# RELATIVITY

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Basics of special theory of relativity

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### RELATIVITY:

RELATIVITY Introduction to Einstein’s theory of relativity Does every assertion make sense: Obviously not . Even if we take some words and link them together in strict accordance with the rules of grammar , the result may be complete nonsense . There is no sense whatsoever ,for example , in the assertion that “water is triangular”. However , not all nonsense is so obvious . All too often an assertion which appears quite reasonable at first glance turns out to be absolute nonsense under closer scrutiny .

### Relativity we are used to:

Relativity we are used to Sir . Albert Einstein Right or left: On what side of the street-right or left-is the house ? You cannot possibly answer this question offhand. If you go from the bridge towards the woods , it will be on your left-hand side , and if you go in the opposite direction , it will be on your right hand side . Speaking of the left-or right hand side of a street you must mention the relative direction.

### Who is Bigger?:

Who is Bigger ? Consider a cow and a cowherd separated by a definite distance . When viewed from near the cowherd , the cow seems to be smaller in size. But when viewed from near the cow , the cowherd seems to be smaller in size . As the two cases are viewed from different points-one closer to the cowherd and the other closer to the cow , it is not the true dimensions of an object that are essential for analysis , but the angle from which they are viewed from . And these angular dimensions of the objects are quite obviously relative . It is senseless to speak about angular dimensions of the objects unless the latter are pinpointed in space . For instance , there is no sense in saying that a tower is seen from an angle of 45 degree .But if you say that a tower of 15metres away from you is seen at an angle of 45 degree , that is quite reasonable . It follows , moreover , that the tower is 15metres high.

### The relative appears absolute: :

The relative appears absolute : If we shift our point of view of observation slightly , the angular dimensions are often used in astronomy . Stellar maps are supplied with angular distances between the stars , i.e., the angles at which the distance between the stars is seen from the Earth. Regardless of our movements on the Earth , and regardless of our point of observation , we shall always see the stars at one and the same distance from each other . This is due to the tremendous , inconceivably great distances that separate us from the stars .compared to them our movement on earth from point to point is so insignificant that we may easily disregard it . Therefore , in this case angular distances may be accepted as absolute distances .

### If we take the rotation of the Earth round the Sun into account , the change of the angular measurement becomes noticeable , though hardly significant . The picture would change radically , however , if we were to shift our observation point to some star-Sirius ,for example . All angular measurements would be different , and we would find the stars , which were far apart in our sky , closer together , and vice versa. :

If we take the rotation of the Earth round the Sun into account , the change of the angular measurement becomes noticeable , though hardly significant . The picture would change radically , however , if we were to shift our observation point to some star-Sirius ,for example . All angular measurements would be different , and we would find the stars , which were far apart in our sky , closer together , and vice versa.

### The absolute turns out to be relative::

We often say “up” and “down” . Are these notions absolute or relative ? At different times people gave different answers to this question . When people did not know that our Earth was round and imagined it to be as flat as a pancake , the vertical direction was regarded as an absolute concept . It was assumed that the vertical direction was one and the same at all points of the Earth’s surface and that it was quite normal to speak of absolute “up” and the absolute ”down”. When it was discovered that Earth was round , the notion “vertical” collapsed. Indeed , the Earth being round , the direction of a vertical line depends essentially on the position of the point on the Earth’s surface through which that line passes. At different points of the globe the vertical direction will be different. Since the notions of “up” and “ down” thus lost sense , unless the exact point on earth is specified , the absolute became relative. The absolute turns out to be relative:

### “Common sense” protests::

All this appears obvious to us today and we do not doubt it in the least . Nevertheless , we know from history that it has not been easy for man to realize the relativity of “up” and ”down” . People are inclined to ascribe absolute sense to concepts if their relativity is not evident from everyday experience. Let us recall the absurd objection to the fact that the Earth was round , which came down to us from the middle ages: how can people walk upside-down ….?! If we did not recognize the relativity of the vertical direction and took it to be absolute in Moscow , for example , then , naturally , people in New Zealand would be walking upside-down . But bear in mind that for New Zealanders muscovites , too , are walking upside-down . There is no contradiction in that at all , since the vertical direction is not really an absolute concept , but a relative one. We begin to feel the true meaning of the relativity of vertical directions only when we consider two points sufficiently far apart on the Earth’s surface-Moscow and New Zealand , for example. But when we take two points close to each other , then we are justified with the absolute concept. “Common sense” protests:

