Physics
Time Dilation
Time dilation is a phenomenon predicted by Einstein's theory of relativity, where time passes at different rates for observers in different gravitational fields or relative velocities. This means that time can appear to move slower for an observer in a strong gravitational field or moving at high speeds compared to an observer in a weaker gravitational field or at rest.
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No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter-3 Time Dilation Time Dilation is a phenomenon (or two phenomena, as mentioned below) described by the theory of relativity. It can be illustrated by supposing that two observers are in motion relative to each other, and/or differently situated with regard to nearby gravitational masses. They each carry a clock of identical construction and function. Then, the point of view of each observer will generally be that the other observer's clock is in error (has changed its rate). Both causes (distance to gravitational mass and relative speed) can operate together. Overview Time Dilation can arise from: 1. the relative velocity of motion between two observers, or 2. the difference in their distance from a gravitational mass. Relative velocity Time Dilation When two observers are in relative uniform motion, and far away from any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of Time Dilation. This case is sometimes called special relativistic Time Dilation. It is often interpreted as time slowing down for the other (moving) clock. But that is only true from the physical point of view of the local observer, and of others at relative rest (i.e. in the local observer's 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 perspective, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always appears to pass at the same rate. Gravitational Time Dilation There is another case of Time Dilation, where both observers are differently situated in their distance from a significant gravitational mass, such as (for terrestrial observers) the
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- 2014(Publication Date)
- Academic Studio(Publisher)
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. ________________________ WORLD TECHNOLOGIES ________________________ Overview of formulae Time Dilation due to relative velocity Lorentz factor as a function of speed (in natural units where c=1). Notice that for small speeds (less than 0.1), γ is approximately 1 The formula for determining Time Dilation in special relativity is: where is the time interval between two co-local events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on his clock) – this is known as the proper time , ________________________ WORLD TECHNOLOGIES ________________________ is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer, is the relative velocity between the observer and the moving clock, is the speed of light, and is the Lorentz factor. Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be running slow. The range of such variances in ordinary life, where , even considering space travel, are not great enough to produce easily detectable Time Dilation effects, and such vanishingly small effects can be safely ignored. It is only when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light) that Time Dilation becomes important. Time Dilation by the Lorentz factor was predicted by Joseph Larmor (1897), at least for electrons orbiting a nucleus. Thus ... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio : (Larmor 1897). Time Dilation of magnitude corresponding to this (Lorentz) factor has been experimentally confirmed, as described below.
eBook - ePub- C. S. Unnikrishnan(Author)
- 2022(Publication Date)
- Jenny Stanford Publishing(Publisher)
Chapter 3 Time and MotionThe most well-known modification of physical time is the Time Dilation of moving clocks in relativity. This is familiar to everyone, being a topic of discussion even in popular literature and films. Slowing down the passage of time significantly is the only hope for even cosmic explorers in fiction to reach the distant worlds in our Universe, within a lifetime.The topic of Time Dilation became an intense topic of discussion and debate within a few years of the publication of the Special Theory of Relativity (STR) by Einstein in 1905 (Einstein, 1905 ), in which he wrote,If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be tv2 /2c2 second slow.The phenomenon was mentioned by J. Larmor earlier in the context of the periodic motion of electrons. However, Einstein’s explicit and clear prediction of Time Dilation of transported clocks was the first general statement on the motional modification of time as a physical phenomenon observable in any type of clock. It became a topic of debate not because the phenomenon was radically strange, but because of the structure of the STR, in which motion was defined only in terms of relative movement; even the kinematical impression of motion was treated as physical motion in the STR.The study of relativity is the study of physical effects during relative motion. Before Einstein, there were two important insights gained by physicists on relativity. One was Galileo’s realization that the state of uniform motion in a straight line could not be distinguished from the state of rest, by any physical means or experiments. This is distilled from our everyday experience; we often face the situation of the apparition that we are moving, while in fact only an external reference background is moving, as with the slowly moving trains in a station. On the other hand, it is a common and familiar situation that we cannot sense our smooth motion, even when it is at a tremendous speed. We do not feel, and cannot prove, the fast motion of the Earth around the Sun, to the extent of not even believing it for centuries. Therefore, it is reasonable to state that only relative motion makes physical sense. Anybody in uniform motion can claim a state of rest, ascribing the whole motion to the rest of the world. All laws of physics should conform to this ‘Principle of Relativity′ (PoR). In other words, the laws of physics are the same in every frame that is in uniform motion. Uniform rectilinear motion is commonly called inertial motion. There is no acceleration in ideal inertial motion,a →= dv →/ d t = 0.
