What is the content of Einstein's theory of relativity?

There may be some duplicate content, but it is by no means plagiarized from the one above.

The theory of relativity is the basic theory about space-time and gravity. It was mainly founded by Einstein and is divided into special relativity (special relativity) and general relativity (general relativity). The basic assumptions of the theory of relativity are the principle of constant speed of light, the principle of relativity and the principle of equivalence. Relativity and quantum mechanics are the two basic pillars of modern physics. Classical mechanics, which lays the foundation for classical physics, is not suitable for high-speed moving objects and objects under microscopic conditions. Relativity solves the problem of high-speed motion; quantum mechanics solves the problem under microscopic subatomic conditions. The theory of relativity has greatly changed mankind's "common sense" concepts about the universe and nature, and proposed brand-new concepts such as "simultaneous relativity", "four-dimensional space-time" and "curved space".

General Relativity

An extremely incredible world

Original translation by Gu Rui: Slaven

Explanation of the basic concepts of general relativity:

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Before we begin reading this short article and understanding the key features of general relativity, we must assume one thing: special relativity is correct. This means that the general theory of relativity is based on the special theory of relativity. If the latter proves wrong, the entire theoretical edifice will collapse.

In order to understand general relativity, we must understand how mass is defined in classical mechanics.

Two different expressions of quality:

First, let’s think about what quality represents in our daily lives. "It's weight"? In fact, we think of mass as something that can be weighed, as we measure it by placing the object whose mass we want to measure on a scale. What properties of quality are we taking advantage of in doing this? It is the fact that the earth and the object being measured are attracted to each other. This mass is called "gravitational mass". We call it "gravitational" because it determines the motion of all the stars and stars in the universe: the gravitational mass between the Earth and the Sun drives the Earth in a nearly circular motion around the latter.

Now, try pushing your car on a flat surface. You can't deny that your car strongly resists the acceleration you want to give it. This is because your car has a very large mass. Moving light objects is easier than moving heavy objects. Mass can also be defined another way: "It resists acceleration." This mass is called "inertial mass".

So we come to this conclusion: we can measure quality in two ways. Either we weigh it (very simple), or we measure its resistance to acceleration (using Newton's laws).

Many experiments have been done to measure the inertial mass and gravitational mass of the same object. All experimental results lead to the same conclusion: inertial mass is equal to gravitational mass.

Newton himself realized that this equality of masses was caused by something that his theory could not explain. But he dismissed the result as a simple coincidence. Einstein, on the contrary, discovered that in this equivalence there existed a passage that superseded Newton's theory.

Everyday experience confirms this equality: two objects (one light, one heavy) will "fall" at the same speed. However, heavier objects experience a greater gravitational pull from the Earth than lighter objects. So why doesn't it "fall" faster? Because it is more resistant to acceleration. The conclusion is that the acceleration of an object in a gravitational field is independent of its mass. Galileo was the first to notice this phenomenon. It is important that you understand that all objects in a gravitational field "fall at the same speed" are the result (in classical mechanics) of the equality of inertial mass and gravitational mass.

Now let’s focus on the expression “whereabouts”. Objects "fall" because the Earth's gravitational mass creates the Earth's gravitational field. Two objects have the same speed in all the same gravitational fields. Whether lunar or solar, they are accelerated at the same rate. This means that their speeds increase by the same amount per second. (Acceleration is the increase in velocity per second)

The equality of gravitational mass and inertial mass is the third assumption in Einstein's argument

Einstein has been looking for "gravity" Mass is equal to inertial mass" explanation. To this end, he made a third assumption known as the "principle of equivalence." It states that if an inertial frame is uniformly accelerated relative to a Galilean frame, then we can consider it (the inertial frame) to be stationary by introducing a uniform gravitational field relative to it.

Let us examine an inertial frame K’, which has a uniformly accelerated motion relative to the Galilean frame. There are many objects around K and K’. This object is stationary relative to K. Therefore these objects have the same accelerated motion relative to K'. This acceleration is the same for all objects and is opposite to the acceleration of K’ relative to K. We said that the magnitude of the acceleration of all objects in a gravitational field is the same, so the effect is equivalent to K’ being stationary and there is a uniform gravitational field.

So if we establish the principle of equality, the equal mass of two objects is just a simple corollary of it. This is why (quality) equivalence is an important argument in favor of the equivalence principle.