### 2.SPACE IS RELATIVE:

One and the same place or not?? Often we say that two events occurred in one and the same place and tend to ascribe absolute meaning to our assertion . But in reality it means nothing . It amounts to saying , “It is five o’clock now”, without specifying where in Moscow or Chicago. To understand this properly , let us imagine that two travellers have arranged to meet every day in one and the same compartment aboard the Moscow-Vladivostik express train and write letters to their husbands . Their husbands would hardly agree that their wives met at one and the same point in space . They would say , and not without reason , that these points were hundreds of kilometres apart . Did they not get the letters from cities. These two events-writing letters on the first and on the second day of the journey-occurred in one and the same place from the point of view of the wives , and in places hundreds of kilometres apart from the point of view of their husbands. 2.SPACE IS RELATIVE

### Who was right-the wives , or their husbands? We have no grounds to side with either of them . It is quite evident to us that the concept “at one and the same space” is relative. The two events may coincide in space only if we mention the bodies in relation to which the events are located. State of rest is lost for ever The amazing fact that a carriage in uniform rectilinear motion has no effect upon the behavior of the bodies in it , compels us to reverse our conception of the state of rest . It develops that the state of rest and the state of uniform and rectilinear motion do not differ . A carriage one which is moving uniformly and rectilinearly relative to the one that is in the state of rest may itself be considered in a state of rest . This means that there is not one absolute state of rest , but a countless number of carriages “in a state of rest” , all of them moving uniformly and rectilinearly relative to each other at various speeds. As the state of rest is not absolute , we have to mention every time in relation to which of the countless carriages moving uniformly and rectilinearly relative to each other we observe the given motion.:

Who was right-the wives , or their husbands? We have no grounds to side with either of them . It is quite evident to us that the concept “at one and the same space” is relative. The two events may coincide in space only if we mention the bodies in relation to which the events are located . State of rest is lost for ever The amazing fact that a carriage in uniform rectilinear motion has no effect upon the behavior of the bodies in it , compels us to reverse our conception of the state of rest . It develops that the state of rest and the state of uniform and rectilinear motion do not differ . A carriage one which is moving uniformly and rectilinearly relative to the one that is in the state of rest may itself be considered in a state of rest . This means that there is not one absolute state of rest , but a countless number of carriages “in a state of rest” , all of them moving uniformly and rectilinearly relative to each other at various speeds. As the state of rest is not absolute , we have to mention every time in relation to which of the countless carriages moving uniformly and rectilinearly relative to each other we observe the given motion.

### 3.The Tragedy of light:

Light does not propagate instantaneously We have convinced ourselves of the principle of the relativity of motion and of the existence of a countless number of “inertial frames” . However , there exists a kind of motion which , at first glance contradicts the principle we have established above . It is the propagation of light. 3.The Tragedy of light

### Principle of relativity of motion seems to be shaken!! The colossal but not infinite velocity of light in vacuum brings us into conflict with the principle of relativity of motion. Imagine a train hurtling along a tremendous speed of 240,000km/sec . We are riding in the head carriage , and an electric bulb is switched on in the tail carriage . Let us see what results we would get if we measured the time necessary for light to travel from one end of the train to the other. It would seem that this would differ from the one we would obtain if the train were at rest . Indeed , relative to a train moving at 240,000km/sec the light should travel at a speed of only 300,000 – 240,000=60,000km/sec . It is as if the light has to catch up with the head carriage . If we place the bulb at the head of the train and measure the time necessary for the light to reach the tail carriage , it would seem that its velocity in the direction opposite to the movement of the train should be 240,000 + 300,000 = 540,000km/sec . The light and the tail carriage move towards each other.:

Principle of relativity of motion seems to be shaken!! The colossal but not infinite velocity of light in vacuum brings us into conflict with the principle of relativity of motion. Imagine a train hurtling along a tremendous speed of 240,000km/sec . We are riding in the head carriage , and an electric bulb is switched on in the tail carriage . Let us see what results we would get if we measured the time necessary for light to travel from one end of the train to the other. It would seem that this would differ from the one we would obtain if the train were at rest . Indeed , relative to a train moving at 240,000km/sec the light should travel at a speed of only 300,000 – 240,000=60,000km/sec . It is as if the light has to catch up with the head carriage . If we place the bulb at the head of the train and measure the time necessary for the light to reach the tail carriage , it would seem that its velocity in the direction opposite to the movement of the train should be 240,000 + 300,000 = 540,000km/sec . The light and the tail carriage move towards each other.

