[Quix]

I think I understand that.

You have been excellent at clarifying my confusion.

Greatly appreciated.

I think the key part that I didn’t appreciate fully enough was that even though one is at 99.9% of the speed of light . . . getting to

99.99%
and then

to 99.999%

and then to 99.9999% and then to 99.99999% etc.

each step takes a huge energy increase. I wasn’t appreciating that fact sufficiently.

[Cboldt]

-- and then to 99.9999% and then to 99.99999% etc. ... each step takes a huge energy increase. ... --

What we rightly see as a "huge" amount of energy doesn't represent much in the way of a mass increase. The atom bomb dropped on Nagasaki converted about 1 gram of mass into energy. Played in reverse, if one could, with perfect efficiency, harness the energy of a 21 thousand tons of TNT explosion, converting ALL of that energy to mass, one would get about one gram of rest mass.

[Cboldt]

-- You have been excellent at clarifying my confusion. ... Greatly appreciated. --

My pleasure. High energy physics is counterintuitive (as is quantum mechanics), and some of the casual conversation by the physicists adds to the confusion; like the "as speed approaches the speed of light, the mass approaches infinity." While technically true, all sense of proportion is lost in the casual statement.

At the extreme end of thought experiment, the theory asserts that if one took half of the mass (I'm leaving some mass hanging around to provide place to watch the moving proton from) and all of the energy in the universe, and concentrated it into one single proton, that proton would still NOT obtain the speed of light in a vacuum. It would be very energetic, it would be very "massive," but it would not be traveling at the speed of light in a vacuum.

[Cboldt]

One other point, it may clarify circular accelerators. The limiting factor of a circular accelerator is not inability to impart more energy into the protons. The limiting factor is keeping them going in a circle. The magnetic field that holds the travel path has to increase in strength as the particles go faster and get heavier. When the particles have an energy (and mass) of 7 Tev, the magnets of the LHC must be at full strength in order to bend the particle path into the 27 km diameter circle. If the particles are driven any faster, they will "fly out" of the desired circular path.

Think of the magnetic field as a string holding the particles in a circular path. The heavier the particles, the stronger the pull on the string.

Most of the energy consumed by the LHC is used to maintain the beam path.

[Cboldt]

The LHC is really an incredible machine. I wonder what the full energy consumption breakdown is, but for basic operation, the energy is used to bring the beam path to a vacuum that has less matter in it than deep space has, and the temperature of the conductors that make the surrounding magnetic filed is just a few degrees above absolute zero. Both of those basic conditions (vacuum and temperature) have to be maintained, or the machine won't work.

Finally, this stuff is just a long standing interest of mine - I am by no means a scientist or physicist. But the nature of matter, the scope and structure of the universe, are just so ephemeral, so hard to "grasp" at bottom. We think we know what 'stuff" is made of, but the closer we look, the more it disappears. And that IS reality.

[HiTech RedNeck]

Unless the particle itself is massless (like photons themselves).