• Choose a category
• All
• Classic-Fiction

By Root 973 0

So Einstein’s theory allows for the possible existence of massless particles. Here is where the experiments come in handy. They have shown us that light is made up of particles called photons and that as far as anyone can tell they have zero mass. As a result, they must travel at the speed c. There is an important point here—if at some point in the future an experiment is performed that reveals that photons actually have a tiny mass, what should we do? Well, hopefully you can answer that question now. The answer is that we do nothing, except go back to Einstein’s second postulate in Chapter 3 and replace it with the statement that “the speed of massless particles is a universal constant.” Certainly c remains unchanged by the new experimental data; what changes is that we should no longer identify it with the speed at which light travels.

This is pretty profound stuff. The c in E = mc2 has something to do with light only because of the experimental fact that particles of light just happen to be massless. Historically, this was incredibly important because it allowed experimentalists like Faraday and theorists like Maxwell to gain direct access to a phenomenon that traveled at the special universal speed limit—electromagnetic waves. This played a key role in Einstein’s thinking, and perhaps without this coincidence, Einstein would not have discovered relativity. We shall never know. “Coincidence” may be the right word because, as we shall see in Chapter 7, there is no fundamental reason in particle physics that guarantees that the photon should be massless. Moreover, there is a mechanism known as the Higgs mechanism that could, in a different universe, perhaps, have given it a nonzero mass. The c in E = mc2 should therefore be seen more correctly as the speed of massless particles, which are absolutely forced to fly around the universe at this speed. From the spacetime perspective, c was introduced so we could define how to compute distances in the time direction. As such, it is ingrained into the very fabric of spacetime.

It may not have escaped your attention that the energy associated with a certain mass carries with it a factor of the speed of light squared. Since the speed of light is so great compared to everyday, run-of-the-mill speeds (the υ inmυ2 ) it ought to come as no surprise that the energy locked away inside even quite small masses is mind-bogglingly large. We are not yet claiming to have proven that this energy can be accessed directly. But if we could get at it, then how huge an energy supply could we be, quite literally, sitting on? We can even put a number on it because we have the relevant formulas on hand. We know that the kinetic energy of a particle of mass m moving with a speed υ is approximately equal tomυ2 and the energy stored up inside the mass is equal to mc2 (we shall assume that υ is small compared to c; otherwise, we would need to use the more complicated formula γmc2). Let’s play around with some numbers to get a better feel for what these equations actually mean.

A lightbulb typically radiates 100 joules of energy every second. A joule is a unit of energy named after James Joule, one of the great figures of Manchester whose intellectual drive powered the Industrial Revolution. One hundred joules every second is 100 watts, named after the Scottish engineer James Watt. The nineteenth century was a century of fantastic progress in science, now commemorated in the way we measure everyday quantities. If a city has 100,000 inhabitants, then a reasonable estimate is that it needs an electrical power supply of around 100 million watts (100 megawatts). To generate even 100 joules of energy requires a fair amount of mechanical effort. It is approximately equal to the kinetic energy of a tennis ball traveling at around 135 miles per hour, which is the service speed of a professional tennis player. You can go ahead and check this number. The mass of a tennis ball is around 57 grams (or 0.057 kilograms) and 135 miles per hour is nearly the same as 60 meters per second. If we put these numbers