Ya follow all that? The Higgs Boson is the theorized to be the thing behind gravity. Dark matter is currently a complete bloody mystery but the entire fate of the Universe hinges upon it.

If I was a gambling man then I reckon they’ll nab the Higgs boson. CERN have quite a track record at this sort of thing. They discovered the W and Z bosons confirming the Salam/Weinburg electroweak unification and also the top quark. As to dark matter? God knows! I suspect it doesn’t exist and something vastly more interesting is going on. My real hope for the LHC is that they provide evidence for Garrett Lisi’s E8 theory and we can dump the extra dimensions of superstring theory. Lisi’s theory is exceptionally simple compare to String Theory. It is potentially accessible to a bright final year undergrad in math or physics. Well, I guess strings are too but they are not at all easy to work with. Perhaps E8 is too beautiful to be true as Kaluza-Klein was but we live in hope.

And anyway, the LHC is magnificent. The US could have had an even bigger one (oh, er missus!) but the Superconducting Super Collider was cancelled by Congress after $2bn had been spent digging tunnels for it in Ellis County, TX. Which is just bloody typical. Congress probably spend more than that on expense account lunches in a year. The Atlas detector at the LHC alone is the size of a cathedral. The kinetic energy of the proton/anti-proton streams is epic (14TeV) or enough to power a Nimitz-class carrier at a stately 8 knots. It is ready and scheduled to go live on the 21st of October. They are currently cooling it to just above absolute zero* because the superconducting magnets need that and also I’m sure the reduction in Brownian motion helps with beam focussing.

Oh and just google the rate LHC will generate data. It’s fucking awesome. It’s so much that CERN have re-jigged the internet to distribute it. ‘net 2 is fast enough to send a Blu-Ray movie from Britain to Japan in 2 seconds. Sometimes, just sometimes, we are magnificent. Bring on the Space Elevator.

*Actually you probably all have in your homes something that operates at a negative Kelvin temperature. Guess what? You probably have several of them actually. There is a reasonable chance you might have one in your car too. Or wear one to the gym or out jogging.

Cats,
You get the cigar! lasers operate at a negative Kelvin temperature because they are essentially a population inversion so you have to stick a negative absolute temperature into the partion function and whatnot.

Sunfish,
I just did. I don’t understand half of this stuff being merely a recovering astrophysicist and not a particle physicist. The short version is that in the 60s Peter Higgs hypothesized an explanation of why gravity is rather different from the other fundamental forces. This machine is the first which can even possibly discover the particle he predicted was doing it. Gravity is the biggy. It is totally mysterious because we have an excellent theory of it (General Relativity) but unlike everything else it hasn’t been brought into line with Q Mech. Many attempts have been made to bring quantise GR and they’ve all ended in tears.

One way of looking at it is that these theories are just ways of getting results and are accurate but not really converging on truth. It’s called instrumenatalism. It’s roughly equivalent to the difference between my tool-box and the Doctors sonic screwdriver. He manages to do everything with on universal tool and I have to lug around a whole panoply of stuff. If the Higgs boson is confirmed as existing we have sometyhing we have experimental confirmation that gravity is a quantum force like the rest. We can can a load of bizarre speculation about everything from Mach’s Principle on up. It will give the ticklish field of Quantum Gravity some kinda reality and that’s something we have lacked for decades.

The GR literature is all over the place. I wrote my MSc thesis on GR (rotating cosmologies) and it’s enouggh to make you seriously doubt the entire concept of a scientific consensus. The Higgs boson is the leveller. It is the point at which some of the more madcap schemes can be discredited. Because the problem, you see, is most particle physics (& cosmology) done over the last 40 years is predicated upon the existence of this particle. If we can get it down either way we can move on with much greater confidence.

Particle physics is a tight-rope walk because in 40 years theories have been advanced all over the place which rely on this particle either existing or not. They are all predicated upon that point. If we can confirm or deny then weeding the garden of physics is much easier because it will mean that some approaches to unification are dead ducks and some are much firmer.

Think of it like this. You’re investigating a murder and you got a suspect and then you find the gun in his dumpster and the ballistics match and you’ve got finger-prints on it and DNA. Makes the DA’s job easier, right? Otherwise you’re chasing phantoms. Did he owe anyone money? Did his wife do it because he was playing around? Was there a family dispute? Without one piece of solid evidence you’re searching every avenue.

This is just for Sunfish.
No reason other than I think he might like it.
Just came across it. Enjoy.
The rest of you can too!
If ya like.
Lazers?
Sometimes you need
A Dark Star…

RAB,
That was…it was zen. It was pure chewing satisfaction. I might even say that it made my whites whiter and my brights brighter.

Nick,
So what you’re telling me is, we know that the Higgs Boson does a whole bunch of stuff. If I understand you right, it is gravity the way photons are light or EM radiation in general. It’s a straight answer to the question ‘who is John Galt?’ We just don’t yet know for sure that it exists.

“If I understand you right, it is gravity the way photons are light or EM radiation in general.”

Not really, but it’s probably as good a non-technical explanation as any.

I personally don’t believe in telling people something is ‘too technical to explain’; if we can’t explain it in terms the intelligent layman can understand, then it means we don’t really understand it ourselves. But if you don’t care about knowing, which many people for some unaccountable reason don’t, then feel free to ignore the following brain-bending exploration of the way the universe secretly works.

