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Relativity for Dummies

The mass gain problem: (For amateur physics nuts, only.)

OMED: E=MC2. In English words, the most famous equation in history says that energy is equal to mass times the speed of light squared. A simple algebraic transformation of that famous equation gives you the following: Mass is equal to energy divided by the speed of light squared. (If you have a big enough bucket sitting out in the open, three pounds of sunlight will land in it from sunrise to sunset on a clear day.)

While the equation in both forms relates to quantities of energy and matter, it may be accurate to say that there is another way to look at this. The first one tells you that if you speed up mass, you get energy. The second one tells you that if you slow down energy, you get mass.

For years I chatted by email with one of the world's leading astrophysicists. This was because I read a lot about physics and astronomy. I don't understand a tenth of what I read, but have a great time, and, when I run across some idea that strikes me as ridiculous, I try to figure out why things work that way. A while back, while re-reading three books on the subject at the same time (Hoyle's Frontiers of Astronomy, Barnett's The Universe and Dr. Einstein and Hawking's A Brief History of Time), I kept running into this business about how things get heavier the faster they go. The scientists would say that mass increases with velocity.

It's an increase whose rate itself increases as you approach the speed of light, designated in formulas as "C," and which to you and me is energy going more than 186,000 miles (about seven times around the Earth) per second. This mass gain exists in anything that is not at rest, and since nothing anywhere in the universe is ever at rest, is part of all matter to one degree or another. If you kick the speed of a chunk of matter up a bit, its mass goes up. Not much for most of the time you have your foot on the accelerator, but when you get up close to the velocity of light, the mass gain takes off like a rocket. Your spaceship gets heavier fast.

At 99.9999% of the speed of light, your ship has almost infinite mass. It has become humongously heavy. Since it takes a lot of rocket juice to make something like that speed up, you eventually reach the point where it would take an infinite amount of power to make it go one mile per hour faster. No gas station offers fuel of infinite octane rating, so it can't be done. Nothing made of ordinary matter can attain lightspeed while remaining in the state we call ordinary matter. (And, perhaps, nothing whose characteristics fit the description of an electromagnetic field can drop below lightspeed without becoming what we call matter.)

While studying this, a question popped into my mind. Where does all the extra weight (mass) come from? I began to work on the problem. The following three emails are what I sent to my astrophysical pal.

Email #1

E=MC2

Energy and mass (OMED: matter) are the two fundamental kinds of existence. Under the proper conditions, each may become the other. At some future time, each may switch back to the opposite state. Regardless of the form involved, a unit of one contains the potential of the other. Mass contains potential energy. Energy contains potential mass.

Or is it something more than just "potential?"

The velocity of light is the speed limit of the universe. .When matter of any kind accelerates, it does so as a result of applied energy, and gains mass. At a velocity close to the speed of light, the mass gain is rapid.. Not potential mass gain, but real mass gain. A dime accelerated to 99.999999% of the velocity of light does not contain just the potential mass that would be expressed in collision with another body, but in addition as a result of the acceleration has actually gained nearly infinite, presently operative mass of its own – mass identical to that of the matter of a slowly moving neutron star in the sense that to add velocity to the dime's journey would require a nearly infinite number of units of real, not potential, energy.

OMED: a problem for the limitation physicists here as I see it is that the fuel of a rocket approaching lightspeed would also gain in mass. Logic suggests that a nearly infinite mass of fuel should have little difficulty in accelerating a nearly infinite mass of ship. E=MC2, after all. Their answer, of course, would be that the problem changes when you try to go from "nearly" to "really." When the playing field becomes infinitely large, no matter how big your bat is, it's impossible to hit a home run into the bleachers.

This explains why Einstein denied us the warp (faster than light, or FTL) drive of the starship, Enterprise. Forget matter. Not even light can go faster than light.

Mathematically speaking, infinite mass and infinite energy cancel each other out, thus disallowing additional acceleration. And, the only reason why acceleration of anything is possible is that the relativistic mass gain curve is end-loaded. There is an imbalance favoring energy at the slow end of the velocity scale. It's a useful imbalance, and wonderfully convenient. That this is true is the only reason anything in the universe can move. Physicists are mostly atheists, and so just accept this "accident" of nature. Ray Bradbury, whose religion, if any, is unknown to me, once told me that the greatest miracle of all is that the universe is here, and works.

The need for ever increasing amounts of energy to accelerate the dime is the result of increased resistance in the direction of travel (if the dime were passing through a medium like air or water), or is the result of inertial resistance of the sort described in Newtonian physics. That is “real” inertia. Real mass resisting a change in uniform motion.

It suggests to me that what we call reaction mass does not push the rocket to the left because it throws mass out to the right. It suggests rather that reaction mass pushes with part of its volume, and transfers part of those of its qualities known as inertial rest mass to the vehicle it is accelerating.

The acceleration process adds weight to the object accelerated. Why then does the accelerated object not weigh more when it comes to rest on a surface? Because the added real mass is transformed into energy during the deceleration process?

Reaction mass acceleration adds real mass to a ship, while reaction mass deceleration subtracts an equal amount of real mass from the same ship? (The mass is shed instantly in the form of heat and radiation during impact, or shed slowly by the braking effects of rockets or some medium like atmosphere.)

In all my reading, I have never seen an explanation of where the mass increase comes from. The above is my best current reasoning on the subject. The problem with it is that if written in one of your treasured formulae, it would state that mass and momentum are equivalent in some degree or other..

M=mv/tf

Where M is momentum, m is mass, v is velocity and tf is a transformation constant of some sort like Hubble's or Planck's, representing a heretofore undesignated mass transfer mechanism activated by the adding of velocity to any body in the state we call matter.

It is no wonder that you people are crazy.

Jacques Clouseau

Email #2

M=mv/tf

That may be backwards

Maybe it's M for mass gain in any given volume of matter is equal to the velocity times the transformation factor.

M=Vtf

But, that doesn't do it either. It's closer, but not right. It doesn't work in a geometric progression, if that's what you call it. Increased increases with each unit of acceleration. You probably have some symbol to attach to the tf function that would identify it as a multiplier with a regularly rising exponent, if that's the right term.

(I know I used mass interchangeably for matter in that other email.)

(Ignore me. You and I both know that I don't know [expletive deleted] about this. It just fascinates me.)

Email #3

M=mv/tf

I'm back to the first one. It expresses a mass value for M (momentum) as defined by an exponential transformation mechanism additive. Momentum is equivalent to mass in some way related to velocity expressed as a percentage of C, and as defined by some sort of progressive rheostat with the high gain numbers on the far end..

Being a progressive, you should love that.

Now, go away and stop bothering me.

If you have any other questions about relativistic physics, just email them to me and I'll get to them when I have space-time.

Postscript: The astrophysicist sent me a note. He said my formula was correct, except for the definition of "tf," the transformational factor. It isn't, he said, a fundamental mathematical expression that desribes a property of the universe like Planck's Constant, but rather a simple (abstract) computational expression, like a fraction. A tool that must be used to predict the values that will result from a particular physical event. At least, I think that's what he said.