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Unformatted text preview: sible to get a massive thing to travel truly at the speed of light energy required is mc2, where as vc so requires infinite energy to get all the way to c But if you are a massless photon... to the outside, your clock is stopped so you arrive at your destination in the same instant you leave your source (by your clock) across the universe in a perceived instant makes sense, if to you the outside world's clock has stopped: you see no "ticks" happen before you hit UCSD Physics 10 E = mc2 as a consequence of relativity Express 4-vector as (ct, x, y, z) describes an "event": time and place time coordinate plus three spatial coordinates factor of c in time dimension puts time on same footing as space (same units) We're always traveling through time our 4-velocity is (c, 0, 0, 0), when sitting still moving at speed of light through time dimension stationary 4-momentum is p = mv(mc, 0, 0, 0) for a moving particle, p = ( mc, px, py, pz) where px, etc. are the standard momenta in the x, y, and z directions the time-component times another factor of c is interpreted as energy conservation of 4-momentum gets energy and momentum conservation in one shot UCSD Physics 10 E = mc2, continued can be approximated as = 1 + v2/c2 + ...(small stuff at low velocities) so that the time component of the 4-momentum c is:
m c2 = mc2 + mv2 + ... the second part of which is the familiar kinetic energy Interpretation is that total energy, E = m c2 mc2 part is ever-present, and is called "rest mass energy" kinetic part adds to total energy if in motion since sticks to m in 4-momentum, can interpret this to mean mass is effectively increased by motion: m m gets harder and harder to accelerate as speed approaches c UCSD Physics 10 Experimental Confirmation We see time dilation in particle lifetimes in accelerators, particles live longer at high speed their clocks are running slowly as seen by us seen daily in particle accelerators worldwide cosmic rays make muons in the upper atmosphere these muons only live for about 2 microseconds if not experiencing time dilation, they would decay before reaching the ground, but they do reach the ground in abundance We see length contraction of the lunar orbit squished a bit in the direction of the earth's travel around the sun E = mc2 extensively confirmed nuclear power/bombs sun's energy conversion mechanism bread-and-butter of particle accelerators UCSD Physics 10 References Relativity Visualized by Lewis Carroll Epstein http://www.anu.edu.au/physics/Searle/ movie Assignments Q/O #3 due today by midnight Partial read of Chapters 9 & 10 (pages on assignment page) Read Chapters 35 & 36 on relativity HW5: 9.R.13, 9.E.9, 9.E.14, 9.E.43, 9.P.7, 10.E.16, 35.R.27, 35.E.6, 35.E.19, 35.E.20, 35.E.37, 35.P.3, 35.P.10, 36.R.7, 36.E.2, 36.E.6...
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