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# Time dilation and length contraction

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#### INTRODUCTION:

Time dilation is a happening (or two phenomena, as stated below) detailed by the theory of relativity. It could be illustrated by supposing that two observers are in movement relative to each other, and/or differently situated with regard to nearby gravitational masses.

Length contraction, regarding to Hendrik Lorentz, is the physical sensation of a reduction in length recognized by an observer in objects that travel at any non-zero velocity in accordance with that observer. This contraction (more formally called Lorentz contraction or Lorentz-Fitzgerald contraction) is usually only visible, however, at a substantial small fraction of the swiftness of light; and the contraction is only in the route parallel to the direction where the observed person is travelling.

#### SPECIAL RELATIVITY :

When such amounts as size, time period and mass are considered in elementary physics, no special point is made about how they are really measured This theory has an array of consequences which were experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity, contradicting the traditional notion that the period of the time period between two situations is equal for those observers. (Alternatively, it introduces the space-time period, which is invariant. ) Combined with other laws and regulations of physics, both postulates of special relativity anticipate the equivalence of matter and energy, as indicated in the mass-energy equivalence solution E=mc2, where c is the swiftness of light in a vacuum. The predictions of special relativity consent well with Newtonian mechanics in their common world of applicability, specifically in experiments where all velocities are small compared with the speed of light. Special relativity shows that c is not merely the speed of a certain phenomenon-namely the propagation of electromagnetic radiation (light)-but rather a simple feature of just how space and time are unified as space time. One of the consequences of the theory is that it is impossible for just about any particle that has recovery mass to be accelerated to the acceleration of light.

#### POSTULATES OF SPECIAL RELATIVITY:

TWO postulates are the following :

1. The regulation of physics will be the same in all inertial structures of guide.
2. The swiftness of light in free space has the same value in all inertial frame of reference.

#### OVERVIEW OF YOUR TIME DILATION :

Time dilation can arise from (1) relative velocity of movement between your observers, and (2) difference in their distance from gravitational mass.

In the truth that the observers are in comparative uniform movement, and far away from any gravitational mass, the idea of view of every will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the comparative velocity, the greater is the rate of your time dilation. This circumstance is sometimes called special relativistic time dilation. It is often interpreted as time "slowing down" for the other (moving) clock. But that is merely true from the physical viewpoint of the local observer, and of others at comparative recovery (i. e. in the local observer's framework of research). The point of view of the other observer will be that again the local clock (this time the other clock) is appropriate, which is the distant moving the one that is sluggish. From an area perspective, time listed by clocks that are at rest with respect to the local structure of reference (and definately not any gravitational mass) always appears to move at the same rate.

There is another case of the time dilation, where both observers are in a different way located in their distance from a substantial gravitational mass, such as (for terrestrial observers) the planet earth or the Sun. One may imagine for straightforwardness that the observers are at relative break (which is not the case of two observers both rotating with the planet earth -- a supplementary factor detailed below). In the simplified case, the general theory of relativity describes how, for both observers, the clock that is closer to the gravitational mass, i. e. deeper in its "gravity well", seems to go slower than the clock that is more distant from the mass (or higher in altitude away from the center of the gravitational mass). That will not mean that both observers fully agree with the fact: each still makes the local clock to be right; the observer more faraway from the mass (higher in altitude) makes the other clock (closer to the mass, reduced altitude) to be slower than the neighborhood right rate, and the observer situated closer to the mass (low in altitude) makes the other clock (further from the mass, higher in altitude) to be faster than the local right rate. They consent at least that the clock nearer the mass is slower in rate, and on the ratio of the difference. This is gravitational time dilation.

#### TIME DILATION:

• t0 is the proper time between happenings A and B for a slow-ticking observer within the gravitational field,
• tf is the coordinate time between occasions A and B for a fast-ticking observer at an arbitrarily large distance from the large subject (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system in which a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at significantly less than that rate),
• G is the gravitational constant,
• M is the mass of the thing creating the gravitational field,
• r is the radial coordinate of the observer (which is analogous to the classical distance from the guts of the object, but is truly a Schwarzschild coordinate),
• c is the rate of light, and r0 = 2GM / c2 is the called the Schwarzschild Radius of M. If a mass collapses so that its surface is situated at less than this radial coordinate (or in other words covers a location of less than 4pG2M2 / c4), then the object exists within the black hole.

