Q This Means Nothing with Mass Can Go Faster Then ______

Notes – Relativity Chapter 26

The Problem:  ______(everything we have done so far in class) can be tested at high speeds by accelerating electrons or other charged particles through a potential difference.  However, experiments have shown, that no matter the size of the accelerating voltage, ______of the electron (or any other particle with mass) will always be ______

 This means nothing with mass can go faster then ______

 Since Newtonian theory no longer worked at high speed, another theory was needed.

The Solution:  In ______Einstein published his general theory of relativity.  Even though this theory is what Einstein is mostly known for, it is not what won him a Nobel Prize o His Nobel Prize was for his explanation of the Photoelectric Effect

 As long as an object’s speed is ______then the speed of light, Newtonian Physics works wonderfully.  However, if an object’s speed starts to approach the speed of light some interesting things occur.  According to the Special Theory of Relativity, two observers moving relative to each other, will measure ______.

 This makes it necessary to choose a ______. The Inertial Reference Frame is:  Any reference frame in which Newtonian Physics is valid.  Any reference frame in which objects that experience ____ forces, move in ______at a ______.

 We will be working with these types of reference frames.

Example: Two students are playing baseball on a train moving at 100 mi/hr. The pitcher throws the ball at 50 mi/hr. According to a stationary observer, how fast is the ball going?

What if instead of a baseball, it was a light pulse? 8  But remember, ______can go faster then 3.0x10 m/s (including ______itself).  Therefore, there must be a problem with the classical addition law for velocities.  And that is where Einstein’s Special Theory of Relativity comes in.

Relativities Two Postulates 1. The principle of Relativity:

2. The Constancy of the speed of light: The speed of light in a vacuum has the same value (c = 2.997 924 58x108m/s, rounded to 3.0 in this class) in all inertial reference frames, regardless of the velocity of the observer or the velocity of the source emitting the light.

Effects of Relativity  Length contraction -

 Time dilation –

Length Contraction  When viewed by an outside observer, moving objects appear to contract ______.  For everyday speeds, the amount of contraction is too small to be measured.  For relativistic speeds, the contraction is noticeable. o A meter stick whizzing past you on a spaceship moving at 87% the speed of light (0.87c) would appear to be only 0.5 m long.

Calculating the length contraction: L = moving length Ls = stationary length (length at rest) v = velocity of the object c = speed of light

Example: A meter stick flies past you at _____% the speed of light. What is it’s apparent length?

Example: How do people on spaceships view their meter sticks? (a) They are smaller then usual, (b) They are the same, (c) They are larger than life

Example: You are packing for a trip to another star, and on your journey you will be traveling at a speed of 0.99c. Can you sleep in a smaller cabin then usual, because you will be shorter when you lie down? Explain.

Time Dilation  Pretend you are in a spaceship at rest in Ms. Stevens’ class. The clock on the wall reads 12-noon. To say it reads “12 noon” is to say that light reflects from the clock and carries the information “12 noon” to you in the direction of sight.  If you suddenly move your head to the side, the light would miss your eye and continue out into space where another observer might see it. The observer in space would then later say “Oh it is 12 noon on Earth right now.” But from your point of view, it isn’t.  Now suppose your spaceship is moving as fast as the speed of light (just pretend!). You would be keeping up with the signal saying “12 noon.” To you on the spaceship, time at home would appear frozen!  This is in essence, time dilation: ______

Consider a light clock  ______, hits a mirror and bounces back into a detector.  Based on how far it traveled and the speed of light, we could calculate the time Now, put the time clock on a spaceship…  Since the speed of light is the same for everyone, time must be running slow for the astronaut.

Calculating time dilation: t = time ts = time if standing still v = velocity c = speed of light Example: The period of a pendulum is measured to be ______s in the inertial frame of the pendulum. What is the period measured by an observer moving at a speed of 0.95c?

Example: If you were moving in a spaceship at a high speed relative to Earth, would you notice a difference in your pulse rate?

Would you notice a difference in the pulse rate of the people left on Earth?

Does time dilation mean that time really does pass more slowly in moving systems or that it only seems to pass more slowly? The Twin Paradox  There are two twins, ______. When they are 20 years old, Speedo, the more adventurous of the two sets off on an epic journey to Planet X, located ______away from Earth. Further, his spaceship is capable of reaching a speed of ______relative to the inertial frame of his twin brother back home.  After reaching Planet X, ______becomes homesick and immediately returns to Earth at the same speed of 0.95c. Upon his return, Speedo is shocked to discover that Goslo is now ______while Speedo is ______.  From Speedo’s point of view, his brother Goslo ______and then back at 0.95c. Therefore, Goslo should now be ______then Speedo. But that isn’t the case.