### :

Thus , it appears that in a moving train light should propagate at different velocities in different directions , while in a train which is at standstill the velocity of light is the same in both directions Boarding a train…. Imagine a train 5,400,000km long moving with a uniform velocity of 240,000km/sec along a straight line. Suppose a lamp is switched on at some instant of time somewhere in the middle of the train . And suppose the automatic doors in the front and rear of the train carriages open the moment the light of the bulb reaches them . What will the people on board the train and those standing on the station platform see?? The people in the middle of the train will see the following: as light travels relative to the train at the same velocity in all directions 300,000km/sec , it will reach the rear and front carriages simultaneously , 9 seconds later (2,700,000:300,000) and both doors will open at the same time. .

### Relative to the station platform the light also travels at the speed of 300,000km/sec , but the rear carriage moves to meet the light beam . Therefore , the beam of light will reach rear carriage after ,:

Relative to the station platform the light also travels at the speed of 300,000km/sec , but the rear carriage moves to meet the light beam . Therefore , the beam of light will reach rear carriage after , 2,700,000/ (300,000+240,000) i.e., 5 seconds . The beam . The beam must catch up with the front carriage and , therefore , will reach it 45 seconds later , 2,700,000/ (300,000-240,000). It will seem to the people on the platform that the doors open at different times-the rear door first and the front door 45-5=40 seconds later.

### Thus , two absolutely identical events-opening of the front and rear doors of the train-will happen at the same time for the people onboard the train and with a 40-second interval for those on the platform. Velocity has its limits Before the second world war the speed of aircraft was far below speed of sound . Today we have supersonic aircraft . Radio waves propagate at a velocity of light . Could we perhaps create “superlight” telegraphy to send signals at velocities greater than that of light?....No that is an impossible thing to do. Indeed , if we could transmit signals at infinite velocities we would be able to establish simultaneity of two events happened simultaneously if the infinitely fast signal about the first event arrived at the same instant as the signal about the second event . Thus , simultaneity of two events would have acquired absolute character independent of the motion of the frame to which this assertion is applies.:

Thus , two absolutely identical events-opening of the front and rear doors of the train-will happen at the same time for the people onboard the train and with a 40-second interval for those on the platform. Velocity has its limits Before the second world war the speed of aircraft was far below speed of sound . Today we have supersonic aircraft . Radio waves propagate at a velocity of light . Could we perhaps create “superlight” telegraphy to send signals at velocities greater than that of light?....No that is an impossible thing to do. Indeed , if we could transmit signals at infinite velocities we would be able to establish simultaneity of two events happened simultaneously if the infinitely fast signal about the first event arrived at the same instant as the signal about the second event . Thus , simultaneity of two events would have acquired absolute character independent of the motion of the frame to which this assertion is applies.

### Earlier and later Let us assume that in our train with the lamp , which we shall call the Einstein’s train , the automatic device has failed and people in the train noticed that the front door opened 15 seconds earlier than the rear one . Conversely , the people on the station platform will notice that the rear door flew open 40-15=25 seconds earlier . An event that occurred earlier in one frame , would take place later for the other. It may occur to us that this relativity of the concepts of “earlier” and “later” should have its limits . It is not likely , after all , that a baby was born prior to the birth of its mother. Suppose a spot is formed on the Sun . Eight minutes later it is detected by an astronomer observing the Sun through the telescope . Anything the astronomer observing does after that will be absolutely later than the appearance of the spot-”later” from the standpoint of any frame from which the Sun and the astronomer are observed . On the contrary , everything that happens to the astronomer earlier than eight minutes before the appearance of the spot takes place absolutely earlier. :

Earlier and later Let us assume that in our train with the lamp , which we shall call the Einstein’s train , the automatic device has failed and people in the train noticed that the front door opened 15 seconds earlier than the rear one . Conversely , the people on the station platform will notice that the rear door flew open 40-15=25 seconds earlier . An event that occurred earlier in one frame , would take place later for the other. It may occur to us that this relativity of the concepts of “earlier” and “later” should have its limits . It is not likely , after all , that a baby was born prior to the birth of its mother. Suppose a spot is formed on the Sun . Eight minutes later it is detected by an astronomer observing the Sun through the telescope . Anything the astronomer observing does after that will be absolutely later than the appearance of the spot-”later” from the standpoint of any frame from which the Sun and the astronomer are observed . On the contrary , everything that happens to the astronomer earlier than eight minutes before the appearance of the spot takes place absolutely earlier.