The first thing you need to know is that there are two sorts of mass, one of them a component of the other, that have wound up with the same label for essentially historical reasons. One of these is called the “rest mass”, and is the mass something has when it’s stationary. It’s a constant for any particular sort of particle, it’s zero for photons, and it can be created and destroyed from nothing. (i.e. photons with zero mass can be turned into electrons and positrons that have plenty of mass. The law of ‘conservation of mass’ doesn’t apply.) The other sort of mass is called ‘relativistic mass’, and it’s what increases when particles move faster in special relativity, it’s the main source of the gravitational field, it’s another word for ‘energy’ as in E = mc2, photons have non-zero relativistic mass, and it is conserved, (it can neither be created nor destroyed). The two versions of mass are equal only when a particle is stationary.

The gravitational field depends on the second form of mass, an the particle that mediates the force of gravity is called the ‘graviton’. This is what most closely matches the role of the photon with the electromagnetic field.

The Higgs boson is what gives particles their rest mass. It’s what makes protons heavier than electrons. It’s what gives matter inertia. It’s what stops everything flying off at the speed of light. Because while photons can act as a source of gravity, they can’t stand still. The Higgs boson is what ties up the energy into a parcel that takes effort to move. It is the treacle in which ponderous matter is stuck.

It’s designed to account for a problem, in that we can’t see any reason in the deep-down foundations of quantum mechanics to explain why particles ever have non-zero rest mass, or to explain why they have the different specific masses they do. The idea is that at the ultra-sub-below-tiny-microscopic level, everything does in fact travel at the speed of light, but some particles can interact with the Higgs field and keep ‘bouncing off’ it. The continual back-and-forth reflections slow the average progress of the particle down, and it can go at less than the speed of light. A lot of their energy is ‘tied up’ and can’t be released, even when the particle stops entirely. The more often it interacts, the harder it is to change its motion, and hence the ‘heavier’ it is.

The maths is very elegant, and ties up a lot of loose ends a lot more neatly than my simplified explanation would suggest, but personally I still feel that it has a heavy air of ‘fudge’ about it. I am highly suspicious. But nobody has had any better idea, or even one half as good, so the Higgs stands.

I don’t know if that was of any interest to you. But you did ask…

Well it certainly was to me Pa.
I have always been facinated by science, but my maths is so poor, that I can double my digital computing capacity, merely by taking my shoes and socks off.

All my mates at Uni were scienists, and if they could explain a theory in words, I could understand it.
You explained the Higgs Boson most eloquently. Thanks

I love explaining this stuff so much, that I find it hard to resist doing so at length. But I’m aware that a lot of people aren’t interested, regarding it as like the boring person at every party who drones on about double entry book-keeping or whatever, that I try to exercise caution before dropping long essays on quantum mechanics in somebody else’s blog. (Unless I’m arguing with them as an opponent, in which case I’ll do it for fun!)

I tend to suspect that the common difficulty with mathematics is down to poor teaching, and that nearly all people could do it if approached in the right way. That anyone would find a subject ‘boring’ after sitting for hours through classes they didn’t fully comprehend and didn’t understand why they should want to. But I don’t really know. The question of whether mathematics is unavoidably boring or difficult for some people is one that is often discussed, but hard to resolve.

Pa,
Now it’s starting to make a little sense. When I had physics in high school, gravity was explained in terms of ‘imagine a sheet stretched out like a hammock with things on it. Heavier things will cause a greater dip in the sheet and so other things will approach them more quickly and with more force.’ “Gravitons” weren’t part of the discussion.

We spent a lot of time fooling around with the ‘what’ but not so much ‘how’ and very little ‘why.’

But your audience here have interests beyond Paris Hilton[1] and the Denver Bronco’s playoff chances. Bring on the physics![2]

[1] When she started making news, I remember seeing something on one of the scandal rags at the supermarket check-out. I thought, ‘why did the French location of an international hotel chain make the front of the Enquirer?’ It was a month or so before I found out that Paris Hilton was a person rather than a hotel.

[2] I always understood that “If it explodes, it’s chemistry. If it smells bad, it’s biology. If it doesn’t work, it’s physics.’

Ah! That marvellous rubber sheet! It is, perhaps, the one thing that everybody knows about general relativity, and it is, in so many ways, totally and utterly wrong. You clearly know me too well; there is no better way to get me to expound at length on general relativity than to mention in my presence the analogy of the rubber sheet.

It is true that space is curved around the Earth, and that the form is somewhat similar to the form of a rubber sheet with a weight in it, but it isn’t the reason objects fall. The aspect of gravity that causes things to fall is the curvature in the time direction. The curvature caused by even a big object like the Earth is tiny, but because you are effectively flying through time at the speed of light (I shall explain this shortly), even a tiny curvature in the time direction can cause big changes. The spatial curvature exists, but is barely detectable. If I’ve got my arithmetic right[1], the Earth’s circumference varies by about 2cm from what you would expect if space was flat. The rubber sheet picture is usually a bit exaggerated!

Right, quick digression to explain special relativity. Everybody knows that you can add a time dimension to the 3 space ones to get a 4D thing called spacetime. Positions are defined by sets of four coordinates. But you can also get 4D analogues of other quantities, like the velocity. However, the velocity is a bit weird, because it turns out that it points more or less in the direction of time, and it is always the same length. This is because if you trace out your path through spacetime, you are always moving along it at one second per second, or because the conversion factor between units of space and units of time is c, at one light-second distance per second time. In other words, at the speed of light.

