Time dilation and length contraction

judgment of conviction distension and duration densificationINTRODUCTION prison term dilatation is a phenomenon (or 2 phenomena, as menti ace(a)d below) exposit by the opening of relativity. It muckle be illust strayd by supposing that twain beh octogenarianers be in inquiry congenator to each former(a), and/or incompatiblely placed with regard to nearby gravitative masses.Length contraction, jibe to Hendrik Lorentz, is the corporal phenomenon of a decrease in length nonice by an renderingator in objectives that conk out at any non-zero fastness recounting to that beholder. This contraction ( more formally called Lorentz contraction or Lorentz-Fitzgerald contraction) is usually only noticeable, however, at a substantial fraction of the amphetamine of sparkling and the contraction is only in the thrill parallel to the direction in which the observed body is snuff itling.SPECIAL opening of relativity When such quantities as length, epoch interva l and mass atomic number 18 considered in elementary physics, no redundant focalize is made slightly how they ar gondola c arful This possible action has a wide range of consequences which pass water been observationally verified, including counter-intuitive unitys such as length contraction, measure dilation and relativity of simultaneity, contradicting the classical notion that the sequence of the cartridge holder interval between two resultant roles is equal for all observers. (On the early(a)(prenominal)(a) hand, it introduces the quad- meter interval, which is invariant.) Combined with other laws of physics, the two postulates of special relativity counter the equivalence of matter and energy, as expressed in the mass-energy equivalence conventionality E=mc2, where c is the further of abstemious in a vacuum.The previseions of special relativity mark well with Newtonian mechanics in their putting surface realm of applicability, specifically in trys i n which all velocities be flyspeck comp ared with the move of electric discharge. Special relativity reveals that c is not just the velocity of a certain phenomenon-namely the propagation of electromag crystaliseic beam of well-fixed ( illumine)- only rather a fundamental feature of the way situation and term are integrate as place cartridge clip. One of the consequences of the scheme is that it is impossible for any fraction that has appease mass to be accelerated to the stop number of light.POSTULATES OF SPECIAL RELATIVITYTWO postulates are as follows The law of physics are the akin in all inertial roams of reference.The hotfoot of light in ease spot has the corresponding value in all inertial bod of reference.OVERVIEW OF condemnation DILATION Time dilation can arise from (1) relation velocity of motion between the observers, and (2) difference in their outer put from gravitative mass.In the outcome that the observers are in intercourse uniform motion, and farther or so past from any gravitational mass, the point of soak up of each impart be that the others ( mournful) measure is ticking at a s overturn rate than the local measure. The faster the copulation velocity, the more is the rate of epoch dilation. This courting is sometimes called special relativistic time dilation. It is often interpreted as time slo realizeg down for the other ( pitiable) quantify. But that is only aline from the physical point of resume of the local observer, and of others at relative equaliser (i.e. in the local observers contour of reference). The point of view of the other observer will be that a crystallize the local quantify (this time the other measure) is correct, and it is the distant mournful atomic number 53 that is slow. From a local aspect, time registered by alfileria that are at rest with mentionfulness to the local frame of reference (and far from any gravitational mass) ceaselessly appears to pass at the same rat e.There is some other case of time dilation, where both observers are differently situated in their hold from a significant gravitational mass, such as (for terrestrial observers) the undercoat or the Sun. One may suppose for simplicity that the observers are at relative rest (which is not the case of two observers both rotating with the Earth an extra grammatical constituent described below). In the simplified case, the general surmise of relativity describes how, for both observers, the quantify that is closer to the gravitational mass, i.e. deeper in its gravity well, appears to go ample-playing than the clock that is more distant from the mass (or higher in altitude away from the center of the gravitational mass). That does not mean that the two observers fully agree each nonetheless makes the local clock to be correct the observer more distant from the mass (higher in altitude) makes the other clock (closer to the mass, 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 l easternmost(prenominal) that the clock nearer the mass is slower in rate, and on the proportion of the difference. This is gravitational time dilation.FORMULAE OF succession DILATION AND LENGTH CONTRACTIONTIME