Elemental forces

Factual Questions
1

I read a book a few years ago on quantum physics that was quite interesting. Unfortunately I can’t remember a lot of things from the book, including two things in particular that are bugging me. I recall the four elemental forces in order of their strength are the strong force, weak force, electromagnetic force, and gravitational force. The strong force, it was written, was once defined as the attractive force between the particles in the nucleus of an atom. That attraction is actually just a residual effect from what we now consider the strong force to be however, which is the attraction of different color quarks within those particles. I think I have the strong force down. I’m curious though, I remember there being quarks that come in twos instead of threes, those being charged with positive and negative instead of red, blue, and green. Are those particles attracted to each other with the electromagnetic force, or the strong force, or even the weak force? For that matter, what is the weak force? I don’t remember it at all.

Those are my two questions, but for the sake of completion, I’ll go over the other two forces briefly. The electromagnetic force is the force between protons and electrons, and causes many phenomena on a greater scale. The gravitational force is pretty obviously the attractive force between any particles or groups of particles with mass. Actually, now that I mention gravity, I have a question about it too. When I’ve read about Einstein’s theories of relativity, he suggested that gravity was caused by a curvature of space. Metaphorically, massive objects caused holes in space which other objects would fall into. I’m sure I’m not the only one who has heard the example with the bedsheet and two balls. However, recently I hear about gravity being caused by particles called gravitons. Has the graviton theory became more popular than Einstein’s? Or are they actually the same theory somehow? I find it odd that string theory supports the particle idea (according to an episode of Nova I watched). It says that gravitons travel into the other dimensions of the multiverse that we cannot perceive. However, assuming gravitons travel in straight lines, I cannot perceive them actually having an affect on our universe. To dumb it down to our number of dimensions, imagine a two-dimensional plane in our universe with a black hole within it. (I’m imagining a black hole as a singularity, for simplicity.) Unless that plane is defined by the path of one or two gravitons, the chance of a graviton just happening to travel along the plane is 0. Thus one can conclude that the two-dimensional universe would not be effected by gravity. What’s different about our three-dimensional universe in a greater multiverse? I have other issues with what I’ve heard about string theory as well, but they’re not within the topic, so maybe some other time. [smiles]

That ended up being a lot more than I intended to say, but hopefully I can get resolution to these questions I’ve been wondering about quantum mechanics and maybe we can start a conversation about the elemental forces.

2

Yes, as far as I understand it (which is just barely).

Whoops! Not quite there!

A quark is characterized by two properties that have acquired the names “color” and “flavor”. There are six flavors, divided into three pairs that have similar masses: the up and down, the strange and charm, and the top and bottom. Each also has an “anti-matter” counterpart: so there is an “up” and an “anti-up”, etc.

Each also carries some electromagnetic charge as well. For instance, the up quark carries a positive charge equal to 2/3 the strength of an electron charge, the down negative charge of 1/3 electron strength.

The colors are three: red, green and blue. There are also anti-red charges, and so forth. The reason for all of this is that the model dictates that baryons consist of three quarks and mesons of two, and they must combine in a way that the color charge disappears, since baryons and mesons do not display color charge properties.

To get a baryon, you combine three differently-color-charged quarks, that is, a red a green and a blue. If two of them (regardless of color) are up and one down, the electromagnetic charge sums to +1 and you have a proton. If you have one up and two downs, they sum to zero and you have a neutron. The three color charges cancel each other out somehow, which is why they were given the names red, green and blue, because, analogously, those three colors of light form “colorless” white light.

For a meson, you mix a quark with an anti-quark. For example, an up and an anti-down create a positively charged pion (an anti-down posessing the opposite electromagnetic charge of a down), and a down and an anti-up create a negatively charged pion. Mesons also do not exhibit color charge properties, so the model declared an anti-color-charge for each color charge. Our pion quarks would have to have color charges of red and anti-red, or blue and anti-blue, for example, which I’m guessing is where you got your erroneous “positive and negative” idea from.

So no, paired quarked are held together by the strong force just like when they are tripled. That is they exchange gluons, in the same way that particles interacting electromagnetically exchange photons.

The weak force is related to radioactive decay. It transforms one quark into another type of quark. The particles carrying the force (the way the photon carries the electromagnetic force and the gluon carries the strong force) are called intermediate vector bosons, and come in three varieties: W+, W-, and Z0.

It was proven a little over twenty years ago that at high energies, the weak and electromagnetic forces are pretty much the same thing, the “electroweak force”. Add in the concept of the Big Bang, which implies that at some point the universe was in just such a state of high energy, and we understand what it might have "looked like’ at that point in its history.

