Tuesday, February 15, Ice Cube Neutrino Facility

Transcription

1 Ice Cube Neutrino Facility

2 Semester Report This Thursday, Feb 17th, due in class: a list of resources (books, websites, articles, etc.), along with title. 1% will be deducted from your paper grade for each day it is late!

3 Exam #1 Delayed by one week to Thu. 2/24. In-class, written answer. Based on all materials in the lectures, and in the online reading and assignments.

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8 It s all relative Space and Time: what could be more basic? Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Isaac Newton Until... Einstein.

9 Special Relativity Einstein, 1905 Two very basic postulates, arrived at independently from any known laws (mechanics/electrodynamics): Speed of Light is invariant Independence of physical laws from the choice of inertial reference frame.

10 Special Relativity Einstein, 1905 Two very basic postulates, arrived at independently from any known laws (mechanics/electrodynamics): Speed of Light is invariant Independence of physical laws from the choice of inertial reference frame.

11 Inertial Reference Frames Impossible to distinguish from a reference frame at rest...have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still. " Galileo

12 Invariant Speed of Light No matter the reference frame, the speed of light is always measured to have the same value: c = 299,792,458 m/s = 670 million mph = miles/sec = 7.5 times around the earth per second. Unlike an arrow shot from a train, the speed of light is not increased by being shot from a moving platform.

13 Galilean Relativity Implies a singe, special, fixed reference frame. For Electromagnetism this was called the Ether, an invisible substrate in which waves propagated in space. Michelson-Morley experiment: no change in speed of light as earth moves relative to ether.

14 Special Relativity Rejects the notion of universal time for all inertial frames: each frame has their own time! Relative velocity between frames bounded by the speed of light. No universal or special frame of reference: all reference frames are equally valid.

15 Lorentz Transform Lengths perpendicular to relative motion must be unchanged. Lengths along the direct of motion appear contracted: the faster the more Time appears to run slower.

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17 Muon Decay Muon lifetime 2.2µs Measure number arriving per second at top of a mountain, compare to number at bottom. Muons traveling relativistically: v=0.9952c More muons arrive than lifetime should allow! From muon s perspective: mountain is shorter. From mountain s perspective: Muon s clock runs slow

18 Apparent Paradoxes Apparent paradoxes arise from the fact that relativity defies common sense. One example: a train 1000ft long approaches an 800ft tunnel at 0.8c.

19 Tunnel Rest Frame Robbers in the tunnel know their relativity, and calculate the train will only be 600ft long when moving at that speed. They will wait until it enters the tunnel, slam the doors at the same time, and trap the train.

20 Train Rest Frame The train driver is not worried. He knows the tunnel, rushing towards him at 0.8c, will appear to him to be only 480ft long. The train won t fit inside.

21 Paradox Explained Either the train is trapped, or it is not! The synchronized Clocks which close the door are, from the train s point of view, out of sync, and they run slow. So the left door closes after the right, by which time the train is past it.

22 Twin paradox Bill Phil