Now this means that a stationary object has a velocity vector that points straight up the time axis (which is where you’re ‘going’), and the three space coordinates are zero. If pick a different set of coordinates (and just as you can freely do this in space, you can can also do it in spacetime), then you might find that the same velocity is no longer pointing along your new time axis, it’s pointing off to the side a bit. Now you’re in a frame of reference where the object is moving. It’s the same object, with the same velocity, with the same length, but the coordinates you use are a bit different. All of special relativity comes down to geometry – it’s what happens to lengths when you look at them from a different angle.

So we can now explain most of the paradoxes of special relativity with a simple picture. Let’s take the clock paradox – two observers are moving relative to each other. Each of them observes the other’s clock to slow down, as the other is moving relative to them. How can both see the other slow? Well, imagine that two people start walking across a field at the same speed, but at a slight angle to each other. Each sees the other start to fall behind themselves as they drift off to the side. Since their forward motion corresponds to progress through time, this corresponds to them seeing the other person’s clock slow down. (And because measured at an angle, lengths are shortened.) Both are correct, but only in their own forwards-sideways coordinate system.

Simple, eh?

There’s one twist to this simple picture, which is that time doesn’t behave quite the same as space. (Which is sort of obvious, really.) And I’m afraid it does involve a tiny bit of maths. To calculate the length of a line in normal space, you use the Pythagoras rule, that the length of the line squared is the sum of the squares of each coordinate. d^2 = x^2 + y^2 + z^2. But in spacetime, the length is slightly modified. We get d^2 = -t^2 + x^2 + y^2 + z^2. The t coodinate has a minus sign in front of it. Often it’s more convenient to use the related distance (called the ‘interval’) which is tau^2 = t^2 – x^2 – y^2 – z^2. Because we normally measure space an time with different units, we have to insert a conversion factor to get things straight. tau^2 = (ct)^2 – x^2 – y^2 – z^2. But people who do this seriously measure their distances in light-seconds, so c comes out to be 1.

Right. You now know special relativity. Bar a bunch of working out the consequences, that’s all there is to it.

Back to general relativity. Einstein’s equation says T(a,b) = G(a,b). Yes, it really is that simple! (I’ve dropped a few constants, which are not important here.) T(a,b) describes matter and what it is doing. It includes mass, but also a bunch of other stuff which are really mass looked at from a different “angle” in spacetime. G(a,b) is a way of describing the curvature.

The a and b are two variable that go through the 4 coordinates, so this equation is really actually 4×4 = 16 equations, but six of them are just repeats of others, so it boils down to 10 equations.

We can write out T(a,b) as a 4×4 table, giving a separate term for each pair of coordinates, like this:

t x y z
———————
t | E -px -py -pz
x |-px Pxx Pxy Pxz
y |-py Pxy Pyy Pyz
z |-pz Pxz Pyz Pzz

Now the one you will be most familiar with is the one in the top left hand corner, which is the energy. (Or the relativistic mass, to use the old terminology.) The other stuff is a bit of a surprise. The (px,py,pz) values are a quantity known to physicists as the momentum. In Newton’s physics, it’s just the mass times the velocity. The Pxx, Pyy, and Pzz terms are really weird, because they’re the pressure in each of the x, y, and z directions. Bizarre as it may seem, pressure acts as a source of gravity. And the other terms are known as the stress, and measure shear forces.

Having introduced all these strange quantities, I’m now going to dispose of them. Because like the velocity in 4 dimensional space, this mysterious 4×4 array of numbers also “points” mainly in the time direction. Each t coordinate has to be multiplied by c to get it into sensible units. For normal, slow matter, the E term is huge (being the mass multiplied by the c conversion factor twice), the momentum terms are big (being multiplied by c once), and the pressure/stress terms are all very small. So the only term that really matters here is the top left term, which is just the relativistic mass, as we expect if this is going to match what we know about gravity.

And this is set equal to the t-t component of the curvature, which can be loosely thought of as the curvature in the time-direction.

So we see the “rubber sheet” curvature of the space dimensions actually corresponds to the smallest components of the curvature, and it’s another bit entirely that makes bricks fall.

What do you think? Too long?

[1] Mathsy stuff: The Schwarzchild metric gives the length distortion as 1/Sqrt(1-2GM/rc^2) where G is Newton’s gravitational constant (0.00000000006674 m^3/kg s^2), M is the mass of the Earth (about 5,973,600,000,000,000,000,000,000 kg), r is the radius of the Earth (6,356,750 m), and c of course is the speed of light (300,000,000 m/s). The expression gives a distortion factor 1.0000000006962, which when multiplied by the circumference of the Earth, gives 0.02 m, or about 2 cm.

By the way, if 2GM/c^2 = r, then a bunch of stuff cancels out and the distortion factor blows up to 1/0 = infinity. This is called the Schwarzchild radius and is the size at which an object becomess a black hole. It’s also about 2cm for the Earth.

So, the rubber sheet is wrong but it isn’t: The object resting on our metaphorical rubber sheet distorts it, but it distorts the sheet in the time dimension as well as the three spatial dimensions and that’s what gravity is? Or do I need to throw out the rubber sheet entirely as being entirely irrelevant?

Where do gravitons come into play, then?

Also, when you compute 4-d distances, why is t^2 negative? It seems to me that, unless the other three terms are pretty large, d ends up being imaginary.

Only throw out the rubber sheet if your bed-wetting has been successfully treated!

Thing is the ol’ rubber sheet is an explanatory tool useful at a certain level. Feynman used in his “Lectures on Physics” a bug on a hot-plate or something. The thing with physics pedagogy and learning is it as much about forgetting as learning. At each stage you get deeper and put away more and more “childish things”. I always had a problem with that. I couldn’t help but feel there was perhaps a better way.

