tim dilation.doc

7/27/2019 tim dilation.doc

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TERM PAPERMODERN PHYSICS AND ELECTRONICS

Topic: Time dilation and length contraction

Submitted to:Mr.Bharpur Singh

Submitted by:Rustam Singh

Registration No:10900942

Roll No:RC6903A06

Section:RC6903

Submitted on: 27.04.2010


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AKNOWLELDGEMENT

As usual large number of people deserves my thanks for the

help they provided me for the preparation for this term

paper.

First of all i would like to thanks my teacher Mr. Bharpur

Singh for her support during the preparation of this topic. I

am very thankful for her guidance.

I would also like to thanks my friends for the encouragementand information about the topic they provided to me during

to me during my effort to prepare this topic.


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INDEX

1. Introduction

2.Overview of time dilation

3.Time dilation and space flight

4. Question may arise in your mind

5. Derivation of Time Dilation

6. Length contraction

7. Example of Time Dilation and LengthContraction

8. Graph of time dilation and length

contraction

9. Reference


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Introduction

Time dilation is aphenomenon (or two phenomena, asmentioned below) described by the theory of relativity. It can beillustrated by supposing that two observers are in motion relativeto each other, and/or differently situated with regard to nearbygravitational masses. They each carry a clock of identicallysimilar construction and function. Then, the point of view ofeach observer will generally be that the otherobserver's clock isin error (has changed its rate). [1]

Overview of time dilation

Time dilation can arise from

(1) relative velocity of motion between the observers(2) Difference in their distance from gravitational mass.

(1) In the case that the observers are in relative uniform motion,and far away from any gravitational mass, the point of view ofeach will be that the other's (moving) clock is ticking at aslower

rate than the local clock. The faster the relative velocity, themore is the rate of time dilation. This case is sometimes calledspecial relativistic time dilation. It is often interpreted as time"slowing down" for the other (moving) clock. But that is onlytrue from the physical point of view of the local observer, and of
http://en.wikipedia.org/wiki/Phenomenonhttp://en.wikipedia.org/wiki/Theory_of_relativityhttp://en.wikipedia.org/wiki/Phenomenonhttp://en.wikipedia.org/wiki/Theory_of_relativity


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others at relative rest (i.e. in the local observer's frame ofreference). The point of view of the other observer will be thatagain the local clock (this time the other clock) is correct, and it

is the distant moving one that is slow. From a local perspective,time registered by clocks that are at rest with respect to the localframe of reference (and far from any gravitational mass) alwaysappears to pass at the same rate.

(2) There is another case of time dilation, where both observersare differently situated in their distance from a significantgravitational mass, such as (for terrestrial observers) the Earth or

the Sun. One may suppose for simplicity that the observers areat relative rest (which is not the case of two observers bothrotating with the Earth -- an extra factordescribed below). In thesimplified case, the general theory of relativity describes how,for both observers, the clock that is closer to the gravitationalmass, i.e. deeper in its "gravity well", appears to go slower thanthe clock that is more distant from the mass (or higher in altitude

away from the center of the gravitational mass). That does notmean that the two observers fully agree: each still makes thelocal clock to be correct; the observer more distant from themass (higher in altitude) makes the other clock (closer to themass, lower in altitude) to be slower than the local correct rate,and the observer situated closer to the mass (lower in altitude)makes the other clock (farther from the mass, higher in altitude)to be faster than the local correct rate. They agree at least that

the clock nearer the mass is slower in rate, and on the ratio ofthe difference. This is gravitational time dilation. [1]
http://en.wikipedia.org/wiki/Frame_of_referencehttp://en.wikipedia.org/wiki/Frame_of_referencehttp://en.wikipedia.org/wiki/Time_dilation#Time_dilation_due_to_mass_and_motion_in_combinationhttp://en.wikipedia.org/wiki/General_theory_of_relativityhttp://en.wikipedia.org/wiki/Gravity_wellhttp://en.wikipedia.org/wiki/Gravitational_time_dilationhttp://en.wikipedia.org/wiki/Frame_of_referencehttp://en.wikipedia.org/wiki/Frame_of_referencehttp://en.wikipedia.org/wiki/Time_dilation#Time_dilation_due_to_mass_and_motion_in_combinationhttp://en.wikipedia.org/wiki/General_theory_of_relativityhttp://en.wikipedia.org/wiki/Gravity_wellhttp://en.wikipedia.org/wiki/Gravitational_time_dilation


