THE PRINCIPLE OF SPECIAL RELATIVITY 10 TH GRADE SCIENCE

MUST DO! In your notebook, write a reflection on the assembly yesterday. What did you appreciate/not appreciate? What inspired/discouraged you? How do you feel about the quest to achieve the IB diploma?

IN THE NINETEENTH CENTURY PHYSICS WAS SOLVED! Scientists had a complete understanding of nature Mechanics had been triumphed!

IN THE NINETEENTH CENTURY PHYSICS WAS SOLVED! Scientists had a complete understanding of nature Mechanics had been triumphed! Applications to engineering!

IN THE NINETEENTH CENTURY PHYSICS WAS SOLVED! Scientists had a complete understanding of nature Mechanics had been triumphed! Applications to engineering! Kepler solved the motion of the planets

IN THE NINETEENTH CENTURY PHYSICS WAS SOLVED! Scientists had a complete understanding of nature Maxwell showed that electricity and magnetism were the same thing (electromagnetism) Hey Gurl…

IN THE NINETEENTH CENTURY PHYSICS WAS SOLVED! Scientists had a complete understanding of nature The kinetic theory of gasses gave us an understanding of matter at a molecular level.

HOWEVER!! (DUHN DUHN DUUHHAAAAA) Two problems defied solution and were threatening to bring down the entire structure of classic mechanics. 1) Physicists were trying to understand the spectrum of “black body radiation.” Which has been resolved and involved photons and quantum mechanics.

HOWEVER!! (DUHN DUHN DUUHHAAAAA) Two problems defied solution and were threatening to bring down the entire structure of classic mechanics. 2) The second problem had to do with the speed of light.

YOUNG EINSTEIN WAS SAID TO HAVE PONDERED…

THIS PUZZLE WAS SOVLED BY… Albert Einstein’s “Special Relativity!”

CREATE A NEW UNIT IN YOUR SCIENCE NOTEBOOK Special and General Relativity Create a Unit cover page Create a new WWK page Create a new “Must do’ page Title the next right blank page “Frames of Reference”

OBJECTIVES (WRITE THESE DOWN) State the meaning of the term frame of reference; State what Galilean relativity means; Solve problems of Galilean relativity; Understand the significance of the speed of light; State two postulates of the principle of relativity; Appreciate that absolute time does not exist and that simultaneity is a relative concept.

WWK Frame of reference – The observer along with the rulers and clocks that he or she uses to measure distances and times. Inertial frame of reference – Frames moving with uniform velocity past each other on straight lines. (When the observer is not accelerated (does not speed up, slow down, or change directions.))

EXAMPLE OF SINGLE FRAME OF REFERENCE In this frame of reference the observer decides that lightning struck at time t = 3 s at position x = 60 m

YOU DO! Use the internets to find an example of a relative frame of reference. Hint: this example must include two frames of reference.

RELATIVE FRAME OF REFERENCE EXAMPLE Consider two observers, one on the ground within sight of a moving train and another in the train. The train moves past the observer on the ground at t = 0s going v = 15 m/s and is struck by lightning three seconds later. Draw a diagram of this scenario Hint: a diagram is not a sketch. A diagram has all important information and, in this case, shows the passage of time.

RELATIVE FRAME OF REFERENCE EXAMPLE With a partner, convert the equation x’ = x – vt into a sentence contextualizing the train problem.

NEWTON SAID… “Absolute, true and mathematical time, of itself, and from its own nature, flows equably without any relation to anything external.”

THE EQUATIONS… x’ = x – vt t’ = t …reflect a Galilean transformation: the relation between coordinates of events when one frame moves past the other with uniform velocity on a straight line. (aka: inertial frames of reference.) It is impossible for one of the observers to claim that he or she is ‘really’ at rest and that the other is ‘really moving’ when there is no acceleration.

VIDEO REVIEW!

GALILEAN RELATIVITY AND THE LAW OF ADDITION OF VELOCITIES Again, imagine the train with the two observers. Consider a ball rolling on the floor of that train with velocity u’ with respect to the observer on the train. Assume t’ = t = 0 s is the point when the ball stars rolling. After time t’ the position can be found at x’ = u’t’ by the train observer. The ground observer records the position of the ball to be at x = x’ + vt (remember t’ = t) Substitute in the equation x’ = u’t’ and you get x = (u’ +v)t

GALILEAN RELATIVITY AND THE LAW OF ADDITION OF VELOCITIES

HOMEWORK! A ball rolls on the floor of the train at 2 m/s (with respect to the floor). The train moves with respect to the gound… a) to the right at 12 m/s, b) to the left at 12 m/s What is the velocity of the ball relative to the ground? If we replace the ball with a beam of light moving with velocity c = 3 x 10 8 m/s, the formula from the example implies that light would be traveling at a higher speed relative to the ground observer. Many experiments have been done to detect variations in the speed of light but none have ever been found!

EINSTEIN’S PRINCIPLE OF SPECIAL RELATIVITY Please title the next right blank page in your notebook “Special Relativity.”

THE SPEED OF LIGHT Remember Maxwel? (1864) By unifying magnetism and electricity he also discovered the electromagnetic nature of light. c = 1/√(ε 0 μ 0 ) ε 0 = electric permittivity μ 0 = magnetic permeability In other words the speed of light doesn't have anything to do with the speed of the object creating the light. Hey Gurl…

THE SPEED OF LIGHT Einstein (1905) resolved the contradiction between Maxwell’s findings and Galilean relativity. Light doesn't need a medium to travel through The speed of light is the same for all observers The laws of physics are the same in all inertial frames of reference. Einstein modified Galilean transformation laws to reflect this. He also had to change Newtonian mechanics to relativistic mechanics.

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THE PRINCIPLE OF RELATIVITY Remember: with inertial frames of reference it is impossible to scientifically prove which observer is moving and which is at rest. Further, both observers would arrive at the same laws of physics if they did the same experiments (Newton’s laws, v=x/t, etc) This leads to the two principles of relativity: 1.The laws of physics are the same in all inertial frames. 2.The speed of light in a vacuum is the same for all inertial observers.

IMPLICATIONS The speed of light in a vacuum is the same for all inertial observers. This means that time is not absolute! “Absolute, true and mathematical time, of itself, and from its own nature, flows equably without any relation to anything external.”

IMPLICATIONS OF RELATIVITY - SPACETIME If the speed of a beam is the same for both observers they must measure different times of travel. Thus observers in motion relative to each other measure time differently. SPACE AND TIME ARE INEVITABLY LINKED AND ARE NOT INDEPENDENT OF EACH OTHER! Space and Time are now Spacetime

IMPLICATIONS OF RELATIVITY – SIMULTANEOUS EVENTS With a partner read and discuss the hand out and answer the final question in your notebooks.

IMPLICATIONS OF RELATIVITY – SIMULTANEOUS EVENTS Events that are simultaneous for one observer and which take place at different points in space, are not simultaneous for another observer in motion relative to the first. On the other hand, if two events are simultaneous foe one observer and take place at the same point in space, they are simultaneous for all other observers as well. SPACE AND TIME ARE INEVITABLY LINKED AND ARE NOT INDEPENDENT OF EACH OTHER!

EXAMPLE QUESTION Observer T is in the middle of a train carriage that is moving with constant speed to the right with respect to the train station. Two light signals are emitted at the same time as far as the observer, T, in the train is concerned. a.Are the emissions simultaneous for observer G on the ground? b.The signals arrive at T at the same time as far as T is concerned. Do they arrive at T at the same time as far as G is concerned? According to G, which signal is first?