Einstein sometimes imagined what it would be like to catch up with a light beam. He knew from Maxwell’s laws of electromagnetism that light must travel at the speed at which it travels. It can never appear stationary the way a vehicle does when you are travelling next to it at the same speed as that vehicle. It must always appear to all observers to be going at its speed, and it always appears to be going this speak regardless of how fast its observers are going. This is true even if the two observers are travelling at totally different speeds, bizarre though this may sound. It was this reality that clued Einstein in to the fact that something must be radically mistaken about how we understand space and time and how they relate to one another and velocity.

Finally, let us consider the famous Einsteinian equation E = mc^2. Some understand this equation simply in terms of replacing the v in the Newtonian understanding with the more complicated equation mentioned a moment ago. This retains the concept of an unchanging mass. Most physicists take this position. However, an earlier way of articulating the equation is 1/V (1 – v^2 / c^2). This entails that mass increases with velocity according to this ratio. this means we have to make a distinction between the mass an object has when it is at rest (its “rest mass”) and the mass that it has when it is moving. The “m” in the formula, therefore, must be be replaced with “m0”, which refers to what the mass of the object is when it iis at rest. Therefore, p = m0v/V (1 – v^2/c^2), or to put it another way, p = mv where m = m0/ V (1 – v^2 / c^2). This is now taken to refer to the mass of the object at such and such a speed.

But how does this mass increase? When an object increases in speed, it also acquires more and more energy. This is its kinetic energy or energy of motion. Energy adds to its mass. Objects are incapable of taking on extra energy without also acquiring the extra mass that goes with kinetic energy. This is because mass (“m”) of the object eventually approaches infinity as velocity approaches the speed of light. This makes it impossible for a force to significantly accelerate an object of infinite mass. This is true regardless of what its magnitude is and for however long it operates on the object.

But have we empirically confirmed this? The high-energy physics laboratory at CERN possesses particle accelerators. They can use powerful electric forces to make tiny subatomic particles form a circular path, going faster and faster. The speed limit is the speed of light. One can push further and further on the particles and their speed more and more closely approaches to that of light but never reaches it. Each machine reaches its speed limit eventually, and larger and larger machines must be built to accommodate larger speeds.

At one accelerator in Stanford, California, electrons, the lightest subatomic particles, were made 40,000 larger than when they began, when placed down a 3-kilometer tube. Once the electrons stop moving, they regain their earlier mass. What about this energy? If one cannot have energy without also having mass, does this not imply that resting particles have mass? Yes, they contain locked-up energy. This energy can be partially released under certain circumstances, and is how we invented the nuclear bomb.

There is energy that is locked up in rest mass. There is also additional energy acquired by a particle’s motion. Basically, E = mc^2 teaches that mass is always associated with energy, and that energy is always associated with increasing mass. The c^2 functions to ensure the mass and energy units are correct. A warmed plate is heavier than a cold plate, since it has more energy, and therefore, greater mass. When it comes to very powerful forces that bind nuclei together, mass differences become significant.

Atoms contain heavy central nuclei. They are surrounded by very light electrons. The 92 elements which constitute all matter consist of differing numbers of electrons; namely, between 1 and 92. These differ in the size of their nuclei. Light nuclei can collide with one another in such a way that creates a heavier nucleus. When a composite nucleus has been constituted, energy is required to pry its components apart. These two smaller nuclei had more energy between them prior to when they were combined as a larger nucleus. This act, therefore, required differences in energy in order to be released. “This is done in the form of heat energy and/or the energy of light. Such then is the process whereby the sun gets its energy – nuclear fusion – the fusion of light nuclei to form larger nuclei.”

Since the larger nucleus has less energy than its earlier components, it must also have less mass than the separated particles. Some of this energy was originally locked up in the form of rest mass energy. Now it becomes transformed into other expressions of energy. This is how the sun converts its hydrogen into helium with loss of 4 million tons of rest mass every second. Nuclear fission, on the other hand, is how we get nuclear bombs. This is also how nuclear power stations are run. Very large nuclei, such as uranium, is unstable. In other words, its neutrons and protons can be packed very tightly and efficiently, provided the larger nucleus is split in order to produce smaller nuclei and other fission products (such as light pulses, electrons and neutrons). Combining certain elements results in nuclear fission powerful enough to create very large amounts of energy. When it comes to creating nuclear explosions or nuclear power:

“A typical process involves the isotope of uranium, 235U, absorbing a neutron to become236U, which then splits to form92Kr (krypton) and141Ba (barium), together with three neutrons and a release of energy – the energy of nuclear fission. The neutrons so released can subsequently go on to get absorbed by other235U nuclei which also split. Hence a chain reaction is set up. If the series of reactions occurs rapidly, there is an explosion (the nuclear bomb); on the other hand, if activated in a controlled manner, then one has a steady release of energy that can be harnessed for peaceful purposes (nuclear power stations).”