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Time dilation and space flight

Time dilation would make it possible for

passengers in a fast-moving vehicle to travelfurther into the future while aging very little, inthat their great speed slows down the rate ofpassage of on-board time. That is, the ship's clock(and according to relativity, any human travellingwith it) shows less elapsed time than the clocks ofobservers on Earth. For sufficiently high speeds theeffect is dramatic. For example, one year of travelmight correspond to ten years at home. Indeed, aconstant 1 g acceleration would permit humans totravel as far as light has been able to travel sincethe big bang (some 13.7 billion light years) in onehuman lifetime. The space travellers could returnto Earth billions of years in the future. A scenariobased on this idea was presented in the novel

Planet of the Apes by Pierre Boulle[1]

Question may arise in your mind

1. Is time dilation true? How big are the effects?

2. Do clocks at speed really run slower, and do

people or things travelling at speed live longer?

One question at a time. Yes, clocks do run more slowly. Planestravel about a million times more slowly than c (so is about1.0000000000005), but atomic clocks are very precise and so
http://en.wikipedia.org/wiki/Standard_gravityhttp://en.wikipedia.org/wiki/Big_banghttp://en.wikipedia.org/wiki/Light_yearhttp://en.wikipedia.org/wiki/Planet_of_the_Apes_(novel)http://en.wikipedia.org/wiki/Pierre_Boullehttp://en.wikipedia.org/wiki/Standard_gravityhttp://en.wikipedia.org/wiki/Big_banghttp://en.wikipedia.org/wiki/Light_yearhttp://en.wikipedia.org/wiki/Planet_of_the_Apes_(novel)http://en.wikipedia.org/wiki/Pierre_Boulle


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this tiny effect effect can actually be measured. In 1971, J.Haefele and R. Keating took atomic clocks on airlinerstravelling both East (with the Earth rotating underneath them:

we could call these "slow frames") and West (these planes havethe Earth's rotation speed plus their own, and return to wherethey came from). Apart from some complications due to thegravitational field variations and their acceleration (which aredealt with by general relativity), this is like the twin paradox,and it gave results in agreement with the relativistic prediction.(See the original paper by J.C. Hafele and R. E. Keating,Science 177, 166 (1972) for details. Do people age more slowly?

We don't know whether people age more slowly, because evencosmonauts don't travel fast enough for the effect to bestatistically observable on their life spans*. However, people'sages are determined by physical and chemical processes in ourbodies. Certainly we expect that people would age more slowlyat relativistic speeds. Particles certainly do. Particle acceleratorsgenerate some short lived particles (e.g. muons or pions) that

travel within a fraction of a percent of c, and (in the laboratoryframe) they survive for much longer than their lifetime when atrest in the lab frame. Muons with a half life of 1.5 microsecondsare also created several tens of km above the Earth in the upperatmosphere by cosmic rays. Travelling 50 km at c would take170 microseconds or 110 half lives, so we should expect theirnumbers to be reduced by a factor of 2110 ~ 1033 (i.e. effectivelynone) to reach the surface. In fact they are measured at sea leveland at various altitudes, with rates that agree with the relativisticdilation of their half lives. Time dilation happens, howevercounter-intuitive it may seem at first.
http://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htmhttp://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm


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* Low orbits are the fastest, travelling around

the Earth in about 90 minutes, which gives of

about 1.0000000003. Suppose that a

cosmonaut spent 2 years in space. Timedilation due to special relativity (neglecting

general relativistic effects) would give an

expected lifetime increase of 20 milliseconds.

