Proper Time

10 Key excerpts on "Proper Time"

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  Special Relativity

  • A.P. French(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Using the same terminology, we introduce the notion of Proper Time. This is time as measured always at some fixed point in a particular frame of reference. The measurement of a time interval between two events is nonproper unless both events are recorded in terms of the same clock. Referring back again to the muon-decay experiment, we can describe the time-dilation phenomenon as a manifestation of the distinction between proper and nonProper Time intervals. And it will perhaps be instructive to rederive the time dilation and length contraction results by applying Einstein’s second postulate (on the universality of c) to some hypothetical but very specific observations involving proper and nonproper measurements. We shall consider a clock that is at rest in a frame S ′ and is moving at constant velocity with respect to another frame S. What sort of clock should it be? Well, it doesn’t matter. If different types of clock responded in different ways to uniform motion, we should have, right there, a means of detecting such motion without reference to the outside world. This would in effect be a determination of absolute velocity, and would be at variance with the principle of relativity. So we have a free choice, and will take a clock whose action is particularly easy to analyze. It consists of a box containing two mirrors between which a light pulse bounces back and forth, and a dial that records one count at each return of the pulse. 1 If the distance between mirrors (i.e., the proper length) is l 0, the interval between successive counts is 2 l 0 / c of Proper Time. Suppose that such a clock moves transversely to its length at speed v with respect to some other inertial frame S (Fig. 4-3). The path of the light pulse with respect to this frame is ABC, and takes a time Δ t as measured by the difference of readings of previously synchronized clocks (at A and C) at rest in S

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  Time: From Earth Rotation to Atomic Physics

  • Dennis D. McCarthy, P. Kenneth Seidelmann(Authors)
  • 2018(Publication Date)
  • Cambridge University Press

    (Publisher)

  Proper Time is measured along the trajectory of an observer in space-time (“world line”). In practice, it is measured by a physical clock accompanying the observer. The clock must be insensitive to environmental conditions, gravity, and accelera- tions. Proper Time is invariant in any coordinate change. Since the second of the Système International (SI) is defined only in terms of the periods of radiation for 7.4 Coordinate and Proper Time 107 the caesium atom, it contains no indication of a specific, gravitational potential, or state of motion. Thus, any observer can realize the SI second as the unit for Proper Times. Proper Time cannot be used to describe phenomena in extended domains, in which cases coordinate time must be used. In special and general relativity, a four-dimensional space-time reference system uses three spatial coordinates (x 1 , x 2 , x 3 ) and a fourth, x o = ct, where t is the coordinate time in this reference system. Coordinate time is an unambiguous way of dating in a specific reference system and is to be used as the time basis in the theory of motion in the system. In metrology, it can be argued that coordinate time cannot be measured, but only computed. The relation of Proper Time of an observer to coordinate time is provided by the metric, which takes into account the surround- ing masses and energy. If two events occur separated by a time dt at the same place in a reference frame, the interval (Equation [7.9]) reduces to: ds 2 ¼ c 2 dt 2 : ð7:10Þ The time t is linked with the place and the new time is called the Proper Time, τ, which describes the local physics of the point. Then the interval (Equation [7.9]) can be written for the general case as: ds 2 ¼ c 2 dτ 2 ¼ c 2 dt 2 þ dx 2 þ dy 2 þ dz 2 : ð7:11Þ This means that for the interval s 2 between two events, the quantity ffiffiffi s 2 p . c equals the difference in readings of a clock moving at a constant velocity between two events.

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  Relativity: The Theory and Its Philosophy

  Foundations & Philosophy of Science & Technology

  • Roger B. Angel, Mario Bunge(Authors)
  • 2014(Publication Date)
  • Pergamon

    (Publisher)

