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RELATIVISTIC MASS AND ENERGY

JOKES OF THE DAY:

CLIP OF A DAY:

• http://www.youtube.com/watch?v=lR4tJr7sMPM&list=PLDA75FE6344666889

UNIVERSAL SPEED LIMIT

• When considering gamma, we know that we must be dealing with real numbers so the value under the root must be positive• Therefore speed (v) cannot be

greater than or equal to the speed of light (c) or the denominator becomes imaginary or zero• This speed limit only applies

to objects with mass (therefore the massless photon can travel at the speed of light)

CERENKOV’S GLOW

• While it is impossible for anything to travel faster than light in a vacuum, it is possible for an object to travel faster than light in a medium

• This is what leads to Cerenkov’s Radiation which is seen in the cooling pools of a nuclear power plant

• The particles in the water are travelling faster than the speed of light in the water and the glow is thus produced

MASS AND ENERGY

• While the gamma term leads to the mathematical understanding that the speed of light is the limit for massive objects, it does not explain why!• The reason is found in Newton’s Second Law and

Einstein’s Special Theory of Relativity• Einstein found that in addition to time dilation

and length contraction, mass is also affected by relativistic effects

RELATIVISTIC MASS

• As a result, the mass increases as an object’s speed increases• m = relativistic

mass• m0 = rest mass

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EXAMPLE:

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• Page 825• 2, 3,4

• Page 830• 7-9

WHERE IS THE ENERGY?

• As an object approaches the speed of light, more energy must be added for each change in speed• Since we know that this

energy must go somewhere, Einstein introduced the following equation:• This means that mass

and energy are the same thing and can be used interchangeably!

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RELATIVISTIC AND CLASSICAL KINETIC ENERGY

o We know that at relativistic speeds, kinetic energy is equal to:o Ek = mc2 – m0c2

o But at classical speeds, kinetic energy is equal to:o Ek = ½mv2

o Let’s prove this does not violate Einstein’s first postulate!

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RELATIVISTIC AND CLASSICAL KINETIC ENERGY

oThis means that both the classical equation we have been using and Einstein’s relativistic equation give the same results at classical speeds

oTherefore, Einstein’s first postulate is upheld

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TOTAL ENERGY:

• The total energy (relativistic mass times the square of the speed of light) of an object is the sum of the rest energy (rest mass times the square of the speed of light) and its kinetic energy.

EXAMPLE:

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THE OTHER ONE: GENERAL RELATIVITY

• In the Special Theory of Relativity, only non-accelerated (inertial) frames of references can be treated• In the General Theory of Relativity, acceleration is

allowed which allows it to be applied to non-inertial frames of reference

SPACETIME

• General relativity often describes spacetime as a flexible sheet

• If the sheet has no masses placed on it, it would be a plane

• However, when masses are placed on the surfact, spacetime is warped which changes the behaviour of objects travelling in spacetime

LIGHT IN SPACETIME

• One of the effects of the warping of spacetime is that light will be bent by gravity• Classically this does

not make sense as light is massless and should not be affected by gravity

GRAVITATIONAL LENSING

• Due to general relativity, the effect of gravitational lensing can be explained• If light from a star travels

close to another star, it will be bent due to the curvature of spacetime and appear in the “wrong” part of the sky

CLIP: SPACETIME

• http://www.youtube.com/watch?v=Cyuc-ncs11k

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• Page 833• 10, 11, 13-16