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Addition of velocities in the Newtonian physics

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

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Addition of velocities in the Newtonian physics

v= speed of the train measured from the platform

w2=man’s speed measured from the platform

w1=man’s speed measured

from the train





If atorch is switched on on the train, from platform we should measure the speed of light as


where v is the train speed and c is light speed from the train






the man on the platform measures the same light speed from the train


the Newtonian physics laws are not valid any more

addition of velocities following einstein s physics
Addition of velocities following Einstein’s physics

So, we need another rule to add velocities







  • In Einstein’s physics:
  • c doesn’t depend on the observer
  • c is a limit speed,
bertozzi s experience
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

bertozzi s results vs classical prediction
Bertozzi’s results vs classical prediction

Instead of following a linear progression the experimental graphic turned out to be like this:


Linear prediction


Limit speed

Speed of electrons

Light speed

Experimental results

Electrons kinetic energy

Once again Newtonian physics is not valid


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

how can muons reach the earth
How can muons reach the Earth?

Muon average lifetime as measured in laboratory is 2,2x10-6s, we’ll call it t.

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 (2x10-5s)= 657m

But we detect them on the earth!

5000 m

muons and time dilation
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 t.

Basing on the value measured in laboratory, we obtain the muon lifetime following this equation



t‘> t


here s the solution
Here’s the solution

Now, let’s apply Einstein’s theory to the muon problem:



2.20x 10-6 s

t‘= = 2,20x10-5 s


1- (0,995c)2/c2


Now muons can reach the earth

5000 m

relativity and common sense
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