The Theory of Relativity. What is it? Why do we need

it?• In science, when a good theory becomes inadequate

to describe certain situations, it is replaced by a more general one.

• This means that the new theory describes more situations than the one it replaces, not that the old one is wrong.

• Relativity describes the situations when 1. either bodies move at speed close to that of the light;2. or gravity is very, very strong;3. or both!

– In these cases Newtonian Theory does not work– But when speeds are much slower than light and

gravity is not too strong, Relativity and Newtonian Theory are exactly the same!

Relativity. What is it. Part I?• Imagine the empty space, with just yourself and

another person in it, and nothing else.• You can tell if you move with uniform motion respect

to that person (or viceversa).• But you cannot say if it is you who is moving, or if it is

the other person , or both.• In fact, it is not possible to define absolute uniform

motion relative to the empty space.• But if this is the case, if all observers in uniform

motion are “equivalent” respect to the empty space. then, all laws of nature must look the same to them– FIRST POSTULATE: The Laws of Physics are the same for all

observers, regardless of their motion (as long as not accelerated)

• otherwise it would be possible to tell one observer from another and define absolute motion.

Relativity. What is it. Part II?• In principle the speed of light through space could either be

infinite, or finite. It turns out (from direct observations) that it is finite.

• Then, all observers MUST measure the same speed of light, regardless of their motion.

• Otherwise, one could use one’s speed relative to light to define absolute motion, which violates the First Postulate.

• Thus, once we have established as a Law of Physics that the speed of light is finite, then all observers must measure that light moves at the same speed.

• This means that if we have two observers in uniform motion respect to each other (one going one way, the other the opposite way), each shining a flashlight, and both measure the speed of light emitted from the other’s flashlight, they find the same speed, regardless of how fast they move

• This is against intuition and common sense derived from observations of slow-moving bodies.

Relativity. What is it. Part III?• The implications are far reaching: for example, this

means that no matter how much energy you spend to accelerate yourself to a higher and higher speed, even infinite energy, you always find that light has the same speed relative to you and that is faster than you.

• If you spend infinite amount of energy, and you still cannot reach the speed of light, it is as if your apparent mass is becoming infinite (thus resisting acceleration). But if your apparent mass increases with energy, this means that energy gets transformed into mass (and viceversa).

• This led Einstein to understand that

– E = m x c2

• Mass and energy are different manifestations of the same physical entity, and transform into each other, given the appropriate conditions.

Other predictions of Relativity

• For high-speed motions (v~c)– Time slows down– Length shrinks in the direction of motion

• For example, if one of two identical twins is accelerated to the nearly the speed of light, kept moving fast for several years, and then slowed back down, he will be younger than the other one, because for him time ticked at a slower pace.

• All these predictions are verified every day in labs using particle accelerators to accelerate sub-atomic particles to speed close to the speed of light.

How much energy is contained within mass?

• Consider 1 kg of matter (about 2 lb)• Recall that c= 3x108 m/s

– This means that c2 = 9x1016 (m/s)2

• So, the energy associated with 2 lb of matter is:– E = 1 kg x 9x1016 (m/s)2 = 9x1016 Joule

• This is roughly the energy liberated by the detonation of 20 million tons of TNT (a powerful H-bomb).

• From only 2 lb of mass…• The conversion of matter into energy is

the power of the Universe.

The General Theory of Relativity

• EQUIVALENCE PRINCIPLE:– Observers cannot distinguish locally between

inertial forces due to acceleration and gravitational forces due to the presence of a mass

To the observer in the room both cases “feel” the same

How do we do that?

• How do we get a body of mass M to act as if it was exerting an inertial force (imparting an acceleration) onto another body?

• Bend the space (and time) around it!

Gravity According to General Relativity

• Mass tells space-time how to curve, and the curvature of space-time tells mass (another mass) how to accelerate

Gravity and General Relativity

• The amount of mass and its size (I.e. density) determines the space-time curvature

Two bodies with the same mass (Sun’s one) but compressed to different size (density) bends the space-time the same way at large distances, but very differently at small distances

Gravity and General Relativity

• The amount of mass and its size (I.e. density) determines the space-time curvature

Two bodies with the same mass (eg. Sun’s one), but compressed to different size (density) bends the space-time the same way at large distances, but very differently at small ones

Empirical Confirmation of GR. I

• The precession of Mercury’s orbit is faster than what expected in Newton’s theory, because close to the Sun, gravity is very, very strong. – GR predicts a precession period 43.03 sec faster than

Newton’s theory– Observations measure a period 43.11+/- 0.45 sec

faster than Newton’s theory

Empirical Confirmation of GR• Curved space-time also expected to bend the

travel path of light– Effect expected to be visible close to the Sun,

because there gravity is very, very strong. Except that sun’s glare makes observations impossible. Except during solar eclipses.

Empirical Confirmation of GR• Bending of the light (by background galaxies)

also observed in proximity of quasars (super-massive black holes) or very, very massive clusters of galaxies (hence, capable of producing very, very strong gravity)

Assigned Reading

• Chapter 5, all of it