### Capricious clocks and rulers “We board the train again” We are riding in the Einstein’s train along an endless railway . The distance between two stations is 864,000,000 km . It will take the travelling train at 240,000km/sec one hour to cover this distance. There are clocks at both stations . A traveller boarding the train at the first station sets his watch by the station clock . On arriving at the second station he is surprised to find that his watch is slow . At the repair shop he was told that his watch is in good order . What was the matter????? :

Capricious clocks and rulers “ We board the train again” We are riding in the Einstein’s train along an endless railway . The distance between two stations is 864,000,000 km . It will take the travelling train at 240,000km/sec one hour to cover this distance. There are clocks at both stations . A traveller boarding the train at the first station sets his watch by the station clock . On arriving at the second station he is surprised to find that his watch is slow . At the repair shop he was told that his watch is in good order . What was the matter?????

### To make it out , let us assume that the traveller sends a beam of light to the ceiling from an electric torch placed on the floor of the carriage . A mirror on the ceiling reflects the beam back to the torch . For the passenger in the train the beam occurs as if the light beam has travelled straight up to the ceiling without deviating , but for an observer on the station platform this appears to be as if the light beam has shifted to a finite distance when received and not straight as observed by the passenger onboard . This deviation appears like as if the light beam traced a triangular path. “Mind you that this observation is made considering Einstein’s train i.e., for velocity of train close to that of light’s . And not applicable for practical velocities”. :

To make it out , let us assume that the traveller sends a beam of light to the ceiling from an electric torch placed on the floor of the carriage . A mirror on the ceiling reflects the beam back to the torch . For the passenger in the train the beam occurs as if the light beam has travelled straight up to the ceiling without deviating , but for an observer on the station platform this appears to be as if the light beam has shifted to a finite distance when received and not straight as observed by the passenger onboard . This deviation appears like as if the light beam traced a triangular path. “ Mind you that this observation is made considering Einstein’s train i.e., for velocity of train close to that of light’s . And not applicable for practical velocities”.

### In the above video two spaceships are considered instead of Einstein’s train as explained in the above paragraph. We notice that to the observer on the platform the beam clearly travelled a greater distance than to those in the train . On the other hand we know that velocity of light is absolute i.e., it is the same for those riding in the train and for those who observe it from the platform . We conclude that a greater time interval elapsed at the station between the departure and return of the beam than in the train !!. ceiling(reflector) X B Y A D C Floor of the train(emitter) Figure(a) Figure(b):

In the above video two spaceships are considered instead of Einstein’s train as explained in the above paragraph. We notice that to the observer on the platform the beam clearly travelled a greater distance than to those in the train . On the other hand we know that velocity of light is absolute i.e., it is the same for those riding in the train and for those who observe it from the platform . We conclude that a greater time interval elapsed at the station between the departure and return of the beam than in the train !!. ceiling(reflector) X B Y A D C Floor of the train(emitter ) Figure(a) Figure(b)

### The figure(a) shows the passenger’s point of view of the beam of light where in the beam projector i.e., X transmits a light beam which is reflected by Y back straight to the projector without getting deviated . But the figure(b) show’s the observer on the platform’s point of view of light beam where in the beam projector projects the light beam which travels distance CB gets reflected by a reflector at B and seems to return to the floor of the train along the path BA . This is considered for theoretical values of velocities of train i.e., travelling close to speed of light . The different observations are due to different frame of observation of the incident . Now the relation is easy to calculate . Suppose the observer on the platform established that 10 seconds elapsed between the departure and return of light . During these 10 seconds the beam travelled 300,000*10=3,000,000km . It follows that sides CB and BA of the isosceles triangle ABC are 1,500,000km each . AC is evidently equal to the distance which the train travels in 10 seconds , i.e., 240,000*10=2,400,000km. Its now easy to calculate height of the carriage which is equal to BD , the height of triangle ABC.:

The figure(a) shows the passenger’s point of view of the beam of light where in the beam projector i.e., X transmits a light beam which is reflected by Y back straight to the projector without getting deviated . But the figure(b) show’s the observer on the platform’s point of view of light beam where in the beam projector projects the light beam which travels distance CB gets reflected by a reflector at B and seems to return to the floor of the train along the path BA . This is considered for theoretical values of velocities of train i.e., travelling close to speed of light . The different observations are due to different frame of observation of the incident . Now the relation is easy to calculate . Suppose the observer on the platform established that 10 seconds elapsed between the departure and return of light . During these 10 seconds the beam travelled 300,000*10=3,000,000km . It follows that sides CB and BA of the isosceles triangle ABC are 1,500,000km each . AC is evidently equal to the distance which the train travels in 10 seconds , i.e., 240,000*10=2,400,000km. Its now easy to calculate height of the carriage which is equal to BD , the height of triangle ABC.

