I've been working hard lately on rationales for some of the conclusions of special relativity including the cosmic speed limit of the speed of light, relativistic mass increase, and mass-energy equivalence.I've come up with rationales that I hope are sound and easily understoodand that involve very basic calculations.

Experiments have demonstrated that the speed of light is about 669,600,000 miles per hour. This speed, unlike the speed of most other physical phenomena, cannot vary and is said to be constant. Following convention, I will use the letter C to represent the speed of light in my calculations.

Let's say I'm in possession of an airplane and an aircraft carrier that can attain speeds close to the speed of light. When the aircraft carrier is moving at 30 mph, I board my plane and from a standstill at the stern of the carrier accelerate my plane to 60 mph and take off from the deck at the bow of the ship. Relative to the surface of the water, at take-off my plane is moving at the speed of the carrier plus the speed of the plane, or 30 mph + 60 mph = 90 mph.

Now, using this basic principle of adding the speeds of the plane and the carrier to find the speed of the plane relative to the water, I set out to prove Einstein wrong when he posited that nothing can move as fast as light (except light and other electromagnetic radiation) or faster than light. I decide to accelerate the carrier to a speed just shy of light, C – 50 mph. I figure that since the plane at the slower speeds can move at 60 mph relative to the deck of the carrier, then adding the speeds of the carrier and the plane, I should take off from the deck at a speed faster than the speed of light. Here's the calculation:

C – 50 mph + 60 mph = C + 10 mph (10 mph faster than light)

Upon attempting this feat, though, I realize it cannot be done. Not only can my plane no longer attain 60 mph relative to the deck of the ship, it cannot even move at 50 mph relative to the carrier's deck. At best, it can move at 49.999 mph or so on the ship's deck. What went wrong?

After some thought, I decide to switch on a headlight on the plane. Since the light is moving forward from the plane, it must move faster than the plane.The plane cannot catch up to the light much less pass it. But, as noted earlier, the speed of light must be constant at C, so by necessity the plane must move slower than light!

Now that we know that nothing except light and other kinds of electromagnetic radiation can move at the speed of light, what effect might this fact have on an object's mass when the object is in motion?

Mass is a measure of inertia. Inertia is the tendency of an object at rest to stay at rest and an object in motion to remain in motion. Inertia can be overcome by applying a shove to an object to put it into motion, stop it, slow it down or speed it up, or change its direction of motion. Since the motion of an object is affected by both its mass and its acceleration, this shove can be said to be equal to mass multiplied by acceleration. In other words, the greater an object's mass at a given acceleration, or the greater its acceleration at its mass, the greater the shove needed to affect its motion. Let's call this shove "force," and relate it to mass and acceleration using the following formula:

f = m X a:

f = force

m = mass

a = acceleration

Now, since we know that nothing except electromagnetic radiation can move at the speed of light,we can conclude that no force, no mater how great, can accelerate any object to the speed of light. To do so would require infinite force which cannot be attained.

Since f = m X a, then, an object with a given mass can be accelerated to a velocity less than light by a finite force. That is, m X a would be a finite number. As we just noted, though, at the speed of light f = m X a would be infinite. Obviously, then,f = m X a increases as we attain greater velocities approaching the speed of light.

So what part of force, f, approaches infinity at such speeds? Is it mass, m, or acceleration, a, or both m and a? The acceleration a, at whatever finite value, will mathematically increase an object's speed to the speed of light given enough time. We need not concern ourselves with acceleration because it can be finite yet eventually reach the speed of light if we ignore the physical restriction.

Using the process of elimination, the mass must be the factor in f = m X a that might approach infinity when an object's speed approaches the speed of light.Since f = m X a approaches infinity when the object's speed approaches the speed of light, then m must also approach infinity. That is, the mass of an object must increase noticeably when approaching light speed!

Finally,since mass increases greatly when approaching the speed of light, the energy of the object moving at that tremendous speed also increases greatly. This relationship indicates that mass and energy are equivalent, or as Einstein put it, E = m X c^2.

I hope this explanation is both sound and easily understood.

Jagella