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244 lines
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<html style><!--
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Page saved with SingleFile
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url: http://www.alternativephysics.org/book/TimeDilation.htm
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saved date: Mon Jul 15 2024 04:48:12 GMT-0400 (Eastern Daylight Time)
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--><meta charset=utf-8>
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<title>Why Time Dilation Must Be Impossible</title>
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<style>body{font-size:100%;font-family:Verdana,Arial,Helvetica,sans-serif}h1{font-size:2.7em;font-family:Calisto MT,Baskerville Old Face,Footlight MT Light,Times New Roman;font-style:italic}h4{font-size:1.0em;font-family:Verdana,Arial,Helvetica,sans-serif}p{font-size:0.875em;font-family:Verdana,Arial,Helvetica,sans-serif}a:link{text-decoration:none}a:visited{text-decoration:none}a:hover{text-decoration:underline}a:active{text-decoration:underline}</style>
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<meta name=referrer content=no-referrer><link rel=canonical href=http://www.alternativephysics.org/book/TimeDilation.htm><meta http-equiv=content-security-policy content="default-src 'none'; font-src 'self' data:; img-src 'self' data:; style-src 'unsafe-inline'; media-src 'self' data:; script-src 'unsafe-inline' data:; object-src 'self' data:; frame-src 'self' data:;"><style>img[src="data:,"],source[src="data:,"]{display:none!important}</style></head>
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<body>
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<p><a href=http://www.alternativephysics.org/index.htm><small>Home</small></a></p>
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<div align=center><center>
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<table border=0 width=650>
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<tbody><tr>
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<td width=100% align=center><h1 align=center>Why Time Dilation<br>
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must be Impossible</h1>
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<p align=left><br>
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A central tenet of Special Relativity (SR) is the idea that the experience of time is a
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local phenomenon. Each object at a point in space can have its own version of time which
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may run faster or slower than at other objects elsewhere. Relative changes in the
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experience of time are said to happen when one object moves toward or away from another
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object. This is called ‘time dilation’ and can cause clocks to run at different
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speeds in different locations.<br>
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<br>
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Here’s how it happens: Suppose we have two clocks: A and B, which are known to be
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very accurate. Clock A is standing still while clock B zooms toward it, narrowly missing.
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As B passes A, we observe that they are perfectly synchronized. Clock B then continues to
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move away from A as pictured below. SR tells us that because B is moving away from A, its
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time will be running slower than A, and will gradually fall behind time-wise.</p>
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<p align=left><img src="data:image/gif;base64,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<p align=left>But wait. Is B moving away from A or is A moving away from B? Since
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velocity is purely relative, there’s no way of knowing. In this case, perhaps A
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should instead be running slower than B; or more properly, perhaps each should be running
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slower than the other. To suggest that two clocks could both run slower than each other is
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a seeming absurdity that defies all logic; even within the difficult ideas that SR asks us
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to follow. It is the mathematical equivalent of saying: A>B and B>A; which is
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impossible.<br>
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<br>
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To complicate the situation a little, let’s say there are three clocks: A, B and C.