By assuming that K’ is stationary and the gravitational field exists, we understand K’ as a Galilean system in which we can study the laws of mechanics. Einstein thus established his fourth principle.

Einstein’s second hypothesis

Original translation by Gu Rui: Slaven

Time and space

We come to a self-contradiction conclusion. The "common sense relativity" we use to convert speed from one frame of reference to another conflicts with Einstein's assumption that "light travels at the same speed in all inertial frames." Einstein's hypothesis is correct only in two cases: either distance is different with respect to the two inertial frames, or time is different with respect to the two inertial frames.

Actually, both are true. The first effect is called "length contraction" and the second effect is called "time dilation."

Length contraction:

Length contraction is sometimes called Lorentz or FritzGerald contraction. Before Einstein, Lorenz and Fritz Grad worked out mathematical formulas to describe contraction. But Einstein realized its significance and built it into his complete theory of relativity. This principle is:

The length of a moving object in the reference frame is shorter than its length at rest

The following graphic illustration is used to facilitate understanding:

Upper graphic It is the ruler that is at rest in the frame of reference. The length of a stationary object in its frame of reference is called its "correct length". The correct length of a yard stick is one yard. The ruler is in motion in the lower image. To put it in longer, more precise terms: relative to a frame of reference, we find it (the ruler) moving. The principle of length contraction states that a ruler moving in this frame of reference should be shorter.

This contraction is not an illusion. As the ruler passes us, any precise test will show that its length is shorter than when it is at rest. The ruler doesn't look shorter, it really is! However, it only contracts in the direction of its motion. In the lower image the ruler moves horizontally, so it becomes shorter horizontally. You may have noticed that the vertical length is the same in both images.

Time dilation:

The so-called time dilation effect is very similar to length contraction. It works like this:

Two events in a certain frame of reference , the time interval when they occur in different places is always longer than the time interval when the same two events occur in the same place.

This is more difficult to understand, so we still use illustrations to illustrate:

Both the two alarm clocks in the picture can be used to measure the time it takes for the first alarm clock to move from point A to point B. time. However, the results given by the two alarm clocks are not the same. We can think of it this way: the two events we mentioned are "the alarm clock leaves point A" and "the alarm clock reaches point B". In our frame of reference, these two events occur at different locations (A and B). However, let's look at this from the frame of reference of the alarm clock itself in the upper half of the picture. From this perspective, the alarm clock in the upper half of the picture is stationary (all objects are stationary relative to themselves), while the lines marking points A and B move from right to left. Therefore, "leaving point A" and "reaching point B" both happen at the same place! (The time measured by the alarm clock in the upper half of the picture is called the "correct time") According to the previously mentioned point of view, the time recorded by the alarm clock in the lower half of the picture will be longer than the time recorded by the alarm clock in the upper half of the picture from A to B. .

A simpler but less precise statement of this principle is: A moving clock runs slower than a stationary clock. The most famous hypothesis about time dilation is often called the twins paradox. Suppose there are twins Harry and Mary. Mary boards a spaceship that flies away from the earth at high speed (for the effect to be obvious, the spacecraft must move at close to the speed of light), and returns very quickly. We can think of two bodies as a clock measuring the passage of time in terms of age. Because Mary moves so quickly, her "clock" runs slower than Harry's "clock." The result is that when Mary returns to Earth, she will be younger than Harry. How young depends on how fast and how far she travels.

Time dilation is not a crazy idea, it has been proven experimentally. The best example involves subatomic particles called mesons. How long it takes for a meson to decay has been measured very precisely. Regardless, it has been observed that a meson moving at nearly the speed of light has a longer lifespan than a stationary or slow-moving meson. This is the relativistic effect. From the perspective of the moving meson itself, it does not exist longer. This is because it is stationary from its own perspective; it is only when we look at the meson relative to the laboratory that we find that its lifespan has been "extended" or "shortened." ?

One sentence should be added: There have been many, many experiments that have confirmed this inference of the theory of relativity. Other corollaries (of relativity) we will be able to verify later. My point is that although we call relativity a "theory", don't make the mistake of thinking that relativity is yet to be proven. It is (actually) very complete.

Einstein’s First Postulate

The entire special theory of relativity is mainly based on Einstein’s two assumptions about the nature of the universe.

