# 28.1 Einstein’s postulates  (Page 2/8)

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## Einstein’s second postulate

The second postulate upon which Einstein based his theory of special relativity deals with the speed of light. Late in the 19th century, the major tenets of classical physics were well established. Two of the most important were the laws of electricity and magnetism and Newton’s laws. In particular, the laws of electricity and magnetism predict that light travels at $c=3\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ in a vacuum, but they do not specify the frame of reference in which light has this speed.

There was a contradiction between this prediction and Newton’s laws, in which velocities add like simple vectors. If the latter were true, then two observers moving at different speeds would see light traveling at different speeds. Imagine what a light wave would look like to a person traveling along with it at a speed $c$ . If such a motion were possible then the wave would be stationary relative to the observer. It would have electric and magnetic fields that varied in strength at various distances from the observer but were constant in time. This is not allowed by Maxwell’s equations. So either Maxwell’s equations are wrong, or an object with mass cannot travel at speed $c$ . Einstein concluded that the latter is true. An object with mass cannot travel at speed $c$ . This conclusion implies that light in a vacuum must always travel at speed $c$ relative to any observer. Maxwell’s equations are correct, and Newton’s addition of velocities is not correct for light.

Investigations such as Young’s double slit experiment in the early-1800s had convincingly demonstrated that light is a wave. Many types of waves were known, and all travelled in some medium. Scientists therefore assumed that a medium carried light, even in a vacuum, and light travelled at a speed $c$ relative to that medium. Starting in the mid-1880s, the American physicist A. A. Michelson, later aided by E. W. Morley, made a series of direct measurements of the speed of light. The results of their measurements were startling.

## Michelson-morley experiment

The Michelson-Morley experiment    demonstrated that the speed of light in a vacuum is independent of the motion of the Earth about the Sun.

The eventual conclusion derived from this result is that light, unlike mechanical waves such as sound, does not need a medium to carry it. Furthermore, the Michelson-Morley results implied that the speed of light $c$ is independent of the motion of the source relative to the observer. That is, everyone observes light to move at speed $c$ regardless of how they move relative to the source or one another. For a number of years, many scientists tried unsuccessfully to explain these results and still retain the general applicability of Newton’s laws.

It was not until 1905, when Einstein published his first paper on special relativity, that the currently accepted conclusion was reached. Based mostly on his analysis that the laws of electricity and magnetism would not allow another speed for light, and only slightly aware of the Michelson-Morley experiment, Einstein detailed his second postulate of special relativity    .

## Second postulate of special relativity

The speed of light $c$ is a constant, independent of the relative motion of the source.

Deceptively simple and counterintuitive, this and the first postulate leave all else open for change. Some fundamental concepts do change. Among the changes are the loss of agreement on the elapsed time for an event, the variation of distance with speed, and the realization that matter and energy can be converted into one another. You will read about these concepts in the following sections.

## Misconception alert: constancy of the speed of light

The speed of light is a constant $c=3.00×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ in a vacuum . If you remember the effect of the index of refraction from The Law of Refraction , the speed of light is lower in matter.

Explain how special relativity differs from general relativity.

Special relativity applies only to unaccelerated motion, but general relativity applies to accelerated motion.

## Section summary

• Relativity is the study of how different observers measure the same event.
• Modern relativity is divided into two parts. Special relativity deals with observers who are in uniform (unaccelerated) motion, whereas general relativity includes accelerated relative motion and gravity. Modern relativity is correct in all circumstances and, in the limit of low velocity and weak gravitation, gives the same predictions as classical relativity.
• An inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force.
• Modern relativity is based on Einstein’s two postulates. The first postulate of special relativity is the idea that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference. The second postulate of special relativity is the idea that the speed of light $c$ is a constant, independent of the relative motion of the source.
• The Michelson-Morley experiment demonstrated that the speed of light in a vacuum is independent of the motion of the Earth about the Sun.

## Conceptual questions

Which of Einstein’s postulates of special relativity includes a concept that does not fit with the ideas of classical physics? Explain.

Is Earth an inertial frame of reference? Is the Sun? Justify your response.

When you are flying in a commercial jet, it may appear to you that the airplane is stationary and the Earth is moving beneath you. Is this point of view valid? Discuss briefly.

what is a kaleidoscope?
A kaleidoscope is an optical instrument with two or more reflecting surfaces tilted to each other in an angle, so that one or more (parts of) objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection.
Onye
well, the reason for the rising of water in capillary tube, Is it the surface tension or adhesive force between water and tube ? Is there any relation of surface tension with adhesive force ? I'm curious to know. Can anyone answer this to me please ?
The adhesive force pull the water up the side of the tube.... While the surface tension holds up the water rising in the tube..... and the keep rising until the surface tension balances the weight of water column....
Abdullateef
what is drift velocity?
avg velocity of a particle in a material due to electric field
Cristiano
what's are maxwells equation on free space??
what is Boltzmann's constant
what is gravitational field strength
Michael
yes ahmed becz a body though with constant speed changes its direction posseses aceleration.
what is Boltzmann constant
Is a body moving with constant speed in a circular path undergoing acceleration?
since it is continually changing its direction I would not say speed but velocity and sinced you said constant then I don't think it is accelerating
Orji
pls what are the formulas for transformers??
Data's.... yes you could write "a" as "g" provided the term used in the question is "acceleration due to gravity"
Second law of motion
Second law of motion States that the rates of change of momentum is proportional to the external unbalanced force... I.e... : F = ma
Abdullateef
Rheostat is used to control current by varying resistance
I little can't understand this can anyone explain it to me.
a ball is kicked with a velocity of 8ms at an angle of 30°to the horizontal. calculate the time of flight of the ball
0.8 seconds. We need vertical speed (y axis) for this task. V final = V initial + a*t. V initial on y axis is 4 m/s, as V initial * sin(30°) = 8 / 2 = 4. Speed of the ball at the start will be equal to its speed when it hits the ground - V final = -4 m/s. a = -10 m/s^2 (acceleration due to gravity)
Data's
rearrange the formula at the beginning and you will get t = (V final - V initial) / a. That is -8 / -10
Data's
you could write "a" as "g"
Data's
(170-L1)÷[L1×(35-10)]=5.5 assume marbles expansion is 5.5