Mass Explained

[Farsight]

MASS EXPLAINED v3.0

 

You know that energy is an intangible thing. You can’t hold pure energy in the palm of your hand. Because energy is stress, which is the same as pressure, which is the same as negative tension, and you need a volume of stress to get the dimensionality right.

 

You know that mass is a tangible thing. You can hold an object in your hand and feel the mass of it. You even know that E=mc², and that the intangible thing called energy can be used to make the tangible thing called mass. But you don’t know how. I’ll explain how.

 

 

The answer is all down to motion. Or the lack of it. You have to get relative, and think in terms of momentum and inertia. You have to stop thinking of momentum as something that a mass has, because a thing can “have” momentum without having the thing you call mass. Like a photon. You know this because you’ve read the physics. You also know this because you’ve felt it yourself, down on the beach, playing in the surf. Along comes a massive wave. You know it’s a travelling stress and you know it has no mass because it’s the water that has the mass. But the wave does have momentum, enough to knock you and your girlfriend flat on your back, laughing and screaming with salt water up your nose. It's both intangible, and it's tangible. You can’t grab hold of it, but it can grab hold of you. And realising this is the first step in grasping how intangible energy can become tangible mass.

 

 

You can get a better feel for this with a gyroscope. Waggle it back and forth. See how light and insubstantial it feels. Now wind the string round the spindle, grasp it tight, and pull. You pulled tension out, so you put energy in. Your gyroscope is now humming, maybe precessing a little. When you try to waggle it you can feel the angular momentum working against you. Now it feels that bit more substantial. And you’re beginning to get a feel for mass.

 

 

Something that has a lot of mass is harder to move. Or harder to stop. Because it’s got a lot of inertia. Or a lot of momentum. And a lot of energy. And these things aren’t quite as different as you might think:

momentum p=mv

 

kinetic energy KE=½mv²

 

energy E=mc²

Consider a mass in motion. Consider a 10 kilogram cannonball travelling at one metre per second in space relative to you. Brace yourself, then apply some constant braking force by catching it in the midriff. Ooof, and you feel the energy/momentum. Kinetic energy is looking at this in terms of stopping distance, whilst momentum is looking at it in terms of stopping time. The measure we call momentum is conserved in the collision because the two objects share a mutual force for the same period of time. The measure we call kinetic energy isn’t conserved, because some of the mass-in-motion is redirected into deformation and heat and bruises, all of which involve mass-in-motion, but scattered motion instead of tidy vector quantities of masses moving relative to you. Or you moving relative to them, because all the while you were never too sure whether it was you moving or the cannonball.

 

When we turn our attention from a cannonball to a photon, we have to express the energy and the momentum in a different way. It’s a travelling volume of stressed space. There is no “mass”, so the energy is hf, and the momentum is hf/c. The h here is Planck’s constant of 6.63 x 10-34 Joule-seconds, and is an “action”, which is a momentum multiplied by a distance. The f is the frequency per second, and our old friend c is distance over time. It converts a stopping-distance measure into a stopping-time measure. A wavelength is a distance, and a frequency is the reciprocal of a time, so we can express c as wavelength multiplied by frequency, or λf . Hence you can also express the energy of the photon as hc/λ, and the momentum as h/λ. Remember that for later. For now all you have to know is that it’s all down to action. A photon is an action, like a shout, or a kick, or a wave in the surf. And you can see how the photon acts upon a mass via Compton scattering:

 

 

When a photon collides with a free electron, the electron gets a bump and goes recoiling off at an angle, while the photon is also deflected and its wavelength is increased. The electron gains some energy/momentum and the photon loses some. The upshot is that their velocity vectors have changed, as have their relative velocities. To get the feel for this you can play “photons” at home with a strip of carpet or better still a rubber mat. Lift one end, grip it tight, and give it a shake. You get a wave travelling down the length of the rubber. It’s a travelling stress that rides on the tension it creates, and you can toss “electrons” with it, be they dollies or eggs.

 

Now remember your Relativity. There is no absolute motion. Look again at the picture above. Imagine you’re that target electron, but you’re not at rest. Imagine it’s you moving instead of the photon. Bump, and you’re sent flying off at an angle. It would feel like you hit something solid instead of a photon. It would feel like a bad flight, with turbulence and so many air pockets it’s like riding over rocks. It would feel like the photon had inertia instead of momentum. It would feel like the photon was a bump, and was something solid. It would feel like the photon had mass.