The Resolution  Consider a third observer traveling in a spaceship at a constant speed of 0.50c ______. To the third observer, Goslo never changes inertial reference frames (his speed relative to the observer is always the same).

 The third observer notes however, that Speedo ______during his journey, changing his reference frame in the process.  To the third observer, the motion of Goslo and Speedo are not the same. Therefore roles played by Goslo and Speedo are not symmetric. So it should not be surprising that time flows differently for each.

Example: How old are Goslo and Speedo when they finally reunite?

Relativity also effects Momentum  With slow moving objects, the momentum of the object is equal to the mass of the object times the velocity of the object. (______)

 However, momentum is ______.

 For this to be true, the relativistic terms for momentum must be considered: Relativistic Momentum: Where: p = momentum (kg.m/s) m = mass (kg) v = velocity Example: An electron, of mass 9.11 x 10-31kg moves at ______. Calculate it’s classical momentum & relativistic momentum. Addition of Velocity: Classical:  Two students are playing baseball on a train moving at 100 mi/hr. The pitcher throws the ball at 50 mi/hr. According to a stationary observer, how fast is the ball going? ______

 A motorcycle moving at 0.80c with respect to a stationary observer. Then the rider throws a ball forward at 0.70c relative to himself.  According to Newton (and classical mechanics), how fast is the ball going? ______(this is a problem!)

Relativistic equation for adding velocities:

v + v v = om ms os v v 1 + om ms c 2

Example: A motorcycle moving at _____ with respect to a stationary observer. Then the rider throws a ball forward at 0.70c relative to himself. How fast is the ball going relative to a person standing still?

One other misconception:  Probably the most famous scientific equation of all time, first derived by Einstein is the relationship ______

 This tells us the ______corresponding to a mass m ______. o What this means is that when mass ______, for example in a nuclear fission process, this amount of ______must appear in some other form. o It also tells us the ______of mass m sitting at rest.

 The misconception: o Many people think that E = mc2 means matter, when traveling at the speed of light transforms into pure energy. . THIS IS NOT TRUE o ______. o ______. 2  What E = mc means:

2  All E = mc means is that mass and energy are two sides of the same coin. ______.

Calculating Energy:  ______: The energy a particle has by simply being a particle (having mass)

 ______- Energy due to movement.

 ______- The total energy a particle has due to the fact it is a particle (______) and the fact that it is moving (______)

General Relativity  Special relativity deals with ______ General relativity deals with ______A Thought Experiment  2 observers are standing inside closed elevators  Elevator 1 is at rest on the surface of the Earth. If Observer 1 throws a ball it will fall toward the floor of the elevator, accelerated by gravity  Now elevator 2 is given an acceleration equal to 9.8m/s2 (g).  The ball stays at rest compared to the background stars. But the elevator floor rushes up toward the ball.  If the ball is given a slight horizontal velocity, it will make a parabolic path as the floor rushes to meet it.  Once it hits, the floor exerts a force of mg on not just the ball, but on Observer 2 as well.  The results of experiments conducted by Observer 2 in his accelerated elevator will have the same results as experiments conducted by Observer 1 back on Earth.  Einstein generalized this result into the Principle of Equivalence The Principle of Equivalence says:

 Thus our observers could not tell (while in the closed elevator) if they are ______in space or sitting in a uniform ______field. Does this effect light?  If Observer 2 at rest has a flashlight, the beam would go straight across the room.  But if the elevator were being accelerated, the beam would hit lower on the wall just like the ball would (because the wall will have moved up). In fact, the beam would even follow a parabolic path.  If this works in an ______frame, then it should work in a ______field too.  And it does. Light will bend in a large gravitational field. The proof: Gravitational Lensing (Proved in 1919) [Draw the picture]

Time and Gravity  ______is also effected by ______fields.  We saw before that moving clocks run slow.  ______as well.  This has also been tested. The Proof: Atomic Clocks  Atomic clocks are extremely accurate. An error for 1 second in 3 million years is typical. This error can be described as about 1 part in 1014.  There are atomic clocks in Boulder, CO and Washington DC.  Boulder is about 1 mile higher in altitude then DC. Which clock runs slow?

 The farther from the center of the Earth one is, the less the gravitational field is. Therefore, ______clock must run slow. And it does!  The ______clock is often 15 nanoseconds (15 x 10-15 seconds) behind the one in ______!  Yes, this isn’t a huge difference, but it is about 17 times larger then the typical error from an atomic clock.