  While this is true, the various observers would contend that the two clocks in The Principle of Special Relativity 71 question were not properly synchronized. Moreover, they would be in disagreement as to which clock was running slow and by how much. In view of the distinguished character of the Lorentz invariant time duration, we call it the proper-time interval between two events. The time interval that is determined by the spreading of time through space, i.e. by spatially separated clocks which have been synchronized by means of a procedure which is appropriate to the particular reference frame in which the clocks are at rest, is called coordinate time. A coordinate-time interval is not an invariant. Symbolically, we label proper-time by τ and coordinate time by t. Intuitively, the nature of the distinction may be illustrated by the following example. Someone takes a trip by car from town A to town B. He notes the departure time on the town hall clock at A and the arrival time on the town hall clock at B. The two public clocks have been synchronized by the standard method, i.e. by means of a radio time signal based on a standard reference clock. The elapsed time measured by the traveller is the 'improper' coordinate-time interval t 2 — t l . However, should the car be equipped with a clock of its own which will, of course, be transported along with the driver, which is to say that it is at rest in the driver's own rest-frame, it will measure an interval Δτ which is less than Δί by the factor yj -v 2 /c 2 . Of course, if the velocity of the car is very small compared with the velocity of light, v <^ c, the Loren tz factor is indiscernible from unity and will be ignored, which is the situation of everyday experience. On the other hand, if v is a significant fraction of c, then the effect will be eminently remarkable.

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  Time: A Philosophical Introduction

  • James Harrington(Author)
  • 2015(Publication Date)
  • Bloomsbury Academic

    (Publisher)

  Time as a Physical Quantity 173 interferometer; timing the trip of one light ray with another. An even simpler version can be seen in Figure 6.5. Most importantly, this result does not depend, either theoretically or experimentally, on the particular composition of our toy system. Theoretically, for any physical system which exhibits regular time dependence, the requirement of the principle of relativity applied to electromagnetism implies that moving copies of otherwise identical systems evolve more slowly relative to the rest frame. Although tiny, time dilation is both experimentally measurable and practically relevant in high precision applications. For the International Space Station, which has an average velocity relative to the surface of the Earth of about 7,700 m/s (27,000 km/h), v 2 / c 2 is about 0.00000000065. However, it is large enough to, for example, interfere with GPS navigation if not corrected for. Similarly, it is responsible for our ability to detect cosmic rays at sea level. Muons have a mean lifetime in their own rest frame of about 2.2 micro seconds; even traveling at 99 percent of the speed of light, they shouldn’t travel more than about 600 meters from their creation in the upper atmosphere. The actual flux at sea level is about 10,000 per square meter per minute. Finally, it is this effect which is responsible for perhaps the most infamous consequence of special relativity, the so-called “twin paradox.” Unlike some of our other paradoxes, this one really doesn’t deserve its name. It is simply a well-confirmed empirical consequence of one of the best confirmed theories ever formulated. The setup is the following. Consider two identical clocks A and B synchronized and located at the same position in a frame of reference, h Light clock at rest in laboratory frame; t = 2 h / c v Light clock moving at velocity, v , in the laboratory frame t ′ = 2 h 2 + u 2 t ′ 2 c = t 1 -u 2 c 2 Figure 6.5 Moving clocks run more slowly.

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  University Physics Volume 3

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  The measurement in the earthbound frame involves comparing the time interval between two events that occur at different locations. The time interval between events that occur at a single location has a separate name to distinguish it from the time measured by the earthbound observer, and we use the separate symbol Δτ to refer to it throughout this chapter. Proper Time The Proper Time interval Δτ between two events is the time interval measured by an observer for whom both events occur at the same location. The equation relating Δt and Δτ is truly remarkable. First, as stated earlier, elapsed time is not the same for different observers moving relative to one another, even though both are in inertial frames. A Proper Time interval Δτ for an observer who, like the astronaut, is moving with the apparatus, is smaller than the time interval for other observers. It is the smallest possible measured time between two events. The earthbound observer sees time intervals within the moving system as dilated (i.e., lengthened) relative to how the observer moving relative to Earth sees them within the moving system. Alternatively, according to the earthbound observer, less time passes between events within the moving frame. Note that the shortest elapsed time between events is in the inertial frame in which the observer sees the events (e.g., the emission and arrival of the light signal) occur at the same point. This time effect is real and is not caused by inaccurate clocks or improper measurements. Time-interval measurements of the same event differ for observers in relative motion. The dilation of time is an intrinsic property of time itself. All clocks moving relative to an observer, including biological clocks, such as a person’s heartbeat, or aging, are observed to run more slowly compared with a clock that is stationary relative to the observer. Chapter 5 | Relativity 191