 

But the photon isn’t sitting in one place, it always travels at c. You can’t nail it down like you can nail down your rubber mat. So how do you keep a travelling volume of stressed space in the same place? It’s easy when you know how. Imagine you’ve got a couple of “free-electron” table tennis bats, and you’re good at topspin. If you bat that photon just right, you can change its direction and give it some more energy/momentum. It’s called an Inverse Compton, like the picture above but with the arrows going the other way. Then you can hit the photon with the other bat to change its direction again. Repeat in rapid succession until you’ve got a kind of hexagon going, a miniature electromagnetic swirl that is your photon going round in circles.

 

 

Now keep batting away, but close your eyes, like you might close your eyes when you’re playing repulsion with a couple of magnets. You can feel something there between your bats. What you can feel is basically mass. You’ve made a “mass”. It isn’t a proper mass because if you stop batting, your photon will be off like a shot. You need to bat faster and harder to get it down smaller. You’re packing more and more stress into a smaller and smaller volume. Then at 511keV or 8.18 x 10-14 Joules, something happens. You suddenly find you don’t have to bat any more. The diameter got down to half a wavelength, and the electric stress in your photon somehow grabbed its own magnetic tail, and now it’s tangled round itself like a moebius-strip bagel. A moebius doughnut. You’ve got yourself a self-sustained soliton of travelling stress that goes round and round all on its own, twisting and turning at the same time. It goes round twice to get back where it started, so it’s got spin ½. It’s a wave and it’s a particle, so it exhibits wave/particle duality. And because it isn’t moving any more with respect to you, when you hit it, it’s you hitting that photon instead of the photon hitting you. It had momentum, and now its got inertia. It’s got mass. And you’ve got yourself an electron.

 

 

This moebius doughnut electron is actually very difficult to depict. It isn’t a solid object, and whilst we can draw a representation of it, it doesn’t have any surface. It’s got as much surface as an ocean wave. The ocean has a surface, but the wave does not. The electron has got as much surface as the repulsion you can feel with a couple of magnets. It’s got just as much surface as a light beam, as the photon that it really is. It’s a jitterbug photon. It’s got the property we call zitterbewegung, and that makes it something else, like a string that’s got knottedness becomes the thing you call a knot. Now we call the photon an electron. It jitters because it twists as it turns as it loops round and round. It’s still travelling at the speed of light, but now it’s going nowhere, so it’s going nowhere fast.

 

But wait, I hear you say, there’s no table tennis bats in particle physics. And a photon always travels at 299,792km/s. You can’t really stop a photon. Yes you can. It’s simple. You use pair production:

 

 

In pair production, a gamma photon of slightly more than 1022KeV is effectively broken over a nucleus to create an electron and a positron of 511KeV apiece. They’re like two half-wavelength “eddies” spinning off in opposite directions. Apart from a little wastage on the motion of the particles, most of the energy/momentum is stopped down from c and re-presented as inertia. We converted travelling kinetic energy or "relativistic mass" into non-travelling energy or "rest mass". If we simplify matters by discarding the positron and considering the electron to be at rest, we can look at those equations again and say:

 

E = hc/λ → mc² therefore m ≡ h/λc

 

That seems to be saying the photon has mass. That sounds wrong, because nowadays we define mass to be rest mass. But we know that both matter and energy cause gravity. Einstein told us that with his mass/energy stress tensor. Energy has what’s called “active” gravitational mass. And since a photon has energy, it has gravitational mass too. A 511KeV photon contributes the same amount of gravitational attraction as an electron. What’s important is that energy causes gravity, not mass. Whilst a mass does cause gravity, that’s because of its energy content.

