Some memorization for a physics test

Usage examples of equations.

Although I avoid technical language and equations, because of the radically new concepts involved the reader may need to pause now and then, to mull over a section here or ponder an explanation there, in order to follow the progression of ideas fully.

For reasons that will become increasingly clear as we proceed, the equations of general relativity and quantum mechanics, when combined, begin to shake, rattle, and gush with steam like a red-lined automobile.

In fact, the mathematics of string theory is so complicated that, to date, no one even knows the exact equations of the theory.

Instead, physicists know only approximations to these equations, and even the approximate equations are so complicated that they as yet have been only partially solved.

If, on the other hand, we were able to grab hold of the sliding clock and move with it at, say, three-quarters the speed of light, the equations of special relativity can be used to show that stationary observers would see our moving clock ticking at just about two-thirds the rate of their own.

For instance, the equations of special relativity show that if an object is moving at about 98 percent of light speed, then a stationary observer will view it as being 80 percent shorter than if it were at rest.

In words, these equations state that the gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them.

Newton accepted the existence of gravity and went on to develop equations that accurately describe its effects, but he never offered any insight into how it actually works.

For this reason, Einstein revisited his equations and modified them by introducing something known as a cosmological constant, an additional term that allowed him to avoid this prediction and once again bask in the comfort of a static universe.

In a now-famous story in the annals of science, Einstein then returned to the original form of his equations, citing his temporary modification of them as the biggest blunder of his life.

Everyone agrees on how to use the equations of quantum theory to make accurate predictions.

Well-formulated physical problems elicit nonsensical answers when the equations of both these theories are commingled.

Calculations that merge the equations of general relativity and those of quantum mechanics typically yield one and the same ridiculous answer: infinity.

The equations of general relativity cannot handle the roiling frenzy of quantum foam.

In theoretical physics research, one is frequently confronted with equations that are just too hard to understand or to analyze.