The first one can be stated like this:

The physical laws in all inertial reference systems are the same

The only slightly difficult thing here is the so-called "Inertial reference frame". A few examples will make this clear:

Suppose you are in an airplane flying level at a constant speed of several hundred miles per hour without any bumps. A man comes across the plane and says, "Can you throw your bag of peanuts over here?" You grab the bag of peanuts, but suddenly stop and think, "I'm sitting on a plane that's spinning at a few minutes per hour." On a plane flying at a speed of 100 miles, how hard should I throw this bag of peanuts before it reaches that person? ”

No, you don’t have to think about this problem at all, you just need to use it with Just throw with the same motion (and force) you would at the airport. The peanut's motion is the same as when the airplane is on the ground.

You see, if the plane is flying in a straight line at a constant speed, the laws of nature that govern the motion of objects are the same as if the plane is stationary. We call the interior of the aircraft an inertial reference frame. (The word "inertia" originally refers to Newton's first law of motion. Inertia is the inherent property of every object to remain stationary or move in a straight line at a uniform speed when there is no external force. The inertial reference system is a series of reference systems in which this law holds true. < /p>

Another example. Let's consider the earth itself. The circumference of the earth is about 40,000 kilometers. Since the earth rotates once every 24 hours, a point on the earth's equator is actually moving at a speed of 1600 kilometers per hour. Moving east. But I bet Steve Young never worried about that when he threw his touchdown pass to Jerry Rice. That's because the ground moves in an approximately straight line. Movement, the surface of the earth is almost an inertial reference frame, so its movement has little effect on other objects, and the movement of all objects behaves as if the earth is at rest.

In fact, unless we are aware of it. Unless the earth is rotating, otherwise some phenomena would be very confusing (that is, the earth is not moving in a straight line, but moving in a large circle around the earth's axis)

For example: many weather (changes). All aspects seem completely contrary to the laws of physics, unless we consider this (the Earth is rotating). Another example is that long-range projectiles do not move in a straight line as they do in the inertial frame, but slightly to the right (in the northern hemisphere) or to the left. (In the Southern Hemisphere). (Outdoor golfers, this doesn't explain your misses.) For most research purposes, we can think of the Earth as an inertial frame of reference. But occasionally, it's non-inertial. The characterization will be very serious (I want to put it more strictly)

Here is a minimum: Einstein's first postulate holds that all the laws of physics in such systems remain unchanged. The examples of airplanes and the earth's surface are just to explain to you that this is a reasonable assumption that people can make without even thinking about it.

Einstein's second hypothesis?

In the middle of the 19th century, people's understanding of electricity and magnetism made a revolutionary leap, represented by the achievements of James Maxwell. Not relevant until Oersted and Ampere showed that electricity produces magnetism; Faraday and Henry showed that magnetism produces electricity. Now we know that electricity and magnetism are so closely related that when When physicists list the forces of nature, they often think of electricity and magnetism as one and the same thing.

Maxwell's achievement was to condense all the then-known knowledge of electromagnetism into four equations:

(If you haven’t taken the three or four semesters of calculus necessary to understand these equations, sit down and look at them for a few minutes and appreciate the beauty.)

Maxwell’s equations are important for Our significance is that, in addition to describing all that is known about electromagnetism, it also reveals some things that people do not know. For example: the electromagnetic fields that make up these equations can propagate through space in the form of vibrating waves. When Maxwell calculated the speed of these waves, he found that they were all equal to the speed of light. This is no coincidence, Maxwell (equations) revealed that light is an electromagnetic wave.

An important thing we should remember is that the speed of light is derived directly from Maxwell's equations, which describe all electromagnetic fields.

Now we return to Einstein.

Einstein's first assumption was that the laws of physics are the same in all inertial reference frames. His second hypothesis was to simply extend this principle to the laws of electricity and magnetism. That is, if Maxwell's hypothesis is a law of nature, then it (and its corollaries) must hold in all inertial frames. One of these corollaries is Einstein's second hypothesis: The speed of light is the same in all inertial systems

Einstein's first hypothesis seems very reasonable, and his second hypothesis continues the first The plausibility of the assumptions. But why doesn't it seem reasonable?

Experiment on the train

To illustrate the rationality of Einstein’s second hypothesis, let us take a look at the following picture on the train.

The train is running at a speed of 100,000,000 meters per second. Dave is standing on the train and Nolan is standing on the ground next to the railway. Dave "fires" photons with the flashlight in his hand.

The photon moves at a speed of 300,000,000 meters per second relative to Dave, and Dave moves at a speed of 100,000,000 meters per second relative to Nolan. So we get that the speed of the photon relative to Nolan is 400,000,000 meters/second.