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As before, A is standing still and B is moving to the right. C is meanwhile moving to the
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left of A with the equal and opposite velocity of B. See diagram:</p>
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<p align=left><img src="data:image/gif;base64,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<p align=left>SR tells us that C and B must be recording time more slowly than A, and A
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should slow down by the same degree relative to C and B. It also tells us that C should be
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going slower than B, by a greater degree than relative to A, and likewise B should
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slowdown the same amount relative to C. Mathematically this is:<br>
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<br>
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<strong>A</strong>><strong>B</strong> and <strong>B</strong>><strong>A</strong> and <strong>C</strong>><strong>A</strong>
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and <strong>A</strong>><strong>C</strong> and <strong>C</strong>>><strong>B</strong>
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and <strong>B</strong>>><strong>C</strong>.<br>
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<br>
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Confused?</p>
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<p align=left> </p>
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<h4 align=left>The Time Travelling Twins</h4>
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<p align=left>A story often told to demonstrate the implications of SR time-dilation is
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that of the travelling twins; also known as the <i>twins paradox</i>. It goes something
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like this:<br>
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<br>
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A pair of identical twins, named Alpha and Beta, decide to journey to a nearby star where
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a new planet has been discovered. The planet is 10 light years away from Earth and the
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twins have at their disposal a space ship that is capable of travelling at near the speed
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of light. However the ship is only big enough for one occupant. So it’s decided that
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Alpha should stay at home while Beta make the journey alone. They estimate the round trip
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should take about 20 years.<br>
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<br>
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The journey begins. Once outside of Earth’s gravity, the ship accelerates at a