Very intersting Pa. I almost lost you for a mo but top-hole! Truly enlightening. I’d never thought about it quite like that.

Have been enjoying the explanations here. Currently reading Lectures on Physics as recommended by NickM, as it happens. Just the other day I read this, in vol1 12-12 (wherein it turns out that gravity can’t be distinguished from an accelerating co-ordinate system):

It might seem all right to consider gravity to be a pseudo force, to say that we are all held down because we are accelerating upward, but how about the people in Madagascar, on the other side of the earth–are the accelerating too? Einstein found that gravity could be considered a pseudo force only at one point in time, and was led by his considerations to suggest that the geometry of the world is more complicated than ordinary Euclidean geometry.

Then some discussion about how objects moving around a sphere in straight lines can appear to attract one another.

If I understand correctly the Higgs boson is not a graviton, replacing the distorted geometry idea of gravity, but rather tidies up some of the maths to do with the explanation of why things have mass.

But it is easy to get confused as a lot of physics seems to be alternative ways of explaining the same thing and we are still working on getting at what is *really* happening.

Really enjoying the book, incidentally, although it is frustrating that it was written in the ’60s and Feynman says “we do not know that yet” and it is hard to tell if that is still true.

FLoP is a tough slog, Rob. “Alternative ways” is a big theme of RPF. He loved it. Note the interstitial lecure on the principle of least action*. Feynman, as a kid, was taken aside by his high-school physics teacher and told about it. I guess it was obvious he was bored at that point. Well, he was a star of the math-team and with a buddy re-working the notation for Calculus at the time.

He was a honest-to-God genius. His collections of annecdotes, starting with, “Surely You’re Joking Mr Feynman” are also brilliant. The story about the door in his frat house at MIT and his defence of “titty bars” in LA are brilliant. They all came about because he was giving drumming lessons to Ralph Leighton’s son in his basement and told stories and then the kid suggested bringing round a tape-recorder. He was enjoying the stories more than the drumming.

“He was enjoying the stories more than the drumming.” I can well believe it. When Feynman talks you want to listen. I’ll keep an eye out for the anecdote collection.

“So, the rubber sheet is wrong but it isnâ€™t: The object resting on our metaphorical rubber sheet distorts it, but it distorts the sheet in the time dimension as well as the three spatial dimensions and thatâ€™s what gravity is? Or do I need to throw out the rubber sheet entirely as being entirely irrelevant?”

It depends what you’re using it for. If it’s just a convenient mental picture for the idea of curvature, it’s fine. If you’re using it thinking it gives you any idea about what is really going on, then you should throw it out.

“Where do gravitons come into play, then?”

Quantum mechanics says things don’t change smoothly, but do so in discrete steps. When the gravitational field changes, the classical picture says it does so by ripples spreading out across the ‘fabric’ of spacetime. If you quantise these ripples into discrete lumps of distortion, they get called gravitons. I’m aware that’s not a very clear explanation, but unfortunately the wave-particle duality requires a very lengthy explanation to make it amenable to visualisation, which I don’t have the time for at the moment. Some day…

Gravitons would not be detectable by any technology we can currently imagine, but ripples of gravitational radiation might be, and have been shown to exist indirectly.

Also, when you compute 4-d distances, why is t^2 negative? It seems to me that, unless the other three terms are pretty large, d ends up being imaginary.

Absolutely correct! Time is “imaginary distance”. (Or vice versa – either way, each is i times the other.) I’m impressed!

The usual way of looking at things is to consider both space and time as real, and then to define two separate non-overlapping “distances” to cover each domain, one being the conventional distance, and the other being the “interval” which measures the time recorded by a clock following such a line. One is valid for the domain of all lines representing objects moving slower than light, the other for points separated so that you would have to go faster than light to get from one to the other.

But there is an alternative view, in which you declare one or other to be imaginary, and use a single common “distance” which follows the usual Euclidean rule, and which can take both real and imaginary values. It’s sometimes called a “Wick rotation”. For many purposes, it makes the maths a lot easier, but it’s somewhat less familiar to the intuition.

This is also the real reason why faster-than-light travel is banned in relativity, because it would make the time experienced as you did it imaginary. Since nobody can figure out how to get their watch to show imaginary time (any suggestions?), it has always been assumed that it doesn’t happen. The related fact that from the point of view of external observers it is also backwards in time is another good reason, but probably wouldn’t be fatal.

For a deeper reason as to why, you probably have to look to Quaternions, which are the next step on from Complex numbers. There are only four complete systems of numbers possible for which the four arithmetical operations (+-*/) behave “nicely”, the real numbers, the complex numbers, the Quaternions, and the Octonions. In many ways, the Complex numbers are the nicest, and the others all suffer from various defects, (Reals don’t have square roots of negatives, for example), but the Quaternions happen to have some eerily familiar properties.

Instead of adjoining one Sqrt(-1) called i, in the Quaternions you adjoin three of them called i, j, and k. So you get numbers like (3+2i+4j+7k) which you can square to get 3^2-2^2-4^2-7^2, because squaring any of i, j, and k gives -1, and the cross terms cancel out because of another property of the Quaternions, which I’ll skip explaining unless you ask. Looks familiar, right?

The mathematical reasons that make these four systems elegant and unique, combined with the observation that the Quaternions are the most elegant choice in which there are enough dimensions to do anything interesting, are the most likely reason for there being 4 dimensions and for one of them to be different to the other three.