eBook - ePubRelativity
An Introduction to Spacetime Physics
- Steve Adams(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
c) and so take longer to complete a cycle. Time Dilation is a reciprocal effect: A sees time slow down in B's frame and B sees time slow down in A's frame. Whichever way we look at it, the ‘moving’ clock always runs slow.Surely there is a paradox here? How is it possible for A's clock to be slower than B's and yet for B's to be slower than A's? We shall face squarely up to problems of this sort later when we consider the twin paradox, but for now an analogy with visual perception might be helpful to bear in mind. Imagine standing some distance away from a friend and then raising your hand at arm's length in front of your face. It is easy to block out their entire image so that they appear smaller than your hand. By the same token they are able to block you out with their hand. Assuming your hands are roughly the same size this could lead to the conclusion that you are smaller than your friend and your friend is smaller than you. There is obviously no great mystery or even a hint of a paradox here, we are very familiar with the effects of perspective.2.6 THE Time Dilation FORMULA.
2.6.1 Comparing Light Clocks.
A simple geometric comparison between light clocks in uniform relative motion leads to a formula that will allow us to calculate the rate at which a ‘moving’ clock ticks. To do this we must compare the time for light to complete one round trip in the ‘moving’ clock with the time for light to complete a similar journey in the ‘stationary’ clock. Before we start we must bear two things in mind. Firstly that ‘stationary’ merely identifies a reference frame from which we intend to make our measurements, that is stationary with respect to us as the observers. The moving frame is moving with respect to us and our measuring apparatus. Secondly, having identified a reference frame from which to make our observations we must remember that all our measured values are on measuring devices fixed in this frame. When we conclude that a moving clock is running slow what we really mean is that if a time t passes between ticks of our own clock then our clock measures a time t’ that is greater than t between ticks on the moving clock. An observer moving with that clock would certainly not think that his or her clock was running slow (in fact, as we have already seen, their conclusion would be that it was our
eBook - PDFGravity from the Ground Up
An Introductory Guide to Gravity and General Relativity
- Bernard Schutz(Author)
- 2003(Publication Date)
- Cambridge University Press(Publisher)
Similar experiments can be done with unstable particles produced at high speeds in accelerators, and the predictions of special relativity are confirmed to a high accuracy. A more practical application of Time Dilation today involves the Global Position- ing System (gps) that we discussed in Chapter 2 as an illustration of the gravita- tional redshift. This redshift produces considerable differences between the rates at which clocks on the ground and in orbit run, and these differences have to be cor- rected often in order for the navigation system to work. What we did not explain in Chapter 2 is that Time Dilation produces differences of a similar size, so that it too has to be calculated and removed with the gravitational redshift: an annoying but unavoidable nuisance for the navigation system! If special relativity were not right, we would quickly learn about it from the gps. Novices to special relativity often worry that the Time Dilation effect is inher- ently self-contradictory, and that this should show up in experiments. The worry goes as follows: if experimenter A measures experimenter B’s clocks to run slowly, simply because B has a speed v relative to A, then the principle of relativity implies that B will also measure A’s clocks to run slowly, since the speed of A relative to B is also v. But this seems to be a contradiction: how could B be slower than A and A be slower than B? This is an important question, and one that goes to the heart of understanding special relativity. I shall give considerable attention to it in a separate section on the so-called twin paradox, at the end of the chapter. But there is a brief answer that we can look at here and see that the appearance of a contradiction comes The length of an object contracts along its motion 199 from comes from comparing what are in fact two different measurements. Let us look carefully at how each experimenter performs the measurement.
