Time dilation and length contraction

Time dilation and continuance condensateINTRODUCTIONTime dilation is a phenomenon (or 2 phenomena, as menti wizd below) describe by the theory of relativity. It can be illust esteemd by supposing that dickens observers be in exercise relative to from each one other, and/or variantly situated with debate to nigh gravitative masses.Length muscle abridgment, according to Hendrik Lorentz, is the physical phenomenon of a decrease in duration detected by an observer in objects that act at any non-zero fastness relative to that observer. This contraction (more form every last(predicate)y called Lorentz contraction or Lorentz-Fitzgerald contraction) is usually only noniceable, however, at a substantial fraction of the reanimate of cloud slight and the contraction is only in the direction parallel to the direction in which the observed body is travelling.SPECIAL RELATIVITY When much(prenominal) quantities as length, beat legal separation and mass argon conside ruddy in elementary physics, no particular propose is made about how they ar c arful This theory has a wide barf of consequences which hurt been experimentally verified, including counter-intuitive ones such as length contraction, meter dilation and relativity of simultaneity, contradicting the classical notion that the duration of the sequence interval among two matters is equal for all observers. (On the other hand, it introduces the topographic point- duration interval, which is invariant.) Combined with other laws of physics, the two postulates of limited relativity predict the equivalence of matter and energy, as expressed in the mass-energy equivalence formula E=mc2, where c is the renovate of sporty in a vacuum.The predictions of special relativity twin well with Newtonian mechanics in their uncouth realm of applicability, specifically in experiments in which all velocities are small compared with the speed of lightly. Special relativity reveals that c is not just the velocity of a certain phenomenon-namely the propagation of electromagnetic radiation (light)-but rather a fundamental feature of the way home and time are unified as quadriceps femoris time. One of the consequences of the theory is that it is impossible for any particle that has relaxation mode mass to be accele mensurable to the speed of light.POSTULATES OF SPECIAL RELATIVITYTWO postulates are as follows The law of physics are the same in all inertial frames of cite.The speed of light in free space has the same abide by in all inertial frame of reference.OVERVIEW OF date DILATION Time dilation can arise from (1) relative velocity of motion between the observers, and (2) residue in their distance from gravitational mass.In the case that the observers are in relative uniform motion, and far away from any gravitational mass, the point of visualize of each go out be that the others ( move) quantify is ticking at a gradual rate than the local quantify. The alacritous the relative velocity, the more is the rate of time dilation. This case is sometimes called special relativistic time dilation. It is ofdecade interpreted as time slowing down for the other ( locomote) time. But that is only rightful(a) from the physical point of view of the local observer, and of others at relative rest (i.e. in the local observers frame of reference). The point of view of the other observer will be that again the local clock (this time the other clock) is correct, and it is the distant moving one that is slow. From a local sight, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always come ons to pass at the same rate.There is some other case of time dilation, where both observers are differently situated in their distance from a significant gravitational mass, such as (for terrestrial observers) the universe 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 particular(a) factor described below). In the simplified case, the general theory of relativity describes how, for both observers, the clock that is ratiocinationr to the gravitational mass, i.e. deeper in its gravity well, appears 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 does not mean that the two observers fully agree each still 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 least that the clock nearer the mass is slower in rate, and on the ratio of the difference. This is gravitational time dilation.FORMULAE OF TIME DILATION AND aloofness CONTRACTIONTIME DILATIONt0 is the proper time between events A and B for a slow-ticking observer within the gravitational field,tf is the array 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 cut back ups, a machinate system where a clock at infinite distance from the massive sphere would tick at one second per second of ordain time, while closer clocks would tick at less than that rate),G is the gravitational unbroken,M is the mass of the object creating the gravitational field,r is the radial orchestrate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild direct),c is the speed of light, and r0 = 2GM / c2 is the called the Schwarzschild Radius of M. If a mass collapses so that its come on lies at less t han this radial coordinate (or in other words c all overs an area of less than 4pG2M2 / c4), then the object exists within a black hole.LENGTH CONTRACTIONThis effect is negligible at every twenty-four hours 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 equation it is assumed that the object is parallel with its line of movement. likewise 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 transformations.AN face OF TIME DILATIONA spaceship is flying a distance of 5lighthours, for exa mple from Earth to the dwarf planet which Earth and Pluto are motionless. law used t.. time indicated by the spaceship clockt.. time indicated by the clocks 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 entrust of the theory of relativity, an observer in the Earth-Pluto-system would see the spacecraft shortened in the direction of motion. This so-called Lorentz contraction was not rewardn 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 operational definitions of simultaneity and length.According to Milne and Bondi the following operational definitions are assigned to simultaneity and length an o bserver moving uniformly along a straight line sends out a light signal at time t0 to a distant point (stationary according to the observer), where it arrives and is immediately reflected at time tr, arriving back 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 reach the reflector. Because light travels at the same speed c in both directions, it takes 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 c onsidered, and their time and length scales compared. The result of the above definitions is that time and length are connected by the Lorentz factor ?PHYSICAL ORIGIN OF LENGTH CONTRACTIONLength contraction as a physical effect on bodies composed of atoms held tog diethyl ether by electromagnetic forces was proposed in myrmecophilously by George FitzGeraldand by Hendrik Lorentz . The following quote from Joseph Larmor is indicatory 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 arise all t old(a) from electromagnetic actions between the system of electrons which constitute the atoms, then the effect of imparting to a steady material system a uniform velocity of ex rate 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 many who prefer Einste ins deduction 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 static forces. Had I emphasized this more, the hypothesis would have created les s of an impression of being invented ad hoc. (emphasis added)The Trouton-Rankine experiment in 1908 showed that length contraction of an object according 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) but in disagreement with FitzGeralds thoughts on length contraction.EXPERIMENTAL