**RELATIVITY**

**Time Dilation**

Relativity of Simultaneity

**Relativist Momentum**

**Length Contraction**

**Principles of Relativity & the Ether Method**

A Brief History

Albert Einstein (1879-1955)

proposed by

Theory of Relativity

Physicists observed that light emitted from some "black body" metals gave up electrons under certain light instead of only absorbing all incident rays thus giving rise to the black body phenomenon.

No full evidence that electomagnetic waves need a medium in order to travel.

Controversy

Through the Theory of Relativity

time dilation is commonly referred to as

the difference of

elasped time

between two events as a result of the observers position either moving relative to the another or from different gravitational standpoints

for example

Inertial Frame of Reference

A frame of reference (co-ordinate system) in which the law of inertia holds.

Due to the laws of nature, time bends changing both the gravity and velocity of space differing from the gravity and velocity recognized on earth. This bend in time is seen when the astronauts have arrived back from their mission and have aged less than the people who remained on earth.

theory states

Space and time are relative concepts rather than absolute.

Through Maxwell's discoveries, physicists could assume that light is a combination of oscillating electric and magnetic fields.

This is represented by the formula:

P= relativistic momentum

M= rest mass

V= speed/velocity

C= speed of light

Rest Mass: mass of an object measured at rest (a.k.a. proper mass)

- the rest mass of an object NEVER changes!

The Principle of Relativity

Relativistic Mass: mass of an object in motion

- always greater than rest mass of an object (equal to rest mass times factor of v)

States that the laws of physics are the same in all inertial frames.

The Ether Method

Relativistic Momentum: is the momentum of objects moving at speeds close to but never reaching the speed of light

The idea of light being a combination of oscillating electric and magnetic fields works under the assumption that electromagnetic waves need a medium in order to travel.

The Universal Speed Limit

Physicists assumed that there must be some sort of medium present in space in order for light to travel

What we know:

-c will always be greater than v

-√ (1 – v2 / c2) is always positive

-no object can reach the speed of light

√ (1 – v2 / c2) > 0

v2 / c2 < 1

c2 > v2

c > v

Two physicists named Michelson and Morley had experimented with light and concluded that the ether medium did not exist.

Lets Apply the Formula!

In Experiments to study the properties of subatomic particles, physicists routinely accelerate electrons to speeds close to the speed of light. An electron has a mass of 9.11 x 10^-31 kg and moves with speed of 0.99c.

Calculate the electron's relativistic momentum.

Simultaneity is the occurrence of two or more events at the same time.

Einstein's total energy equation for special relativity:

Simultaneity is absolute and it depends on the measurement of time.

E = total energy

M = rest mass

C = speed of light

If two observers are in different frames of reference their measurement of time relative to the event can be different.

Rest Energy: the amount of energy an object has at rest (it is a property of matter)

V = 0

M = rest mass

C = speed of light

Relativistic Kinetic Energy: the energy of an object in excess of its rest energy

-It is equal to total energy minus rest energy

Every observation is correct in respects to their frames of reference.

Relativity of simultaneity works together with time dilation and length contraction to ensure that no reference frame is preferred.

The length of objects moving at relativistic speeds undergoes a contraction along the dimension of motion.

Applications of Conservation of Mass-Energy

-Nuclear Fusion

-Nuclear Weapons

-Nuclear Powers

-Nuclar reactions

This equation is known as the conservation of mass-energy. It is the principle that rest mass and energy are equivalent!

The average home in Canada uses 3.6 x 10^10 J of energy per day. Imagine that a cabbage with a rest mass of 0.75kg could be completely converted to another form of energy.

Calculate how much energy is released by the cabbage.

Mass-Energy Equivalence

An observer at rest (relative to the moving object) would observe the moving object to be shorter in length

Lm = length observed by an observer in relative motion with respect to the object

Ls = length of object by an observer at rest relative to the object

V = velocity between observer and moving object

C = speed of light

The object is actually contracted in length as seen from the stationary reference frame.

-The first being in agreeance with Newton’s law, also requires the laws of physics to be the same in all inertial frames of reference.

-The second postulate law states that the speed of light is not oblivious, and is the same in every reference frame

Newton's postulate theory

Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. The separation of the mirrors is L and the clock ticks once each time the light pulse hits a given mirror.

So to show time dilation between 2 observers, we can theoretically say if a railway car was moving at high speed on a railway track in a straight line, given a straight motion, how does this motion affect the operation of the light clock if the clock moves with constant horizontal speed (v) relative to a clock at rest?

Velocity and gravitational time dilation combined-effect tests

The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the travel. But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel

picture of Halefeand Kaeting

• The Global Positioning System can be considered a continuously operating experiment in both special and general relativity