Time-space view dynamics Length contraction Time dilation Relative nature of simultaneity Principle of relativity Lorentz transformation Relativity
Einstain ’ s theory took us into a world far beyond that of ordinary experience,it led us to a deeper and more satisfying view of the nature of space and time
In modern long range navigation,the precise location and speed of moving craft are continuously monitored and updated.A system of navigation satellites called NAVSTAR permits locations and speeds anywhere on earth to be determined to within about 16m and 2cm/s.However if relativity effects were not taken into account,speeds could not be determined any closer than about 20cm/s,which is unacceptable for modern navigation systems.How can something as abstract as Einstain ’ s relativity be involved in something as practical as navigation?
A pair of twins,A remains on earth,and B make the milk run to a nearby solar system in high speed,when B come back,who ’ s younger?
Take an account on a event in two different frame 1.Galileo transformation §1 Galileo relativity principle
Even though electromagnetism shares with mechanics concept such as energy and momentum.there appear to be a major difference between these two fundamental discipline.the laws of mechanics look the same in all inertial frames,but electromagnetism appears to violate the general law.According to Maxwell ’ s equation,electromagnetic waves propagate at speed C,with no restrictions on the state of the source of detector,this suggests the existence of an absolute frame for electromagnetism.
1.the relativity postulate:the laws of physics are the same for observers in all inertial reference frames.no frames is preferred 2.the speed postulate:the speed of light in vacuum has the same value c in all direction and in all inertial reference frames Einstein relativity develop Newton’s theory discussion physics rule Mechanics rule §2 the postulates
The light speed invariability is opposed to Galileo velocity transformation Difference in view Newton Time scale Length scale Mass measure Has no relation with frame relativity Time,space,mass has relation with reference frame C is constant
transformation Inverse transformation 2.lorentz transformation 1.transformation formula
Galileo transformation << discussion Has relation with
No meaning.Maximum Speed is C > 4.procedure to solve the problem 1)establish coordinate 2)determine the moving frame and rest frame 3)u is the positive speed of S ’ to S 4)use formula to get relation among x, t, x ’ t’ and solve problem
Example:two persons a,b observe lighting pulses, from point of a, x 1 =6 10 4 m ， t 1 =2 10 -4 s ； x 2 =12 10 4 m ， t 2 =1 10 -4 s ， from the point of b, two events happen at the same time （ 1 ） find the relative velocity of b to a （ 2 ） find the space separation of lighting pulses measured by b Solution:
Example:a race track with length 100m,a sports man Run from the origin point to end point with time interval 10s,a craft with velocity 0.8c fly along the direction of run way.from the point of craft man find the space separation and time interval Solution: x=100, t=10s,u=0.8c Negative sign means the sportsman run in the opposite direction
§ 2 time and space of relativity 1 、 relative nature of simultaneity But in Einstain theory: In Newton ’ s theory so ， Relative nature of simultaneity 。 if We have
Conclusion:in general,two events that appear simultaneous in one frame of reference don ’ t appear simultaneous in a second,unless the two events happen in the same place.
