• Prologue: Something to Think About   Say for example that a crew of astronauts was on the space station orbiting Earth – some inside and some out on space walks, perhaps performing delicate maneuvers of parts and machinery. Suddenly, a huge speeding asteroid comes hurtling out of nowhere and has a very close call with the space station, but misses it. The asteroid weighs countless thousands of times what the space station does, so its gravity abruptly lurches the entire station, crew and all, out of position and onto a new trajectory. What sort of casualties and damages could one expect from this calamity? Well none of course; that's right, none. Except for seeing the asteroid draw close and then veer away at a different angle, the crew on the station wouldn't even perceive a significant event occurring. And what's more, even if the astronauts used an instrument that could measure the local velocity of light, in all directions, and with utter precision; no such instrument could deliver evidence of the asteroid encounter and subsequent lurch off course. That is because gravity affects all things, in a locality, with exact uniformity, and now we've learned that that includes light itself. A human wouldn't sense the lurch in the above example, because the liqueous matter in the brain would be accelerated in perfect harmony with its containing cavity, the skull – not so the lurch of any artificial thrust (eg. cars, rockets). So too, scientific instruments can sense gravitational fluxes only by sampling data over a wider area.
  
  

  
  

  • Minor qualification    If the asteroid were extremely immense and came very very close, then the space station might creak and groan a bit – or be damaged – by the so-called ‘tidal forces’. But for the most part, these effects can be discounted as negligible.
    
    

  
  

• Relativity in a nutshell   Our universe respects no preferred frame of reference, so there is no such thing as a body's unequivocal motion through space, proper. Indeed any thing, any place, is a proprietary platform per se, a basal world of supreme stature, owing deference to no greater realm. And the laws of Physics bestow unerring homage to each and every such arbitrarily-defined vantage as if it, and seemingly it alone, constitutes some hallowed special ground.
  
  

  
  

• The age old quandary   When you look up to the sky you see the Sun going around the Earth. But we're taught that this viewpoint is scientifically incorrect because, in fact, the Earth spins about its own axis once every 24 hours, which more correctly accounts for the Sun's apparent transit. Well, relativity may have changed that, and here's how.
  
  

  
  

• A venerable proof?   If indeed the Earth is spinning in space, then with our superfine electronic gadgetry we ought to be able to verify this beyond any shadow of a doubt. Consider if you will two towns, some miles apart, each located on the Equator, and each with a prominent high tower. Since the Earth is supposedly spinning in the direction that we know by convention as Eastward, then clearly, an ethereal signal (such as a light or radio pulse), sent from the tower of the Westernmost town to the tower of its Eastern counterpart, would take a fraction of a second longer to transit than a signal sent in the opposite direction; because the Easternmost town is RECEDING in space from where the signal originates... yet in the opposite case, the tower is actually coming to meet the signal. We now possess the technology, the very precise instrumentation, that could detect such a discrepancy in signal transit time, but WHOA! we find that it takes exactly the same time for the Eastbound signal to traverse as the Westbound one. Those results would seem to indicate that the Earth is stock still in space, rather than spinning.
  
  

  
  

  • Advisory note    Of course we've known for ages that light does not inherit velocity from it's source, like a ball would if it's tossed about inside a moving vehicle; hence the scenario above examines and debunks the second most likely supposition: that light somehow moves relative to an absolute space/grid.
    
    

  
  

• Nevermind media   Remember that light can travel through a vacuum, so the above result has nothing to do with the presence of Earth's atmosphere (which is dragged along with Earth’s rotation) serving as a medium. For we can do a like experiment on ANY spinning body, such as on our Moon, where no atmosphere is present; and the results of those time trials, when gauged by instrumentation there, would again show no difference between an Eastbound and a Westbound light signal about the Moon's equator. Amazing, huh?
  
  

  
  

• Light clinches it    So, where's the catch?? Referring to the Sun as the system center, around which all nine planets are slued by gravity, is by far more gratifying then any alternate orientation. But indeed, relativity tells us that one viewpoint is every bit as accurate as another, so long as the behavior of light signals betrays no express bias.
  