### Let us recall that in a right angled triangle the square of the hypotenuse CB is equal to sum of squares of legs CD and BD . The equation √CB²=CD²+BD² helps us find that the height of carriage BD=√(CB²-CD²) . √(1,500,000²-1,200,000²)=900,000 km . Quite a height that , although it is not too surprising , considering the astronomical dimensions of the Einstein’s train. Point of view of the passenger , the path travelled by the beam from the floor to the ceiling and back again is obviously double the height , that is , 2*900,000=1,800,000 km . It will take 1,800,000/300,000=6 seconds for the beam to travel this distance. ClOcK pArAdOx While 10 seconds elapsed at the railway station , only 6 seconds passed on the train . This means that if the train arrived one hour after its departure according to the station clock , it travelled only (60*6)/10=36- minutes by the passenger’s watch . In other words , in an hour his watch was 24 minutes behind the station’s clock. It is easily seen that the greater the speed of the train the greater the time lag difference . In deed the closer the train approaches speed of light the closer the leg AD indicating the path of the train approaches the hypotenuse CB indicating the path travelled by the light beam in the same time interval. :

Let us recall that in a right angled triangle the square of the hypotenuse CB is equal to sum of squares of legs CD and BD . The equation √CB²=CD²+BD² helps us find that the height of carriage BD=√(CB²-CD²) . √(1,500,000²-1,200,000²)=900,000 km . Quite a height that , although it is not too surprising , considering the astronomical dimensions of the Einstein’s train. Point of view of the passenger , the path travelled by the beam from the floor to the ceiling and back again is obviously double the height , that is , 2*900,000=1,800,000 km . It will take 1,800,000/300,000=6 seconds for the beam to travel this distance. ClOcK pArAdOx While 10 seconds elapsed at the railway station , only 6 seconds passed on the train . This means that if the train arrived one hour after its departure according to the station clock , it travelled only (60*6)/10=36- minutes by the passenger’s watch . In other words , in an hour his watch was 24 minutes behind the station’s clock. It is easily seen that the greater the speed of the train the greater the time lag difference . In deed the closer the train approaches speed of light the closer the leg AD indicating the path of the train approaches the hypotenuse CB indicating the path travelled by the light beam in the same time interval.

### Consequently , all travelling clocks and watches lag behind timepieces in a state of rest . Time machine Now , let us assume that the Einstein’s train travels along a circular railway and not in a straight line . It will then return after a certain time to its point of departure . As we have already established , The passenger will discover that his watch is slow , and the faster the train goes the slower his watch will be . By increasing the speed of the train we may reach a point where only a day passes for stationmaster . So many years may elapse , as a matter of fact , that on returning home to the station of departure after a day’s journey (by his own watch) , our passenger will learn that all his relatives and friends are long since dead. During this journey by the circular railway the time of only two timepieces is compared-in the train and at the station of departure . :

Consequently , all travelling clocks and watches lag behind timepieces in a state of rest . Time machine Now , let us assume that the Einstein’s train travels along a circular railway and not in a straight line . It will then return after a certain time to its point of departure . As we have already established , The passenger will discover that his watch is slow , and the faster the train goes the slower his watch will be . By increasing the speed of the train we may reach a point where only a day passes for stationmaster . So many years may elapse , as a matter of fact , that on returning home to the station of departure after a day’s journey (by his own watch) , our passenger will learn that all his relatives and friends are long since dead. During this journey by the circular railway the time of only two timepieces is compared-in the train and at the station of departure .

### Travelling to a star:

Travelling to a star There are stars in the sky which are so far away from us that a beam of light takes 40 years to reach them . Since we already know that it is impossible to travel faster than the speed of light , we can well draw the conclusion that the star cannot be reached in less than 40 years . However this inference is erroneous , because we did not consider the time contraction involved in motion.