The problem arises: This is inconsistent with Einstein’s second hypothesis! Einstein said that the speed of light relative to Nolan's frame of reference must be exactly the same as the speed of light in Dave's frame of reference, which is 300,000,000 meters/second. So which one is wrong, our "common sense feeling" or Einstein's hypothesis?

Well, the experiments (results) of many scientists support Einstein’s hypothesis, so we also assume that Einstein is right and help everyone find out what is wrong with the common sense theory of relativity.

Remember? The decision to add up the speeds came very easily. One second later, the photon has moved to 300,000,000 meters in front of Dave, and Dave has moved to 100,000,000 meters in front of Nolan. There are only two possibilities if the distance is not 400,000,000 meters:

1. The distance of 300,000,000 meters for Dave is not also 300,000,000 meters for Nolan

2. A second to Dave is different from a second to Nolan

As strange as it sounds, both are actually correct.

Einstein’s Second Postulate

Time and Space

We come to a contradictory conclusion. The "common sense relativity" we use to convert speed from one frame of reference to another conflicts with Einstein's assumption that "light travels at the same speed in all inertial frames." Einstein's hypothesis is correct only in two cases: either distance is different with respect to the two inertial frames, or time is different with respect to the two inertial frames.

Actually, both are true. The first effect is called "length contraction" and the second effect is called "time dilation."

Length contraction:

Length contraction is sometimes called Lorentz or FritzGerald contraction. Before Einstein, Lorenz and Fritz Grad worked out mathematical formulas to describe contraction. But Einstein realized its significance and built it into his complete theory of relativity. This principle is: the length of a moving object in the reference system is shorter than its length at rest. The following graphic illustration is used to facilitate understanding:

The upper graphic shows the ruler at rest in the reference system. The length of a stationary object in its frame of reference is called its "correct length". The correct length of a yard stick is one yard. The ruler is in motion in the lower image. To put it in longer and more precise terms: relative to a frame of reference, we find it (the ruler) moving. The principle of length contraction states that a ruler moving in this frame of reference should be shorter.

This contraction is not an illusion. As the ruler passes us, any precise test will show that its length is shorter than when it is at rest. The ruler doesn't look shorter, it really is! However, it only contracts in the direction of its motion. In the lower image the ruler moves horizontally, so it becomes shorter horizontally. You may have noticed that the vertical length is the same in both images.

Time dilation:

The so-called time dilation effect is very similar to length contraction. It works like this:

Two events in a certain frame of reference , the time interval when they occur in different places is always longer than the time interval when the same two events occur in the same place.

This is more difficult to understand, so we still use illustrations to illustrate:

Both the two alarm clocks in the picture can be used to measure the time it takes for the first alarm clock to move from point A to point B. time. However, the results given by the two alarm clocks are not the same. We can think of it this way: the two events we mentioned are "the alarm clock leaves point A" and "the alarm clock reaches point B". In our frame of reference, these two events occur at different locations (A and B). However, let's look at this from the frame of reference of the alarm clock itself in the upper half of the picture. From this perspective, the alarm clock in the upper half of the picture is stationary (all objects are stationary relative to themselves), while the lines marking points A and B move from right to left. Therefore, "leaving point A" and "reaching point B" both happen at the same place! (The time measured by the alarm clock in the upper half of the picture is called the "correct time") According to the previously mentioned point of view, the time recorded by the alarm clock in the lower half of the picture will be longer than the time recorded by the alarm clock in the upper half of the picture from A to B. .

A simpler but less precise statement of this principle is: A moving clock runs slower than a stationary clock. The most famous hypothesis about time dilation is often called the twins paradox. Suppose there are twins Harry and Mary. Mary boards a spaceship that flies away from the earth at high speed (for the effect to be obvious, the spacecraft must move at close to the speed of light), and returns very quickly.

We can think of two bodies as a clock measuring the passage of time in terms of age. Because Mary moves so quickly, her "clock" runs slower than Harry's "clock." The result is that when Mary returns to Earth, she will be younger than Harry. How young depends on how fast and how far she travels.

Time dilation is not a crazy idea, it has been proven experimentally. The best example involves a subatomic particle called a meson. How long it takes for a meson to decay has been measured very precisely. Regardless, it has been observed that a meson moving at nearly the speed of light has a longer lifespan than a stationary or slow-moving meson. This is the relativistic effect. From the perspective of the moving meson itself, it does not exist longer. This is because it is stationary from its own perspective; it is only when we look at the meson relative to the laboratory that we find that its lifespan has been "extended" or "shortened." ?