Lives, let alone life expectancies, are not

measured that precisely!

How big are time dilation effects?

Note the shape of the curve above: only starts to become largeat speeds close to c. At 0.99*c, is 7. But in many moderndevices, electrons are accelerated to higher speeds than this. In a

typical electron accelerator used to treat cancers, the electronshave an energy of 20 MeV The speed of such electrons is0.9997*c and is 40.

Now of course an electron cannot go much faster than this, but itcan have a lot more energy. In the Large Electron-Positroncollider in Europe's nuclear research lab CERN, electrons (andpositrons, or anti-electrons) were accelerated to energies of

100 GeV. For such particles, v = 0.999 999 999 95*c and is200,000. Yes, time is slowed down by that factor. And themomentum is increased by that factor too: something that israther important in the design of the collider because theseelectrons must be turned to go in a circle.


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Nature can produce even larger particle energies. Some particlesstriking the Earth's upper atmosphere have energies that exceed2*1020 eV. If such particles are protons (with mass of about

1 GeV), their speeds would be0.999 999 999 999 999 999 999 995 c. For them, is 1011. Nowthe age of the universe is about 13 billion years for us, but forsuch particles, the age of the universe would be about (13 billionyears/1011), i.e. about a month. Such a particle could cross thevisible universe in a matter of months (their time). [2]

Derivation of Time Dilation

This is a derivation of the time dilation formula. This will becovered in detail in class, but here it is just in case it goes by toofast. Refer to Fig. 1.

A clock is made by sending a pulse of light toward a mirror at adistance L and back to a receiver. Each "tick" is a round-trip tothe mirror. The clock is shown at rest in the "Lab" frame in Fig.1a, or any time it is in its own rest frame. Consequently, it alsorepresents the clock at rest in rocket#1. Figure 1b is the way theclock looks in the lab when the clock is at rest in rocket#1,which is moving to the right with velocity v.


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Actually, our clock "ticks" once every round-trip of the lightpulse. So, we should use ct=2L, etc. But since both legs of the

round-trip are the same, we'll just use the one-way times forsimplicity.

Some notation:

t = time for light to reach the mirror in the lab for a clock at restin Rocket #1 (Fig. 1b)t' = time for light to reach the mirror in Rocket#1 in its own rest

frame (Fig. 1a)L = distance to mirror

So, the times and distances are related as follows:L = ct'L2 + v2*t2 = c2*t2 (Pythagorean Theorem)

Eliminate L from the equations:

c2

*t'2

= c2

*t2

- v2

*t2

t' = t*(1-v2/c2)

Since (1-v2/c2)


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Go back to Fig. 1c. Rocket#2 is moving with velocity v to theleft. Those clocks would also appear slow to observers in thelab. But, it is also the way a clock at rest in the lab appears in

rocket#1. So, lab clocks also appear slow to observers in the lab.Relativity is symmetrical! [3]

Length contraction

You have probably noticed that, in Jasper's versionof events, Zoe's car has shrunk. And vice versa. We

haven't proved that yet, but it's logically simple.

Suppose that Zoe and Jasper choose to measure

lengths in lightyears, lightseconds, and

lightnanoseconds* etc: i.e. they measure distance

by how long light takes to cover the distance. Ifthey agree on the speed of light, but disagree on

measurements of time, they must inevitably

disagree on length as well. If you observe

someone's clocks run slowly by a factor , you will

also observe her rulers to be short by a factor of :

that's the only way that she can measure the

speed of light to have the same value you get.

* The lightnanosecond is a convenient unit. c is

about 3 108 metres per second, and a

nanosecond is 10-9 seconds, so a


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lightnanosecond is 0.3 metres. (Americans,

who use British imperial units, can therefore

remember that the speed of light is about one

foot per nanosecond. The rest of us canremember it as 30 centimeters per

nanosecond.)