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comfortable rate of 9.8 m/s<sup>2</sup> (equal to Earth’s gravity), and reaches light
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speed in just under a year. To fit within the SR speed limit, we’ll say that the
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ship’s top speed is 99.99% of light speed. The ship then cruises at a constant
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velocity for the next 10 years. As it approaches the planet, it then decelerates at the
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same rate until it stops.<br>
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<br>
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Beta then gets out, takes pictures, collects samples etc, and then climbs back into the
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ship for the journey home. The return journey follows the same pattern of acceleration,
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cruising and deceleration as before, until it reaches Earth. A chart of the ship’s
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velocity would look like this:</p>
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<p align=left><img src="data:image/gif;base64,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
|
|||
|
|
<p align=left>Many years later, Beta’s ship returns to Earth. It lands gently and,
|
|||
|
|
as the roar of its mighty engines subside, a crowd of onlookers gather round. Twenty years
|
|||
|
|
have passed and Alpha is waiting anxiously by the docking bay for the return of his
|
|||
|
|
brother. As he stands waiting, we notice that he is visibly different. The sands of time
|
|||
|
|
have aged him: his face, hair, and body no longer hold the youthful looks he once had when
|
|||
|
|
Beta departed all those years ago<br>
|
|||
|
|
<br>
|
|||
|
|
The hatch opens, and as Beta steps out, Alpha notices that his brother has barely aged,
|
|||
|
|
looking much like the day when he left. In fact while everything on the Earth has moved
|
|||
|
|
twenty years forward in time, Beta has aged little over a year. All of the ship’s
|
|||
|
|
time keeping instruments have likewise barely moved in comparison to Earth’s clocks.<br>
|
|||
|
|
<br>
|
|||
|
|
SR tells us that Beta has experienced time-dilation. The closer Beta got to the speed of
|
|||
|
|
light, the slower his clocks ticked, and the slower he aged, relative to Alpha. Beta had
|
|||
|
|
no awareness of this because all his bodily functions, and even his thoughts, slowed
|
|||
|
|
similarly.<br>
|
|||
|
|
<br>
|
|||
|
|
But hang on a minute... Was Beta moving away from Alpha or was Alpha moving away from
|
|||
|
|
Beta? Both classical mechanics and SR tell us that velocity has no absolute measure and
|
|||
|
|
can only be measured relative to something else. Beta looks out his rear window and sees
|
|||
|
|
Alpha moving away from him at the same speed as Alpha sees Beta’s ship move away from