DILATIONt0 is the proper time between take downts A and B for a slow-ticking observer within the gravitational k right offledge domain,tf is the organise time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild line ups, a coordinate organisation where a clock at infinite distance from the massive heavens would tick at one second per second of coordinate time, speckle closer filaree would tick at less than that rate),G is the gravitational regular,M is the mass of the object creating the gravitational field of operations,r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, that is real a Schwarzschild coordinate),c is the step on it of light, and r0 = 2GM / c2 is the called the Schwarzschild Radius of M. If a mass collapses so that its surface lies at less than this radial coordinate (or in other words covers an area of less than 4pG2M2 / c4), then the object exists within a black hole.LENGTH CONTRACTIONThis imprint is negligible at habitual speeds, and can be ignored for all regular purposes. It is only when an object approaches greater speeds, that it becomes important. At a speed of 13,400,000 m/s, the length is 99.9% of the length at rest and at a speed of 42,300,000 m/s still 99%. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant, as can be seen from the formulaNote that in this compare it is off-key that the object is parallel with its line of movement. Also note that for the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object. For more general conversions, see the Lorentz translations.AN EXAMPLE OF TIME DILATIONA spaceship is flying a distance of 5lighthours, for pillow slip from Earth to the dwarf planet which Earth and infernal region are nonmoving. formulation lend oneselfd t.. time indicated by the spaceship clockt.. time indicated by the measure of the Earth-Pluto-systemv.. speed of the spacecraft relatively to the system of Earth and Plutoc.. speed of lightREMARKSIn a simplifying way there was assumed an inertial system in which Earth and Pluto are motionless especially the motion around the Sun was neglected.According to an important allow of the theory of relativity, an observer in the Earth-Pluto-system would see the spacecraft abbreviated in the direction of motion. This so-called Lorentz contraction was not pull in ones hornsn into consideration in order to make it possible to read off the spaceships clock.BASIS IN RELATIVITYThe origin of length contraction in the special theory of relativity can be traced to the operable definitions of simultaneity and length.According to Milne and Bondi the following operational definitions are assigned to simultaneity and length an observer moving uniformly along a straight line sends out a light call for at time t0 to a distant point ( nonmoving consort to the observer), where it arrives and is immediately reflected at time tr, arriving spine at the observer at time ta. What time does the observer ascribe to the time of reflection tr, or, what event is simultaneous with the reflection? Let l be the distance to the point of reflection. An observer, with his or her definition of c,says it takes time l / c for light to distort the reflector. Because light travels at the same speed c in both directions, it ta kes the same time both ways, so it returns to the observer at time ta = t0 + 2 l / c, or in other words, the distance to the point of reflection is l = c ( ta t0 ) / 2, and the time at which reflection occurred is simultaneous with the clock registering ( t0 + ta ) / 2. With these operational definitions for determining length and simultaneous events, two observers in constant relative motion at velocity v are considered, and their time and length scales compared. The result of the supra definitions is that time and length are connected by the Lorentz factor ? carnal ORIGIN OF LENGTH CONTRACTIONLength contraction as a physical effect on bodies composed of atoms held together by electromagnetic forces was proposed on an individual basis by George FitzGeraldand by Hendrik Lorentz . The following quote from Joseph Larmor is indicative of the pre-relativity view of the effect as a consequence of James Clerk Maxwells electromagnetic theory if the internal forces of a material system ar ise totally from electromagnetic actions between the system of electrons which constitute the atoms, then the effect of conveyancing to a steady material system a uniform velocity of translation is to produce a uniform contraction of the system in the direction of motion, of amount (1-v2/c2)1/2The extension of this specific result to a general result was (and is) considered ad hoc by umpteen who prefer Einsteins certainty of it from the Principle of relativity without reference to any physics.In other words, length contraction is an inevitable consequence of the postulates of special relativity. To gain a little physical insight on why length contractions occur, consider what those postulates involve by requiring the speed of light (a quantity dependent on the fundamental properties of space and time) to be invariant in all frames of reference (including ones in motion) one