SPECIAL RELATIVITY Albert Einstein (1879 1955) Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 OUTLINES • Einstein’s Postulates • Lorentz Transformation • The Lorentz Velocity Transforma[.]
SPECIAL RELATIVITY Albert Einstein (1879-1955) Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 OUTLINES • • • • • • • • • Einstein’s Postulates Lorentz Transformation The Lorentz Velocity Transformation Relativity of Simultaneity Relativity of Length –Contraction of length Relativity of Time interval –Time dilatation Invariance of Space –Time interval Relativistic Dynamics Relativistic Energy, Relativistic Kinetic energy Einstein’s Postulates Einstein’s first postulate, called the principle of relativity,states:The laws of physics are the same in all inertial frames of reference dW Einstein’s second postulate states: The dt speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source The Ultimate Speed Limit Einstein’s second postulate immediately implies the following result: It is impossible for an inertial observer to travel at c, the speed of light in vacuum We can prove this by showing that travel at c implies a logical contradiction Suppose that the spacecraft is moving at the speed of light c relative to an observer on the earth, so that If the spacecraft turns on a headlight, the second postulate now asserts that the earth observer measures the headlight beam to be also moving at c Thus this observer measures that the headlight beam and the spacecraft move together and are always at the same point in space But Einstein’s second postulate also asserts that the headlight beam moves at a speed relative to the spacecraft, so they cannot be at the same point in space This contradictory result can be avoided only if it is impossible for an inertial observer, such as a passenger on the spacecraft, to move at c As we go through our discussion of relativity, you may find yourself asking the question Einstein asked himself as a 16-yearold student, “What would I see if I were traveling at the speed of light?” Einstein realized only years later that his question’s basic flaw was that he could nottravel at c All observers see light flashes go by them with the same speed v No matter how fast the guy on the rocket is moving!! Both guys see the light flash travel with velocity = c c Even when the light flash is traveling in an opposite direction v c Both guys see the light flash travel past with velocity = c The Lorentz Coordinate Transformation Event A observed in reference frame O at (x,y,z,t) , is observed at in ereference frame O’(x’,y’,z’,t’) The relationships between (x,y,z,t) and (x’,y’,z’,t’) are given by the Lorentz Coordinate Transformation t=t’=0 , OO’ x' 1 x 1 v c2 t’ V=const x’ O’ x ; y' y; z' z; ; y y' ; z z' ; v c2 x ' vt ' t O z x vt y’ y z’ v x c t' v2 1 c v t ' x ' c t v2 1 c t Derivation of The Lorentz Coordinate Transformation y’ y t=t’=0 , OO’ t x ' ( x vt ) x ( x ' vt ' ) ct ' (ct vt ) ct (ct ' vt ' ) c tt ' (c v ) tt ' v2 1 c v ct ' (ct x ) c v t' (t x) c O t’ V=const x’ O’ x z x x ' vt ' 1 v2 c z’ t ' ; y y' ; z z' ; t v c 1 x' v2 c2 The Lorentz Velocity Transformation The relationships between The velocity of a point mass in the RF O and RF O’ u(u x , u y , u z ), u' (u'x , u'y , u'z ) u 'x ux v v 1 ux c v ux v u'x c u 'x ; u 'y u y 1 1 v c ; uy v2 c 1 1 v u'x uz 1 1 v c v2 c c ; u 'z ux u 'y 2 ; uz u 'z 1 1 v c c2 ux 2 v2 v2 c2 u'x u(u x , u y , u z ), u' (u'x , u'y , u'z ) DERIVATION: dx ' dx vdt 1 v2 dt ; dy' dy, dz ' dz, dt ' c dx vdt v2 dx v ux v dx ' c dt u ' x v v dx v dt ' dt dx 1 ux c c dt c 1 1 v2 c2 v2 dy v2 v2 dy 1 u y 1 dy' c dt c u ' c y v v dx v dt ' dt dx 1 1 ux c c dt c v2 dz v2 v2 dz 1 uz 1 dt dz ' c c u ' c z v v dx v dt ' dt dx 1 1 ux c c dt c v c 1 dx v2 c2 ... Postulates Lorentz Transformation The Lorentz Velocity Transformation Relativity of Simultaneity Relativity of Length –Contraction of length Relativity of Time interval –Time dilatation Invariance of Space... energy Einstein’s Postulates Einstein’s first postulate, called the principle of relativity, states:The laws of physics are the same in all inertial frames of reference dW Einstein’s second postulate... observer, such as a passenger on the spacecraft, to move at c As we go through our discussion of relativity, you may find yourself asking the question Einstein asked himself as a 16-yearold student,