Quaternions are often used in 3D graphics for computer games because they are a fast way to do rotations without the ‘gimbal lock’ you get around the poles when you use more conventional rotation angles. If you’ve got either OpenGL or DirectX, you’ve got implementations of Quaternions on your computer. But they do have a reputation for being rather strange and difficult to understand.

Free speech is about the state dictating what is or is not acceptable, it is not about free people freely expressing contempt for contemptible behaviour.

Refusal to finance a platform for thugs to spew their venomous bile does not constitute censorship.

"I would remind you that extremism in the defense of liberty is no vice! And let me remind you also that moderation in the pursuit of justice is no virtue."

Counting Cats (CC) was taken to task by several other commenters for being too squeamish and perhaps even morally neutral about who are the good guys and who are the bad guys here. While I don't share CC's reaction to the video, I rejoice in his (her?) existence. What kind of a world would it be if people like CC didn't exist or if they had to hide their views? Who knows, we might all be living in something akin to Somalia.
...
CC's civilized response is precisely why our military is a force for good in the world.

A negative Kelvin temperature? Below absolute zero?

Um.

Otherwise? You talking lasers?

Nick,

Can you translate that into terms that a gentleman’s-C biologist can understand?

Cats,

You get the cigar! lasers operate at a negative Kelvin temperature because they are essentially a population inversion so you have to stick a negative absolute temperature into the partion function and whatnot.

Sunfish,

I just did. I don’t understand half of this stuff being merely a recovering astrophysicist and not a particle physicist. The short version is that in the 60s Peter Higgs hypothesized an explanation of why gravity is rather different from the other fundamental forces. This machine is the first which can even possibly discover the particle he predicted was doing it. Gravity is the biggy. It is totally mysterious because we have an excellent theory of it (General Relativity) but unlike everything else it hasn’t been brought into line with Q Mech. Many attempts have been made to bring quantise GR and they’ve all ended in tears.

One way of looking at it is that these theories are just ways of getting results and are accurate but not really converging on truth. It’s called instrumenatalism. It’s roughly equivalent to the difference between my tool-box and the Doctors sonic screwdriver. He manages to do everything with on universal tool and I have to lug around a whole panoply of stuff. If the Higgs boson is confirmed as existing we have sometyhing we have experimental confirmation that gravity is a quantum force like the rest. We can can a load of bizarre speculation about everything from Mach’s Principle on up. It will give the ticklish field of Quantum Gravity some kinda reality and that’s something we have lacked for decades.

The GR literature is all over the place. I wrote my MSc thesis on GR (rotating cosmologies) and it’s enouggh to make you seriously doubt the entire concept of a scientific consensus. The Higgs boson is the leveller. It is the point at which some of the more madcap schemes can be discredited. Because the problem, you see, is most particle physics (& cosmology) done over the last 40 years is predicated upon the existence of this particle. If we can get it down either way we can move on with much greater confidence.

Particle physics is a tight-rope walk because in 40 years theories have been advanced all over the place which rely on this particle either existing or not. They are all predicated upon that point. If we can confirm or deny then weeding the garden of physics is much easier because it will mean that some approaches to unification are dead ducks and some are much firmer.

Think of it like this. You’re investigating a murder and you got a suspect and then you find the gun in his dumpster and the ballistics match and you’ve got finger-prints on it and DNA. Makes the DA’s job easier, right? Otherwise you’re chasing phantoms. Did he owe anyone money? Did his wife do it because he was playing around? Was there a family dispute? Without one piece of solid evidence you’re searching every avenue.

This is just for Sunfish.

No reason other than I think he might like it.

Just came across it. Enjoy.

The rest of you can too!

If ya like.

Lazers?

Sometimes you need

A Dark Star…

RAB,

That was…it was zen. It was pure chewing satisfaction. I might even say that it made my whites whiter and my brights brighter.

Nick,

So what you’re telling me is, we know that the Higgs Boson does a whole bunch of stuff. If I understand you right, it is gravity the way photons are light or EM radiation in general. It’s a straight answer to the question ‘who is John Galt?’ We just don’t yet know for sure that it exists.

Sunfish,

“If I understand you right, it is gravity the way photons are light or EM radiation in general.”Not really, but it’s probably as good a non-technical explanation as any.

I personally don’t believe in telling people something is ‘too technical to explain’; if we can’t explain it in terms the intelligent layman can understand, then it means we don’t really understand it ourselves. But if you don’t care about knowing, which many people for some unaccountable reason don’t, then feel free to ignore the following brain-bending exploration of the way the universe secretly works.

The first thing you need to know is that there are two sorts of mass, one of them a component of the other, that have wound up with the same label for essentially historical reasons. One of these is called the “rest mass”, and is the mass something has when it’s stationary. It’s a constant for any particular sort of particle, it’s zero for photons, and it can be created and destroyed from nothing. (i.e. photons with zero mass can be turned into electrons and positrons that have plenty of mass. The law of ‘conservation of mass’ doesn’t apply.) The other sort of mass is called ‘relativistic mass’, and it’s what increases when particles move faster in special relativity, it’s the main source of the gravitational field, it’s another word for ‘energy’ as in E = mc2, photons have non-zero relativistic mass, and it is conserved, (it can neither be created nor destroyed). The two versions of mass are equal only when a particle is stationary.