|
|||
|
|
Earth. In other words, this:</p>
|
|||
|
|
<p align=left><img src="data:image/gif;base64,R0lGODlhsAGXAPcAAAAAAAC1EAC1GAC9CAgAAAgICAiMUgiMWgiUQgiUSgicMQicOQicQgilKQilMQitGAitIQitKQi1EAi1GAi1IRAAABAQEBBjlBBjnBBrhBBrjBBzexBzhBB7axB7cxCEWhCEYxCMWhCcQhCtKRCtMRC1IRC1KRC9GBgYGBg51hg53hhCxhhCzhhC1hhKvRhKxhhSrRhStRhapRharRhjnBicWhitORitQhi1KRi1MRi9IRi9KSEAACEhISEh/yEp7yEp9yEp/yEx3iEx5yF7jCGlSiGtQiG1MSG9MSkpKSmcYymtUimtWim9OTEAADExMTFK3jGlazGtYzG1UjG9OTG9Qjk5OTk5/zm1Wjm1Yzm9SkIAAEJCQkKta0K9Y0LGUkoAAEpKSkqUjEqte0q9Y0rGY0rOUkrOWlJSUlJS/1KthFK9e1LGa1LOY1paWlprtVqUtVq9hFrOY1rOa2NjY2O1lGO9jGPGe2POa2tra2tr/3MAAHNzc3Nz/3O1pXt7e3u1rXvGnISEhISE/4S1vYTWlIwAAIyMjIzWnIzejJSUlJTWpZTnlJycnJyc/5zWrZzetZznpaWlpaXetaXevaXnpaXnra0AAK2tra3eva3exrW1tbW1/7XexrXezrXvtb0AAL29vb3ezsbGxsbn3sbvxs7Ozs7O/87n587vzs73ztYAANbW1tb31t7e3t733ufn5+fn/+f35+f/5+/v7+//7/f39/f/9/8AAP8ICP8QEP8YGP8hIf8pKf8xMf85Of9CQv9KSv9SUv9aWv9jY/9ra/9zc/+EhP+MjP+UlP+cnP+lpf+trf+1tf+9vf/Gxv/Ozv/e3v/n5//39////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////ywAAAAAsAGXAAAI/gCpCRxIsKDBgwgTKlzIsKHDhxAjSpxIsaLFixgzatzIsaPHjyBDihxJsqTJkyhTqlzJsqXLlzBjypxJs6bNmzhz6tzJs6fPn0CDCmVoa6hRnUWPKl16kZUgPoJMMZ260pZTqFKpat1qUJIFAGBRhOJKFqRXsADEll27lNYTtGC5JGVLl6JbuADk1t3rk9VXuCjm8h280C/ewIQT23SFAm8PwYojC2TsGLLkyylthcHLBzNmWmg4ex6tklWYAgAs0KFFWrJp1AVWt55d0hYsNKMs095rG40p3buDa7SVB5ZwxcSNH1++cVSSP6yZ7x3V448t4NKzL8TEhQsaNK6w/mtXiimMle+uNOYJw94NnUbix9tsFIbVRFu0nrrKwyqUm7E8LcMLLgQWaOCBCCao4IIMNujggxAyeFB+fOzX338HRVigEzyAAQaHAGyh4YgklmjiiQfyIowxy9TUQ2wTuYLGIUXxYRwt7/FkDIo89ugjigbJSCM1NlKDYyMGkegEGAYaAsAlP0Yp5ZQL8tJiTKMAwIcF8RlkihtZUVOcQLT88Ydy8hllCh2/CTSmkWaiOdETYRAECwCCpEnQM8sY8wuBwsSUhxV3SvKQLZKggaYtRQpkSyNosNKlnjQhCh5BjVLzqG8V0UnQJgBsQqlBAuKCzEu2WHAINd05ZIsi/nxEN1AesgrEypuj8gRrrYzKSc2tvj70xHOC/EGHapNm9wwuvLyECQDpNQKtQ7RYhutA1ebaU7YFXUtmsgY9UQAKKHwVG7jSEfgSGlyQWUBnFWWq7VTyYuSpo5IA4Ma8BKnbEi0FhNGIIo30gBhF3koHzTHMkJWwRfcO5AYAteYqjb8sKZIWueSGalcYwQYnjTLD6MKsMlzRwkXIndZJEB0AsCxfNMLgYoxLVrQ7UKpoUIRJD0gKN00zxfSCiy7CJBNNWT8HrVHE1DCWxLzPIDMgL0uz5AoAihQEs8wJ2UKHJLLR5gwwuRTYCzFssw0MlXAjGPbYZWc4ohMVOKG3/hMEEABK3IAHfqIw0rgkSMwFgbpqRKb8QY0iotLGjC8H+hKMMJcPKDjcCTX+eOR2a7iHh6TvscrmqKeeoIrPwMRHHgbZgga8h+YhlSm00zb0MWgzmzQ002hF3O258yvfKHwURZx9zD2TzDC7HA1Mw0whrzx/xuvJR5ihOD5eNMsUg/JSt2w/UPfZy4c7QbS4UXH6O62PrfvwSyd2mAIpgkn9Pd1fkCKG4t9x1gQZV9ABXQJUCQELYkAEJnAvhxjFQf7AvAfaJIITrKAFRwOLAx6kew7coEg6qBsQinA0+kPIq0J4wo+k8CArbGFkOMGJPrxBDDaQwAB0KIEJkMAI/mS4QyVYKEON5KaInuHEINLggybGwAA7jGIUeRhFEejBEadAohZPeIolNtEHQfCBC0RAxSmakYoc+KIeOLHFNqYvFo5gIhh9IAQZdAACOjTjGQcgRQlIQAhhVGMW3UhI+ZSCDDXogCI7EAIFTICPeqRiHss4yQ3MMZA+uIIjYlHITgrnE03QIx8lucdJ9tGMC8BkGDE5CE568pWYKUUVIknKWo6ylLf0YxMDycsvDgKWwCSMLNpgy2Le8pR53OMAJtDLXTozk2wMpjTLEokT2PKU2DSmLUHwTFU+Mw2unKY4lVKLM1Ayl9nEJTKPKYIffNGb3WyiI8ZJT6GUAgfr/tSmMtdpxnbO8Zn/3MAEHrCBITRRD+Gsp0JxkohrkpKfptSnAwx6yXj6QARRfAANgJDJhC70ozGRQwDUGdFI4tKUUYQAIN/5xX+GsQGSXIAGXvCDaIL0piy5xRccalKeorSWLwDoKgHqgJLqsAFeSAVOl3qSWszypz1N5zmvKQOXsvSqZDzpCUrB1K6GpBZHOKlJSRrVUXrgqt7sZQemmkuuevWtGrlFFdiaT2Xqc4oL4Cg8MflPH9CgpKecQCvgSliLfAGix3xoWY26w5X2tZfeHEJUqagDWRT2shCZgz4feldtbtSqAH3sRRlryiPUArOoVQgjFotOwJI1ohy1/mhF++qDGNhVj19IrW4Lkgq6XnOyieXnD/Z6VWcGsqiI5WEhdrvbWuAAsJwVK2lNGlTiGhegLoAuMpXKXNQSE7hlrStUqZiBZoJWqGBcq1ijaNruXrYSxrztdMWbSxK0lLjE/cEIoLpHNriXsLUowVjZOt/4PnQFkC3ueX0gg9fuUAJu/W9X8XBO6Q74tlENAW3Tit4gAOEBBebjESTc1VaM1MDBtXBwjSkEvRaXr+YNAXh5iAgSL1ULF56udtd7zhA0c6jodeYGorvHEhDRxlqUBYHly2SfmnQFCzavKjNAX1MuF8kLPQWTEVtX8EZSBGgN82xBsOQzluAWWFZo/hoeGV0dNzm56AyqbM07RwhsuYw1TvM4T+EDmK64tX9mrZN1KILYnjfBDGbsbUesZ3EyMQFwVjSKgRtRF4g2yvoV9Bkz0WhpxiK9nXUwj7usQ25eGp4+CIFv+TmALHQ6mI5oIg3QeWdaL3nVkwxBbFHdSw8AWtASOPKr65eGMGbX1oB2M3/bfEwNS/mqZB41Yx8xbE/yGYwscDKp/7zZ1hqAw48dAk9VzIRqd3IQgRQCpaXN2m1reMMAbfCtkR3FCQTP3G6UYxiZzWV+h5qKur5uPGU83jfrUBP4dqNLsyrqQbe7wu+GMUvFnWxutzYO9054ETnxTA68udZuFmvA/oPcRA04XNIDKILGtYhuZ2bbwSjXbjKZLYGIxzOQ+430YiWwciTq+4tZLfjHu03kAYyczkFIgb8tbkZS9FyGoo2Bsn/NbwyT0uYsDeSsq6xiCfjh6S1EbwJWPeOyt/nbYgY1yJkeB7CLkBN0boEfdY7ipff40F8cMtXLHkUluH2DHD+vyZFNdiLXPYpHt6jSca1pI/zdgnoAdxAIvvZ1VxiwWL+5C/zM+CU34PEP1ENoA/kD5Ma84pfn+sgv/U4WwCDnnUcmz0EvwMgL
|
|||
|
|
<p align=left>Is the same as this:</p>
|
|||
|
|
<p align=left><img src=data:image/gif;base64,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
|
|||
|
|
<p align=left>So why not have Alpha stay young and let Beta age instead? It’s the
|
|||
|
|
same thing. Or let’s take it to the extreme and say that, when the ship returns, they
|
|||
|
|
are both younger than each other? This is the same situation that I’ve described
|
|||
|
|
above with the moving clocks, albeit with one small difference...</p>
|
|||
|
|
<p align=left> </p>
|
|||
|
|
<h4 align=left>Effects of Acceleration</h4>
|
|||
|
|
<p align=left>Opponents of the above argument may point out that we cannot simply
|
|||
|
|
reverse the roles of Alpha and Beta because they do have a difference; namely that Beta
|
|||
|
|
experienced acceleration whereas Alpha did not. That’s true. Beta experienced both
|
|||
|
|
acceleration and deceleration in shifting between rest and near-light speeds. However I
|
|||
|
|
would argue that this acceleration cannot account for the time differences for the
|
|||
|
|
following reasons:<br>
|
|||
|
|
<br>
|
|||
|
|
1. Time dilation calculations are based mainly on velocity, not acceleration. If speed was
|
|||
|
|
not an issue, then it shouldn’t make much difference if the top speed was only 90%
|
|||
|
|
light speed instead of 99.99%. But the Lorentz factor for 0.9<strong>c</strong> (<strong><big><font face="Times New Roman">γ</font></big></strong>=2.3) is very different from 0.9999<strong>c</strong>
|
|||
|
|
(<strong><big><font face="Times New Roman">γ</font></big></strong>=71)<br>
|
|||
|
|
<br>
|
|||
|
|
2. The acceleration/deceleration occurs over only brief periods of the trip – see the
|
|||
|
|
above velocity chart. If acceleration was the deciding factor for time-dilation, then it
|
|||
|
|
should make no difference if the destination was 20 light years away instead of 10. Better
|
|||
|
|
yet we could simply remove the cruising portion of trip; i.e. immediately decelerate after