can appreciate that it would require the distortion of the measures of length and time. Apparently Lorentz did not agree to the criticism that his proposal was ad hoc. the interpretation given by me and FitzGerald was not artificial. It was more so that it was the only possible one, and I added the comment that one arrives at the hypothesis if one extends to other forces what one could already say about the influence of a translation on motionless forces. Had I emphasized this more, the hypothesis would have created less of an impression of macrocosm invented ad hoc. (emphasis added)The Trouton-Rankine experiment in 1908 showed that length contraction of an object correspond to one frame, did not cause changes in the resistance of the object in its rest frame. This is in agreement with some current theories at the time (Special Relativity and Lorentz ether theory) tho in disagreement with FitzGeralds ideas on length contraction.EXPERIMENTAL CONFIRMATIONTime dilation has been tested a issuance of times. The routine work carried on in particle accelerators since the 1950s, such as th ose at CERN, is a continuously running test of the time dilation of special relativity. The specific experiments includeVelocity time dilation testsIves and Stilwell (1938, 1941), An experimental study of the rate of a moving clock, in two parts. The stated purpose of these experiments was to verify the time dilation effect, predicted by Lamor-Lorentz ether theory, repayable to motion through the ether using Einsteins suggestion that Doppler effect in canal rays would provide a suitable experiment. These experiments measured the Doppler shift of the radiation emitted from cathode rays, when viewed from directly in front and from directly behind. The high and low frequencies detected were not the classical values predicted.Rossi and Hall (1941) compared the population of cosmic-ray-produced muons at the spend of a mountain to that observed at sea level. Although the travel time for the muons from the top of the mountain to the base is several muon half- alerts, the muon take in a t the base was only moderately reduced. This is explained by the time dilation attributed to their high speed relative to the experimenters. That is to say, the muons were decaying about 10 times slower than if they were at rest with respect to the experimenters.Hasselkamp, Mondry, and Scharmann(1979) measured the Doppler shift from a reference book moving at right angles to the line of sight (the transverse Doppler shift). The about general relationship between frequencies of the radiation from the moving sources is given byas deduced by Einstein (1905). For phi = 90circ(cosphi = 0,) this reduces to fdetected = frest?. Thus there is no transverse Doppler shift, and the lower frequency of the moving source can be attributed to the time dilation effect alone.Gravitational time dilation tests tucker out, Rebka in 1959 measured the very slight gravitational red shift in the frequency of light emitted at a lower height, where Earths gravitational field is relatively more intense. The results were within 10% of the predictions of general relativity. Later Pound and Snider (in 1964) derived an even closer result of 1%. This effect is as predicted by gravitational time dilation.Velocity and gravitational time dilation combined-effect testsHafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners, to compare the progress time against that of a clock that remained at the US Naval Observatory. Two opposite effect came into play. The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound, Rebka). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel. The gravitational effect was the larger, and the clocks suffered a net gain in elapsed time. To within experimental error, the net gain was conformable with the difference betw een the predicted gravitational gain and the predicted velocity time loss. In cc5, the National Physical Laboratory in the United dry land reported their limited replication of this experiment. The NPL experiment differed from the master key in that the caesium clocks were sent on a shorter trip (London-Washington D.C. return), but the clocks were more accurate. The reported results are within 4% of the predictions of relativity.The Global localization System can be considered a continuously operating experiment in both special and general relativity. The in-orbit clocks are right for both special and general relativistic time dilation make as described above, so that (as observed from the Earths surface) they run at the same rate as clocks on the surface of the Earth. In addition, but not directly time dilation related, general relativistic discipline terms are built into the model of motion that the satellites broadcast to receivers uncorrected, these effects would result i n an approximately 7-metre (23ft) oscillation in the pseudo-ranges measured by a receiver over a cycle of 12 hours. mu-meson lifetimeA comparison of muon lifetimes at different speeds is possible. In the laboratory, slow muons are produced, and in the atmosphere very fast moving