#### LENGTH CONTRACTION:

This impact is negligible at everyday speeds, and can be ignored for everyone regular purposes. It is merely when an subject approaches greater speeds, it becomes important. At a acceleration of 13, 400, 000 m/s, the space is 99. 9% of the space at rest with a rate of 42, 300, 000 m/s still 99%. As the magnitude of the velocity approaches the speed of light, the result becomes dominant, as can be seen from the method:

Note that in this formula it is assumed that the object is parallel with its line of activity. Also remember that for the observer in relative movement, the distance of the thing is measured by subtracting the together measured distances of both ends of the object. For more general conversions, start to see the Lorentz transformations.

#### AN EXAMPLE OF TIME DILATION:

A spaceship is flying a distance of 5lighthours, for example from Globe to the dwarf planet which Globe and Pluto are motionless. Formula used :

• t. . time mentioned by the spaceship clock
• t. . time mentioned by the clocks of the Earth-Pluto-system
• v. . speed of the spacecraft relatively to the machine of Globe and Pluto
• c. . acceleration of light

#### REMARKS:

1. In a simplifying way there was assumed an inertial system in which Earth and Pluto are motionless; especially the action around the Sun was neglected.
2. According to an important result of the theory of relativity, an observer in the Earth-Pluto-system would see the spacecraft shortened in direction of movement. This so-called Lorentz contraction had not been taken into consideration in order to make it possible to learn from the spaceship's clock.

#### BASIS IN RELATIVITY:

The origins of span contraction in the special theory of relativity can be traced to the functional definitions of simultaneity and size. Matching to Milne and Bondi the following operational meanings are designated to simultaneity and size: an observer moving uniformly along a direct line delivers out a light indication at time t0 to a faraway point (stationary according to the observer), where it comes and is also immediately reflected at time tr, arriving back at the observer at time ta. What time does the observer ascribe to enough time of representation tr, or, what event is simultaneous with the representation? Let l be the distance to the point of representation. An observer, with his or her explanation of c, says it requires time l / c for light to reach the reflector. Because light vacations at the same quickness c in both directions, it takes once both ways, so that it comes back to the observer at time ta = t0 + 2 l / c, or quite simply, the distance to the idea of reflection is l = c ( ta - t0 ) / 2, and the time at which reflection happened is simultaneous with the clock registering ( t0 + ta ) / 2. With these functional definitions for identifying size and simultaneous events, two observers in frequent relative motion at velocity v are considered, and their time and duration scales compared. The consequence of the above meanings is that point and size are connected by the Lorentz factor ?:

#### PHYSICAL ORIGIN OF Period CONTRACTION:

Length contraction as a physical effect on bodies made up of atoms held along by electromagnetic causes was proposed independently by George FitzGeraldand by Hendrik Lorentz. The next quotation from Joseph Larmor is indicative of the pre-relativity view of the result as a consequence of James Clerk Maxwell's electromagnetic theory:

". . . if the internal forces of the material system happen wholly from electromagnetic activities between your system of electrons which constitute the atoms, then your aftereffect of imparting to a reliable materials system a uniform speed of translation is to produce a uniform contraction of the machine in direction of motion, of amount (1-v2/c2)1/2

The extension of this specific lead to a general consequence was (and it is) considered "random" by many who like Einstein's deduction of it from the Process of Relativity without reference to any physics. In other words, length contraction is an inevitable result of the postulates of special relativity. To get a little physical understanding on why length contractions occur, consider what those postulates entail: by requiring the rate of light (a amount dependent on the essential properties of space and time) to be invariant in every frames of guide (including ones in motion) you can appreciate that it would require the "distortion" of the options of duration and time. Apparently Lorentz did not agree to the criticism that his proposal was "random".

". . . the interpretation distributed by me and FitzGerald had not been artificial. It was way more that it was the only possible one, and I added the comment that one finds the hypothesis if one extends to other pushes what one could already say about the influence of your translation on electrostatic forces. Experienced I emphasized this more, the hypothesis would have created less of the feeling of being developed ad hoc. " (emphasis added)

The Trouton-Rankine experiment in 1908 showed that span contraction associated with an object according to one frame, didn't cause changes in the level of resistance of the object in its snooze frame. This is in agreement with some current ideas at that time (Special Relativity and Lorentz ether theory) but in disagreement with FitzGerald's ideas on length contraction.