|
|||
|
|
reaching top speed, and get the same result.<br>
|
|||
|
|
<br>
|
|||
|
|
3. The acceleration experienced by Beta is mild; it is only Earth’s gravity strength.
|
|||
|
|
If acceleration of such mild degree could allow Beta to take 20 years off his life, then I
|
|||
|
|
propose we could sit in a spinning centrifuge for a few years to achieve the same. Since
|
|||
|
|
the direction of the acceleration is unimportant (the net acceleration of Beta’s
|
|||
|
|
journey was zero), it shouldn’t matter that the centrifuge’s acceleration is
|
|||
|
|
constantly changing direction.</p>
|
|||
|
|
<p align=left> </p>
|
|||
|
|
<h4 align=left>The reference frames argument</h4>
|
|||
|
|
<p align=left>This leads us to the standard explanation of this anomaly, known as the
|
|||
|
|
‘accelerated vs. inertial reference frames’ argument. Basically it states that
|
|||
|
|
Beta shifted into a different ‘time frame’ due to his initial acceleration
|
|||
|
|
– whereas Alpha did not accelerate and stayed in the same frame. This made Beta
|
|||
|
|
experience time dilation rather than Alpha. An important point about the argument is that
|
|||
|
|
acceleration is not what determines the degree of dilation – that is still done via
|
|||
|
|
velocity. Rather, acceleration is what enables dilation to occur.<br>
|
|||
|
|
<br>
|
|||
|
|
From a logical perspective this makes no sense because it says nothing about the amount of
|
|||
|
|
acceleration required. Essentially it is saying that, while zero acceleration won’t
|
|||
|
|
change a ‘reference frame’, a non-zero acceleration of any amount changes it
|
|||
|
|
completely. For example Beta’s acceleration may be a billion-trillion times weaker
|
|||
|
|
than Earth’s gravity, yet that is all that’s needed to make Beta age 71 times
|
|||
|
|
slower than Alpha, rather than vice-versa. If acceleration was a determining factor in the
|
|||
|
|
degree of dilation then it should be incorporated into the LT describing it. But the fact
|
|||
|
|
is, it’s not.<br>
|
|||
|
|
<br>
|
|||
|
|
And from a practical perspective the ‘frames argument’ fails completely. Because
|
|||
|
|
Alpha, left behind on earth, cannot stand perfectly still and will be accelerating all the
|
|||
|
|
time. As the earth rotates and orbits the sun he experiences acceleration. Even if both he
|
|||
|
|
and the earth were somehow completely motionless, the molecules in his body will be
|
|||
|
|
constantly vibrating with heat, and vibration involves acceleration. Therefore an argument
|
|||
|
|
that favours non-zero accelerating bodies over zero-accelerating ones could never apply in
|
|||
|
|
a real situation.</p>
|
|||
|
|
<p align=left> </p>
|
|||
|
|
<h4 align=left>Dual changes in time</h4>
|
|||
|
|
<p align=left>One might argue that time-dilation may yet be possible if it affected both
|
|||
|
|
bodies equally. This is not a belief of SR but I’ll discuss it here.<br>
|
|||
|
|
<br>
|
|||
|
|
In the example above with two clocks, if both clocks slow down by the same amount when in
|
|||
|
|
motion, then each would still show the same time afterward. In other words, time dilation
|
|||
|
|
may have occurred but we would have no way of knowing it. This argument holds true for two
|
|||
|
|
clocks but it falls apart with three. In the example with three clocks A, B and C (above),
|
|||
|
|
B ran slower than A, and slower again than C. So it is not possible for all three clocks
|
|||
|
|
to run slow by an equal amount.</p>
|
|||
|
|
<p align=left> </p>
|
|||
|
|
<h4 align=left>Directionally dependent time changes</h4>
|
|||
|
|
<p align=left>A final consideration is the possibility that time dilation could occur if
|
|||
|
|
it changed with direction. E.g. Beta could age more slowly than Alpha while travelling
|
|||
|
|
away from Earth, then age more quickly during the return trip, restoring his age to match
|
|||
|
|
Alpha. The net result is that time dilation would have occurred but neither twin would
|
|||
|
|
know it. This is not a belief of SR either but it should be addressed for completeness.<br>
|
|||
|
|
<br>
|
|||
|
|