muons are introduced by cosmic rays. Taking the muon lifetime at rest as the laboratory value of 2.22 s, the lifetime of a cosmic ray produced muon traveling at 98% of the speed of light is about five times longer, in agreement with observations. In this experiment the clock is the time taken by processes leading to muon decay, and these processes take place in the moving muon at its own clock rate, which is much slower than the laboratory clock.TIME DILATION AND SPACE escapismTime dilation would make it possible for passengers in a fast-moving fomite to travel further into the future while aging very little, in that their great speed slows down the rate of passage of on-board time. That is, the ships clock (and tally to relativity, any valet travelling with it) shows less elapsed time than the clocks of observers on Earth. For sufficiently high speeds the effect is dramatic. For archetype, one year of travel might correspond to ten long time at home. Indeed, a constant 1g acceleration would permit humans to travel as far as light has been able to travel since the big bang (some 13.7 billion light long time) in one human lifetime. The space travellers could return to Earth billions of years in the future. A scenario base on this idea was presented in the clean Planet of the Apes by Pierre Boulle.A more presumable use of this effect would be to enable humans to travel to nearby brainiacs without spending their entire lives aboard the ship. However, any such application of time dilation during Interstellar travel would require the use of some new, advanced system of propulsion.Current space flight technology has fundamental theoretical limits based on the practical problem tha t an increasing amount of energy is necessitate for propulsion as a craft approaches the speed of light. The likelihood of shock with small space debris and other particulate material is another practical limitation. At the velocities presently attained, however, time dilation is not a factor in space travel. Travel to regions of space-time where gravitational time dilation is taking place, such as within the gravitational field of a black hole but outside the event celestial horizon (perhaps on a hyperbolic trajectory exiting the field), could also yield results consistent with present theory.LORENTZ TRANSFORMATIONIn physics, the Lorentz transformation, named after 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 others frames of reference. It reflects the surprising fact that observers moving at different velocities may measure different distances, e lapsed times, and even different orderings of events.The Lorentz transformation was originally the result of attempts by Lorentz and others to explain observed properties of light propagating in what was presumed to be the luminiferous aether Albert Einstein later reinterpreted the transformation to be a statement about the nature of both space and time, and he independently re-derived the transformation from his postulates of special relativity. The Lorentz transformation supersedes the Galilean transformation of Newtonian physics, which assumes an dogmatic space and time (see Galilean relativity). According to special relativity, this is only a good approximation at relative speeds much smaller than the speed of light.LORENTZ TRANSFORMATIONRELATIVISTIC LENGTH CONTRACTIONOne of the peculiar aspects of Einsteins theory of special relativity is that the length of objects moving at relativistic speeds undergoes a contraction along the dimension of motion. An observer at rest (relativ e to the moving object) would observe the moving object to be shorter in length. That is to say, that an object at rest might be measured to be 200 feet long yet the same object when moving at relativistic speeds relative to the observer/measurer would have a measured length which is less than 200 ft. This phenomenon is not due to actual errors in measurement or ill-timed observations. The object is actually contracted in length as seen from the stationary reference frame. The amount of contraction of the object is dependent upon the objects speed relative to the observer.Temporal coordinate systems and clock synchronizationIn Relativity, temporal coordinate systems are set up using a outgrowth for synchronising clocks, discussed by Poincar (1900) in relation to Lorentzs local time (see relativity of simultaneity). It is now usually called the Einstein synchronization procedure, since it appeared in his 1905 paper.An observer with a clock sends a light signal out at time t1 accord ing to his clock. At a distant event, that light signal is reflected buttocks to, and arrives back to the observer at time t2 according to his clock. Since the light travels the same elbow room at the same rate going both out and back for the observer in this scenario, the coordinate time of the event of the light signal being reflected for the observer tE is tE = (t1 + t2) / 2. In this way, a wizard observers clock can be used to define temporal coordinates which are good anywhere in the universe.Symmetric time dilation occurs with respect to