One sentence should be added: There have been many, many experiments that have confirmed this inference of the theory of relativity. Other corollaries (of relativity) we will be able to verify later. My point is that although we call relativity a "theory", don't make the mistake of thinking that relativity is yet to be proven. It is (actually) very complete.

Gamma parameter (γ)

Now you may be wondering: why have you never noticed length contraction and time dilation effects in your daily life? For example, based on what I just said, if you drive from Oklahoma City to Kansas City and back, then when you get home, you should reset your watch. Because when you're driving, your watch should run slower than a watch that's at rest at home. If the time is 3 o'clock when you get home, then your watch at home should show a later time. Why have you never noticed this happening?

The answer is: Whether this effect is significant or not depends on the speed of your movement. And you are moving very slowly (you may think your car is going very fast, but this is extremely slow according to the theory of relativity). The effects of length contraction and time dilation are only noticeable when you move close to the speed of light. The speed of light is approximately 186,300 miles/second (or 300 million meters/second). In mathematics, relativistic effects are usually described by a coefficient, which physicists usually refer to as the Greek letter γ. This coefficient depends on the speed of the object's movement. For example, if a meter stick (correct length is 1 meter) flies quickly in front of us, its length relative to our frame of reference is 1/γ meter. If it takes 3 seconds for a clock to move from point A to point B, then relative to our handicap, it is /γ seconds.

To understand why we don't notice relativistic effects in reality, let's look at the formula for γ: The key here is v2/c2 in the denominator. v is the speed of the object we are discussing, and c is the speed of light. Because the speed of any normal-sized object is much less than the speed of light, v/c is very small; when we square it it is even smaller. Therefore, for all objects of normal size in real life, the value of γ is 1. So for ordinary speeds, the length and time we get after multiplication and division have not changed. To illustrate this, here is a table of gamma values ??corresponding to different speeds. (Where) the last column is the length of the meter stick when moving at this speed (i.e. 1/γ meter).

C in the first column still represents the speed of light. .9c is equal to nine-tenths of the speed of light. For reference, here's an example: The Saturn V rocket travels at about 25,000 miles per hour. You see, for any reasonable speed, γ is almost always 1. So there is little variation in length and time. In real life, relativistic effects occur only in science fiction (in which spacecraft are much faster than the Saturn V) and in microphysics (where electrons and protons are often accelerated to velocities very close to the speed of light). This effect is not apparent on a flight from Chicago to Denver.

The Adventures of the Cosmic Law Enforcer

The cosmic law enforcer AD was captured by the evil Dr. EN on Planet A. Dr. EN gave AD a glass of poisonous wine that would occur 13 hours later, and told AD that the antidote was on Planet B, which is 40,000,000,000 kilometers away. After AD learned of this situation, he immediately boarded his interstellar spacecraft with 0.95 times the speed of light and flew to Star B. Then:

Can AD reach Star B and obtain the antidote?

We make the following calculations:

The distance between planets A and B is 40,000,000,000 kilometers. The speed of the spacecraft is 1,025,000,000 kilometers/hour. Dividing these two numbers, we get 39 hours from Planet A to Planet B.

Then AD will definitely die.

Wait a minute! This is only for people standing on Planet A. Since poisons must be metabolized in the body of AD (before they can take effect), we must study this issue from the frame of reference of AD. There are two ways we can do this that will lead to the same conclusion.

1. Imagine a large ruler extending uniformly from planet A to planet B. This ruler is 40,000,000,000 kilometers long. However, from AD's perspective, the ruler flew past him at nearly the speed of light.

We already know that such objects undergo length contraction. In the AD frame of reference, the distance from planet A to planet B shrinks with the parameter γ. At 95% of the speed of light, the value of γ is approximately equal to 3.2. Therefore AD believes that this distance is only 12,500,000,000 kilometers away (40 billion divided by 3.2). We divide this distance by AD's speed and get 12.2 hours. AD will arrive at Planet B nearly 1 hour earlier!

2. An observer on planet A will find that it takes approximately 39 hours for AD to reach B. However, this is a post-expansion time. We know that AD's "clock" slows down by parameter γ (3.2). To calculate time in the AD frame of reference, we divide 39 hours by 3.2 to get 12.2 hours. That leaves about 1 hour for the AD (which is good because it gives the AD 20 minutes to leave the ship and another 20 minutes to find the antidote).