#### EXPERIMENTAL Verification:

Time dilation has been tested a number of that time period. The tedious work continued in particle accelerators since the 1950s, such as those at CERN, is a constantly running test of that time period dilation of special relativity. The specific experiments include:

#### Velocity time dilation tests

• Ives and Stilwell (1938, 1941), "An experimental analysis of the rate of your moving clock", in two parts. The explained reason for these tests was to confirm the time dilation effect, expected by Lamor-Lorentz ether theory, due to action through the ether using Einstein's recommendation that Doppler result in canal rays would give a suitable experiment. These experiments assessed the Doppler change of the radiation emitted from cathode rays, when seen from directly in front and from straight behind. The high and low frequencies recognized were not the classical principles predicted.
• Rossi and Hall (1941) likened the population of cosmic-ray-produced muons at the top of a mountain to that detected at sea level. Even though the travel time for the muons from the most notable of the mountain to the base is several muon half-lives, the muon test at the base was only reasonably reduced. This is explained by the time dilation attributed to their broadband relative to the experimenters. That is to say, the muons were decaying about 10 times slower than if indeed they were at snooze with regards to the experimenters.
• Hasselkamp, Mondry, and Scharmann(1979) measured the Doppler move from a source moving at right sides to the type of vision (the transverse Doppler shift). The most general romantic relationship between frequencies of the radiation from the moving resources is distributed by:

as deduced by Einstein (1905). For \phi = 90^\circ(\cos\phi = 0\, ) this reduces to fdetected = frest?. Thus there is absolutely no transverse Doppler switch, and the low regularity of the moving source can be attributed to the time dilation effect by itself.

#### Gravitational time dilation tests

• Pound, Rebka in 1959 assessed the very little gravitational red change in the occurrence of light emitted at a lesser elevation, where Earth's gravitational field is relatively more extreme. The results were within 10% of the predictions of standard relativity. Later Pound and Snider (in 1964) produced a straight closer result of 1%. This result is as expected by gravitational time dilation.

#### Velocity and gravitational time dilation combined-effect tests

• Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the united states Naval Observatory. Two other effects arrived to play. The clocks were likely to age more quickly (show a more substantial elapsed time) than the research clock, since they were in a higher (weaker) gravitational potential for almost all of the trip (c. f. Pound, Rebka). But also, contrastingly, the moving clocks were expected to age more gradually as a result of speed of their travel. The gravitational result was the larger, and the clocks endured a world wide web gain in elapsed time. To within experimental mistake, the net gain was steady with the difference between the predicted gravitational gain and the predicted velocity time loss. In 2005, the Country wide Physical Laboratory in the United Kingdom reported their limited replication of the experiment. The NPL experiment differed from the initial in that the caesium clocks were directed over a shorter trip (London-Washington D. C. come back), but the clocks were more accurate. The reported results are within 4% of the predictions of relativity.
• The Global Setting System can be viewed as a continuously working experiment in both special and general relativity. The in-orbit clocks are corrected for both special and standard relativistic time dilation results as referred to above, so that (as detected from the Earth's surface) they run at the same rate as clocks on the surface of the Earth. Furthermore, but not straight time dilation related, basic relativistic correction terms are built into the model of motion that the satellites transmit to receivers - uncorrected, these effects would result in an around 7-metre (23ft) oscillation in the pseudo-ranges assessed by a receiver over a routine of 12 time.

A assessment of muon lifetimes at different rates of speed is possible. Within the laboratory, poor muons are produced, and in the atmosphere extremely fast moving muons are created by cosmic rays. Taking the muon life-time at break as the laboratory value of 2. 22 s, the duration of a cosmic ray produced muon visiting at 98% of the velocity of light is approximately five times longer, in arrangement with observations. With this test the "clock" is the time taken by operations resulting in muon decay, and these processes happen in the moving muon at its "clock rate", which is much slower than the lab clock.