This leads to the possibility that the strong force, at some even higher energy, combines with the electroweak force into some single force. Various versions of how this might work, known as “Grand Unified Theories” are floating around, but it’s more or less impossible to build an accelerator large enough to try any of them out.

Well, what I said above leads to the thought that gravity, the other fundamental force, can also be lumped in at an even higher energy. This is known as the “Theory of Everything”. On the quantum side, you need a force carrying particle, currently called the graviton. There have been several efforts to actually observe a graviton, but as far as I am aware, nothing’s turned up yet, although I believe it was shown within the last year or so that the gravitational force travels at light speed, so it’s most likely just be a matter of time until the right experiment turns up the graviton.

Then of course you have to reconcile the existence of the graviton with Einstein’s general theory of relativity and the curvature of space time, which has plenty of observations backing THAT up. Hasn’t been figured out yet.

The grantor’s favorite candidate for figuring it out has been string theory for years now, but my personal speculation is that it’s going to eventaully be regarded as a dead end.

3

Yes, that’s exactly what I was talking about. You answered that and most of my other questions quite outstandingly.

I kind of agree. It does seem like an unlikely, although intriguing, theory. Of course I probably would have said the same about relativity back in the day. All we can do is sit back and wonder for now.

So just one question remains: how gravitons effect mass on the three-dimensional “plane” when they’re supposedly travelling out in all dimensions of the multiverse, according to string theory.

4

Ow, scotandrsn’s post made my brain hurt.

Think back to your two-dimensional example. The gravitons are leaving from every angle. This includes a 360 degree circle that is parallel to the plane. Those gravitons affect the plane and the rest don’t.

5

Assuming there is a finite number of gravitons leaving an object, then no, they wouldn’t be leaving at every angle. You can’t possible have a finite number of particles traveling at an infinite number of angles. And there is 0 chance a random particle will be travelling along a preselected two-dimensional plane. The chances do not change for 20 dectillion particles, again, assuming the plane isn’t defined by one of the particles.

6

Why is that?

7

Well think of it in terms of polar coordinates. For a two-dimensional plane, you have x (the angle; actually it’s theta I think, but I can’t make that symbol) and d (the distance). For a three-dimensional plane, it introduces a third angle, y. Now in order for a point to rest on the plane, y would have to equal 0. However, since y can be an infinite number of values, and 0 is one of them, and 1 / infinity is 0, the chances of y being 0 if chosen with true randomness is 0. (Yes, 1 / infinity is actually undefined, but in most practical cases including this one, it ends up being 0.) So while it is technically possible for a point to be on a particular plane, there is a 0 chance of it. Thus unless there are an infinite number of gravitons emitted per time (which I can’t imagine) or there is some force acting upon the particles causing some of them to stick to our plane, I see no reason why any should. A curvature of space does, however, could extend in infinite directions so I would think it would fit the bill of string theory a bit better.

8

There are a couple of small errors with my last post. Y is the second angular variable, not the second. Also, y could also be 180, but there’s still a 0 chance of it being one of two exact values out of an infinite number of them.

9

scotandersn did a bang-up job on most of your question.

A nitpick: there have been no experiments designed to detect gravitons, which are much too weakly interacting for current technology. (Maybe you were thinking of gravitational wave expts, which are looking for the classical, not the quantum , version.)

I think your question about the gravitons in multidimensional space is a good one. (Damn, I just love writing “gravitons in multidimensional space”. Makes all those years of physics grad school worthwhile.) I think what you’re missing is that gravity works by graviton exchange: one object emits a graviton and another object absorbs it. So both ends of the trajectory are tied down to our slice of spacetime. The small changes to the gravity force law that experiments are looking for are due to gravitons wandering off into the extra dimensions before ending up back in our slice.

But I want to emphasize, any talk of “gravitons” or “string theory” is completely speculative: these ideas have not been verified by any experiments, they are simply the way some physicists think the world “ought to be”.

10

scotandrsn has already covered most of what I would have said, but I’ll just make a few addenda. First, the weak force is weaker than electromagnetism, not stronger. Anything that electromagnetism can do, the weak force can do also, but we can usually disregard it because it’s so much weaker. In fact, the Z particle (one of the three particles which carries the weak force) is basically a massive photon (photons carry the electromagnetic force). So for any valid electromagnetic interaction, with particles exchanging photons, you could replace all of the photons with Zs, and have a valid weak phenomenon. What makes the weak force interesting, though, is the W particles (positive and negative): Interactions involving those can also change the flavor of quarks.