temporal coordinate systems set up in this manner. It is an effect where another clock is being viewed as running slowly by an observer. Observers do not consider their own clock time to be time-dilated, but may find that it is observed to be time-dilated in another coordinate system.SIMPLE INFERENCE OF TIME DILATION Time dilation can be inferred from the observed fact of the constancy of the speed of light in all reference frames.This con stancy of the speed of light means, counter to intuition, that speeds of material objects and light are not additive. It is not possible to make the speed of light appear faster by approaching at speed towards the material source that is emitting light. It is not possible to make the speed of light appear slower by receding from the source at speed. From one point of view, it is the implications of this unexpected constancy that take away from constancies expected elsewhere. figure a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. The separation of the mirrors is L, and the clock ticks once each time it hits a given mirror.In the frame where the clock is at rest (diagram at right), the light pulse traces out a path of length 2L and the period of the clock is 2L divided by the speed of lightFrom the frame of reference of a moving observer traveling at the speed v (diagram at lower right), the light pulse traces out a longer, angled path. The s econd postulate of special relativity states that the speed of light is constant in all frames, which implies a lengthening of the period of this clock from the moving observers aspect. That is to say, in a frame moving relative to the clock, the clock appears to be running more slowly. Straightforward application of the Pythagorean theorem leads to the known prediction of special relativityThe spacetime geometry of velocity time dilationTime dilation in transverse motion.The putting surface dots and red dots in the vivification represent spaceships. The ships of the green decease have no velocity relative to each other, so for the clocks onboard the individual ships the same amount of time elapses relative to each other, and they can set up a procedure to maintain a synchronized standard hand time. The ships of the red fleet are moving with a velocity of 0.866 of the speed of light with respect to the green fleet.The blue dots represent pulses of light. One cycle of light-pul ses between two green ships takes two seconds of green time, one second for each leg.As seen from the perspective of the reds, the transit time of the light pulses they exchange among each other is one second of red time for each leg. As seen from the perspective of the commons, the red ships cycle of exchanging light pulses travels a diagonal path 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 green time.)One of the red ships emits a light pulse towards the greens every second of red time. These pulses are received by ships of the green fleet with two-second intervals as measured in green time. Not shown in the animation is that all aspects of physics are proportionally involved. The light pulses that are emitted by the reds at a particular frequency as measured in red time are received at a lower frequency as measured by the detectors of the green fleet that measure against green time, and vice versa.The animation cycles between the green perspective and the red perspective, to emphasize the symmetry. As there is no such social occasion as unconditional motion in relativity (as is also the case for Newtonian mechanics), both the green and the red fleet are authorise to consider themselves motionless in their own frame of reference.Again, it is vital to earn that the results of these interactions and calculations reflect the real state of the ships as it emerges from their situation of relative motion. It is not a mere quirk of the method of measurement or communication.The quartet dimensions of space timeIn Relativity the world has four dimensions deuce-ace space dimensions and one dimension that is not exactly time but related to time. In fact, it is time multiplied by the square stalk of -1. Say, you move through one space dimension from point A to point B. When you move to another space coordinate, you automatically cause your commit on the time c oordinate to change, even if you dont notice. This causes time to elapse. Of course, you are always travelling through time, but when you travel through space you travel through time by less than you expect. Consider the following exampleTime dilation the twin paradoxThere are two twin brothers. On their thirtieth birth solar day, one of the brothers goes on a space journey in a superfast rocket that travels at 99% of the speed of light. The space traveller stays on his journey for precisely one year, whereupon he returns to Earth on his 31st birthday. On Earth, however, seven years have elapsed, so his twin brother is 37 years old at the time of his arrival. This is due to the fact that time is stretched by factor 7 at approx. 