The relativity equations explain it well to a mathematician, but most of us have an instinctive need for picture that matches our experiences. The only picture I can offer is the one that comes from

**my own model**, as follows:

The known particles, like electrons, protons, etc., are composed of more fundamental particles. The most fundamental particles consist of pairs (or perhaps groups) of photons orbiting one another. Since they are photons, they can only move at the speed of light, even when they are locked in orbit around one another. The center of the particle is the center of the orbit. When the particle moves relative to any reference frame, the path of the orbit in that frame is necessarily longer than the path of the center.

For an analogy, consider a bola [thanks, imatfaal, for the correction] (two or more heavy balls tied to the ends of ropes). When you throw a bolero, the balls orbit around the center of the ropes. If you trace the paths of the balls and the center, you will see that the balls travel farther than the center, but in the same amount of time. Obviously, the center of the bola can't move faster than the balls spinning around it. [

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The rest mass of the particle is the combined mass of its constituent orbiting photons. I can hear you general relativity people shouting and laughing, "Photons have no mass! Ha, ha!" [

] I'm going to have take a slight detour to satisfy the general relativists before I can resume answering the question.

I'm not saying GR is wrong; it just uses the same words we learned in high school, but with different meanings. It may be true that, in GR, a photon has no mass; that's because "mass" doesn't mean the same thing in Minkowski space-time as it does in Euclidean space. In Euclidean space, gravity bends the path of light; in Minkowski space-time, the path of light is the definition of a straight line. Near a white dwarf or black hole, the Euclidean space is still there, but things that are spherical in Minkowski space-time are distorted in the Euclidean space. When you see a diagram of a black hole with curvy lines to represent light beams, your actually looking at the black hole in Euclidean space; there is no way to illustrate it in Minkowski space-time unless your visual cortex is wired like a modern computer.

Now, as I was saying: A photon has mass in Euclidean space. In a gravitational field, the force of gravity changes the momentum of the photon. At relativistic speeds, force is not equal to mass times acceleration; instead, force is the rate of change of momentum. The equation, f = dp/dt, works for particles with rest mass as well as for photons, regardless of the velocity. Near the speed of light, dp = mdv + vdm. Mdv = ma, and since dm is not zero at high velocities, f ≠ ma.

To satisfy conservation of momentum and Newton's third law, the force of gravity pulling a photon toward a star must be matched by an equal and opposite force pulling the star toward the photon. So the photon has gravitational mass as well as inertial mass in Euclidean space.

Let's get back to the question, shall we.

The rest mass of the particle is the combined mass of its constituent orbiting photons. To accelerate the particle, you must transform its waveform into a different reference frame. Applying the formulas of special relativity to small increments of velocity, you find that the energy of the orbiting photons is greater in a reference frame that is moving relative to the center of the particle. The greater the velocity difference between particles own reference frame and the moving reference frame, the greater the energy of the orbiting photons. Since acceleration increases the energy of the orbiting photons, it also increases the mass of the particle. The rest mass of the particle remains unchanged because it is the mass measured in reference frame of the particle.

Actually, the picture ain't quite that simple, because the orbiting photons are sometimes moving in the direction of relative motion, sometimes opposite the relative motion, and most of the time at an angle to the relative motion. You have to be pretty good mathematician to prove that the sum of masses of the orbiting photons is always equal to the total mass of the particle. (By the way, I'm not a mathematician.)

And that brings us to the standard explanation of why it takes infinite energy to accelerate a particle to the speed of light. If the center of the particle is moving at the speed of light in a given reference frame, and the particle still has its original rest mass in its own reference frame, then the equations of special relativity can only be satisfied by assuming that the particle has infinite mass. Anyway, how are the photons supposed to orbit? They must take infinite time in the part of their orbit where they move in the direction of relative motion, and zero time coming around the other side of the particle. [

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For those of you who are wondering how photons can orbit one another, it’s the Higgs force. I'm working on an explanation of how that works, but it’s not yet posted on my website. Long story short: Dark energy pushes photons less on the side facing one another, but only if they are properly matched for wavelength and aligned for phase, polarity and distance. Then, zero point energy sucks them into a potential well so deep that they become blue shifted and their mass increases by a factor greater than a million to one.

Now, kiddies, you must forget everything I've said because you'll get an F if you mention any of this in your school work. It's pure heresy. Bad thoughts! [xx(] Nasty! Get them out of your mind, right now!