While this possibility holds true for two observers, it falls apart for three. Suppose we
|
|||
|
|
have the three observers A, B and C as pictured.</p>
|
|||
|
|
<p align=left><img src=data:image/gif;base64,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 width=199 height=48></p>
|
|||
|
|
<p align=left>A and C are motionless with respect to each other, while B moves away from
|
|||
|
|
A and toward C. If time dilation was directionally dependent then B’s clocks should
|
|||
|
|
move slower than A’s, but faster than C’s (or vice-versa, if you prefer). But
|
|||
|
|
this would contradict the relation between A and C whose clocks need to move at the same
|
|||
|
|
speed. Mathematically that’s:<br>
|
|||
|
|
<br>
|
|||
|
|
<strong>A</strong>><strong>B</strong> and <strong>B</strong>><strong>C</strong>
|
|||
|
|
and <strong>A</strong>=<strong>C</strong><br>
|
|||
|
|
<br>
|
|||
|
|
Again, another impossibility.</p>
|
|||
|
|
<p align=left> </p>
|
|||
|
|
<h4 align=left>Conclusion</h4>
|
|||
|
|
<p align=left>SR proponents would have us believe that the fountain of youth awaits us
|
|||
|
|
inside a high speed rocket ship, or on a lifetime of non-stop jet travel, if only we can
|
|||
|
|
make them fast enough. Nice if it were true.<br>
|
|||
|
|
<br>
|
|||
|
|
Based on the reasoning that any time-shift which might occur as the result of moving
|
|||
|
|
bodies should occur equally in each, because each body moves in equal relation to the
|
|||
|
|
other, I conclude that such time-dilation between moving bodies must be impossible.<br>
|
|||
|
|
<br>
|
|||
|
|
An interesting aspect of this argument is that it appears to have been overlooked by
|
|||
|
|
mainstream science texts.<br>
|
|||
|
|
<br>
|
|||
|
|
Here is an exercise you can try: Pick up a physics text book that discusses relativity and
|
|||
|
|
see if it covers the ‘Twins’ analogy, or something similar. Or search the
|
|||
|
|
internet for the phrase ‘Einstein twins’. If you find it, see if the authors
|
|||
|
|
also address the above arguments about contradictions in time-dilation. Chances are they
|
|||
|
|
give a lot of double-talk about reference frames; perhaps in the hopes of bluffing the
|
|||
|
|
reader into agreement. Or they make no mention of it, only to label it an enigma and leave
|
|||
|
|
it at that.<br>
|
|||
|
|
<br>
|
|||
|
|
Calling something an enigma makes it sound almost romantic, like you should sit back in
|
|||
|
|
awe at the mysteries of the universe and not consider the argument too deeply. But it
|
|||
|
|
should not be called that. It would be better to call it a flaw, a limitation, or
|
|||
|
|
even a mistake in the SR theory.<br>
|
|||
|
|
<br>
|
|||
|
|
There’s nothing wrong with having flaws in a theory; many theories have them. But we
|
|||
|
|
should acknowledge such limitations so that better theories may be sought to replace the
|
|||
|
|
ineffective ones. Otherwise students, and even teachers, of science will be stuck with
|
|||
|
|
wrong information and flawed thinking. And such must be detrimental to scientific
|
|||
|
|
progress.</p><br>
|
|||
|
|
<table style=text-align:center;width:400px border=1 cellpadding=5 cellspacing=2>
|
|||
|
|
<tbody>
|
|||
|
|
<tr><td>
|
|||
|
|
<p> Need more? Try the <a href=http://www.alternativephysics.org/book/RelativityChallenge.htm>Relativity Challenge</a>.</p>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</td>
|
|||
|
|
</tr>
|
|||
|
|
</table>
|
|||
|
|
</center></div>
|
|||
|
|
<p> </p>
|
|||
|
|
<div align=center><center>
|
|||
|
|
<table border=0 width=400>
|
|||
|
|
<tbody><tr>
|
|||
|
|
<td width=33%><a href=http://www.alternativephysics.org/book/LorentzWrong.htm>Previous</a></td>
|
|||
|
|
<td width=33% align=center><a href=http://www.alternativephysics.org/book/index.htm><small>Contents</small></a></td>
|
|||
|
|
<td width=34% align=right><a href=http://www.alternativephysics.org/book/TimeDilationExperiments.htm>Next chapter</a></td>
|
|||
|
|
</tr>
|
|||
|
|
</table>
|
|||
|
|
</center></div>
|
|||
|
|
<p><br>
|
|||
|
|
<font color=#808080><small>Copyright © 2010 Bernard Burchell, all rights reserved.</small></font></p>
|