99% of the speed of light, which means that in the space travellers reference frame, one year is equivalent to seven years on earth. Yet, time appears to have passed normally to both brothers, i.e. both still regard five minutes to shave each morning in thei r single reference frame.As it can be seen from the above function, the effect of time dilation is negligible for common speeds, such as that of a car or even a jet plane, but it increases dramatically when one gets close to the speed of light. Very close to c, time virtually stands still for the outside observer.Time expands, space contractsInterestingly, while time expands from the perspective of the stationary observer, space contracts from the perspective of the moving observer. This phenomenon is known as Lorentz contraction, which is exactly the mutual of the above time dilation formula l=l*sqr(1-v/c). Thus the space traveller passing by Earth at a speed of 0.99c would see its shape as an ellipsis with the bloc parallel to his flight direction contracted to a seventh of its original diameter. That is of course, if he sees it at all, given the enormous speed. Therefore, space travel is shortened with the velocity of the traveller. A journey to the 4.3 light-years distant Alp ha Centauri C, the closest star to our Sun, would take only 7.4 months in a space ship moving at 0.99c.The effect of time dilation has been experimentally confirmed convey to very precise caesium clocks that can measure exceedingly small periods of time. Unfortunately, time dilation is completely outside of human experience, because we have not yet devised a way of travelling at speeds where relativistic effects become noticeable. Even if you spent your whole life in a jet plane that moves at supersonic speed, you would barely win a second over your contemporaries on the ground. And, not even todays astronauts can perceive the Lorentz contraction. Imagine you are a cosmonaut on board of space station Mir, moving at 7700 meters per second relative to Earth. Looking down upon Europe from space, you would see the entire 270 kilometre east to west extent of Switzerland contracted by a mere 0.08 millimetres. put up we travel at the speed of light?The hope that one day mankind will be a ble to travel at near-to-speed-of-light velocities seems farfetched, because of the improbable amounts of energy needed to accelerate a spacecraft to these speeds. The forces are likely to destroy any vehicle before it comes even close to the compulsory speed. In addition, the navigational problems of near-to-speed-of-light travel pose another tremendous difficulty. Therefore, when passel say they have to hurry in order to win time, they likely dont mean it in a relativistic way.Kant Space and time are properties of thoughtThe German philosopher, Immanuel Kant (1724-1804), maintained that time and space are a priori particulars, which is to say they are properties of perception and thought imposed on the human mind by nature. This subtle spotlight allowed Kant to straddle the well-known differences about the reality of space and time that existed between Newton and Leibniz. Newton held that space and time have an absolute reality, in the sense of being quantitative objects. Le ibniz held against this that space and time werent really things, such as cup and a table, and that space and time have a different quality of being. Kants position agrees with Newton in the sense that space and time are absolute and real objects of perception, hence, science can make valid propositions about them. At the same time, he agrees with Leibniz by saying that time and space are not things in themselves, which means they are fundamentally different from cups and tables. Of course, this view of space and time also introduces new problems. It divides the world into a phenomenal (inner) reality sphere and an noumenal (outer) reality sphere. From this academic separation arise many contradictions in epistemology. We will, however, not deal with this particular problem at this point. life in a spacetime cubicleFrom Relativity we learn that time and space is seemingly independent of human experience, as the example of time dilation suggests. Since our own perception of time and space is bound to a single reference frame, time appears to be constant and absolute to us. Physics teaches us that this is an illusion and that our perception deceived us within living memory. Thanks to Einstein, we are now able to draw relativistic spacetime diagrams, compute gravitational fields, and predict trajectories through the four-dimensional spacetime continuum. Still, we are hardly able to visualise this spacetime continuum, or deal with it in practical terms, because human consciousness is bound to the human body, which is in turn bound to a single reference frame. We live within the confinements of our own spacetime cubicle.Considering that in Relativity, spacetime is independent of human perception, the Kantian spirit of space and time as a priori particulars seems to be obsolete. They are no longer properties of perception, but properties of nature itself. But, there is more trouble looming for Kant. Relativity stretches the distincti