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Lorentz Transformation

This document discusses key concepts from special relativity including Lorentz transformations, length contraction, and time dilation. It provides equations for Lorentz transformations and explains that length is contracted and time is dilated in a moving reference frame compared to a stationary frame. Length is greatest and time passes most quickly in the frame where an object is at rest.

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Bhupendra Kumar Arjun
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218 views8 pages

Lorentz Transformation

This document discusses key concepts from special relativity including Lorentz transformations, length contraction, and time dilation. It provides equations for Lorentz transformations and explains that length is contracted and time is dilated in a moving reference frame compared to a stationary frame. Length is greatest and time passes most quickly in the frame where an object is at rest.

Uploaded by

Bhupendra Kumar Arjun
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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ENGINEERING PHYSICS

Topic :
• Lorentz Transformation
•Length Contraction
•Time Dilation

Name :
Branch : B.Tech
Computer Science (1)
Lorentz Transformation

The primed frame moves with velocity v in the x direction


with respect to the fixed reference frame. The reference
frames coincide at t=t'=0. The point x' is moving with the
primed frame.
S S’

P(x, y, z) in fixed frame P(x’, y’, z’) in moving frame

Lorentz Transformation implies: c2 t2 – (x2 + y2 + z2) = c2 t’2 – (x’2 + y’2 + z’2) (Lorentz
invariant)

x2 + y2 + z2 x’2 + y’2 + z’2


c2 = = is the same (speed of light )2 in the two frames
t2 t’2
t and t’ cannot be equal

Two “events” (x1, t1) and (x2, t2) at the same time t1 = t2 in S are do not happen at the same time in
S’, t1’ ≠ t2’.
Lorentz Transformation Equations

y = y’ z = z’

The reverse Lorentz


Transformation Equations

Direct Lorentz Transformation


Equations
Length Contraction

The length of any object in a moving frame will appear


foreshortened in the direction of motion, or contracted.
The amount of contraction can be calculated from the
Lorentz transformation. The length is maximum in the
frame in which the object is at rest.
Time Dilation

A clock in a moving frame will be seen to be running


slow, or "dilated" according to the Lorentz
transformation. The time will always be shortest as
measured in its rest frame. The time measured in the
frame in which the clock is at rest is called the "proper
time".
If the time interval T0  t '2 t '1 is measured in the moving reference
frame, then T  t2  t1 can be calculated using the Lorentz transforma tion

vx'2 vx'1
t '2  2  t '1  2 The time measurements made
T  t2  t1  c c in the moving frame are made at
the same location, so the
v2
1 2 expression reduces to:
c
T0
T  T0 
2
v
1
c2
For small velocities at which the relativity factor is very
close to 1, then the time dilation can be expanded in a
binomial expansion to get the approximate expression:

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