Special Relativity

Contents:• The End of Physics• Michelson Morley• Postulates of Special Relativity• Time Dilation

The End Of Physics

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1900 +/- 5The End of physicsBlack Body Radiation -> Quantum mechanicsVelocity of light With Respect to etherMaxwell’s Equations…

But what does light move through?

Ether

oo

c

1

Michelson Morley

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Path parallel to ether should take a bit longerTried it in JanuaryTried it in June…The Earth is at rest in etherOr the path parallel to the ether shrinksOr, there is no ether

So what does light travel through ?

Einstein’s Gedanken

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If we caught up to an EM wave what would we see:

                               

B and E fields with nothing to create themThis is impossibleTherefore we cannot catch up to light waves…

Postulates of Special Relativity

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First Postulate:• The laws of physics are the same in all inertial frames of reference

• There is no experiment you can do to ascertain whether you are moving.

• (i.e. all motion is relative)Second Postulate:• The speed of light is the same no matter

what speed the source or observer is going• (i.e the speed of light is a law of physics)

(examples of this with cars/observers/galilean vs relativistic transforms)

                               

The speed of the photons was independent of the speed of the pion

Time Dilation

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How the clock worksWhat proper time is

                               

Time Dilation

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Earth observer sees light traveling at speed of lightTime is longer (i.e the clock runs slower)DeriveMoving clocks run slowerExamples: (time elapsed, velocity, factor of c)

                               

Factor Vs V

012345678

0 0.5 1 1.5

Speed in c

Fa

cto

r

You can safely ignore relativistic effects to about .2 c

Lorentz factor:

?, ?, 10.2 s, 11.5 s

Example 1: If you drive by the school at 40.0 m/s, how long do we see your watch take to register 10.0 seconds? What about 40,000. m/s? .200 c? .500 c?

.55c

Example 2: If we see your watch take 12 seconds to register 10. seconds, how fast are you going?(Show solution for c)

Length Contraction

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Moving objects shrink in the direction of motion

lo l

2

2

1c

vLL o

This reconciles the frames of reference

Mass Dilation

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Moving objects gain mass

2

2

1c

v

mm o

(The gained mass is energy mass as in E = mc2)

Electron at restmo = 0.511 MeV

Electron with 1.0 MeV Ke:m = 1.00 MeV + 0.511 MeV=1.511 MeV

e e

4.0 m

Example 3: A car that is 5.0 m long is going .60 c past us. How long is the car in our frame of reference?

0.592 c

Example 4: What is the speed of an electron if it has a mass of 0.634 MeV. (Its rest mass is 0.511 MeV) (What is its kinetic energy? through what potential was it accelerated?)

Whiteboards: Time Dilation, Length Contraction, Mass Dilation

1 | 2 | 3 | 4

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W19 s

Moe and Joe have clocks that tick every 10.00 seconds. Joe is flying by at .85 c. What time does Moe see Joe’s clock take to tick? (trick with c)

W.75 c or 2.24 x 108 m/s

Two stopwatches, one sitting still, one moving in a very large circle. The clock at rest ticks every .800 s, the moving one ticks every 1.200 s. What speed is the moving watch going?

Show the general solution

W7.9 s

Moe and Joe both have identical watches. Joe is moving with respect to Moe at .85c. If 15 s elapse on Moe’s clock, how much time has elapsed on Joe’s clock?

answer

W.53c, 1.6 x 108 m/s, 415 m

Muons have a mean life of 2.2 x 10-6 s at rest. What speed are they traveling if they they have an average lifetime of 2.6 x 10-6 s?How far would they travel before decaying on the average?

answer

W0.941 c

An electron has a rest mass of 0.511 MeV, and a moving mass of 1.511 MeV. What is its speed ?

answer

W0.46 c

What speed does a 45 foot long bus need to go to fit exactly into a tunnel that is 40. feet long?

answer

Paradoxes

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Joe stays on earthMoe goes to planet x that is 30 Ly away at .99 cComes backHow old Moe is/Joe isDoes this violate Special relativity?Inertial means no accelerationWhat they see

                               

Planet X

Paradoxes

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It’s all relativeMoe sees our clocks slow down tooPostulates only apply to inertial frames of reference

                               

Planet X

Planet X