AD will survive and continue the fight against evil.

If you study my description carefully, you will find many specious and very subtle things. When you think about it deeply, typically you'll end up asking the question: "Wait a minute, in AD's frame of reference, EN's clock runs slower, so in AD's frame of reference, space travel should cost Longer, not shorter...

If you are interested or confused about this issue, you should probably read the following article "The Adventures of the Space Law Enforcer - Subtle Time". Or you can take my word for it that "if you figure out all the cause and effect, then all (these) are correct" and skip to the Mass and Energy chapter

Cosmic Enforcer. The Adventures of Subtle Time

Okay, that's what we just saw. We've discovered time dilation in AD relative to the EN frame of reference. In the EN frame of reference, AD is in motion. , so AD's clock runs slower. As a result, EN's clock runs 39 hours during this flight, and AD's clock runs 12 hours. This often leads people to the following question:

Relatively. In AD's system, EN is moving, so EN's clock should run slower. So when AD reaches planet B, who is right?

Good question. When you ask this question, I know you are already entering the situation. Before I start to explain, I must state that in the situation I described, everything is correct. AD can get the antidote in time. Now let's explain this paradox. This is related to a corollary of "simultaneity" that I haven't mentioned yet: two events in the same frame of reference occur at the same time (but in different places). events do not occur simultaneously with respect to another frame of reference

Let's examine some simultaneous events

First, let's assume that EN and AD leave planet A at the same time. Press the stopwatch at the same time. According to EN's watch, the trip to Planet B will take 39 hours. In other words, EN's watch reads 39 hours when AD reaches Planet B. Because of time dilation, AD's watch reads 12.2 at the same time. hours. That is, the following three things happened at the same time:

1. EN’s meter read 39

2. AD arrived at Planet B

3. AD's meter reads 12.2

These events occur simultaneously in EN's frame of reference.

Now in AD's frame of reference, the above three events cannot occur simultaneously. Furthermore, since we know that EN's meter must slow down by the parameter γ (where γ is approximately 3.2), we can calculate that when AD's meter reads 12.2 hours, EN's meter reads 12.2/3.2=3.8 hours. Therefore, in AD's system, these things happen at the same time:

1. AD reaches planet B

2. AD's clock reads 1.2

The first two items are the same in both systems because they occur in the same place - Planet B. Two events occurring in the same place either occur at the same time or they do not occur at the same time, and here the frame of reference does not play a role.

It may be helpful to look at this issue from another perspective. The events you are interested in are from AD leaving planet A to AD arriving at planet B. An important note: AD is present in both events. That is, in AD's frame of reference, these two events occurred at the same place. Thus, events in the AD frame of reference are called "correct time" and times in all other frames will be longer than in this frame (see the principle of time dilation). Anyway, if you're confused about time dilation in AD adventures, hopefully this clears things up a bit. If you weren't confused before, I hope you aren't confused now either.

Mass and Energy

In addition to length contraction and time dilation, the theory of relativity has many corollaries. The most famous and important of these is about energy.

Energy has many states. Any moving object has what physicists call "kinetic energy" due to its own motion. The amount of kinetic energy is related to the speed and mass of the object.

("Mass" is very similar to "Weight", but not exactly the same) An object placed on a shelf has "gravitational potential energy". Because if the shelf is removed, it has the potential to gain kinetic energy (due to gravity).

Heat is also a form of energy that is ultimately attributed to the kinetic energy of the atoms and molecules that make up matter, and there are many other forms of energy.

The reason that links the above phenomena to energy, that is, the connection between them, is the law of conservation of energy. This law says that if we add up all the energy in the universe (we can describe energy quantitatively in units like joules or kilowatt hours), the total amount never changes. That is, energies are never created or destroyed, although they can be transformed from one form to another. For example, a car is a device that converts heat energy (in the cylinders of the engine) into kinetic energy (the motion of the car); a light bulb (can) convert electrical energy into light energy (which are again two forms of energy).

In his theory of relativity, Einstein discovered another form of energy, sometimes called "rest energy." I have pointed out that a moving object possesses energy by virtue of its motion. But Einstein discovered that the same object also has energy when it is stationary. The amount of static energy in an object depends on its mass and is given by the formula E = mc2.