2. Addition of velocities in the Newtonian physics V v= speed of the train measured from the platform w 1 =man’s speed measured from the train w1w1 w 2 =man’s speed measured from the platform w 2 =v+w 1

3. If a torch is switched on on the train, from platform we should measure the speed of light as w=v+c V where v is the train speed and c is light speed from the train c w>c

4. Actually the man on the platform measures the same light speed from the trainso the Newtonian physics laws are not valid any more the Newtonian physics laws are not valid any more

5. Addition of velocities following Einstein’s physics w2=w2= v+w 1 1+ vw 1 c2c2 So, we need another rule to add velocities w 2 =v+w 1 In Einstein’s physics: c c doesn’t depend on the observer c is a limit speed,

6. Bertozzi’s experience In 1968 professor Bertozzi used the linear accelerator of the MIT to verify Einstein’s Theories. Bertozzi used the accelerator to accelerate clusters of electrons. According to the Newtonian physics the speed of electrons should proportionally increase as we add energy without any limit

7. Bertozzi’s results vs classical prediction Instead of following a linear progression the experimental graphic turned out to be like this: Once again Newtonian physics is not valid Linear prediction Experimental results Limit speed V C Electrons kinetic energy Speed of electrons Light speed

8. Muons Muons are subnuclear particles which are created by interaction of cosmic rays with high atmosphere

9. How can muons reach the Earth? Muon average lifetime as measured in laboratory is 2,2x10 -6 s, we’ll call it . After their creation, muons run toward the earth at 0,995 c Since muons are created at 5000m from earth surface, with a simple computation we find out that they can’t reach the earth: 0,995c x (2x10 -5 s)= 657m But we detect them on the earth! 5000 m

10. Muons and time dilation Einstein gives us the answer to this problem. In Einstein’s physics time is not absolute: every time evaluation must be referred to a specific observer.  Muons lifetime is actually longer than  Basing on the value measured in laboratory, we obtain the muon lifetime following this equation  ‘= 1-v 2 /c 2   ‘> 

11. Here’s the solution Now, let’s apply Einstein’s theory to the muon problem:  ‘= = 2,20x10 -5 s 1- (0,995c) 2 /c 2  x 10 -6 s (0,995c)(2.2x10 -5 )=6570m Now muons can reach the earth  ‘= 1-v 2 /c 2  5000 m

12. Relativity and common sense Anyway, Newtonian physics is still valid and useful in many situations in everyday life. Relativistic effects are not measurable at everyday speed. For example, travelling on the Space Shuttle, nowadays the fastest human vehicle, at 28000 km/h: Time delay per second is only 0, 000000000333 s. So, a clock positioned on the shuttle will be one second late in 100 years Supervision: Prof. Barbara Ranco