761 Words4 Pages

The Car in the Garage ”Paradox”

Sudarshan Neopane

BSc. Phy 3 rd Yr

26/02/2017

1

Introduction

It was 1905 when Albert Einstein published his papers on Special Relativity.

These papers changed our views on space, time, matter ,energy and simul- taneity. Special Relativity concerns itself with motions that are comparable with the speed of light.It has several counter-intuitive consequences. One of such is the car in the garage paradox. It’s one of the version of the pole in the barn paradox. It is a paradox resulting from the phenomenon of length contraction. 2

Brief Overview of Special Relativity

Special Relativity applies to the object in the inertial frame of reference. It is based on two postulates: the laws of physics are same on all inertial frames and speed of light in vacuum is constant in all inertial frames, regardless of the speed of the observer or source.

The consequences of these postulates are: length contraction, time dilation, mass increment and relative nature of simultaneity. According to special relativity,the length of an object in the direction of motion is shorter as com- pared to it’s length when it is at rest. Also the events that are simultaneous in one inertial frame are not simultaneous in another inertial frame in motion with respect to the first one ie. simultaneity is relative in nature.

We have the equation for length of an object l with velocity v and proper length l 0 (length as observed in rest frame) as, s l = l 0 1 − where, c=3 × 10 8 m/s

1

Sudarshan Neopane

BSc. Phy 3 rd Yr

26/02/2017

1

Introduction

It was 1905 when Albert Einstein published his papers on Special Relativity.

These papers changed our views on space, time, matter ,energy and simul- taneity. Special Relativity concerns itself with motions that are comparable with the speed of light.It has several counter-intuitive consequences. One of such is the car in the garage paradox. It’s one of the version of the pole in the barn paradox. It is a paradox resulting from the phenomenon of length contraction. 2

Brief Overview of Special Relativity

Special Relativity applies to the object in the inertial frame of reference. It is based on two postulates: the laws of physics are same on all inertial frames and speed of light in vacuum is constant in all inertial frames, regardless of the speed of the observer or source.

The consequences of these postulates are: length contraction, time dilation, mass increment and relative nature of simultaneity. According to special relativity,the length of an object in the direction of motion is shorter as com- pared to it’s length when it is at rest. Also the events that are simultaneous in one inertial frame are not simultaneous in another inertial frame in motion with respect to the first one ie. simultaneity is relative in nature.

We have the equation for length of an object l with velocity v and proper length l 0 (length as observed in rest frame) as, s l = l 0 1 − where, c=3 × 10 8 m/s

1

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