CONFIRMATIONTime dilation has been tested a number of times. The routine work carried on in particle accelerators since the 1950s, such as those at CERN, is a continuously running test of the time dilation of special relativity. The specific experiments include fastness 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, due to motion done the ether using Einsteins suggestion t hat Doppler effect in canal rays would provide a suitable experiment. These experiments measured the Doppler exchange 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 guide 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-lives, the muon sample at 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 source moving at right angles to the line of sight (the transverse Doppler shift). The most 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 testsPound, 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. subsequently 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 elapsed time against that of a clock that remained at the US Naval Observatory. Two opposite effects 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 consistent with the difference between the predicted gravitational gain and the predicted velocity time loss. In 2005, the National Physical Laboratory in the United Kingdom 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 globular P ositioning System can be considered a continuously operating experiment in both special and general relativity. The in-orbit clocks are correct for both special and general relativistic time dilation effects 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 correction terms are built into the model of motion that the satellites broadcast to receivers uncorrected, these effects would result in an approximately 7-metre (23ft) oscillation in the pseudo-ranges measured by a receiver over a cycle of 12 hours.Muon alivenessA comparison of muon lifetimes at different speeds is possible. In the laboratory, slow muons are produced, and in the automatic teller machine 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 traveli ng 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 FLIGHTTime dilation would make it possible for passengers in a fast-moving vehicle 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 according to relativity, any gay travelling with it) shows less elapsed time than the clocks of observers on Earth. For sufficiently high speeds the effect is dramatic. For example, one year of travel might correspond to ten years at home. Indeed, a constant 1g acceleration would permit human races to travel as far as light has been able to travel since the freehand bang (some 13.7 billion light years) in one human lifetime. The space travellers could return to Earth billions of years in the future. A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle.A more likely use of this effect would be to enable humans to travel to nearby stars 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 method of propulsion.Current space flight technology has fundamental theoretical limits based on the practical problem that an increasing amount of energy is required for propulsion as a craft approaches the speed of light. The likelihood of collision 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 hol e but outside the event horizon (perhaps on a hyperbolic flight of stairs 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, elapsed times, and even different orderings of events.The Lorentz transformation was sea captainly 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 absolute 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 holding of motion. An observer at rest (relative 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 faulty observations. The object is actually contracted in length as seen from the stat ionary 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 procedure for synchronizing 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 according 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. Since the light travels the same path 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 single observers clock can be used to define temporal coordinates whi ch 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 constancy 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 e lsewhere.Consider 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 second 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 perspective. 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 well-known prediction of special relativityThe spacetime geometry of velocity time dilationTime dilation in transverse motion.The immature dots and red dots in the animation represent spaceships. The ships of the green conk 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 fleet 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-pulses 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 greens, 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 fo r 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 thing as absolute motion in relativity (as is also the case for Newtonian mechanics), both the green and the red fleet are entitled to consider themselves motionless in their own frame of reference.Again, it is vital to understand that the results of these interactions and calculations reflect the real state of the ships as it emer ges from their situation of relative motion. It is not a mere quirk of the method of measurement or communication.The four dimensions of space timeIn Relativity the world has four dimensions three space dimensions and one dimension that is not exactly time but related to time. In fact, it is time multiplied by the square root 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 position on the time coordinate 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 birthday, 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 on the button one ye ar, 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 need five proceeding to shave each morning in their respective 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 phenom enon is known as Lorentz contraction, which is exactly the reciprocal 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 axis 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 Alpha 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 thanks to very minute caesium clocks that can measure extremely 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 su personic 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 klick east to west extent of Switzerland contracted by a mere 0.08 millimetres.Can we travel at the speed of light?The hope that one day mankind will be able to travel at near-to-speed-of-light velocities seems farfetched, because of the incredible amounts of energy needed to accelerate a spacecraft to these speeds. The forces are likely to abate any vehicle before it comes even close to the required speed. In addition, the navigational problems of near-to-speed-of-light travel pose another tremendous difficulty. Therefore, when people say they have to hurry in order to win time, they probably dont mean it in a relativistic way.Kant Space and time are pro perties of thoughtThe German philosopher, Immanuel Kant (1724-1804), maintain 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 position 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 spirit of being quantifiable objects. Leibniz held against this that space and time werent really things, such as cup and a table, and that space and time have a different choice 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 an d 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 trammel 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, opine 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 judgement 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