eBook - PDFFrom Atoms to Galaxies
A Conceptual Physics Approach to Scientific Awareness
- Sadri Hassani(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
Time Dilation The slowing down of clocks (including biological clocks such as aging) in motion. 26.5.3 Review Questions 26.1. What is proper time interval? What is coordinate time interval? Which one is shorter? 26.2. What is the ultimate speed for sending information? Is it possible for a massive object to move at the speed of light? What does this say about the mass of a photon? 26.3. What is Time Dilation? Is it possible for a father to be as old as his child? Can he be older? Can these happen without traveling? 26.4. What is the rest length? What is the moving length? Which one is longer? Is it possible to see length contraction of ordinarily moving objects? 26.5. What is the twin paradox? Why is it called a paradox? 26.6. How much does the fastest and largest man-made object, a 100-meter-long satellite moving at 18,000 mph shrink as it passes by? (See the beginning of Section 26.4.) 26.7. What is the relationship between relativity and Newtonian physics? What happend to relativity theory when the speed of objects under investigation is much much smaller than light speed? 26.5.4 Conceptual Exercises 26.1. One clock is on a spaceship that goes from Earth to a distant planet. Another clock is at the space center on Earth. For the time interval between the two events, take-off from Earth and landing on the planet, which clock, if any, measures the proper time? 26.2. One clock is on a spaceship that goes from Earth to a distant planet, turns around immediately and comes back to Earth. Another clock is at the space center on Earth. For the time interval between the two events, take-off from Earth and landing on Earth, which clock, if any, measures the proper time? Section 26.5 End-of-Chapter Material 389 26.3. Light travels from a star to Earth in 60 years. The captain of Enterprise gets only 5 years older when he goes from Earth to that star. Is there something wrong with these statements? Has he traveled faster than light? 26.4.
eBook - PDFTime and Man
Pergamon International Library of Science, Technology, Engineering and Social Studies
- L.R.B. Elton, H. Messel(Authors)
- 2014(Publication Date)
- Pergamon(Publisher)
It is often stated to be a prediction of E i n s t e i n ' s Theory of Relativity. This i s , of course, true. It is not, however, a consequence of long complicated theoretical argument, but q u a l i -tatively follows immediately from the experimental fact that we must assume the velocity of l i g h t always to be ο no matter who measures it or how he is moving. In the years that have passed since E i n s t e i n ' s theory there have been several experiments which indicate that the Time Dilation effect really occurs. One such experiment concerns the muon, which i s another of the unstable particles created in high energy nuclear reactions. It has a measured lifetime of only about two millionths of a second, after which it changes into an electron. Muons that are created by cosmic ray bombardment in the upper atmosphere at heights of about 30 km with speeds approaching that of l i g h t have been found to reach ground l e v e l , although even at the speed of light this distance takes one ten-thousandth of a second to travel. This i s possible, because according to the observer on the ground the muon clock ticks much more slowly than his own. Using the above formula for time d i l a t i o n , we find that in order to stretch the muon's life by the necessary factor of about 50, the speed of the muon must be within 1/10 per-cent of the velocity of l i g h t . To see why we have not ourselves observed this Time Dilation effect before, let us look in more detail at the expression Time and Relativity 43 1 which is plotted against v/c in F i g . 5 . 5 . Clearly, as long as ν is much smaller than o 9 the expression differs l i t t l e from unity, and not until ν is of the order 0.2 c , i.e. ν = 60,000 km/sec which is a very large velocity indeed, can a departure from unity be detected on the graph. After that growth is increasingly rapid and, as ν comes close to c , the expression tends to infinity.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Simultaneity is not absolute. We might have guessed (incorrectly) that if light is emitted simultaneously, then two observers halfway between the sources would see the flashes simultaneously. But careful analysis shows this cannot be the case if the speed of light is the same in all inertial frames. This type of thought experiment (in German, “Gedankenexperiment”) shows that seemingly obvious conclusions must be changed to agree with the postulates of relativity. The validity of thought experiments can only be determined by actual observation, and careful experiments have repeatedly confirmed Einstein’s theory of relativity. 