The chances are pretty good that you immediately assumed you are in a stationary position (if you're reading this at home), and by means of your personal frame of reference, you'd be correct. However, the Earth is constantly revolving around the sun, and by comparing the reference frame of the Earth to that of the sun, the average velocity of the Earth about the sun is approximately 107,225 km/h, or about 66,627 miles per hour. [1] Furthermore, the solar system is orbiting the Milky Way at an approximate rotational velocity, Θo, of 220 km/s. [2] To assume that you are stationary is to assume a local inertial reference frame.
The establishment of independent inertial reference frames is an important concept to know if you're to further study special relativity (SR). Simply put, an inertial reference frame is one in which the law of inertia holds. [3] In physics you can choose any metric you wish, including a geocentric one. This however, makes future calculations with respect to your non-moving reference incredibly difficult. [4] In Einstein's theory of special relativity, he established two very important postulates that are vital to the theory:
1. The laws of physics are the same in all inertial reference frames. [5]
2. The speed of light in a vacuum is constant and is independent of the motion of the source. [6]
Although these postulates are reasonable independently, they seem to violate common sense when they are coupled together. Examples of this include a contraction of length, an inability to add velocities relative to another reference frame, an increase in relativistic momentum and kinetic energy, and a dilation of time. [7]
When measuring time dilation, consider two reference frames: S in a stationary position, and S' moving with some velocity. If each observer carries an identical clock, an observer in reference frame S will measure a longer time interval than an observer in S'. Consider that an event taking place between the two reference frames has a duration of Δt0. An observer in the S reference frame moving with respect to S' will measure a longer time interval of Δt for this event than S' will measure for the same occurrence, such that Δt = Δto (1-v^2/c^2)^-(1/2). [8] The interval Δt is always longer than Δto regardless of the magnitude of the velocity. This means that time is expanding, not contracting: time is getting longer and not shorter. [9] Einstein himself stated that "...the time which elapses between two strokes of the clock is not one second, but ... a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest." [10]
When choosing a reference frame between the two, it is important to note that the speed of the clock ticking in each is constant. It is only perceived to slow down when comparing one reference frame to another. However, the fact that time is variant between S and S' does not mean that time does not exist; likewise, a variant length does not entail that length does not exist, and this is quite an absurd notion to hold. In fact, time must exist for movement to even be detected, as movement itself requires a change in position with regard to time.
To date, several experiments have upheld the predictions made by relativity in regards to time dilation by measuring the decay of muons [11] and pions [12], and many other predictions including an advance in the perihelion of Mercury, gravitational lensing, gravitational waves and the gravitational redshift of light against a gravitational field have all upheld Einstein's theory of relativity. There is a consensus amongst physicists (and the Global Satellite Positioning system) that relativity is sound. [13] [14]
Footnotes and References
1 [149 597 887*2*pi/365.2564*24] is 2*pi*semi-major axis of orbit/revolutionary time in hours. Of course the Earth actually orbits around the sun in the form of an ellipse, but this is an approximate value. To learn more about the orbits of the planets and their actual velocities read up on Kepler's Laws.2 This is the value of rotational velocity adopted by the International Astronomical Union in 1985. Zeilik M, Gregory SA. Introductory astronomy and astrophysics. Fourth edition: Thomson Learning; 1998. 387 p.
3 Recall that the law of inertia is Newton's first law and simply states that if the sum of all forces on an object is zero then the object is traveling at a constant velocity and is not subject to an acceleration. Once an object changes its velocity (speed or direction) then SR fails and the theory of general relativity must be invoked––this is quite a beast, indeed. Tipler PA, Llewellyn RA. Modern physics. Fourth edition: W. H. Freeman and company; 2003. 3 p.
4 A metric is a chosen coordinate system (to put it simply). For example, the Minkowski metric of flat spacetime is best used to explain transformations in SR, but the Schwarzchild metric is more suited for measuring the curvature of space around a black hole. Hartle JB. Gravity: an introduction to Einstein’s general relativity. First edition: Benjamin-Cummings Publishing; 2002. 256-252 pp.
5 This implies that no inertial system holds preference to another, and thus that no absolute motion can be detected. Tipler PA, Llewellyn RA. Modern physics. Fourth edition: W. H. Freeman and company; 2003. 15 p.
6 This is a common property of electromagnetic waves. Tipler PA, Llewellyn RA. Modern physics. Fourth edition: W. H. Freeman and company; 2003. 15 p.
7 These relatavistic effects are minute at lower velocities (in fact, negligible) but become tremendous at velocites greater than roughly 60% the speed of light. The process of calculating these differences between reference frames are the result of performing Lorentz transformations assuming that one reference frame measures another. Krane K. Modern physics. Second edition: John Wiley and Sons, Inc.; 1996. 26-51 pp.
8 This is literally the mathematical summary of time dilation. If you need help understanding this further, feel free to consult a dictionary over the word "dilate." Krane K. Modern physics. Second edition: John Wiley and Sons, Inc.; 1996. 26-27 pp.
9 Kenneth Krane states that "all clocks run more slowly according to an observer in relative motion, biological clocks included. Even the growth, againg, and decay of living systems are slowed by the time dilation effect." A superb example of this phenomena is the Twin Paradox if you care to read up on it. Krane K. Modern physics. Second edition: John Wiley and Sons, Inc.; 1996. 27 p.
10 Einstein A. Relativity. First edition: Barnes and Noble, Inc.; 2008. 37 p.
11 Measurements of relativistic time dilatation for positive and negative muons in a circular orbit. J. Bailey et al., Nature 268, 301 (1977).
12 Measurements of the Lifetimes of Positive and Negative Pions. D. S. Ayres et al., Physical Review D 3, 1051 (1971).
13 The GPS system consists of 24 satellites, each with a 12-hour orbit. To maintain an accuracy of 2 meters (required by the military), each unit must have an approximate time accuracy to within 0.000000006 seconds. This means that each unit must make a fractional correction in rate for time dilation (~0.00000000008 seconds) and a fractional correction in rate for the gravitational potential of the Earth (~0.00000000016 seconds) for each signal. Without accounting for these relativistic effects, it would take less than a minute for the entire GPS system to begin to catastrophically fail. Hartle JB. Gravity: an introduction to Einstein’s general relativity. First edition: Benjamin-Cummings Publishing; 2002. 69, 124-126 pp.
14 As a testament to the outstanding quality of my physics education, very few undergraduate physicists ever see Einstein's general theory of relativity at all in their studies, and such a course is usually given late in the Master's level of education. I, however, had the good fortune to have this man teach an entire course dedicated to the study of GR. Dr. Bolen is easily one of the greatest men I have ever known, and it was quite a treat to have him teach us directly as he had done his Ph.D. thesis on quantum gravity and had worked with the LIGO experiment at his alma mater at Ole Miss. I received an A in the course. < /brag>
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