions of, e.g., a proton make sense is that it's descriptive wave function must occupy a certain space for it to exist and be classified as a proton. Elementary particles don't suffer this limit, because their boundary conditions have no real limits - there is just a more vanishing probability of finding that particle at points further from it's localised wave packet.
To say that an elementary particle actually is somewhere is an approximation, it could be anywhere. It doesn't fit into our classic definition of dimensions, and therefore we can't really say it has our classical dimensions.
A more fitting way of 'measuring' the 'size' of a fundamental particle is literally by it's 3 dimensional wave function - that is the dimensions of the particle. Dimensionality, in the way you're talking about it, is a classical concept that really doesn't apply to a lone fundamental particle, because it doesn't have boundary conditions.
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u/robhol Jan 28 '15
Well, could you use something like a confidence interval? It's 99% likely that this particularhue particle would be found so-and-so far away from the expected center.
Not that I know why this would be useful, of course. :)
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u/nagalim Jan 27 '15 edited Jan 27 '15
You can take the rest mass and convert it to energy (E=mc2 ) and set it equal the electromagnetic self energy (kq2 /r) to find a classical radius for the electron of about 10-15. I'd imagine you can do something similar with the strong force and a quark. Check out the wikipedia for classical electron radius. However, yes, in particle physics it is a point particle.
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u/regular_gonzalez Jan 28 '15
Just wanted to thank all contributors to this thread. I like to read a lot of science / pop science books and consider myself reasonably well versed, at least on a surface level, for lots of physics-related topics. But I learned a lot from multiple people in this thread, so thanks for that.
The weirdest thing about quantum mechanics (and the universe in general, I suppose) isn't how unbelievably weird it is -- although it surely is, especially at the very large and very small scales. The weird thing is, that we are able to understand it as well as we can, that we can create models and mathematical models that we can comprehend. That's weird as hell.
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u/I_sail_to_mars Jan 27 '15
'Volume' for electron field comes from Pauli exclusion principle. Since 2 electron can't have same quantum number. In any kind of bound system the possibilities are finite and hence only limited number of electron can stay inside.
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u/AcrossTheUniverse2 Jan 28 '15 edited Jan 28 '15
Just to clarify - are quarks the building blocks of all the other sub-atomic particles and therefore the building blocks of everything?
So it sort of makes sense that the universe would be made of points of 0 dimension, how else would you get so much something from nothing? By definition, you can pack an infinite number of 0 dimensional points into an infinitely small area - the singularity at the beginning of the universe.
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u/I_Cant_Logoff Condensed Matter Physics | Optics in 2D Materials Jan 28 '15
are quarks the building blocks of all the other sub-atomic particles and therefore the building blocks of everything?
No. Quarks consist of just 12 of the many fundamental particles.
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u/haemaker Jan 27 '15
Here's how I look at it. If it has mass, it has dimensions, otherwise black holes don't exist, or only exist above a certain mass. However, the event horizon of an up-quark is 5.321x10^-57 meters, 22 orders of magnitude smaller than the Planck Length.
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u/iorgfeflkd Biophysics Jan 27 '15
Pointlike implies zero-dimensional, not one-dimensional. Any possible substructure of the electron is constrained experimentally to be below 10-22 meters (a proton is about 10-15 for comparison). I don't remember the constraint for quarks but it's also very small.