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  The Nature of Time

  • J. Woods Halley(Author)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)

  CHAPTER 5 Relativity and Time

  DOI: 10.1201/9781003037125-5

  “Time,” he said, “is what keeps everything from happening at once.” Ray Cummings, “The Girl in the Golden Atom”, All-Story Weekly (1919) sometimes attributed to Albert Einstein

  “‥the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” Albert Einstein, “On the Method of Theoretical Physics,” the Herbert Spencer Lecture, Oxford, June 10, 1933, often paraphrased as “Things should be as simple as possible, but not simpler”

  5.1 INTRODUCTION

  A few decades before quantum mechanics was found as a way to describe non-Newtonian behavior of particles on very small scales, physicists found another problem with the Newtonian description of particles moving at very high velocities. The solution to the problem was the special theory of relativity, which describes how the space and time separations of events differ when recorded in frames of reference moving at rapid velocities with respect to one another. There is a second aspect to relativity, called general, as opposed to special, relativity, which is basically a theory of gravity, also differing from Newton's description but reducing to it in low gravitational fields and velocities. In this chapter I will be mainly concerned with the special theory.

  5.2 WARPING NEWTONIAN TIME

  To try to make these matters as clear as possible, I begin with the description of a wave moving on water, say on a lake, with some velocity, which I will call

  c

  w a t e r

  , in a straight line (no curves). Now we imagine that the wave is passing by a dock and that a person has set up a measurement scheme to measure the velocity of waves moving past the dock. (See Figure 5.1 .) The person has made two marks on the dock, a distance, call it

  Δ x

  , apart. She also has some kind of stopwatch in order to measure the time, call it

  Δ t

  , between the moment when a wave passes the first mark and the time when it passes the second mark a distance

  Δ x

  away from the first mark along the dock. She simply starts the stopwatch when the wave passes the first mark and stops it when the wave passes the second mark. The person on the dock then has enough information to calculate the speed of the wave (

  c

  w a t e r

  = Δ x / Δ t

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  Philosophy of Physics

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  (ISO 31-1). What exactly time is and how it works follows from the above definition. Physicists use theory to predict how time is measured. Time then can be combined mathematically with the fundamental quantities of space and mass to derive concepts such as velocity, momentum, energy, and fields. ________________________ WORLD TECHNOLOGIES ________________________ Both Newton and Galileo, as well as most people up until the 20th century, thought that time was the same for everyone everywhere. Our modern conception of time is based on Einstein's theory of relativity and Hermann Minkowski's spacetime, in which rates of time at separate places run differently, and space and time are merged into spacetime. Time may be quantized, with the theoretical smallest time being the Planck time. Einstein's general relativity as well as the redshift of the light from receding distant galaxies indicate that the entire Universe and possibly space-time itself began about 13.7 billion years ago in the big bang. Whether and how the universe will ever end are open questions.

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  The Fourth Dimension

  Enigma of Time

  • Dayalanand Roy, Ph.D.(Authors)
  • 2021(Publication Date)
  • BrownWalker Press

    (Publisher)

  time is a measurement of the extension of objects in their fourth dimension, a measurement of their age —and remove all its mysteries; thanks to Einstein and his relativity principle that enables us to reach this probable explanation of time. This meaning sees time as an effect, as a property; not as a cause or an entity. On the other hand, if we derive an indirect meaning of Feynman’s statement- since time has gone slow for the guy going by in the spaceship, all his processes are getting slow; time will remain undefined. It will appear to be an entity, a cause behind the processes while it is not. After all, Einstein, too, said; time is what a clock measures. And what else can it measure except its extension into its own fourth dimension?

  Time, therefore, does not seem to be independent of objects. In the words of Lincoln Barnett too-

  “… Relativity tells us there is no such thing as a fixed interval of time independent of the system to which it is referred. There is indeed no such thing as simultaneity, there is no such thing as now, independent of a system of reference.”68

  Special Theory of Relativity is about relative measurement of space and time in different reference frames. A man runs for 1 hour on a track. Another man flies for 1 hour in a spaceship. How do they come to know they have run or flied for 1 hour? Invariably they have to depend on some clock like device to know this. They can depend upon a mechanical clock, an atomic clock, or they can depend upon some of their biological clocks- number of breathes, pulses, heartbeats or something like that. Whether it is a clock- mechanical or atomic, or a biological clock; all of them are aging (getting old), that is, extending into their own fourth dimension and measuring their own time. By comparing with these devices, we measure the fourth dimension- time- of other things, like our own. And it is by no means guaranteed that things in all circumstances will age equally and identically—that is, extend equally and identically into their fourth dimension. The heartbeats, pulse rates or breaths of the runner on the track may vary from that of the flier; likewise, their clocks may also vary in what they read.