#### TIME DILATION AND SPACE FLIGHT:

Time dilation would make it possible for passengers in a fast-moving vehicle to travel further in to the future while ageing very little, for the reason that their great quickness slows down the rate of passing of on-board time. That is, the ship's clock (and regarding to relativity, any individual travelling with it) shows less elapsed time than the clocks of observers on Earth. For sufficiently high speeds the effect is dramatic. For instance, twelve months of travel might correspond to ten years at home. Indeed, a continuous 1g acceleration would allow humans to travel so far as light has had the opportunity to travel since the big bang (some 13. 7 billion light years) in a single human lifetime. The space travellers could return to Earth vast amounts of years in the future. A scenario based on this idea was offered in the book World of the Apes by Pierre Boulle.

A more likely use of the effect would be to enable humans to travel to nearby superstars without spending their complete lives aboard the ship. However, such software of time dilation during Interstellar travel would require the use of some new, advanced method of propulsion.

Current space flight technology has important theoretical limits predicated on the practical problem that an increasing amount of energy is necessary for propulsion as a craft approaches the velocity of light. The likelihood of collision with small space dirt and other particulate materials is another functional limitation. In the velocities presently achieved, however, time dilation is not a factor in space travel. Travel to parts of space-time where gravitational time dilation is taking place, such as within the gravitational field of the black opening but beyond your event horizon (perhaps on a hyperbolic trajectory exiting the field), may possibly also yield results constant with present theory.

#### LORENTZ TRANSFORMATION:

In physics, the Lorentz change, named following the Dutch physicist Hendrik Lorentz, describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's casings of guide. It reflects the shocking reality observers moving at different velocities may assess different distances, elapsed times, and even different orderings of incidents.

The Lorentz transformation was originally the result of endeavors by Lorentz as well as others to explain discovered properties of light propagating in that which was presumed to be the luminiferous aether; Albert Einstein later reinterpreted the change to be a statement about the type of both space and time, and he individually re-derived the transformation from his postulates of special relativity. The Lorentz change supersedes the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). Regarding to special relativity, this is merely a good approximation at comparative speeds much smaller than the acceleration of light.

#### RELATIVISTIC Period CONTRACTION:

One of the peculiar aspects of Einstein's theory of special relativity is that the length of things moving at relativistic rates of speed undergoes a contraction along the dimension of movement. An observer at rest (in accordance with the moving subject) would take notice of the moving object to be shorter in length. That is to say, that an subject at rest might be measured to be 200 toes long; yet the same object when moving at relativistic speeds relative to the observer/measurer would have a measured duration which is significantly less than 200 ft. This phenomenon is not credited to actual errors in measurement or defective observations. The object is actually contracted long as seen from the fixed reference frame. The amount of contraction of the object is dependent upon the object's acceleration in accordance with the observer.

#### Temporal coordinate systems and clock synchronization

In Relativity, temporal coordinate systems are set up using a process of synchronizing clocks, talked about by Poincar (1900) with regards to Lorentz's local time (see relativity of simultaneity). It is now usually called the Einstein synchronization technique, since it appeared in his 1905 paper.

An observer with a clock delivers a light sign out at time t1 relating to his clock. At a distant event, that light signal is reflected back to, and arrives back to the observer at time t2 according to his clock. Because the light trips the same course at the same rate heading both out and back again for the observer in this scenario, the coordinate time of the function of the light indication being reflected for the observer tE is tE = (t1 + t2) / 2. In this way, an individual observer's clock can be used to determine temporal coordinates which are good any place in the world.

Symmetric time dilation occurs regarding temporal coordinate systems set up in this manner. It is an effect where another clock is being viewed as working little by little by an observer. Observers do not consider their own clock time for you to be time-dilated, but could find that it is discovered to be time-dilated in another coordinate system.

#### SIMPLE INFERENCE OF ENERGY DILATION :

Time dilation can be inferred from the discovered reality of the constancy of the speed of light in all reference frames.

This constancy of the swiftness of light means, counter to intuition, that rates of speed of material things and light aren't additive. It is not possible to help make the speed of light appear faster by approaching at speed towards materials source that is emitting light. It is not possible to make the acceleration of light appear slower by receding from the source at speed. In one point of view, it is the implications of this unpredicted constancy that eliminate from constancies expected elsewhere.

Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. The parting of the mirrors is L, and the clock ticks once each and every time it hits a given mirror.

