08-26-2010, 12:46 AM | #76 |
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A more practical application of time dilation is in GPS technology. As I understand it, accurate positioning requires comparing the time the signals depart different GPS satellites with the time they arrive at the GPS receiver on the jet plane, helicopter or your Toyota. Because of the speed of the satellites, the GPS processors have to factor time dilation into. Here are the details
The current GPS configuration consists of a network of 24 satellites in high orbits around the Earth. Each satellite in the GPS constellation orbits at an altitude of about 20,000 km from the ground, and has an orbital speed of about 14,000 km/hour (the orbital period is roughly 12 hours - contrary to popular belief, GPS satellites are not in geosynchronous or geostationary orbits). The satellite orbits are distributed so that at least 4 satellites are always visible from any point on the Earth at any given instant (with up to 12 visible at one time). Each satellite carries with it an atomic clock that "ticks" with an accuracy of 1 nanosecond (1 billionth of a second). A GPS receiver in an airplane determines its current position and heading by comparing the time signals it receives from a number of the GPS satellites (usually 6 to 12) and triangulating on the known positions of each satellite. The precision is phenomenal: even a simple hand-held GPS receiver can determine your absolute position on the surface of the Earth to within 5 to 10 meters in only a few seconds (with differential techiques that compare two nearby receivers, precisions of order centimeters or millimeters in relative position are often obtained in under an hour or so). A GPS receiver in a car can give accurate readings of position, speed, and heading in real-time! To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy. Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion. Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day. The engineers who designed the GPS system included these relativistic effects when they designed and deployed the system. For example, to counteract the General Relativistic effect once on orbit, they slowed down the ticking frequency of the atomic clocks before they were launched so that once they were in their proper orbit stations their clocks would appear to tick at the correct rate as compared to the reference atomic clocks at the GPS ground stations. Further, each GPS receiver has built into it a microcomputer that (among other things) performs the necessary relativistic calculations when determining the user's location. |
08-26-2010, 02:06 AM | #77 |
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Personally I enjoy this book called Black-Holes Wormholes and Time Machines.
http://www.amazon.co.uk/Black-Holes-.../dp/0750305606 Has anyone read it? |
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08-26-2010, 09:49 AM | #78 | |
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08-26-2010, 02:23 PM | #79 | |
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But somehow I found the sections on how they view a 1-dimensional universe as revealing, and how a 3D universe appears to them in Flatland. Thus an extrapolation on why any higher dimensions than our own, are nearly impossible to understand. |
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08-26-2010, 03:44 PM | #80 |
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Looking further at "Flatlandia" I see I mostly skipped the first 10 or so chapters, after getting bored during the beginning. "Section 2" wherein the Flatlander meets 'Other Worlds' -- the other dimensional worlds -- was good.
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08-26-2010, 04:27 PM | #81 |
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08-26-2010, 05:24 PM | #82 |
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WOW!
Wow, I didn't expect this kind of reaction when I started this thread. I am thrilled to be exposed to so many theories and ideas!
The reason I started this thread was because of my lifelong obsession with time. If you have followed this thread you may know my full time job is a professional musician. Since music travels through time, I have spent my entire life being under the rigourous demands that time imposes upon the creation of music. It made me start to wonder; What would music be like without the contraints of time? That led me to ponder the even more perplexing question; What would an existance be like without any time at all? This has led me to write about this topic, and struggle with the very essence of understanding something that to me, is purely a human explanation of how we exist. I truly believe time is a mystery, the hope is that we can continue to explore the concept and see the world beyond the limits that time may impose. |
08-26-2010, 07:47 PM | #83 |
Bah, humbug!
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Every time I see this thread, I'm reminded of this quote:
.....What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know. ..........— Augustine of Hippo (13 – 430), Christian theologian, North African bishop, Doctor of the Roman Catholic Church, philosopher. Confessions (c. 397), XI, 14. |
08-26-2010, 11:55 PM | #84 | |
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Cheers, Marc |
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08-27-2010, 12:28 AM | #85 |
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That whistling sound you hear when you tip your head sideways; that's time flying by!
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08-27-2010, 11:41 PM | #86 | |
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08-28-2010, 07:55 AM | #87 |
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08-28-2010, 10:26 PM | #88 |
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08-29-2010, 10:39 PM | #89 | |
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08-30-2010, 10:54 PM | #90 |
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I'm not sure if anyone realized this, but I was actually refering to the magazine. LOL, wow, that was a poor attempt at humor.
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