{"id":96,"date":"2019-04-01T17:45:32","date_gmt":"2019-04-01T21:45:32","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/?post_type=chapter&p=96"},"modified":"2019-04-12T18:44:57","modified_gmt":"2019-04-12T22:44:57","slug":"chapter-review","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/chapter\/chapter-review\/","title":{"raw":"Chapter 1 Review","rendered":"Chapter 1 Review"},"content":{"raw":"
\r\n

Key Terms<\/span><\/h3>\r\n
\r\n \t
classical (Galilean) velocity addition<\/dt>\r\n \t
method of adding velocities when v<<c;<\/span><\/span>\u00a0<\/span>velocities add like regular numbers in one-dimensional motion: u=v+u\u2032,\u00a0<\/span>where\u00a0<\/span>v<\/em>\u00a0<\/span>is the velocity between two observers,\u00a0<\/span>u<\/em>\u00a0<\/span>is the velocity of an object relative to one observer, and u\u2032<\/span><\/span>\u00a0<\/span>is the velocity relative to the other observer<\/dd>\r\n<\/dl>\r\n
\r\n \t
event<\/dt>\r\n \t
occurrence in space and time specified by its position and time coordinates (x<\/em>,\u00a0<\/span>y<\/em>,\u00a0<\/span>z<\/em>,\u00a0<\/span>t<\/em>) measured relative to a frame of reference<\/dd>\r\n<\/dl>\r\n
\r\n \t
first postulate of special relativity<\/dt>\r\n \t
laws of physics are the same in all inertial frames of reference<\/dd>\r\n<\/dl>\r\n
\r\n \t
Galilean relativity<\/dt>\r\n \t
if an observer measures a velocity in one frame of reference, and that frame of reference is moving with a velocity past a second reference frame, an observer in the second frame measures the original velocity as the vector sum of these velocities<\/dd>\r\n<\/dl>\r\n
\r\n \t
Galilean transformation<\/dt>\r\n \t
relation between position and time coordinates of the same events as seen in different reference frames, according to classical mechanics<\/dd>\r\n<\/dl>\r\n
\r\n \t
inertial frame of reference<\/dt>\r\n \t
reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force<\/dd>\r\n<\/dl>\r\n
\r\n \t
length contraction<\/dt>\r\n \t
decrease in observed length of an object from its proper length L0<\/span><\/span>\u00a0<\/span>to length\u00a0<\/span>L<\/em>\u00a0<\/span>when its length is observed in a reference frame where it is traveling at speed\u00a0<\/span>v<\/em><\/dd>\r\n<\/dl>\r\n
\r\n \t
Lorentz transformation<\/dt>\r\n \t
relation between position and time coordinates of the same events as seen in different reference frames, according to the special theory of relativity<\/dd>\r\n<\/dl>\r\n
\r\n \t
Michelson-Morley experiment<\/dt>\r\n \t
investigation performed in 1887 that showed that the speed of light in a vacuum is the same in all frames of reference from which it is viewed<\/dd>\r\n<\/dl>\r\n
\r\n \t
proper length<\/dt>\r\n \t
L0; the distance between two points measured by an observer who is at rest relative to both of the points; for example, earthbound observers measure proper length when measuring the distance between two points that are stationary relative to Earth<\/dd>\r\n<\/dl>\r\n
\r\n \t
proper time<\/dt>\r\n \t
\u0394\u03c4<\/span><\/span><\/span>\u00a0<\/span>is the time interval measured by an observer who sees the beginning and end of the process that the time interval measures occur at the same location<\/dd>\r\n<\/dl>\r\n
\r\n \t
relativistic kinetic energy<\/dt>\r\n \t
kinetic energy of an object moving at relativistic speeds<\/dd>\r\n<\/dl>\r\n
\r\n \t
relativistic momentum<\/dt>\r\n \t
p\u2192,<\/span><\/span><\/span>\u00a0<\/span>the momentum of an object moving at relativistic velocity; p\u2192=\u03b3mu\u2192<\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
relativistic velocity addition<\/dt>\r\n \t
method of adding velocities of an object moving at a relativistic speeds<\/dd>\r\n<\/dl>\r\n
\r\n \t
rest energy<\/dt>\r\n \t
energy stored in an object at rest: E0=mc2<\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
rest frame<\/dt>\r\n \t