In the frame where in fact the clock is at break (diagram at right), the light pulse traces out a avenue of period 2L and the time of the clock is 2L divided by the velocity of light:

From the framework of reference of any moving observer traveling at the speed v (diagram at lower right), the light pulse traces out a longer, angled path. The next postulate of special relativity says that the swiftness of light is continuous in all frames, which implies a lengthening of the time of the clock from the moving observer's perspective. In other words, in a frame moving relative to the clock, the clock is apparently running more slowly. Straightforward request of the Pythagorean theorem leads to the well-known prediction of special relativity:

#### Time dilation in transverse motion.

The inexperienced dots and red dots in the computer animation represent spaceships. The ships of the renewable fleet haven't any velocity relative to each other, so for the clocks onboard the individual boats the same amount of time elapses in accordance with each other, plus they can create a procedure to keep a synchronized standard fleet time. The boats of the "red fleet" are moving with a speed of 0. 866 of the rate of light with respect to the inexperienced fleet.

The blue dots stand for pulses of light. One routine of light-pulses between two green ships calls for two seconds of "green time", one second for every leg.

As seen from the perspective of the reds, the transit time of the light pulses they exchange among the other person is one second of "red time" for each and every knee. As seen from the point of view of the greens, the red ships' pattern of exchanging light pulses trips a diagonal way that is two light-seconds long. (As seen from the green perspective the reds travel 1. 73 (\sqrt3) light-seconds of distance for every two seconds of renewable time. )

One of the red ships emits a light pulse towards the greens every second of red time. These pulses are received by boats of the green fleet with two-second intervals as measured in green time. Not shown in the animation is that all areas of physics are proportionally engaged. The light pulses that are emitted by the reds at a specific consistency as measured in red time are received at less consistency as measured by the detectors of the renewable fleet that strategy against renewable time, and vice versa.

The animation cycles between your green perspective and the red perspective, to emphasize the symmetry. As there is no such thing as complete motion in relativity (as is also the situation for Newtonian mechanics), both renewable and the red fleet are entitled to consider themselves motionless in their own frame of reference.

Again, it is essential to comprehend that the results of the interactions and computations reflect the true express of the boats as it emerges off their situation of comparative motion. It is not only quirk of the technique of way of measuring or communication.

#### The four sizes of space time

In Relativity the entire world has four measurements: three space dimensions and one dimensions that's not exactly time but related to time. Actually, its about time multiplied by the rectangular reason behind -1. Say, you undertake one space dimension from point A to point B. Once you move to another space coordinate, you automatically cause your position on enough time coordinate to improve, even if you don't notice. This triggers period to elapse. Certainly, you are always exploring through time, however when you travel through space you travel through time by significantly less than you anticipate. Consider the following example:

#### Time dilation; the twin paradox

There are two twin brothers. On their thirtieth birthday, one of the brothers goes on a space voyage in a superfast rocket that travels at 99% of the swiftness of light. The area traveller stays on his trip for precisely twelve months, whereupon he comes back to Globe on his 31st birthday. ON THE PLANET, however, seven years have elapsed, so his twin brother is 37 years of age during his arrival. This is because of the fact that point is extended by factor 7 at approx. 99% of the acceleration of light, which means that in the area traveller's reference body, one year is the same as seven years on earth. Yet, time appears to have approved normally to both brothers, i. e. both still need 5 minutes to shave every day in their particular reference structure.

As it can be seen from the above function, the effect of time dilation is negligible for common rates of speed, such as that of an automobile or even a jet plane, but it does increase significantly when one gets close to the quickness of light. Very near c, time nearly stands still for the outside observer.

#### Time expands, space contracts

Interestingly, while time expands from the perspective of the stationary observer, space contracts from the perspective of the moving observer. This happening is known as Lorentz contraction, which is exactly the reciprocal of the above time dilation formula: l'=l*sqr(1-v†/c†). Thus the area traveller moving by Earth at a quickness of 0. 99c would see it's shape as an ellipsis with the axis parallel to his airfare way contracted to a seventh of its original diameter. That's of course, if he considers it by any means, given the substantial rate. Therefore, space travel is shortened with the speed of the traveller. A trip to the 4. 3 light-years distant Alpha Centauri C, the closest celebrity to our Sun, would take only 7. 4 weeks in a space ship moving at 0. 99c.