The gravitational field depends on the

secondform of mass, an the particle that mediates the force of gravity is called the ‘graviton’. This is what most closely matches the role of the photon with the electromagnetic field.The Higgs boson is what gives particles their

rest mass. It’s what makes protons heavier than electrons. It’s what gives matterinertia. It’s what stops everything flying off at the speed of light. Because while photons can act as a source of gravity, they can’t stand still. The Higgs boson is what ties up the energy into a parcel that takes effort to move. It is the treacle in which ponderous matter is stuck.It’s designed to account for a problem, in that we can’t see any reason in the deep-down foundations of quantum mechanics to explain why particles ever have non-zero rest mass, or to explain why they have the different specific masses they do. The idea is that at the ultra-sub-below-tiny-microscopic level, everything

doesin fact travel at the speed of light, butsomeparticles can interact with the Higgs field and keep ‘bouncing off’ it. The continual back-and-forth reflections slow the average progress of the particle down, and it can go at less than the speed of light. A lot of their energy is ‘tied up’ and can’t be released, even when the particle stops entirely. The more often it interacts, the harder it is to change its motion, and hence the ‘heavier’ it is.The maths is very elegant, and ties up a lot of loose ends a lot more neatly than my simplified explanation would suggest, but personally I still feel that it has a heavy air of ‘fudge’ about it. I am highly suspicious. But nobody has had any better idea, or even one half as good, so the Higgs stands.

I don’t know if that was of any interest to you. But you did ask…

Well it certainly was to me Pa.

I have always been facinated by science, but my maths is so poor, that I can double my digital computing capacity, merely by taking my shoes and socks off.

All my mates at Uni were scienists, and if they could explain a theory in words, I could understand it.

You explained the Higgs Boson most eloquently. Thanks

Thanks RAB!

I love explaining this stuff so much, that I find it hard to resist doing so at length. But I’m aware that a lot of people aren’t interested, regarding it as like the boring person at every party who drones on about double entry book-keeping or whatever, that I try to exercise caution before dropping long essays on quantum mechanics in somebody else’s blog. (Unless I’m arguing with them as an opponent, in which case I’ll do it for fun!)

I tend to suspect that the common difficulty with mathematics is down to poor teaching, and that nearly all people

coulddo it if approached in the right way. Thatanyonewould find a subject ‘boring’ after sitting for hours through classes they didn’t fully comprehend and didn’t understand why they should want to. But I don’t really know. The question of whether mathematics isunavoidablyboring or difficult for some people is one that is often discussed, but hard to resolve.Pa. Keep on keeping on!

Between you and Nick, your combined passion for science is almost tasteable.

This is a fledgling site.

Spread your wings.

Hell yes, we interested!

Pa,

Now it’s starting to make a little sense. When I had physics in high school, gravity was explained in terms of ‘imagine a sheet stretched out like a hammock with things on it. Heavier things will cause a greater dip in the sheet and so other things will approach them more quickly and with more force.’ “Gravitons” weren’t part of the discussion.

We spent a lot of time fooling around with the ‘what’ but not so much ‘how’ and very little ‘why.’

But your audience here have interests beyond Paris Hilton[1] and the Denver Bronco’s playoff chances. Bring on the physics![2]

[1] When she started making news, I remember seeing something on one of the scandal rags at the supermarket check-out. I thought, ‘why did the French location of an international hotel chain make the front of the Enquirer?’ It was a month or so before I found out that Paris Hilton was a person rather than a hotel.

[2] I always understood that “If it explodes, it’s chemistry. If it smells bad, it’s biology. If it doesn’t work, it’s physics.’

Ah! That marvellous rubber sheet! It is, perhaps, the one thing that everybody knows about general relativity, and it is, in so many ways, totally and utterly

wrong. You clearly know me too well; there is no better way to get me to expound at length on general relativity than to mention in my presence the analogy ofthe rubber sheet.It is true that space is curved around the Earth, and that the form is somewhat similar to the form of a rubber sheet with a weight in it, but it isn’t the reason objects fall. The aspect of gravity that causes things to fall is the curvature in the

timedirection. The curvature caused by even a big object like the Earth is tiny, but because you are effectively flying through time at the speed of light (I shall explain this shortly), even a tiny curvature in the time direction can cause big changes. The spatial curvature exists, but is barely detectable. If I’ve got my arithmetic right[1], the Earth’s circumference varies by about 2cm from what you would expect if space was flat. The rubber sheet picture is usually a bit exaggerated!Right, quick digression to explain special relativity. Everybody knows that you can add a time dimension to the 3 space ones to get a 4D thing called spacetime. Positions are defined by sets of four coordinates. But you can also get 4D analogues of other quantities, like the velocity. However, the velocity is a bit weird, because it turns out that it points more or less in the direction of time, and it is always the same length. This is because if you trace out your path through spacetime, you are always moving along it at one second per second, or because the conversion factor between units of space and units of time is c, at one light-second distance per second time. In other words, at the speed of light.

Now this means that a stationary object has a velocity vector that points straight up the time axis (which is where you’re ‘going’), and the three space coordinates are zero. If pick a different set of coordinates (and just as you can freely do this in space, you can can also do it in spacetime), then you might find that the same velocity is no longer pointing along your new time axis, it’s pointing off to the side a bit. Now you’re in a frame of reference where the object is moving. It’s the same object, with the same velocity, with the same length, but the coordinates you use are a bit different. All of special relativity comes down to geometry – it’s what happens to lengths when you look at them from a different angle.

So we can now explain most of the paradoxes of special relativity with a simple picture. Let’s take the clock paradox – two observers are moving relative to each other.