188 Chapter 5 | Relativity This OpenStax book is available for free at http://cnx.org/content/col12067/1.4 5.3 | Time Dilation Learning Objectives By the end of this section, you will be able to: • Explain how time intervals can be measured differently in different reference frames. • Describe how to distinguish a proper time interval from a dilated time interval. • Describe the significance of the muon experiment. • Explain why the twin paradox is not a contradiction. • Calculate Time Dilation given the speed of an object in a given frame. The analysis of simultaneity shows that Einstein’s postulates imply an important effect: Time intervals have different values when measured in different inertial frames. Suppose, for example, an astronaut measures the time it takes for a pulse of light to travel a distance perpendicular to the direction of his ship’s motion (relative to an earthbound observer), bounce off a mirror, and return (Figure 5.4). How does the elapsed time that the astronaut measures in the spacecraft compare with the elapsed time that an earthbound observer measures by observing what is happening in the spacecraft? Examining this question leads to a profound result. The elapsed time for a process depends on which observer is measuring it.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
37-9 (Δt = γ Δt 0 ) for Time Dilation. (Note that we can use that equation because one of the time mea- sures is a proper time. However, we get the same relation if we use a Lorentz transformation.) Calculation: Solving Eq. 37-9 for Δt 0 and substituting γ from (a) and Δt from (b), we find Δt 0 = Δt γ = 9.8 × 10 4 y 3.198 × 10 11 = 3.06 × 10 −7 y = 9.7 s. (Answer) In our frame, the trip takes 98 000 y. In the proton’s frame, it takes 9.7 s! As promised at the start of this chapter, relative motion can alter the rate at which time passes, and we have here an extreme example. Additional examples, video, and practice available at WileyPLUS The Postulates Einstein’s special theory of relativity is based on two postulates: 1. The laws of physics are the same for observers in all inertial reference frames. No one frame is preferred over any other. 2. The speed of light in vacuum has the same value c in all directions and in all inertial reference frames. The speed of light c in vacuum is an ultimate speed that cannot be exceeded by any entity carrying energy or information. Coordinates of an Event Three space coordinates and one time coordinate specify an event. One task of special relativity is to relate these coordinates as assigned by two observers who are in uniform motion with respect to each other. Simultaneous Events If two observers are in relative motion, they will not, in general, agree as to whether two events are simultaneous. Time Dilation If two successive events occur at the same place in an inertial reference frame, the time interval Δt 0 between them, measured on a single clock where they occur, is the proper time between the events. Observers in frames moving relative to that frame will measure a larger value for this interval. For an observer moving with relative speed v, the measured time interval is Δt = Δt 0 √1 − (v/c) 2 = Δt 0 √1 − β 2 = γ Δt 0 (Time Dilation).
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Under these conditions, the measured interval is a proper time interval, and we can label it Δt 0 as we have previously labelled proper times. Thus, with that label our result becomes Δt = Δt 0 , which is exactly the Time Dilation equation. Thus, Time Dilation is a special case of the more general Lorentz equations. Length contraction If a rod lies parallel to the x and x ′ axes in our arrangement of frames S and S ′ and is at rest in reference frame S ′ , an observer in S ′ can easily measure its length. One way to do so is by subtracting the coordinates of the end points of the rod. The value of Δx ′ that is obtained will be the proper length L 0 of the rod because the measurements are made in a frame where the rod is at rest. Pdf_Folio:904 904 Fundamentals of physics Suppose the rod is moving in frame S. This means that Δx can be identified as the length L of the rod in frame S only if the coordinates of the rod’s end points are measured simultaneously — that is, if Δt = 0. Let’s apply equation 1 ′ of table 37.2, Δx ′ = (Δx − v Δt) , (37.21) substituting Δx ′ = L 0 for the length in S ′ , Δx = L for the length in S, and Δt = 0 for the simultaneous measurement in S. We find L = L 0 , which is exactly the length‐contraction equation. Thus, length contraction is a special case of the more general Lorentz equations. 37.4 The relativity of velocities LEARNING OBJECTIVES After reading this module, you should be able to: 37.4.1 with a sketch, explain the arrangement in which a particle’s velocity is to be measured relative to two frames that have relative motion 37.4.2 apply the relationship for a relativistic velocity transformation between two frames with relative motion. KEY IDEA • When a particle is moving with speed u ′ in the positive x ′ direction in an inertial reference frame S ′ that itself is moving with speed v parallel to the x direction of a second inertial frame S, the speed u of the particle as measured in S is u = u ′ + v 1 + u ′ v∕c 2 .