The effect of time dilation has been experimentally established because of very precise caesium clocks that can evaluate extremely small intervals. Sadly, time dilation is totally outside of human being experience, because we've not yet devised a means of venturing at speeds where relativistic results become noticeable. Even though you spent your whole life in a aircraft plane that moves at supersonic rate, you would scarcely win another over your contemporaries on the floor. And, not today's astronauts can understand the Lorentz contraction. Consider you are a cosmonaut on board of space train station Mir, moving at 7700 meters per second relative to Earth. Looking down after European countries from space, you'll see the entire 270 kilometre east to western world scope of Switzerland contracted by only 0. 08 millimetres.

#### Can we travel at the rate of light?

The anticipation that one day mankind can travel at near-to-speed-of-light velocities seems farfetched, because of the incredible amounts of energy had a need to accelerate a spacecraft to these speeds. The forces will probably demolish any vehicle before it comes even close to the required rate. Furthermore, the navigational problems of near-to-speed-of-light travel pose another incredible difficulty. Therefore, when people say they have to hurry to be able to "win time", they probably don't mean it in a relativistic way.

#### Kant: Space and time are properties of thought

The German philosopher, Immanuel Kant (1724-1804), preserved that point and space are a priori particulars, which is to say they are really properties of belief and thought imposed on the individual mind by nature. This simple position allowed Kant to straddle the well-known differences about the reality of space and time that been around between Newton and Leibniz. Newton held that space and time have an absolute simple fact, in the sense to be quantifiable objects. Leibniz held against this that space and time weren't really "things", such as cup and a stand, and that space and time have another type of quality of being. Kant's position will abide by Newton in the sense that space and time are overall and real things of perception, hence, science can make valid propositions about them. At the same time, he agrees with Leibniz by stating that time and space are not "things in themselves, " this means they are really fundamentally different from cups and desks. Of course, this view of space and time also introduces new problems. It divides the globe into a phenomenal (interior) truth sphere and an noumenal (outer) reality sphere. Out of this academic separation come up many contradictions in epistemology. We will, however, not package with this particular problem at this point.

#### Life in a spacetime cubicle

From Relativity we learn that time and space is seemingly unbiased of real human experience, as the example of time dilation suggests. Since our own perception of your time and space will a single research frame, time appears to be constant and definite to us. Physics teaches us that can be an illusion and that our understanding deceived us within living storage area. Thanks to Einstein, we are now able to bring relativistic spacetime diagrams, compute gravitational areas, and anticipate trajectories through the four-dimensional spacetime continuum. Still, our company is hardly in a position to visualise this spacetime continuum, or package with it in practical terms, because human consciousness will the body, which is subsequently bound to an individual reference body. We live within the confinements of our very own spacetime cubicle.

Considering that in Relativity, spacetime is 3rd party of human perception, the Kantian understanding of space and time as a priori particulars seems to be obsolete. They are simply no more properties of perception, but properties of character itself. But, you can find more trouble looming for Kant. Relativity exercises the difference between phenomenal simple fact, i. e. that that can be experienced, and noumenal simple fact, i. e. whatever is solely intelligible and non-sensory, to a qualification where these principles almost appear grotesque. For instance, the question arises, whether time dilation falls in to the noumenal or phenomenal category? Since it can be measured, it must be remarkable, however, since individual perception is bound to a single guide frame, it must also be noumenal. The differentiation between noumenon and occurrence is thus blurred and perhaps invalidated.

We can try to consider relativistic models by making use of appropriate mathematical models, but cannot experience it immediately, at least not until someone builds a near-to-speed-of-light spacecraft. Thanks to Einstein, we're able to look beyond the phenomenal actuality of space and time, and we recognize that there is more to it than commonsense belief tells us. In a way, Einstein has freed our intellects from the spacetime cubicle.

#### BIBLOGRAPHY:

• http://www. thebigview. com/spacetime/timedilation. html
• en. wikipedia. org/wiki/Time_dilation
• en. wikipedia. org/wiki/Gravitational_time_dilation
• www. walter-fendt. de/ph14e/timedilation. htm
• www. physicsclassroom. com
• en. wikipedia. org/wiki/Size_contraction
• hyperphysics. phy-astr. gsu. edu/hbase/relativ/tdil. html
• Modern Physics by Arthur Beiser
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