frame of reference in which the observer is at rest<\/dd>\r\n<\/dl>\r\n
\r\n \t
rest mass<\/dt>\r\n \t
mass of an object as measured by an observer at rest relative to the object<\/dd>\r\n<\/dl>\r\n
\r\n \t
second postulate of special relativity<\/dt>\r\n \t
light travels in a vacuum with the same speed\u00a0<\/span>c<\/em>\u00a0<\/span>in any direction in all inertial frames<\/dd>\r\n<\/dl>\r\n
\r\n \t
special theory of relativity<\/dt>\r\n \t
theory that Albert Einstein proposed in 1905 that assumes all the laws of physics have the same form in every inertial frame of reference, and that the speed of light is the same within all inertial frames<\/dd>\r\n<\/dl>\r\n
\r\n \t
speed of light<\/dt>\r\n \t
ultimate speed limit for any particle having mass<\/dd>\r\n<\/dl>\r\n
\r\n \t
time dilation<\/dt>\r\n \t
lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location)<\/dd>\r\n<\/dl>\r\n
\r\n \t
total energy<\/dt>\r\n \t
sum of all energies for a particle, including rest energy and kinetic energy, given for a particle of mass\u00a0<\/span>m<\/em>\u00a0<\/span>and speed\u00a0<\/span>u<\/em>\u00a0<\/span>by E=\u03b3mc2,<\/span><\/span>\u00a0where\u00a0\u03b3=11\u2212u2c2<\/span><\/span><\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
world line<\/dt>\r\n \t
path through space-time<\/dd>\r\n<\/dl>\r\n<\/div>\r\n
\r\n

Key Equations<\/span><\/h3>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time dilation<\/td>\r\n\u0394t=\u0394\u03c41\u2212v2c2=\u03b3\u03c4<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Lorentz factor<\/td>\r\n\u03b3=11\u2212v2c2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Length contraction<\/td>\r\nL=L01\u2212v2c2=L0\u03b3<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Galilean transformation<\/td>\r\nx=x\u2032+vt,y=y\u2032,z=z\u2032,t=t\u2032<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Lorentz transformation<\/td>\r\nt=t\u2032+vx\u2032\/c21\u2212v2\/c2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
<\/td>\r\nx=x\u2032+vt\u20321\u2212v2\/c2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
<\/td>\r\ny=y\u2032<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
<\/td>\r\nz=z\u2032<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Inverse Lorentz transformation<\/td>\r\nt\u2032=t\u2212vx\/c21\u2212v2\/c2<\/td>\r\n<\/tr>\r\n
<\/td>\r\nx\u2032=x\u2212vt1\u2212v2\/c2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
<\/td>\r\ny\u2032=y<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
<\/td>\r\nz\u2032=z<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Space-time invariants<\/td>\r\n(\u0394s)2=(\u0394x)2+(\u0394y)2+(\u0394z)2\u2212c2(\u0394t)2<\/td>\r\n<\/tr>\r\n
<\/td>\r\n(\u0394\u03c4)2=\u2212(\u0394s)2\/c2=(\u0394t)2\u2212[(\u0394x)2+(\u0394y)2+(\u0394z)2]c2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Relativistic velocity addition<\/td>\r\nux=(ux\u2032+v1+vux\u2032\/c2),uy=(uy\u2032\/\u03b31+vux\u2032\/c2),uz=(uz\u2032\/\u03b31+vux\u2032\/c2)<\/td>\r\n<\/tr>\r\n
Relativistic Doppler effect for wavelength<\/td>\r\n\u03bbobs=\u03bbs1+vc1\u2212vc<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Relativistic Doppler effect for frequency<\/td>\r\nfobs=fs1\u2212vc1+vc<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Relativistic momentum<\/td>\r\np\u2192=\u03b3mu\u2192=mu\u21921\u2212u2c<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Relativistic total energy<\/td>\r\nE=\u03b3mc2,where\u03b3=11\u2212u2c2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Relativistic kinetic energy<\/td>\r\nKrel=(\u03b3\u22121)mc2,where\u03b3=11\u2212u2c2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section><\/div>\r\n
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Summary<\/span><\/h3>\r\n
\r\n
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1.1<\/span>\u00a0<\/span><\/span>Invariance of Physical Laws<\/span><\/a><\/h4>\r\n