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
3. The time interval between those two events as mea- sured in the proton’s reference frame is the proper time interval Δt 0 because the events occur at the same location in that frame—namely, at the proton itself. 4. We can find the proper time interval Δt 0 from the time interval Δt measured in the Earth–Milky Way frame by using Eq. 37.1.9 (Δt = γ Δt 0 ) for Time Dilation. (Note that we can use that equation because one of the time measures is a proper time. However, we get the same relation if we use a Lorentz transformation.) Calculation: Solving Eq. 37.1.9 for Δt 0 and substituting γ from (a) and Δt from (b), we find Δ t 0 = Δt __ γ = 9.8 × 10 4 y ___________ 3.198 × 10 11 = 3.06 × 10 −7 y = 9.7 s. (Answer) In our frame, the trip takes 98 000 y. In the proton’s frame, it takes 9.7 s! As promised at the start of this chapter, rela- tive motion can alter the rate at which time passes, and we have here an extreme example. Additional examples, video, and practice available at WileyPLUS 1215 REVIEW & SUMMARY The Postulates Einstein’s special theory of relativity is based on two postulates: 1. The laws of physics are the same for observers in all inertial reference frames. No one frame is preferred over any other. 2. The speed of light in vacuum has the same value c in all directions and in all inertial reference frames. The speed of light c in vacuum is an ultimate speed that cannot be exceeded by any entity carrying energy or information. Coordinates of an Event Three space coordinates and one time coordinate specify an event. One task of special rela- tivity is to relate these coordinates as assigned by two observers who are in uniform motion with respect to each other. Simultaneous Events If two observers are in relative motion, they will not, in general, agree as to whether two events are simultaneous.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
(This is in accord with our conclusion in Module 37-1.) The time interval between the events in S will be Δt = γ v Δx′ c 2 (simultaneous events in Sʹ ). Thus, the spatial separation Δxʹ guarantees a temporal separation Δt. Time Dilation Suppose now that two events occur at the same place in Sʹ (thus Δxʹ = 0) but at different times (thus Δtʹ ≠ 0). Equation 37-23 then reduces to Δt = γ Δtʹ (events in same place in Sʹ ). (37-24) This confirms Time Dilation between frames S and Sʹ. Moreover, because the two events occur at the same place in Sʹ, the time interval Δtʹ between them can be measured with a single clock, located at that place. Under these conditions, the measured interval is a proper time interval, and we can label it Δt 0 as we have previously labeled proper times. Thus, with that label Eq. 37-24 becomes Δt = γ Δt 0 (Time Dilation), which is exactly Eq. 37-9, the Time Dilation equation. Thus, Time Dilation is a special case of the more general Lorentz equations. Length Contraction Consider Eq. 1ʹ of Table 37-2, Δxʹ = γ(Δx – v Δt). (37-25) If a rod lies parallel to the x and xʹ axes of Fig. 37-9 and is at rest in reference frame Sʹ, an observer in Sʹ can measure its length at leisure. One way to do so is by subtracting the coordinates of the end points of the rod. The value of Δxʹ that is obtained will be the proper length L 0 of the rod because the measurements are made in a frame where the rod is at rest. 992 CHAPTER 37 RELATIVITY x b for the burst; Δt is also a positive quantity because the time t e of the explosion is greater (later) than the time t b of the burst. Planet–moon frame: We seek Δxʹ and Δtʹ , which we shall get by transforming the given S-frame data to the planet – moon frame Sʹ . Because we are considering a pair of events, we choose transformation equations from Table 37-2 — namely, Eqs. 1ʹ and 2ʹ : Δxʹ = γ(Δx – v Δt) (37-27) and Δt′ = γ ( Δt − v Δx c 2 ) .
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