Einstein train rest frame In train There ’ s a signal source Give a signal In the middle Einstain ’ s train experiment
Event 1Receive flash Event 2 Receive flash Receive the flash at same time Two events happen in different time Give a signal Move with Receive light early than Give a signal S
discussion 1 ） simultaneous is absolutely only when two events happen in same place
2) Relative nature of simultaneous is the result of constant c 3) When speed is far more less than C,the result in two inertial frame is same A君A君 B君B君
Example:two trains leave from two station A,B with space separation 1000km at the same time,a craft with u=9km/s along the direction ab,find The interval from the point of spaceman Solution: x=10 6 t=0 Negative means b train go first
1)proper time a time interval between two events at the same space point in a frame is called a proper time in that frame 2. Time dilation
2 、 proper time is shortest time in all frames Take an account on a clock in Time dilation,proper time is minimum time In s,from lorentz transformation
3)physics reason of time dilation y′ x′ u d u tu t d l M′ A′ C′ In S ′ ， there ’ s a light source in A ′ M′is a reflected mirror
y′ x′ u d u tu t d l M′ A′ C′ In S ： Time dilation
(2)the proper time is the shortest one in all frames discussion （ 1 ） time dilation is the space-time effect of relativity,it has no relation with the structure of clock （ 3 ） there ’ re a lot of experiment to proof the time dilation effect
example a rocket v=0.95c ， the time interval is 10min measured in rocket ， how long is it in earth frame ？ Solution:
Example:the lifelong time for is 2.5×10 -8 s while in rest,if its u=0.99c,the passing distance is 52m,is this ok ？ Solution:if with t′=2.5 ×10 -8 s times u ， we get 7.4m 。 Take account of time dilation So s=uΔt=53m,it’s ok
3.length contraction 1 、 proper length A length measured in the rest frame of the body is called proper length 2 、 proper length is the longest in all frames (length contraction)
Notes:in S we measure the rod length,we must measure end points in same time From lorenze transformation
Proper length is longest discussion 1)Relativity effect 2) In low speed Galileo transformation 4)length contraction is relativity effect,it ’ s different from what we say that the body become smaller. 3)proper length is the longest,
Example:a length of rocket measured in rocket frame is 15m, suppose v=0.95c,find the length in earth frame ？ Solution:
Example:a 1m rod rest in O ’ x ’ y ’ 。 the angle is 45 0 with x ’ axis measured from s ’ 。 find the length of the rod and angle with x in s 。 The related velocity is solution: z y y'y' S S'S' v O O z'z' x x'x' ly'ly' lx'lx' '' l'l'
Conclusion:not only the rod have contraction,but also rotate in some angle.
Example:in 6000m altitude ， a meson fly to earth with v=0.998c 。 Suppose meson ‘s life span in its rest frame is 2 10 -6 s ， from relativity ， 1)can meson arrive in earth from earth frame ？ 2) from meson Frame? solution ： 1) proper time for meson is t 0 =2 10 -6 s 。 Because of time dilation ， the life span from earth The distance for to travel It can go straight through the earth
2 ） from frame The distance for to travel in frame It can go straight through the earth
4 、 comparison of two time-space view space,time is absolutely,there’r no relation among time,space and the motion of body Classic view
4 、 light speed is c,which is utmost speed of motion body Relativity view 1 、 there are relation among time space and the motion of body 2 、 every inertial frame has its own time scale,and found that the clock in other frame go slow 3 、 every inertial frame has its own space scale,and found the ruler in other frame become shorter.
§ 5 the dynamic of relativity 1 、 momentum and dynamic equation But the utmost of v is c Must change with speed A:It can be proofed
notes ： （ 1 ） if ， （ 2 ） if ， （ 3 ） if ， B: dynamic equation if (4) v>c ， m is negative,no meaning
2 、 mass and energy 1 、 kinetic energy If v<
"name": "2 、 mass and energy 1 、 kinetic energy If v<
三、相对论能量 质能关系 Rest energy Kinetic energy Total energy Mass and energy formula 56 2 、 energy
Notes: （ 1 ） a body in rest,it still has substantial energy 。 （ 2 ） mass is not the measure of inertial,but also the energy （ 3 ） change in mass implies change in energy （ 4 ） to isolated system,the total energy keeps constant
Example: m 0 of electron is known （ 1 ） find the E 0 ；（ 2 ） find the work for the particle moving from rest to 0.60c 2 ） the work for accelerating particle solution ：（ 1 ） rest energy of electronic
Example: two rest particle with rest mass m 0 each collide head on with v to become a combined particle 。 Find the rest mass and speed of the combined particle 。 Solution from the conservation law of momentum and energy Notes:the rest mass of combined particle is larger than 2m 0 ， the difference The difference of rest mass comes from kinetic energy V=0 (1) (2) We ’ v