  We cannot prove that atomic clocks are unaffected by a wide range of speeds. And we have no reason to think so, because in different conditions of movements, the components of things may behave differently, age differently and gain different amount of extensions into their fourth dimension. Therefore, time must vary in different conditions of movement. One hour of the track runner may not agree with one hour of the flier, both according to relativity as well as according to the model of time adopted here- time is a property of objects, the fourth dimension of objects.

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  The Sciences

  An Integrated Approach

  • James Trefil, Robert M. Hazen(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  Historically, two striking experiments verified the theory: 1. In 1971, scientists conducted experiments in which extremely accurate atomic clocks were flown around the world in commercial airliners, and the time they registered was compared to that registered on identical clocks on the ground (Figure 7.4). The results met the predictions of relativity (both special and general). d tick tock Mirror Light Detector (a) (b) Stationary light clock Moving light clock d v v tick tock FIGURE 7.3 A light clock incorporates a flashing light and a mirror. A light pulse bounces off the mirror and returns to trigger the next pulse. Two light clocks, one stationary (a) and one moving (b), illustrate the phenomenon of time dilation. Light from the moving clock must travel farther, and so it appears to the stationary observer to tick more slowly. 7.2 | Special Relativity 191 2. Many of the elementary particles we will meet in Chapter 13 are unstable and decay in a fraction of a second. A particle called the muon (pronounced MEW- on), for example, will decay in a millionth of a second or so in its rest frame. Thus, these particles are a kind of clock that ticks only one time. Because they are continually being produced by the collision of cosmic rays with atoms in the upper atmosphere, we can calculate how many muons would make it to the ground if there were no time dilation. Experiments that measured muon fluxes on mountaintops and then on the ground shows that far too many of the particles reached the ground to be explained by any cause other than time dilation. The Size of Time Dilation We have tried, in general, to talk about science in everyday terms and stay away from formulas in this book. But we have now run into a rather fundamental question that requires some simple mathematics to answer. In this section, you’ll be able to follow the kind of thought process used by Einstein when he first formulated his revolution- ary theory.

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  Modern Physics

  • Gary N. Felder, Kenny M. Felder(Authors)
  • 2022(Publication Date)
  • Cambridge University Press

    (Publisher)

  (You can take a picture of what happens at an event and everyone will agree about what’s in the picture.) For example, everyone agrees that, at the event “ship passes Station Alpha,” the ship clock and the station clock both say 0. That is a “frame-independent” statement. But anything that involves comparing two events cannot be directly measured. What time did Station Beta’s clock say at the moment the ship passed Station Alpha? How much time did it take the ship to get from Station Alpha to Station Beta? How long is the ship? These are “frame-dependent” questions that can only be answered in the context of a particular reference frame. The Spacetime Interval One of the most important properties of any coordinate transformation is its “invariants”: the quantities that remain the same through the transformation. For instance, if you rotate your x and y axes, the x and y coordinates of every point change, but for any two points the new and old systems agree about the distance  x 2 + y 2 . So distance is invariant under rotation. 40 1 Relativity I: Time, Space, and Motion When we change reference frames in relativity we know that distances are not invariant, and neither are time intervals. However, in Problem 22 you will show that the following quantity is invariant under the Lorentz transformations: s =  c 2 t 2 − x 2 − y 2 − z 2 The spacetime interval. (1.7) Take a moment to convince yourself that s is real and positive for two events with a timelike separation, imaginary for a spacelike separation, and zero for a lightlike separation. 2 Coordinate Time, Proper Time, and Spacetime Interval The spacetime interval is important because, mathematically, any invariant quantity can be a great aid in problem solving. (See for instance Problem 11.) But Equation (1.7) also suggests some important physical interpretations.

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