Zoe, who is a graffiti artist in her spare time, will

demonstrate this: she decides to tag the two ends

of the verandah. (The paint can is green, and it

sprays purple paint.) For Jasper, the distancebetween the tags will be his proper length, i.e.

the length measured in his frame, because they

are stationary with respect to him. Zoe can

measure the time between the two tags, and thus

get her measurement of the length of the

verandah.

Both agree that the time between the two tags - the time Zoetakes to go past the verandah - is two ticks of Zoe's clock. Thisis 2T' for Zoe, so the length that Zoe measures is 2vT'. But forJasper, two ticks of Zoe's clock takes 2T = 2T'. The length thatJasper measures for the verandah is 2vT = 2vT'. Jaspermeasures the verandah to be times longer than Zoe measures

it.

Further, the situation is symmetrical: Jasper observes the car tobe shrunk with respect to the verandah, while Zoe concludes thatthe verandah has shrunk with respect to the car. The proper


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length is always longer than a measure of the length fromanother frame. But can't one make a paradox from this? See the"pole in the barn" paradox. [2]

Example of Time Dilation and Length

Contraction:Suppose there are two vehicles. One is moving slightly fasterthan the other. You are sitting in the slower vehicle and want to

measure the speed of the faster vehicle right from your seat. Inorder to do that it is assumed that the faser vehicle is coming

from behind the slower vehicle. As soon as the faster advancingvehicle comes exactly in your X-axis or exactly in your right

or left front whatever the case may be, you begin measuring the

distance per second. It was found that the distance covered

by the faster moving vehicle just beside you was one half ofyour vehicle's length as you are measuring it with respect toyour

vehicle that is when it exactly juxtaposed your vehicle, yourecorded a time t0,and when it excelled your vehicle about one

half of your vehicle's length ,you recorded a time t1.The timedifference between the two intervals is one second as you kept

it so, so t1-t0=1Sec.Now stop your vehicle and measure its
http://www.phys.unsw.edu.au/einsteinlight/jw/module4_pole_paradox.htmhttp://www.phys.unsw.edu.au/einsteinlight/jw/module4_pole_paradox.htm


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length, divide it by two to get the half,.......Suppose it comes outto

be 2meters if your vehicle is 4meters long. You measured thedistance covered by the faster vehicle sitting in your own

slower moving vehicle, so your frame of reference is movingwith respect to the faster moving vehicle.Let repeat this experiment again but this time the frame ofreference will be at rest (apparent rest no absolute rest is there in

the universe as every thing keep moving with respect to oneanother), that is to say a standing person is measuring the

distance travelled by the faster vehicle in one second. No soonerdoes the faster vehicle cross the standing person on the

road, then he records a time t0 and there is an other friend on thefootpath and has been assigned the duty of marking the

field when he hears the sound form his friend. After one secondthe person yells at his friend and he marks the field just in

sideway front of the vehicle, and he record a time t1.The timedifference must be one second as he kept it so. Now they

measurs the distance between the mark and the person standingthat.........Suppose comes out to be 10meters.The

supposition is based upon the actual happening and every one


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with normal brain or common sense will agree to it.Why the length or distances covered by the same faster vehiclediffer when measured by the two obsevers?

It is because the length or distance is contracted in accordancewith the special theory of relativity.The length is shortened

in the direction of the motion when your frame of reference ismoving with respect to the item being measured.A relative

stationary frame of reference will not show this contraction.Thisis what we call length contraction.