 

It can get a little confusing because there are lots of different ways of talking about mass. Whilst the accepted definition is rest mass, this is also called “invariant mass” or “intrinsic mass” or “proper mass”. The term “relativistic mass” is really a measure of energy, which is why it applies to a massless photon. When you apply it to a cannonball travelling at 1000m/s, it’s a measure that combines the rest mass and the kinetic energy into total energy. There’s also “inertial mass”, which is a measure of how much force you need to apply to accelerate an object according to the equation F=ma. If you think of decelerating the cannonball using sheets of cardboard, it’s clear that this is the same thing as relativistic mass. There’s also “passive gravitational mass”, which is a a measure of how much an object is attracted by gravity. But it’s best not to get hung up on all these terms, because what’s important is this:

 

A photon has no rest mass, because rest mass is just rest energy, and the photon is never at rest. Because when it is at rest, it’s not a photon any more.

 

Rest mass is mass, and mass is just energy that isn’t going anywhere because it’s going nowhere fast. It’s a travelling stress travelling in such a tight little twist that it looks like it’s not travelling any more. You can't treat mass as something fundamental like energy, because you can “create” it and you can “destroy” it. All you have to do stop and start the energy. You stop the energy with pair production to produce an electron and a positron. To get it moving again you shove them back together. You need them both, because whether it's an electron or a positron, that tight little twist means you can’t undo it unless you’ve got the opposite twist to hand. When you do, and you do shove your electron and positron back together: bang, annihilation sends out two photons of 511KeV apiece. It’s like the electron is a twist in your tight taut fishing line, and the positron is the opposite twist. Slide them together and: twang, gone.

 

 

Interestingly, the motion of the electron and the positron in a magnetic field echoes the eddies created in pair production. We’ll come back to that later. The thing to note is that a magnetic field is all you need to shove an electron round. A magnetic field is produced by moving an electric field, so all you need is another electron, moving. Or a table tennis bat that’s full of them.

 

It’s much easier to think in terms of a table tennis bat. When you give your electron a little face-on tap with your table tennis bat, you effect a photon deflection as per the Inverse Compton. But this is a photon tied tight as a nut at 511KeV, so the deflection doesn’t alter the wavelength. It can only alter the photon velocity vector. It alters all the subsequent velocity vectors in the moebius doughnut electron. It translates into motion, so the electron as a whole moves with respect to you. In very simple terms the electron is a photon travelling in a circle, and if the electron moves past you, you see it as a cycloid or helix. The whole helix represents the relativistic mass, the total energy of the thing. The circular component represents the rest mass, denoting how much energy is going nowhere fast. The helix less the circle represents the kinetic energy of your electron, and denotes how much that energy that’s going nowhere fast is.. going somewhere.

 

 

This is why a moving mass is like a spring. To get it moving you had to deform the circle like you were making a split-ring helical spring. It then traces a helical path. To stop it moving you have to push it back into a circle. It’s rather like stretching and compressing a spring. And in case you didn’t notice, you can’t get it moving faster than the light from which its made. That’s the real trick to it. We’re made out of these circles of light. Everything is, be they our atoms, our brains, or our rulers or our clocks. If you’re moving, my circles look helical to you, and yours look helical to me. Everything is relative, be it our motion or our energy or momentum. And mass is just relative too. It’s just a measure of energy that’s relatively at rest with respect to us, because it’s going nowhere fast.

 

And it’s going nowhere fast for a very simple reason. Look at the picture of the moebius doughnut. Look at the line with the arrowheads. Now look at the picture of the balloon. The travelling stress is going nowhere fast because it’s tied in a knot.

 

 

All this means we don’t need the Higgs Boson. We converted a photon into an electron via pair production. The photon is boson enough, it’s the “mediator” of the electromagnetic force. An electron is a fermion, and it’s got mass, and it’s easy to see how mass comes from the electromagnetic field. So we don’t need the Higgs field. We don’t need to couple to it. The electromagnetic field is field enough, and it’s a vector field. Yet the Higgs field is a scalar field. Which means it can’t be right. It has to be a mathematical abstraction. It has to be wrong.

 

It gets worse. All we’re talking about is stress volumes travelling in space, and tying them into three-dimensional surfaceless solitons of variable tightness, complexity, energy, mass. It means “particle physics” is the stuff of boy scouts. It’s like they’re trying to tie knots of energy, and most of them come undone in a nanosecond because the particles just aren’t stable. What it all means is that the Large Hadron Collider is not just some misguided search for the Higgs Boson. The Large Hadron Collider is just playing with knots.