  
  
  

• Closet space is one thing...    Now, how can this be? Well, part of the problem is that 'space' is just a convenient invention of the human mind. In real nature, physically, there is no fundamental set of rectilinear x-y-z axes that we can assign to our greater cosmic reality, and so there truly is no all-encompassing reference frame which can serve as the standard preferred over all others. Not even the pervasive background of seemingly fixed stars, deep in the heavens, can serve as a standard reference... no, because light just doesn’t behave that way. The problem crept into our discussion and analysis when we surmised that the Earth spins in SPACE... and there's no such animal.
  
  

  
  

• Textured Space   Out there in the Cosmos, instead of plain-jane space, and far more pertinent, we find a complex web of interwoven gravitational fields. Also note that, except in the human mind, there is no specific reality as a ‘straight line'. Modern science has discovered that light follows no ‘absolute’ straight line on the large scale, such as when traversing intergalactic spans. Specifically, light is bent, diverted by gravitational pulls – only a minuscule amount normally, mind you, but significant nonetheless. With the myth of rectilinear space exploded, and the myth of light following a straight course exploded, we are left with only a few cornerstone assumptions about the physics of our world.
  
  

  
  

• Relativity Rudiments   When an object, such as a star or planet or spaceship, drifts along impelled only by gravity, it is said to be in freefall, also known as a geodesic trajectory. Every object on a geodesic trajectory lays claim to a consistent (regular) space/time continuum uniquely all its own – the place is a veritable ‘Terra Firma’ and can rightly claim to be stock still, The Unmoving Center of All. From the perspective of such an observatory, any object in motion – regardless if that motion be toward, away or transverse – is literally moving somewhat toward the past, as moving clocks are unsynchronized along the direction of travel, with leading clocks lagging in time. Of course, the moving object, though moving toward the past, never actually moves into the past because the clocks are ticking, so that by the time the object reaches any point ahead, the clocks there have progressed to what has become the future. The effect is telling however, such that clocks on board moving objects progress more slowly overall with respect to the presumed still observer. (By ‘clocks run slow’ it is meant, in fact, that time itself is slowed, and applies to all temporal processes.) But realize that this effect is mutual, ie. covariant: according to the perspective of the moving party or object, it is he who is still and it is the first party whose clocks go slow and who is moving somewhat toward the past. And finally, there is one last mutual distortion at play between observers moving relative to one another: distances in the moving frame are shortened – only along the direction of movement – by the reckoning of a presumed stationary observer. These covariant effects are hard to grasp, but may be thought of as akin to viewing an apartment building askew, say, from diagonally away across an intersection. Because of perspective, the individual windows, or units, are not quite as long or as wide as they would appear face on. The distortion is mutual, equally affecting viewers from that building looking at your own. This analogy may however be less than satisfactory.
  
  

  
  

  • A better analogy  But a similar seeming paradox is grasped in everyday life: one man hails another from a couple hundred yards away. To each man, the other one's stature appears small, and the other man's voice seems muffled. This is not so much an illusion as it is a mutual (or covariant) warping of physical measures. And so it is in relativity.
    
    

    
    

  • Contradictory it’s not  But one might well ask, "If the other fellow's clock is running slow simply by virtue of his relative motion, then when he should return to me, his clock will show less time elapsed... and how can that be covariant? either his clock shows less time elapsed or mine does! how can my time be slowed to him and his time slowed to me, both??" Not to worry: the answer lies in the fact that each body on a geodesic trajectory has its own proprietary and perfectly valid time continuum. The clock that will show missing time upon reunion is the clock on board the spacecraft that purposely fired its rocket engines to take leave of its own freefall reference frame and come to join up with the other party's trajectory. What is propelled by rocketry is no longer in freefall! The effect of thrusting toward that other craft is unequivocal: it speeds up the distant freefalling craft’s time – as reckoned by the thrusting one – which more than compensates for the otherwise accrued discrepancy. This should dispel any seeming paradox about, say, two spaceships drifting past one another deep in space.
    
