# 5.5 The lorentz transformation

 Page 1 / 12
• Describe the Galilean transformation of classical mechanics, relating the position, time, velocities, and accelerations measured in different inertial frames
• Derive the corresponding Lorentz transformation equations, which, in contrast to the Galilean transformation, are consistent with special relativity
• Explain the Lorentz transformation and many of the features of relativity in terms of four-dimensional space-time

We have used the postulates of relativity to examine, in particular examples, how observers in different frames of reference measure different values for lengths and the time intervals. We can gain further insight into how the postulates of relativity change the Newtonian view of time and space by examining the transformation equations that give the space and time coordinates of events in one inertial reference frame in terms of those in another. We first examine how position and time coordinates transform between inertial frames according to the view in Newtonian physics. Then we examine how this has to be changed to agree with the postulates of relativity. Finally, we examine the resulting Lorentz transformation equations and some of their consequences in terms of four-dimensional space-time diagrams, to support the view that the consequences of special relativity result from the properties of time and space itself, rather than electromagnetism.

## The galilean transformation equations

An event    is specified by its location and time ( x , y , z , t ) relative to one particular inertial frame of reference S . As an example, ( x , y , z , t ) could denote the position of a particle at time t , and we could be looking at these positions for many different times to follow the motion of the particle. Suppose a second frame of reference $S\prime$ moves with velocity v with respect to the first. For simplicity, assume this relative velocity is along the x -axis. The relation between the time and coordinates in the two frames of reference is then

$x=x\prime +vt,\phantom{\rule{0.5em}{0ex}}y=y\prime ,\phantom{\rule{0.5em}{0ex}}z=z\prime \text{.}$

Implicit in these equations is the assumption that time measurements made by observers in both S and $S\prime$ are the same. That is,

$t=t\prime \text{.}$

These four equations are known collectively as the Galilean transformation    .

We can obtain the Galilean velocity and acceleration transformation equations by differentiating these equations with respect to time. We use u for the velocity of a particle throughout this chapter to distinguish it from v , the relative velocity of two reference frames. Note that, for the Galilean transformation, the increment of time used in differentiating to calculate the particle velocity is the same in both frames, $dt=dt\prime .$ Differentiation yields

${u}_{x}={u}_{x}^{\prime }+v,\phantom{\rule{0.5em}{0ex}}{u}_{y}={u}_{y}^{\prime },\phantom{\rule{0.5em}{0ex}}{u}_{z}={u}_{z}^{\prime }$

and

${a}_{x}={a}_{x}^{\prime },\phantom{\rule{0.5em}{0ex}}{a}_{y}={a}_{y}^{\prime },\phantom{\rule{0.5em}{0ex}}{a}_{z}={a}_{z}^{\prime }.$

We denote the velocity of the particle by u rather than v to avoid confusion with the velocity v of one frame of reference with respect to the other. Velocities in each frame differ by the velocity that one frame has as seen from the other frame. Observers in both frames of reference measure the same value of the acceleration. Because the mass is unchanged by the transformation, and distances between points are uncharged, observers in both frames see the same forces $F=ma$ acting between objects and the same form of Newton’s second and third laws in all inertial frames. The laws of mechanics are consistent with the first postulate of relativity.

#### Questions & Answers

can someone explain normalization condition
1 millimeter is How many metres
1millimeter =0.001metre
Gitanjali
The photoelectric effect is the emission of electrons when light shines on a material.
What is photoelectric effect
it gives practical evidence of particke nature of light.
Omsai
particle nature
Omsai
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
Anil
what are the applications of quantum mechanics to medicine?
Neptune
application of quantum mechanics in medicine: 1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles. 2) in Genomic medicine 3) in protein folding 4) in radio theraphy(MRI)
Anil
Quantam physics ki basic concepts?
why does not electron exits in nucleaus
electrons have negative
YASH
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
Amalesh
.......proton and neutron....
Amalesh
excuse me yash what negative
Rika
coz, electron contained minus ion
Manish
negative sign rika shrestha ji
YASH
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
Amalesh
yes yash ji
Rika
yes friends
Prema
koantam theory
Laxmikanta
yes prema
Rika
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
Prema
proton and nutron nuclear power is best than proton and electron kulamb force
Laxmikanta
what is de-broglie wave length?
Ramsuphal
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
expression for photon as wave
Are beta particle and eletron are same?
yes
mari
how can you confirm?
Amalesh
sry
Saiaung
If they are same then why they named differently?
Amalesh
because beta particles give the information that the electron is ejected from the nucleus with very high energy
Absar
what is meant by Z in nuclear physic
atomic n.o
Gyanendra
no of atoms present in nucleus
Sanjana
Note on spherical mirrors
what is Draic equation? with explanation
what is CHEMISTRY
it's a subject
Akhter
it's a branch in science which deals with the properties,uses and composition of matter
Eniabire
what is a Higgs Boson please?
god particles is know as higgs boson, when two proton are reacted than a particles came out which is used to make a bond between than materials
M.D
bro little abit getting confuse if i am wrong than please clarify me
M.D
the law of refraction of direct current lines at the boundary between two conducting media of