And there have been no attempts to detect individual gravitons, nor do we expect to ever be able to do so. Gravitational waves can be regarded as streams of gravitons, though, in much the same manner that electromagnetic waves can be regarded as streams of photons, and we do hope to detect gravitational waves within a few years. The difficulties are twofold: First of all, gravity is so incredibly weak compared to the other forces, so gravitons would have an exceedingly low probability of interacting with matter (including the matter your hypothetical detector is made out of). Second, the typical sources we expect to produce gravitational waves would produce wavelengths of kilometers or more. Gravitons are expected to have the same relationship between wavelength and the energy of a particle as do photons, which means that an individual graviton would have an energy of 10[sup]-10[/sup] eV or less.

On the question of gravitons propagating through higher dimensional space, the “extra” dimensions are generally regarded as being compact, or “rolled up” on a very small scale. To illustrate, let’s take your example and step it down a dimension: A point source in a plane, emitting gravitons in all directions in the plane. If you picked any single line, the chances of any graviton exactly falling on that line would be infinitesimal. However, suppose you now roll that plane up into something resembling a drinking straw. It’s still two-dimensional, but if you zoom out, it looks one-d. Now, put your point source on the surface of that straw. If you zoom in very close to your point source, it still looks the same as before, two dimensional. But on larger scales, gravitons start winding around the straw forming helices. The net effect is gravitons moving away from the source along the axis of the straw, on (or rather, very close to) a one-dimensional line. This is something which is, in principle, testable: On normal scales, gravity scales with the inverse square of the distance, reflecting the fact that it’s spreading out in 3-dimensional space. But if, on a smaller scale, you have these extra dimensions, then for very short distances, gravity should be proportional to the inverse cube (or inverse fourth, etc.) of the distance. Experiments have been done down to the millimeter scale, or so, and the results have all been null thus far (that is, we’re pretty sure that the largest extra dimension is smaller than a millimeter).

11

Ah. That explains it quite well. I hadn’t thought of the extra dimensions being wrapped as the first three are sometimes believed to be, especially on a small scale. I understand now. I think I’ll play some Scorched Earth with wrapped walls turned on.

12

:smack:

Yes, I was thinking of an underground experiment I saw on NOVA once, that was designed to detect gravity waves, not gravitons, although as Chronos points out detecting the one would imply the other.

I was also thinking of the JPL/ESA LISA mission, which for some reason I had thought already launched, but is in fact, still very much on the drawing board. :smack: :smack:

But that too, is designed to detect gravity waves, not gravitons. :smack: :smack: :smack:

13

Don’t we need also to remember that once we place ourwselves in the context of string theory’s 10 curled and uncurled dimensions of space and time, we must also stop thinking of a graviton and the other particles as essentially zero-dimensional entities traveling around, and start thinking of them in terms of one-dimensional strings vibrating through these dimensions (or multi-dimensional p-branes wobbling and roving)?

14

As I understand it, particle/wave duality manifests itself as a function of frequency/wavelength:

The lower the frequency/longer the wavelength, the more apt the field phenomena manifests itself as a wave.

The higher the frequency/shorter the wavelength, the more apt you will detect individual particles.

To apply this to gravity, we need a strong source of high frequency gravitons.

A quantum singularity.

Since we do not have immediate access to a Black Hole nor a Romulan Warbird, we won’t be seeing gravitons any time soon.

15

Frequency and wavelength are both characteristics of waves. Try again, you’re sort of in the ballpark.

16

Yes, I know frequency and wavelength are attributes of waves; specifically, the distance between the peaks (or troughs) of a sine wave and the time interval for the wave to cycle itself.

I just believed that at higher frequencies and shorter wavelengths, the phenomena presents itself less like a wave and more like a particle.

17

Not quite. The “particle-like” behavior emerges with the packet structure. Think (for simplicity) of a massive bosonic quantum field on a line, that is a square-integrableC-valued function satisfying the 1+1-dimensional Klein-Gordon wave equation

d[sup]2[/sup]u/dx[sup]2[/sup] - d[sup]2[/sup]u/dt[sup]2[/sup] = m[sup]2[/sup]

The Hilbert space of solutions has an easy base: the trigonometric functions. These are the wave solutions, and on second-quantization they are the basic excitations of the field. The particle behavior you seem to be referring to is the localization, which these waves don’t have at all. However, we can integrate across a spectrum of these waves to get a solution with compact support as small as we choose, and a suitable collection of these form another base.

In other words, the relation is (like in the Uncertainty principle) through a Fourier transform: “wave-like” behavior comes from a momentum-space basis (used in the solution of the K-G equation), while “particle-like” behavior comes from a position-space basis.