The Galilean transformation nevertheless violates Einstein’s postulates, because the velocity equations state that a pulse of light moving with speed
c along the
x -axis would travel at speed
$c-v$ in the other inertial frame. Specifically, the spherical pulse has radius
$r=ct$ at time
t in the unprimed frame, and also has radius
$r\prime =ct\prime $ at time
$t\prime $ in the primed frame. Expressing these relations in Cartesian coordinates gives
This cannot be satisfied for nonzero relative velocity
v of the two frames if we assume the Galilean transformation results in
$t=t\prime $ with
$x=x\prime +vt\prime .$
To find the correct set of transformation equations, assume the two coordinate systems
S and
$S\prime $ in
[link] . First suppose that an event occurs at
$(x\prime ,0,0,t\prime )$ in
$S\prime $ and at
$(x,0,0,t)$ in
S , as depicted in the figure.
Suppose that at the instant that the origins of the coordinate systems in
S and
$S\prime $ coincide, a flash bulb emits a spherically spreading pulse of light starting from the origin. At time
t , an observer in
S finds the origin of
$S\prime $ to be at
$x=vt.$ With the help of a friend in
S , the
$S\prime $ observer also measures the distance from the event to the origin of
$S\prime $ and finds it to be
$x\prime \sqrt{1-{v}^{2}\text{/}{c}^{2}}.$ This follows because we have already shown the postulates of relativity to imply length contraction. Thus the position of the event in
S is
This set of equations, relating the position and time in the two inertial frames, is known as the
Lorentz transformation . They are named in honor of H.A. Lorentz (1853–1928), who first proposed them. Interestingly, he justified the transformation on what was eventually discovered to be a fallacious hypothesis. The correct theoretical basis is Einstein’s special theory of relativity.
The reverse transformation expresses the variables in
S in terms of those in
$S\prime .$ Simply interchanging the primed and unprimed variables and substituting gives:
Spacecraft
$S\prime $ is on its way to Alpha Centauri when Spacecraft
S passes it at relative speed
c /2. The captain of
$S\prime $ sends a radio signal that lasts 1.2 s according to that ship’s clock. Use the Lorentz transformation to find the time interval of the signal measured by the communications officer of spaceship
S .
Solution
Identify the known:
$\text{\Delta}t\prime ={t}_{2}\prime -{t}_{1}\prime =1.2\phantom{\rule{0.2em}{0ex}}\text{s};\phantom{\rule{0.2em}{0ex}}\text{\Delta}x\prime =x{\prime}_{2}-x{\prime}_{1}=0.$
Identify the unknown:
$\text{\Delta}t={t}_{2}-{t}_{1}.$
Express the answer as an equation. The time signal starts as
$\left(x\prime ,{t}_{1}\prime \right)$ and stops at
$\left(x\prime ,{t}_{2}\prime \right).$ Note that the
$x\prime $ coordinate of both events is the same because the clock is at rest in
$S\prime .$ Write the first Lorentz transformation equation in terms of
$\text{\Delta}t={t}_{2}-{t}_{1},$$\text{\Delta}x={x}_{2}-{x}_{1},$ and similarly for the primed coordinates, as:
torque is actually the rotational equivalent of linear force....as this equation tells..... however in general terms it is the turning effect of applied force
ashwani
Torque is moment of Force if a force is applied at some finite distance from COM of a body it produce rotation.
For pure rotation we need to apply Couple not Torque...
All matter is composed of two sets of three dimensions. The first set (1,2,3) decay with a positive charge. The second set (4,5,6) decay with a negative charge. As they decay, they create space (7 8,9) dimensions.
John
Two sets of (1,2,3,4,5,6) dimensions create a proton, a neutron, and an electron. This is the primordial atom.
John
A 10kg mass lift to a height of 24m and release. what is the total energy of the system
عند قذف جسم إلى أعلى بسرعة إبتدائية فإنه سيصل إلى ارتفاع معين (أقصى ارتفاع) ثم يعود هابطاً نحو سطح الأرض .
إذا قُذِفَ جسم إلى أعلى ووجد أن سرعته 18 م / ث عندما قطع 1/4 المسافة التي تمثل أقصى ارتفاع سيصله فالمطلوب إيجاد السرعة التي قُذِف بها بالمتر / ث . إن هذه السرعة هي واحدة من الإجابات التالية
light energy (photons) through semiconduction of N-P junction into electrical via excitation of silicon purified and cristalized into wafers with partially contaminated silicon to allow this N-P function to operate.
Michael
i.e. Solar pannel.
Michael
Photoelectric emission is the emission of electrons on a metal surface due to incident rays reflected on it
Benita
If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well.Why not?
it has everything to do with the angle the UV sunlight strikes your sunglasses.
Jallal
this is known as optical physics. it describes how visible light, ultraviolet light and infrared light interact when they come into contact with physical matter. usually the photons or light upon interaction result in either reflection refraction diffraction or interference of the light.
Jallal
I hope I'm clear if I'm not please tell me to clarify further or rephrase