Материал готовится,

пожалуйста, возвращайтесь позднее

пожалуйста, возвращайтесь позднее

E n e rg y

The aim of this chapter is to present the most famous

equation of physics: E = mc2. This equation underlies nu-

clear power and the atom bomb. It says that if you convert

one pound of matter entirely into energy, you could keep

the lights on in a million American households for a year.

E = mc2 also underlies much of string theory. In particular,

as we’ll discuss in chapter 4, the mass of a vibrating string

receives contributions from its vibrational energy.

What’s strange about the equation E = mc2 is that it relates

things you usually don’t think of as related. E is for energy,

like the kilowatt-hours you pay your electric company for

each month; m is for mass, like a pound of flour; c is for the

speed of light, which is 299,792,458 meters per second, or

(approximately) 186,282 miles per second. So the first task

is to understand what physicists call “dimensionful quan-

tities,” like length, mass, time, and speed. Then we’ll get

back to E = mc2 itself. Along the way, I’ll introduce metric

units, like meters and kilograms; scientific notation for big12

numbers; and a bit of nuclear physics. Although it’s not nec-

essary to understand nuclear physics in order to grasp string

theory, it provides a good context for discussing E = mc2.

And in chapter 8, I will come back and explain efforts to

use string theory to better understand aspects of modern

nuclear physics.

Length, mass, time, and speed

Length is the easiest of all dimensionful quantities. It’s what

you measure with a ruler. Physicists generally insist on using

the metric system, so I’ll start doing that now. A meter is

about 39.37 inches. A kilometer is 1000 meters, which is

about 0.6214 miles.

Time is regarded as an additional dimension by physicists.

We perceive four dimensions total: three of space and one

of time. Time is different from space. You can move any di-

rection you want in space, but you can’t move backward in

time. In fact, you can’t really “move” in time at all. Seconds

tick by no matter what you do. At least, that’s our everyday

experience. But it’s actually not that simple. If you run in a

circle really fast while a friend stands still, time as you expe-

rience it will go by less quickly. If you and your friend both

wear stopwatches, yours will show less time elapsed than

your friend’s. This effect, called time dilation, is impercepti-

bly small unless the speed with which you run is comparable

to the speed of light.

Mass measures an amount of matter. We’re used to think-

ing of mass as the same as weight, but it’s not. Weight has

to do with gravitational pull. If you’re in outer space, you’re

weightless, but your mass hasn’t changed. Most of the mass

in everyday objects is in protons and neutrons, and a little bit

more is in electrons. Quoting the mass of an everyday object

basically comes down to saying how many nucleons are in it.

A nucleon is either a proton or a neutron. My mass is about 75

kilograms. Rounding up a bit, that’s about 50,000,000,000,

000,000,000,000,000,000 nucleons. It’s hard to keep track of

such big numbers. There are so many digits that you can’t

easily count them up. So people resort to what’s called scien-

tific notation: instead of writing out all the digits like I did

before, you would say that I have about 5 × 1028 nucleons in

me. The 28 means that there are 28 zeroes after the 5. Let’s

practice a bit more.

The aim of this chapter is to present the most famous

equation of physics: E = mc2. This equation underlies nu-

clear power and the atom bomb. It says that if you convert

one pound of matter entirely into energy, you could keep

the lights on in a million American households for a year.

E = mc2 also underlies much of string theory. In particular,

as we’ll discuss in chapter 4, the mass of a vibrating string

receives contributions from its vibrational energy.

What’s strange about the equation E = mc2 is that it relates

things you usually don’t think of as related. E is for energy,

like the kilowatt-hours you pay your electric company for

each month; m is for mass, like a pound of flour; c is for the

speed of light, which is 299,792,458 meters per second, or

(approximately) 186,282 miles per second. So the first task

is to understand what physicists call “dimensionful quan-

tities,” like length, mass, time, and speed. Then we’ll get

back to E = mc2 itself. Along the way, I’ll introduce metric

units, like meters and kilograms; scientific notation for big12

numbers; and a bit of nuclear physics. Although it’s not nec-

essary to understand nuclear physics in order to grasp string

theory, it provides a good context for discussing E = mc2.

And in chapter 8, I will come back and explain efforts to

use string theory to better understand aspects of modern

nuclear physics.

Length, mass, time, and speed

Length is the easiest of all dimensionful quantities. It’s what

you measure with a ruler. Physicists generally insist on using

the metric system, so I’ll start doing that now. A meter is

about 39.37 inches. A kilometer is 1000 meters, which is

about 0.6214 miles.

Time is regarded as an additional dimension by physicists.

We perceive four dimensions total: three of space and one

of time. Time is different from space. You can move any di-

rection you want in space, but you can’t move backward in

time. In fact, you can’t really “move” in time at all. Seconds

tick by no matter what you do. At least, that’s our everyday

experience. But it’s actually not that simple. If you run in a

circle really fast while a friend stands still, time as you expe-

rience it will go by less quickly. If you and your friend both

wear stopwatches, yours will show less time elapsed than

your friend’s. This effect, called time dilation, is impercepti-

bly small unless the speed with which you run is comparable

to the speed of light.

Mass measures an amount of matter. We’re used to think-

ing of mass as the same as weight, but it’s not. Weight has

to do with gravitational pull. If you’re in outer space, you’re

weightless, but your mass hasn’t changed. Most of the mass

in everyday objects is in protons and neutrons, and a little bit

more is in electrons. Quoting the mass of an everyday object

basically comes down to saying how many nucleons are in it.

A nucleon is either a proton or a neutron. My mass is about 75

kilograms. Rounding up a bit, that’s about 50,000,000,000,

000,000,000,000,000,000 nucleons. It’s hard to keep track of

such big numbers. There are so many digits that you can’t

easily count them up. So people resort to what’s called scien-

tific notation: instead of writing out all the digits like I did

before, you would say that I have about 5 × 1028 nucleons in

me. The 28 means that there are 28 zeroes after the 5. Let’s

practice a bit more.

Загрузка...

Выбрать следующее задание

Ты добавил

Выбрать следующее задание

Ты добавил