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Links 1 through 10 of 34 by Chad Orzel tagged relativity

Science fiction writers can make use of worm holes or warp drives to overcome this restriction, but it is not clear that such things can ever be made to work in reality.  Another way to get around the problem may be to use the relativistic effects of time dilation and length contraction to cover large distances within a reasonable time span for those aboard a space ship.  If a rocket accelerates at 1g (9.81 m/s2) the crew will experience the equivalent of a gravitational field with the same strength as that on Earth.  If this could be maintained for long enough they would eventually receive the benefits of the relativistic effects which improve the effective rate of travel.

What then, are the appropriate equations for the relativistic rocket?

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It may sound like a strange setup, but the somewhat kooky concept works well for explaining a field of physics that can sound, well, kooky to the uninitiated. Emmy is the stand-in for the everyman (or everydog) who has never quite managed to grasp the idea of spacetime, or why moving clocks tick slower than stationary ones. The imagined back-and-forth banter between author and dog keeps the book engaging while Orzel lays out the theoretical framework of particle physics, explains why neither dogs nor neutrinos can move faster than light and describes what happens to cats that get sucked into black holes.

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By the 1860s, the classical theory of electricity and magnetism was on a very solid theoretical footing. Maxwell's equations describing the interplay of charges and currents with electric and magnetic fields were on paper by 1862, and with some changes in notation they're the exact same today. Relativity wouldn't be invented for another half-century or so, and that makes it all the more remarkable that Maxwell's equations don't actually need to be modified at all to work in a relativistic framework. Lorentz covariance is built right in, though it's a bit hidden.
But Maxwell and Faraday and Ampere and the rest didn't know that. There were some tantalizing hints though, and in fact it was the exploration of classical electrodynamics that led Einstein to the theory of special relativity. It's entertaining to take a look at some of those hints, which are lurking right there in second-semester intro physics.

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"The best stories in the history of physics are those in which someone comes from humble origins and, seemingly out of nowhere, makes a brilliant discovery that changes everything.  Such stories, however, can give a very misleading impression of the nature of scientific progress: science is a continuous process, and a closer inspection of any incredible breakthrough always reveals that there were numerous earlier discoveries that anticipated it.

A great case study of this is Einstein’s special theory of relativity, introduced in 1905.  Einstein’s groundbreaking work transformed mankind’s perceptions of space and time, provided answers to puzzling problems and led directly to other major discoveries, including the harnessing of nuclear energy.  However, Einstein’s revelations were preceded by some twenty years of gradual progress, during which time researchers put forth tantalizing hypotheses that came closer and closer to the truth."

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"This is an epic result," adds Clifford Will of Washington University in St. Louis. An expert in Einstein's theories, Will chairs an independent panel of the National Research Council set up by NASA in 1998 to monitor and review the results of Gravity Probe B. "One day," he predicts, "this will be written up in textbooks as one of the classic experiments in the history of physics."Time and space, according to Einstein's theories of relativity, are woven together, forming a four-dimensional fabric called "space-time." The mass of Earth dimples this fabric, much like a heavy person sitting in the middle of a trampoline. Gravity, says Einstein, is simply the motion of objects following the curvaceous lines of the dimple.If Earth were stationary, that would be the end of the story. But Earth is not stationary. Our planet spins, and the spin should twist the dimple, slightly, pulling it around into a 4-dimensional swirl. This is what GP-B went to space in 2004 to check.

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"As your velocity increases, time as you experience it slows down relative to something moving slower than you. A passenger on a spaceship traveling near the speed of light would appear to have aged less than his friends when he returned to Earth, for instance. Similarly, a fast runner appears to gain time compared to a slow runner.

Einstein’s Pedometer brings special relativity to your daily activities, showing how much time you gain by moving."

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"In the July issue of APS News we pointed out that Einstein's field equations for general relativity appear unexpectedly under the opening credits of the animated feature film "The Triplets of Belleville," directed by Sylvain Chomet of France.
We asked our readers for their interpretation, and offered copies of the book "Physics in the 20th Century" for particularly convincing explanations.
We received many intriguing replies. We reprint some of them here, and, at the end, a communication that may, in fact, resolve the mystery of how those equations came to be featured in the film."

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"Apart possibly from high-energy accelerators, there are no other engineering systems in existence today in which both special and general relativity have so many applications. The system is based on the principle of the constancy of c in a local inertial frame: the Earth-Centered Inertial or ECI frame. Time dilation of moving clocks is significant for clocks in the satellites as well as clocks at rest on earth. The weak principle of equivalence finds expression in the presence of several sources of large gravitational frequency shifts. Also, because the earth and its satellites are in free fall, gravitational frequency shifts arising from the tidal potentials of the moon and sun are only a few parts in and can be neglected."

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"You're taking your morning shower and a thought occurs to you. "In classical electrodynamics, an accelerating charge radiates. In general relativity, acceleration is equivalent to a gravitational field. Therefore a stationary charge should radiate simply by virtue of being in a gravitational field. What's up with that?"

You wonder about what the radiated power would be for a given gravitational field. You figure maybe you could use the Larmor formula with the Stefan-Boltzmann law to estimate the equivalent thermal radiation but you don't remember either one of those equations exactly and you're pretty sure you'd have to finagle some spatial factors anyway (the Stefan-Boltzmann law has a factor of surface area).

One alternative is to try to construct a quantum field theory in curved spacetime, but this is ludicrously tough even if you're not in the shower without pen and paper. But we might be able to just juggle some constants around and get an estimate."

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"Relativity enthusiasts will be excited to learn that in a few months, twin brothers will meet in space for the very first time! But who will age more, the brother spending six months in orbit, or the brother on the quick shuttle hop to the International Space Station?"

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