MASS EXPLAINED v2.1

F

Farsight

MASS EXPLAINED

You know that energy is an intangible thing. You can’t hold energy in the palm of your hand. Because energy is to do with 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 a thing 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.

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The answer is all down to motion. Or the lack of it. You have get relative, and think in terms of momentum and inertia. You have to stop thinking that momentum is something that a mass has, because a thing can have momentum without 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 think 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. 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.

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You can get a better feel for this with a gyroscope. Waggle it back and forth. See how light 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. And you’re beginning to get a feel for mass.

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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.

energy E=mc² kinetic energy KE=½mv² momentum p=mv inertial mass=m

Consider a 10 kilogram cannonball travelling at 1 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 momentum is conserved in the collision because the two objects shared a mutual force for the same period of time. The kinetic energy isn’t conserved, because some of the mass-in-motion was 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.

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When we turn our attention from a cannonball to a photon, we have to express the energy and the momentum in a different way. 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, which converts a stopping-distance measure into a stopping-time measure. It’s just wavelength over frequency or λ/f , so you can also express the momentum as h/λ. And you can see how that momentum affects a mass via Compton scattering:

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When a photon collides with a free electron the electron gets a bump and goes recoiling off at an angle, while the photon is similarly deflected and its wavelength is increased. The electron has gained some kinetic energy and the photon has lost some momentum. Or vice versa. Their velocity vectors have changed, as have their relative velocities. 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 big shake. You can see 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. Hours of endless fun. Better than an egg in the microwave for four minutes.

Now remember your Relativity. There is no absolute motion. Imagine you’re that free electron, only it’s you moving instead of the photon. Bump, and you’re sent flying off at an angle. It feels like you hit something solid instead of a volume of stressed space. Like a bad flight with so much turbulence it’s like riding over rocks. It felt like the photon had inertia instead of momentum.

But the photon isn’t sitting in one place, and you can’t nail it down like you can nail down your rubber mat. So how do you keep that bump of momentum in the same place? There’s only one tool in the box. More of the same. 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 energy. It’s called an Inverse Compton, like the picture above but with the arrows going the other way. Then you can hit it 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 vortex.

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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 and 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 goes click and suddenly you don’t have to bat any more. The volume got down to half a wavelength, and the 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 stress eddy that goes round and round all on its own twisting at the same time. This means it goes round twice to get back where it started, so it’s got spin ½. It also means the negative charge variation stays on the outside, so it’s got negative charge. It’s a wave and it’s a particle, so it exhibits wave/particle duality. And because it isn’t going anywhere any more, 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.


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This meobius-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 surfaces. It’s got as much surface as the repulsion you can feel with a couple of magnets. It’s like an ocean wave - the sea has a surface, but the wave doesn’t. But anyhow, you could do the same sort of thing to make a positron. It’s got the twist wrapped the other way, with the positive charge on the outside. But wait, I hear you say, there’s no table tennis bats in particle physics. And a photon always travels at 300,000km/s. You can’t stop a photon. Yes you can. It’s simple. You use pair production:

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In pair production a gamma photon of at least 2 * 511KeV is “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, most of the energy/momentum is stopped down from c and re-presented as inertia. Mass. We converted travelling kinetic energy or "relativistic mass" into non-travelling energy or "rest mass" aka “inertial mass”. If we simplify matters by discarding the positron and considering the electron to be at rest, we can say:

E = hc/λ → mc² therefore m ≡ h/λc

Whoa. That’s like saying the photon has mass. That sounds wrong. But wait a minute, we know that both mass and energy cause gravity. Energy has gravitational mass. And since a photon has energy, it has gravitational mass. Which means gravitational mass must relate to relativistic mass rather than rest mass. A photon has the former but not the latter because it’s never at rest. When it is “at rest” following pair production it isn’t a photon any more. No wonder the photon has no rest mass. It’s because rest mass is just rest energy.

That’s all inertial mass is. Energy that isn’t going anywhere. A travelling stress that is travelling in such a tight little loop that it looks like it’s not travelling. You can't treat inertial or rest 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. But whether it's an electron or a positron, that tight little twist means you can’t do that unless you’ve got the opposite twist to hand. But if you have, all you have to do is shove your electron and positron back together again, and 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 mirror image twist. Slide them together, and voila, twang, gone.


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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 another time. The thing to note is that all you need to shove an electron around is a magnetic field. A magnetic field is produced by moving an electric field, so all you need is another electron, moving. It’s easier to thing 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 locked tight at 511KeV, so the deflection is only a change in the photon velocity vector, not the wavelength. It adds to all the velocity vectors in the moebius doughnut. It translates into motion, so the electron as a whole moves with respect to you.

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What you get is a spiral. The spiral represents the relativistic mass, the energy. The circular component represents the rest mass, denoting how much energy isn’t going anywhere. The spiral less the circle represents the kinetic energy of your rest mass, and denotes how much the energy that isn’t going anywhere, is going somewhere. This is why a moving mass is rather like a spring. It evens looks like a spring. To get it moving you had to push the circle into a spiral, and to stop it moving you have to push it back into a circle. And 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, our spaceships, or our clocks. If you’re moving my circles look like spirals, and yours do too to me. Everything is relative, be it our motion and time, our momentum and energy. So maybe mass ought to be relative too. Maybe we don’t even need mass. No, I think we just need to make things clearer, and say mass is energy at rest.
One thing that is clear, is that the photon is the mediator of the electromagnetic field. And this field is a vector field. So we don’t need a scalar field called Higgs. I'll talk some more about these things, about particle physics and the standard model, about charge and space, and whether energy is a property of space or makes it the thing that it is. But first, I need to explain a matter of some gravity...

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Acknowledgements: to J.G. Williamson and M.B. van der Mark for Is the electron a photon with toroidal topology? see http://members.chello.nl/~n.benschop/electron.pdf to Peter M Brown for his many mass papers on his excellent website http://www.geocities.com/physics_world/ , to Robert A Close for The Other Meaning of Special Relativity http://home.att.net/~SolidUniverse/Relativity/Relativity.html, to R F Norgan likewise see http://www.aethertheory.co.uk/pdfRFN/Aether_Why.pdf, to all the forum guys with their relevant posts and links, Wikipedia contributors, and to anybody who I’ve forgotten or whose pictures I’ve used. And Albert Einstein. Thanks guys.
 
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OK, this is an improved version of mass explained. I've also kept all the images by splitting it across several posts.

It doesn't belong in pseudoscience.
 
You know that mass is a tangible thing. You can hold a thing in your hand and feel the mass of it.
Click to expand...

Can you give me 2 kg of raw mass?
 
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