Mass Explained

[Farsight]

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. 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.

[Farsight]

I'm not quite sure if I've got this essay right, so I'd appreciate any feedback to put me straight or point out any cringing howlers. Thanks in advance.

[arkain101]

I really enjoyed reading this popular.

 

Good work, and those dark field microscopy images were great. I looked at the video clips and it was quite something.

 

Do you happen to know what exactly those images and clips are of? What specific item they are viewing?

 

Thanks and I will reply again later.

 

 

Oh and this was a really interesting article.

 

It's some interesting points about relativity.

[Farsight]

Thanks arkain.

 

The pictures were something to do with proteins and microtubules. I've just had a look to find out more, but the downloadable thesis is in 3Meg chunks, and in French to boot.

 

Hmmn, interesting article. I was rather put off by the evolution and creationism that followed, and as far as I can recall √(1-v2 /c2 ) is derived simply from Pythagoras' Theorem. But thanks, it is interesting. I'll look out for more on this. I'm especially interested because it's GRAVITY EXPLAINED next.

[cwes99_03]

I have to say that without reading it, you had a fine presentation with the images and what not. I think more people need to use images and graphs on this site. I think I'll give you a bit of rep just for that.

 

On the other hand, this thread seems to be being discussed on multiple threads. While I understand not wanting to have your presentation lost in the shuffle, perhaps a better title should be thought up and applied.

[LJP07]

If you can hold mass in your hand and mass is a form of energy, then are you technically not holding energy in the palm of your hand?

[Farsight]

Thanks cewes. The title is what it is because this is part of a set, and it's in response to discussions about this and those other subjects on other threads. If there's some threads in particular that I should look at, please can you let me know.

 

If you can hold mass in your hand and mass is a form of energy, then are you technically not holding energy in the palm of your hand?

 

There's an analogy here with money and a house. A house is made out of bricks, not money. You use the money to make the bricks and put them in place. Likewise you use energy to make matter out of space, so I tend to think it's stressed space we're holding in the palm of our hand. But space might be nothing without energy, so I could be inclinded to agree with your point. Interestingly, if you make a fist you can feel the blood pressure in the end of your thumb, so you've got a fist-sized volume of pressure. That's a way of holding energy in your hand.

[LJP07]

What's the weight of the smallest amount of energy/mass known and why is it that figure?

[Farsight]

I don't know Prolu. I guess a low-energy photon. Here's a paper that popped up when I googled just now:

 

http://ceta.mit.edu/pier/pier55/06.0503071.Puccini.pdf

[Farsight]

A poster called Good Elf on another forum showed me this. I really liked the way Qiu-Hong talks about grasp and intuition as opposed to the abstraction of mathematics. He talks about mass being action (=momentum) constrained by curved spacetime.

 

"The Nature of the Electron" by Qiu-Hong Hu

 

http://arxiv.org/pdf/physics/0512265

[Farsight]

See the end of the first paragraph on page 105 of Lee Smolin's The Trouble with Physics:

 

"..because mass is the measure of a particle's energy when it is motionless".

 

NB: there's a typo in the essay on post 1. This is the corrected paragraph:

 

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. A wavelength is a distance and a frequency is the reciprocal of a time, so we can express c as wavelength times frequency or λf . Hence you can also express the energy as hc/λ and momentum as h/λ. Anyway, you can see how the photon momentum acts upon a mass via Compton scattering:

[Moontanman]

I'm not quite sure if I've got this essay right, so I'd appreciate any feedback to put me straight or point out any cringing howlers. Thanks in advance.

 

Extremely good read, I felt like I was actually seeing what you were describing. You have a gift of describing the un seeable, I'm not qualified to debate the complete accuracy of your math but you made it completely real to me, please continue on!

 

Michael

[Farsight]

Thanks for that, Moontanman. Much appreciated.

 

I've written a set of essays, you can find them here:

 

http://hypography.com/forums/physics-mathematics/10787-relativity.html

 

I will be resequencing them. The TIME EXPLAINED essay offers a rather difficult concept and can be off-putting, so it's best to read them in this order:

 

MONEY EXPLAINED

ENERGY EXPLAINED

MASS EXPLAINED

CHARGE EXPLAINED (this is new, it's in its own thread)

REFERENCE FRAMES (this is new, it's in its own thread)

TIME EXPLAINED

GRAVITY EXPLAINED.

 

I've got further essays in progress, but I've got a few things to check over before I can consider them finished. Any feedback will be gratefully appreciated.