Eachof them observes theother’sclock to slow down, as the other is moving relative to them. How canbothsee the other slow? Well, imagine that two people start walking across a field at the same speed, but at a slight angle to each other. Each sees the other start to fall behind themselves as they drift off to the side. Since their forward motion corresponds to progress through time, this corresponds to them seeing the other person’s clock slow down. (And because measured at an angle, lengths are shortened.) Both are correct, but only in their own forwards-sideways coordinate system.Simple, eh?

There’s one twist to this simple picture, which is that time doesn’t behave

quitethe same as space. (Which is sort of obvious, really.) And I’m afraid it does involve a tiny bit of maths. To calculate the length of a line in normal space, you use the Pythagoras rule, that the length of the line squared is the sum of the squares of each coordinate. d^2 = x^2 + y^2 + z^2. But in spacetime, the length is slightly modified. We get d^2 = -t^2 + x^2 + y^2 + z^2. The t coodinate has a minus sign in front of it. Often it’s more convenient to use the related distance (called the ‘interval’) which is tau^2 = t^2 – x^2 – y^2 – z^2. Because we normally measure space an time with different units, we have to insert a conversion factor to get things straight. tau^2 = (ct)^2 – x^2 – y^2 – z^2. But people who do this seriously measure their distances in light-seconds, so c comes out to be 1.Right. You now know special relativity. Bar a bunch of working out the consequences, that’s all there is to it.

Back to general relativity. Einstein’s equation says T(a,b) = G(a,b). Yes, it really is that simple! (I’ve dropped a few constants, which are not important here.) T(a,b) describes matter and what it is doing. It includes mass, but also a bunch of other stuff which are really mass looked at from a different “angle” in spacetime. G(a,b) is a way of describing the curvature.

The a and b are two variable that go through the 4 coordinates, so this equation is really actually 4×4 = 16 equations, but six of them are just repeats of others, so it boils down to 10 equations.

We can write out T(a,b) as a 4×4 table, giving a separate term for each pair of coordinates, like this:

t x y z

———————

t | E -px -py -pz

x |-px Pxx Pxy Pxz

y |-py Pxy Pyy Pyz

z |-pz Pxz Pyz Pzz

Now the one you will be most familiar with is the one in the top left hand corner, which is the energy. (Or the relativistic mass, to use the old terminology.) The other stuff is a bit of a surprise. The (px,py,pz) values are a quantity known to physicists as the momentum. In Newton’s physics, it’s just the mass times the velocity. The Pxx, Pyy, and Pzz terms are really weird, because they’re the

pressurein each of the x, y, and z directions. Bizarre as it may seem, pressure acts as a source of gravity. And the other terms are known as thestress, and measure shear forces.Having introduced all these strange quantities, I’m now going to dispose of them. Because like the velocity in 4 dimensional space, this mysterious 4×4 array of numbers also “points” mainly in the time direction. Each t coordinate has to be multiplied by c to get it into sensible units. For normal, slow matter, the E term is huge (being the mass multiplied by the c conversion factor

twice), the momentum terms are big (being multiplied by c once), and the pressure/stress terms are all very small. So the only term that really matters here is the top left term, which is just the relativistic mass, as we expect if this is going to match what we know about gravity.And this is set equal to the t-t component of the curvature, which can be loosely thought of as the curvature in the time-direction.

So we see the “rubber sheet” curvature of the space dimensions actually corresponds to the smallest components of the curvature, and it’s another bit entirely that makes bricks fall.

What do you think? Too long?

[1] Mathsy stuff: The Schwarzchild metric gives the length distortion as 1/Sqrt(1-2GM/rc^2) where G is Newton’s gravitational constant (0.00000000006674 m^3/kg s^2), M is the mass of the Earth (about 5,973,600,000,000,000,000,000,000 kg), r is the radius of the Earth (6,356,750 m), and c of course is the speed of light (300,000,000 m/s). The expression gives a distortion factor 1.0000000006962, which when multiplied by the circumference of the Earth, gives 0.02 m, or about 2 cm.

By the way, if 2GM/c^2 = r, then a bunch of stuff cancels out and the distortion factor blows up to 1/0 = infinity. This is called the Schwarzchild radius and is the size at which an object becomess a black hole. It’s also about 2cm for the Earth.

Ooops! wrong name! I’m so used to Samizdata filling it in, I didn’t notice Firefox picking me another one. Oh, well.

So, the rubber sheet is wrong but it isn’t: The object resting on our metaphorical rubber sheet distorts it, but it distorts the sheet in the time dimension as well as the three spatial dimensions and that’s what gravity is? Or do I need to throw out the rubber sheet entirely as being entirely irrelevant?

Where do gravitons come into play, then?

Also, when you compute 4-d distances, why is t^2 negative? It seems to me that, unless the other three terms are pretty large, d ends up being imaginary.

Only throw out the rubber sheet if your bed-wetting has been successfully treated!

Thing is the ol’ rubber sheet is an explanatory tool useful at a certain level. Feynman used in his “Lectures on Physics” a bug on a hot-plate or something. The thing with physics pedagogy and learning is it as much about forgetting as learning. At each stage you get deeper and put away more and more “childish things”. I always had a problem with that. I couldn’t help but feel there was perhaps a better way.

Very intersting Pa. I almost lost you for a mo but top-hole! Truly enlightening. I’d never thought about it quite like that.

Well you guys do what you do best

And I’ll attempt the same.

I have been exposed to all sorts of weiredness in my time,

And this isn’t even off topic really!

See what you think.

