Conceptual Physics

35.13 - Gotchas

If you measure the speed of light from a star that is moving toward you, you will get a higher value than if you measure the speed of light from a

star that is moving away from you. No! You will measure the same speed. The speed of light does not change based on motion of source or

observer. This is one of Einstein’s postulates.

You are flying from Earth to Alpha Centauri at a constant speed of 150,000,000 m/s. Given your incredible speed, you should expect some of

the laws of physics to change. No, Einstein’s other postulate is that the laws of physics are the same in any inertial reference frame. You are

moving at a constant speed, so you are in an inertial reference frame.

I’m watching an airplane flying overhead at 400 km/hr. The pilot throws and catches a ball, measuring the time with a stopwatch. Her stopwatch

measures the proper time. Yes, that is correct.

Since you are standing still as you watch the plane pass by, you measure its proper length. No. You have to be at rest relative to an object to

measure its proper length. However, in the case of an airplane, the difference is negligible í not so for relativistic speeds!

Einstein was very smart. Yes.

35.14 - Summary

Einstein radically changed our perception of space and time with his two postulates

of special relativity. The first postulate states that the laws of physics are the same

for observers in any inertial reference frame. The second postulate states that the

speed of light in a vacuum is the same in all inertial reference frames.

An event is specified by giving its space and time coordinates. Observers who are in

different inertial reference frames will assign different coordinates to the same

event.

Observers in a reference frame where two events occur at the same place measure

a time interval between those events called the proper time. Observers moving

relative to that frame will always measure a longer time interval. This effect is known

as time dilation.

The inability to agree on time intervals led to Einstein’s thought experiment about

the concept of simultaneity. In this thought experiment, he showed that observers in

reference frames moving relative to one another would not agree that there was

zero time interval between separated events í in short, they would disagree about

whether events occurred simultaneously or not.

Special relativity also correctly predicts that different observers may not agree on

the spatial interval between two events. The length of an object at rest in an inertial

reference name is known as its proper length. Observers who are moving relative to

that frame will always measure a shorter length than the proper length. This effect is

known as length contraction.

The Doppler effect applies to light. The astronomer Hubble used this effect to argue

that the universe is expanding.

The intertwining of space and time means that a relativistic definition of linear

momentum must be accepted if consistent relations among them are to be retained

at both low and high speeds, and for observers in all inertial reference frames.

Special relativity reveals a previously unseen connection between two fundamental

concepts: mass and energy. A mass has a tremendous amount of rest energy

locked up, ready to be released either in a terrifying chain reaction or in a controlled,

useful manner. Meanwhile, the converse is also true: Energy has a mass equivalent

and may be transformed into matter.

Time dilation

t = Ȗt 0

Lorentz factor

Length contraction

Doppler shift

Source/observer closing:

Source/observer separating:

Relativistic momentum

Rest energy

E 0 = mc^2

Total energy

E = Ȗmc^2

(^654) Copyright 2007 Kinetic Books Co. Chapter 35