### Suppose we fly to a star in an Einstein’s rocket at a speed of 240,000 km/sec . For people on Earth we will reach the star in (300,000*40)/240,000=50 years . But for us , on board the rocket , flying time at the mentioned speed will shrink at a ratio of 10:6 . Hence , we shall reach the star in (6/10)*50=30 years , and not in 50 years . We shall reduce this flying time indefinitely by raising the speed of our Einstein rocket until it approaches the speed of light . Theoretically , travelling at a speed of light we can reach the star and return to Earth within a minute !! But on Earth 80 years will have passed just the same. To all appearances , we thus possess a way of prolonging human life , though only from the point of view of other people , since man ages according to “his” own time . To out regret , however this prospect is illusory if we take a closer look at it. To begin with , the human body is not adapted to a state of prolonged acceleration exceeding noticeably the acceleration due to gravity of Earth . It will require considerable time to accelerate to speeds close to velocity of light . Calculations show that in six months of travelling at an acceleration equal to that due to gravity our gain will amount to a mere six weeks . If we prolong our trip the gain in time will increase sharply . Twelve months in a flying rocket will yield an additional gain of 18 months , two years of travelling will give a gain of 28 years , and if we spend three years in interplanetary travel we will gain more than 360 years.:

Suppose we fly to a star in an Einstein’s rocket at a speed of 240,000 km/sec . For people on Earth we will reach the star in (300,000*40)/240,000=50 years . But for us , on board the rocket , flying time at the mentioned speed will shrink at a ratio of 10:6 . Hence , we shall reach the star in (6/10)*50=30 years , and not in 50 years . We shall reduce this flying time indefinitely by raising the speed of our Einstein rocket until it approaches the speed of light . Theoretically , travelling at a speed of light we can reach the star and return to Earth within a minute !! But on Earth 80 years will have passed just the same. To all appearances , we thus possess a way of prolonging human life , though only from the point of view of other people , since man ages according to “his” own time . To out regret , however this prospect is illusory if we take a closer look at it. To begin with , the human body is not adapted to a state of prolonged acceleration exceeding noticeably the acceleration due to gravity of Earth . It will require considerable time to accelerate to speeds close to velocity of light . Calculations show that in six months of travelling at an acceleration equal to that due to gravity our gain will amount to a mere six weeks . If we prolong our trip the gain in time will increase sharply . Twelve months in a flying rocket will yield an additional gain of 18 months , two years of travelling will give a gain of 28 years , and if we spend three years in interplanetary travel we will gain more than 360 years.

### Very comforting figures , don’t you think ?? The matter is less cheerful when we come to expenditure of energy . A rocket weighing a mere one ton and flying with a speed of 260,000 km/sec (the speed required to “double the time , i.e., for a year in the rocket to be equal to two on Earth) consumes 250,000,000,000,000 Kilo-watt-hours an amount which it takes the world several months to produce. However that is only what the rocket consumes in flight . We still have to figure out how much power it takes to accelerate our vehicle to a speed of 260,000 km/sec . Moreover , at the flight the spaceship will have to be decelerated for safe landing . How much power would that require ? It would still be 200 times as much as the amount we cited above , even if we had fuel enough to produce a jet escaping the engine at the highest speed possible-the speed of light . In other words , we would have to consume an amount of power that the world produces in several dozen years . Actually the jet escape velocity is scores of thousands of times less than the speed of light , making the power expenditure required for our imagined flight fabulously great. :

Very comforting figures , don’t you think ?? The matter is less cheerful when we come to expenditure of energy . A rocket weighing a mere one ton and flying with a speed of 260,000 km/sec (the speed required to “double the time , i.e., for a year in the rocket to be equal to two on Earth) consumes 250,000,000,000,000 Kilo-watt-hours an amount which it takes the world several months to produce. However that is only what the rocket consumes in flight . We still have to figure out how much power it takes to accelerate our vehicle to a speed of 260,000 km/sec . Moreover , at the flight the spaceship will have to be decelerated for safe landing . How much power would that require ? It would still be 200 times as much as the amount we cited above , even if we had fuel enough to produce a jet escaping the engine at the highest speed possible-the speed of light . In other words , we would have to consume an amount of power that the world produces in several dozen years . Actually the jet escape velocity is scores of thousands of times less than the speed of light , making the power expenditure required for our imagined flight fabulously great.