Have been enjoying the explanations here. Currently reading Lectures on Physics as recommended by NickM, as it happens. Just the other day I read this, in vol1 12-12 (wherein it turns out that gravity can’t be distinguished from an accelerating co-ordinate system):

Then some discussion about how objects moving around a sphere in straight lines can appear to attract one another.

If I understand correctly the Higgs boson is not a graviton, replacing the distorted geometry idea of gravity, but rather tidies up some of the maths to do with the explanation of why things have mass.

But it is easy to get confused as a lot of physics seems to be alternative ways of explaining the same thing and we are still working on getting at what is *really* happening.

Really enjoying the book, incidentally, although it is frustrating that it was written in the ’60s and Feynman says “we do not know that yet” and it is hard to tell if that is still true.

FLoP is a tough slog, Rob. “Alternative ways” is a big theme of RPF. He loved it. Note the interstitial lecure on the principle of least action*. Feynman, as a kid, was taken aside by his high-school physics teacher and told about it. I guess it was obvious he was bored at that point. Well, he was a star of the math-team and with a buddy re-working the notation for Calculus at the time.

He was a honest-to-God genius. His collections of annecdotes, starting with, “Surely You’re Joking Mr Feynman” are also brilliant. The story about the door in his frat house at MIT and his defence of “titty bars” in LA are brilliant. They all came about because he was giving drumming lessons to Ralph Leighton’s son in his basement and told stories and then the kid suggested bringing round a tape-recorder. He was enjoying the stories more than the drumming.

*something I’m inordinately fond of…

“He was enjoying the stories more than the drumming.” I can well believe it. When Feynman talks you want to listen. I’ll keep an eye out for the anecdote collection.

Wow, I think my brain just grew another lobe.

Thanks for the explanations, I’ll be re-reading them with a pen and paper later.

Hi Sunfish,

“So, the rubber sheet is wrong but it isnâ€™t: The object resting on our metaphorical rubber sheet distorts it, but it distorts the sheet in the time dimension as well as the three spatial dimensions and thatâ€™s what gravity is? Or do I need to throw out the rubber sheet entirely as being entirely irrelevant?”It depends what you’re using it for. If it’s just a convenient mental picture for the idea of curvature, it’s fine. If you’re using it thinking it gives you any idea about what is

reallygoing on, then you should throw it out.“Where do gravitons come into play, then?”Quantum mechanics says things don’t change smoothly, but do so in discrete steps. When the gravitational field changes, the classical picture says it does so by ripples spreading out across the ‘fabric’ of spacetime. If you quantise these ripples into discrete lumps of distortion, they get called gravitons. I’m aware that’s not a very clear explanation, but unfortunately the wave-particle duality requires a very lengthy explanation to make it amenable to visualisation, which I don’t have the time for at the moment. Some day…

Gravitons would not be detectable by any technology we can currently imagine, but ripples of gravitational radiation might be, and have been shown to exist indirectly.

Also, when you compute 4-d distances, why is t^2 negative? It seems to me that, unless the other three terms are pretty large, d ends up being imaginary.Absolutely correct! Time is “imaginary distance”. (Or vice versa – either way, each is i times the other.) I’m impressed!

The usual way of looking at things is to consider both space and time as real, and then to define two separate non-overlapping “distances” to cover each domain, one being the conventional distance, and the other being the “interval” which measures the time recorded by a clock following such a line. One is valid for the domain of all lines representing objects moving slower than light, the other for points separated so that you would have to go faster than light to get from one to the other.

But there is an alternative view, in which you declare one or other to be imaginary, and use a single common “distance” which follows the usual Euclidean rule, and which can take both real and imaginary values. It’s sometimes called a “Wick rotation”. For many purposes, it makes the maths a lot easier, but it’s somewhat less familiar to the intuition.

This is also the real reason why faster-than-light travel is banned in relativity, because it would make the time experienced as you did it imaginary. Since nobody can figure out how to get their watch to show imaginary time (any suggestions?), it has always been assumed that it doesn’t happen. The related fact that from the point of view of external observers it is also backwards in time is another good reason, but probably wouldn’t be fatal.

For a deeper reason as to

why, you probably have to look toQuaternions, which are the next step on from Complex numbers. There are only four complete systems of numbers possible for which the four arithmetical operations (+-*/) behave “nicely”, the real numbers, the complex numbers, the Quaternions, and the Octonions. In many ways, the Complex numbers are the nicest, and the others all suffer from various defects, (Reals don’t have square roots of negatives, for example), but the Quaternions happen to have some eerily familiar properties.Instead of adjoining one Sqrt(-1) called i, in the Quaternions you adjoin

threeof them called i, j, and k. So you get numbers like (3+2i+4j+7k) which you can square to get 3^2-2^2-4^2-7^2, because squaring any of i, j, and k gives -1, and the cross terms cancel out because of another property of the Quaternions, which I’ll skip explaining unless you ask. Looks familiar, right?The mathematical reasons that make these four systems elegant and unique, combined with the observation that the Quaternions are the most elegant choice in which there are enough dimensions to do anything interesting, are the most likely reason for there being 4 dimensions and for one of them to be different to the other three.

Quaternions are often used in 3D graphics for computer games because they are a fast way to do rotations without the ‘gimbal lock’ you get around the poles when you use more conventional rotation angles. If you’ve got either OpenGL or DirectX, you’ve got implementations of Quaternions on your computer. But they do have a reputation for being rather strange and difficult to understand.

Where do you download some blue ray movie trailers in HD ?`”,