Now, just think opposite of the above experiment. If the vehiclewere to move 2meters per second with respect to the standing

person,it would have taken 5Secs to cover the 10 meters.Itmeans that in moving vehicle ,time slowed down,that is it

dropped from 5secs to 1sec,or in other words time has been

dilated with respect to the stationary person.It means that each

five seconds of the standing person equals one second of theperson sitting in the slower moving vehicle.This is what we

call Time Dilation and it's a real phenomenon.It follows that thestanding person's life is reduced by 5secs and the life of the

person sitting in the vehicle is just reduced by 1sec,that is to saythat time is different in different frames of reference. The

faster your frame of reference moves, the slower is your agingprocess or the slower your time passes.


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Prove that no absolute space (a body in rest) is possible:No absolute space is possible because of the fact the fact that allbodies in the universe keep moving. The faster they

move, the slower their time will pass .When their speed equalsspeed of light, their time stops, it do not pass any further. Light

Speed is the Ultimatum as it is so fast that it do not allow time topass by.Conversely thinking, the slower body moves, the faster it's timewill pass. Moreover when a body comes to rest, then its time

will be so much faster that it will not give the body its existenceas it would be for a very brief time that is negligible or in

other words rest things are non-existant in this universe becauseof the fact that when a body gets the speed of light ,it's

time stops,it never ages......likewise is the case of the oppositeextreme that is if the a body gets zero speed then there is no

time associated with it so it does not exist as the time will be atits fastest movement.......quite for a blank of eye.If there is movement, there is time, there is an object.........Ifthere is time, there is movement, there is an object.....If there isobject, there is time, and there is movement. If there is rest, thereis no object, there is no movement, and there is no time.Conclusively......................If there is life there isMovement.....otherwise nothing exist.So life has three very basiccomponents...............Movement.....by what........by Object....in


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[1] http://en.wikipedia.org/wiki/Time_dilation

[2]

http://www.phys.unsw.edu.au/einsteinlight/jw/mod

ule4_time_dilation.htm

[3]http://www.drphysics.com/syllabus/time/time.html

[4]http://hubpages.com/hub/Time-Dilation-and-Length-

Contraction

[5] http://www.britannica.com/EBchecked/topic-

art/458757/86705/Length-contraction-and-time-

dilation-As-an-object-approaches-the
http://en.wikipedia.org/wiki/Time_dilationhttp://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htmhttp://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htmhttp://www.drphysics.com/syllabus/time/time.htmlhttp://hubpages.com/hub/Time-Dilation-and-Length-Contractionhttp://hubpages.com/hub/Time-Dilation-and-Length-Contractionhttp://var/www/apps/conversion/tmp/scratch_2/5%5D%20http://www.britannica.com/EBchecked/topic-art/458757/86705/Length-contraction-and-time-dilation-As-an-object-approaches-thehttp://var/www/apps/conversion/tmp/scratch_2/5%5D%20http://www.britannica.com/EBchecked/topic-art/458757/86705/Length-contraction-and-time-dilation-As-an-object-approaches-thehttp://var/www/apps/conversion/tmp/scratch_2/5%5D%20http://www.britannica.com/EBchecked/topic-art/458757/86705/Length-contraction-and-time-dilation-As-an-object-approaches-thehttp://en.wikipedia.org/wiki/Time_dilationhttp://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htmhttp://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htmhttp://www.drphysics.com/syllabus/time/time.htmlhttp://hubpages.com/hub/Time-Dilation-and-Length-Contractionhttp://hubpages.com/hub/Time-Dilation-and-Length-Contractionhttp://var/www/apps/conversion/tmp/scratch_2/5%5D%20http://www.britannica.com/EBchecked/topic-art/458757/86705/Length-contraction-and-time-dilation-As-an-object-approaches-thehttp://var/www/apps/conversion/tmp/scratch_2/5%5D%20http://www.britannica.com/EBchecked/topic-art/458757/86705/Length-contraction-and-time-dilation-As-an-object-approaches-thehttp://var/www/apps/conversion/tmp/scratch_2/5%5D%20http://www.britannica.com/EBchecked/topic-art/458757/86705/Length-contraction-and-time-dilation-As-an-object-approaches-the

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