### Length contraction Time , as we have just seen , is not really an absolute concept . It is relative and requires precise indication of the frame from which it is observed. We found that space is relative . Yet despite the relativity of space we attributed an absolute character to the dimensions of bodies . In other words , we considered them to be the properties of the body which did not depend on the frame of reference . However , the theory of relativity forces us to abandon this conviction as well . Like our notion about time being absolute , it is a prejudice we have developed because we always deal with speeds infinitely smaller than the speed of light . Let us imagine that the Einstein train rushes past a platform 2,400,000 km long . The train travels from one end of the platform to the other in 2,400,000/240,000=10 seconds by the station clock . But by the passengers’ watches it will take the train only 6 seconds . The passengers will be fully justified to conclude that the platform is not 2,400,000 km but 240,000*6=1,440,000 km long. The length of the platform , as we see , is greater from the point of view of the frame which is stationary relative to it , than from the point of view of the frame relative to which the platform is moving . All moving bodies contract in the direction of their movement. However this contraction does not prove at all that motion is absolute . Likewise , the passengers will find that the platform has contracted , while the people on the platform will think that it is the train that has become shorter(ratio of 6:10):

Length contraction Time , as we have just seen , is not really an absolute concept . It is relative and requires precise indication of the frame from which it is observed. We found that space is relative . Yet despite the relativity of space we attributed an absolute character to the dimensions of bodies . In other words , we considered them to be the properties of the body which did not depend on the frame of reference . However , the theory of relativity forces us to abandon this conviction as well . Like our notion about time being absolute , it is a prejudice we have developed because we always deal with speeds infinitely smaller than the speed of light . Let us imagine that the Einstein train rushes past a platform 2,400,000 km long . The train travels from one end of the platform to the other in 2,400,000/240,000=10 seconds by the station clock . But by the passengers’ watches it will take the train only 6 seconds . The passengers will be fully justified to conclude that the platform is not 2,400,000 km but 240,000*6=1,440,000 km long. The length of the platform , as we see , is greater from the point of view of the frame which is stationary relative to it , than from the point of view of the frame relative to which the platform is moving . All moving bodies contract in the direction of their movement. However this contraction does not prove at all that motion is absolute . Likewise , the passengers will find that the platform has contracted , while the people on the platform will think that it is the train that has become shorter(ratio of 6:10)

### To sum up Precise and very convincing experiments force us to admit the validity of the theory of relativity , which reveals most amazing features in the world about us , the features evading us at the first glance . Does this mean that PHYSICS developed long before the proposal of the theory of relativity is to be thrown over board like a useless shoe ??? If this were so then new theories can crush the old ones just as said before…!! Without old theories there won’t exist a will to propose new theories to rectify the old ones . The word RESEARCH will lose its sense and there wont be any kind of advancement in technology as technology is based on research. The idea of Einstein’s theory of relativity may be obvious and also challenges common sense . This is theoretical PHYSICS and is not been achieved practically till the present day . Dealing with the velocities which are highly impossible to achieve this theory is gnawing PHYSISTS till this day. Imagine a passenger riding in an ordinary train adjusting his watch because , according to this theory , it would be behind the clock at the station . Everyone would make a laughing stock of him . The effect of , say , a jolt on a highly precise watch is far greater , not to mention the fact that the difference in time amounts to a microscopic fraction of a second. Theory of relativity is an imaginary experiment and valid for extremely high profile initializations. :

To sum up Precise and very convincing experiments force us to admit the validity of the theory of relativity , which reveals most amazing features in the world about us , the features evading us at the first glance . Does this mean that PHYSICS developed long before the proposal of the theory of relativity is to be thrown over board like a useless shoe ??? If this were so then new theories can crush the old ones just as said before…!! Without old theories there won’t exist a will to propose new theories to rectify the old ones . The word RESEARCH will lose its sense and there wont be any kind of advancement in technology as technology is based on research. The idea of Einstein’s theory of relativity may be obvious and also challenges common sense . This is theoretical PHYSICS and is not been achieved practically till the present day . Dealing with the velocities which are highly impossible to achieve this theory is gnawing PHYSISTS till this day. Imagine a passenger riding in an ordinary train adjusting his watch because , according to this theory , it would be behind the clock at the station . Everyone would make a laughing stock of him . The effect of , say , a jolt on a highly precise watch is far greater , not to mention the fact that the difference in time amounts to a microscopic fraction of a second. Theory of relativity is an imaginary experiment and valid for extremely high profile initializations .