# Mass Explained

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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 units right. Because stress is force per unit area and energy is force times distance.

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.

The answer is all down to motion. Or the lack of it. You have to 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 having the thing you think is 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.

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.

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. 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 probably 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. 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 λ/c or wavelength over frequency, so you can also express the momentum as h/λ. And you can see how that momentum affects a mass via Compton scattering:

When a photon collides with a free electron the electron gets a bump and goes flying 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 imagine you’re the 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 would feel 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 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.

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, a funny thing happens. The volume will fit only a single wavelength, and the stress in your photon kind of tangles round itself like a moebius-strip bagel, spinning and rolling around itself like a smoke ring, and suddenly you’ve got yourself a self-sustaining vortex that you don’t have to bat any more. You’ve got yourself something that goes round twice to get back where it started, so it’s got spin ½. All the negative charge variation is on the outside, so it’s got negative charge. And most importantly, because it isn’t going anywhere, when you hit it, it’s you hitting the 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.

It’s wrapped into tight little loop, and you can’t undo it. When you give it a little tap with a bat you can still think in terms of the Compton picture. But now the whole thing is tied into a single wavelength and since it isn’t kept in place by some atomic nucleus acting like a tetherpole, you can’t stretch it with a little tap. All you get is the deflection. That deflection is a change in the photon velocity vector, it adds to all the velocity vectors in the moebius loop. It translates into motion, so the electron as a whole moves with respect to you.

You can do the same sort of thing to make a positron. It’s got the twist wrapped the other way, with the positive charge variation on the outside. But there’s no table tennis bats in particle physics. In practice you fire a mega-electron-volt photon at an atomic nucleus, whereupon it splits into two to create an electron and a positron at the same time for conservation of charge. The positron won’t last long because it will meet an electron, and the two will annihilate to create a pair of 511keV gamma-wave photons flying off in opposite directions. It’s like the electron is a twist in your fishing line and the positron is the mirror image twist. Slide them together, and voila, twang, gone.

Now when we go back to your cannonball we can see how it’s a whole heap of whirling stress, a trundling bundle of energy. But is the cannonball moving or is it you moving, and what’s its mass? Is the rest mass calculated from the transverse velocity vector of those racing photons, or is it the relativistic mass of whatever path they trace through space? Take your pick, but I pick the latter. Which means in my eyes photons have momentum, and energy, and mass too. It’s all relative really, because we’re made out of these things, they’re like our light clocks. If you’re racing past me, yours look like this /\/\/\ to me and mine look the same to you. But our own look like this | to each of us. Our length contraction of 1/√(1-v2/c2) is relative, like our time dilation, and our momentum and energy, so I think our mass might as well be relative too.

Anyhow. That’s why a moving mass is rather like a spring. It looks like a spring stretched out rather than a spring compressed. That’s why a moving mass has something that looks like tension, sorry negative tension volume, that thing called energy. I will talk some more about these things. I will talk about electromagnetism and space, and whether energy is a property of space or makes it the thing that it is. And I will talk about particle physics and string theory, and matter.

But first, I need to try to explain a matter of some gravity...

Acknowledgements: thanks 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 A New Interpretation of Special Relativity, 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 Paul Dirac. Thanks guys.

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Thnx, I think I might use that ocean waves pic as a backdrop

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OK guys, what do you think? If anybody could point out why this layman's explanation falls flat on its face I'll be sad, but grateful.

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Farsight,

This is not a simple explanation at root level, to do that only basic defintions can be used that anyone would understand without requiring to work through what is theoretical here and what is fact.

I define empty space as empty with no properties t do anything until someone can show me some empty space actually doing something rather than infer attributes through other means.

Given empty space is accepted as empty then all I have is energy to create any mass at all. So I have mass is energy.

However energy can take many forms and what science considers mass consists of matter so it is the matter rather than the mass that needs explaining.

I have taken on board your answer from another thread and feel it justifies the explanation of matter. If a quark or electron is simply an energy particle then what exactly is the matter they represent?

Given only the energy and the empty space then it is the constraint on the empty space within the energy that constitutes the matter.

Now with atoms all having empty space constrained within energy then the cannonball would be a massive amount of matter consisting of empty space constrained by energy, any other matter colliding with this would normally be repulsed but that depends on the comparitive mass of each object etc.

Now energy constraining empty space may not seem like a particularly solid item but as is known the atom takes a little persuading to give up its energy protection of the space it contains.

john

jck

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Impressive post there farsight :¬)

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jck: it's a tricky one. Things have properties, but some things are maybe nothing but properties. It all gets kinda fuzzy.

Thanks alan.

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The answer is all down to motion. Or the lack of it.

Consider a 10 kilogram cannonball travelling at 1 metre per second in space relative to you... 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

Now imagine you’re the electron, only it’s you moving instead of the photon.

Imagine the electron and all other things which display the characteristic of mass temporally flowing at C and a photon that, except for oscillations which we observe as frequency, has dropped out of the generalized temporal flow, and the electron which remains embedded in the temporal flow runs into the photon.

Other than that, I don't think your electron/photon scattering is supported by observation. I think the general consensus is that the original photon will be absorbed and another photon of different frequency/oscillation will be 'emitted' in the majority view, and 'left behind' in my speculative scenerio.

aguy2

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Farsight,

I do not have anything as fuzzy. The clarity of empty space being absolutely empty allows no arguement for it to have substance or properties.

As all particles and properties are energy based then it is only energy that can create mass, if the energy constrains empty space and the particle formed then has properties then it is the energy that is responsible.

This of course is simply my solution which is logic based and requires certain definitions rather than fuzzy definitions so that the certain answers can be compared to the fuzzy ones.

john

jck

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Imagine the electron and all other things which display the characteristic of mass temporally flowing at C and a photon that, except for oscillations which we observe as frequency, has dropped out of the generalized temporal flow, and the electron which remains embedded in the temporal flow runs into the photon.

I really don't think there is any temporal flow, aguy. See the Time Explained essay for details:

Other than that, I don't think your electron/photon scattering is supported by observation. I think the general consensus is that the original photon will be absorbed and another photon of different frequency/oscillation will be 'emitted' in the majority view, and 'left behind' in my speculative scenerio.

Thanks, I'll check that out.

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jck: I think we both agree that you need space and energy to make mass. Perhaps we can agree to differ for now on whether space or energy is the prime ingredient.

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Farsight,

I am happy to accept your views as they do not fundamentally differ from the total concept of mass. The tune may played in different ways but the melody remains.

john

jck

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• 2 weeks later...

I have a problem with your words: "...imagine now the electron moving at the photon." Because of the relativistic nature of both, especially the photon, there is no frame of reference in which it is stationary. Indeed this is what distinguishes mass.

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