    

    
    

  • Again, texture   Yet, in such a case, if a reunion should occur without rocket propulsion, induced solely by the two ships’ mutual gravitational pull, then the two clocks would agree on the time elapsed, as no specific force breaks the symmetry. In the real world though, there’s never perfect symmetry – distant heavenly bodies will add their subtle bias. This is clarified below, under Equivalent Pseudo-Forces.
    
    

    
    

  • Simultaneity is moot  Truly, under Relativity, no unerring truth can be asserted how two differently moving clocks compare until there’s a reunion. Synchronicity between disparate frames works out to be a moot point; undefined, nebulous.
    
    
    

  
  

• The Key Thrust  This warping of clockworks and measures in one reference frame as cited by another (moving) one, is precisely such that it results in light being assessed as traveling at the fixed speed of 186,282 miles per second, by all observers, irregardless. (diagramed as an appendix below) So in essence, light and similar electromagnetic (eg. radio) messages DEFY the relativity of motion: their motions are distinctly absolute. Material objects dance only in relative motion, while ethereal signals move only at absolute light speed (unless they interact with matter).
  
  

  
  

• The Vital Truth   Scientists assert that no material thing can ever reach or exceed the speed of light. But they're not talking about an object's ABSOLUTE speed, such as relative to a hypothetical macro scale set of x-y-z axes of our universe/space, which is a myth... NO, they mean that no object can move as fast as light as assessed from another object's reference frame. This perhaps is an even greater constraint than the first, because it means that every single object in the world must comply in relation to every other possible citing object! and in relation to any conceivable vantage or trajectory. Another way to phrase this particular rule of Relativity Principle is: no object can OUTRUN being viewed by others. That truth is inviolate and universal.
  
  

  
  

  • Example   Consider Earth, and a spacecraft takes off from it moving at three quarters the speed of light (.75c). From the other side of Earth another spacecraft takes off also moving at three quarters the speed of light, but in the opposite direction. Doesn't then craft A outrun any possible light transmissions from craft B and vice versa?? Crazily, no! and B is not moving at one and a half times light speed relative to A either. Here's why: A has only Earth's word for it that B is moving at .75c (in relation to Earth) but Earth's measurements are SUSPECT to A, because Earth is undeniably a reference frame in motion relative to craft A. In order to cite the velocity measurements supplied by Earth and make them viable in A’s perspective, A must employ a specific complex transformation computation based on the known speed of the frame being cited. After applying that formula, craft A will conclude that the velocity of craft B, relative to Earth, is NOT .75c as claimed, but rather it is only about .21c. That then, when added to the .75c that Earth is known to be moving, yields a sum of around .96c for the speed of craft B in craft A's frame. It's unbelievable, but true! The scenario is fully diagramed as an appendix below. Remember, in relativity, the observer’s frame of reference is the one presumed to be stock still, in any computation... it’s the other guy who’s moving.
    
    

  
  

• Equivalent Pseudo-Forces  Gravity affects clocks just as the equivalent acceleration would – ie, the effect is to slow clocks, relative to any time continuum where gravity is less or absent. G-forces/fields don’t actually have a physical effect on clocks, rather it’s just that a bias needs be applied to such a frame’s dynamics, when citing measurements therefrom. Again, it’s more of a perspective thing. But unlike the perspective corrections already discussed – those of speed-derived relativity (SR) – the transforms for G-force relativity (GR) won’t be covariant between frames but instead have an unambiguous orientation and pitch (distant clocks off in the direction of tug need be assessed slower-ticking; those in the opposite direction faster-ticking, than one’s own). Hence we hold the view that gravitating bodies ‘shape’ the space-time fabric around them.
  
  

  
  

  • Example  An astronaut in a spacecraft drifts in freefall (with rockets idle), so he floats in his cabin... he feels no specific pull, so 'gravity is absent'. He is in freefall and can be rightly assessed as standing stock still... as no local study of the behavior of light would reveal any different. But when he fires his rockets, he and all objects aboard succumb to an inexorable tug in one and only one direction. That tugging is in every way equivalent to, and as causative as, what we normally think of as real gravity, ie. the pull exerted by massive bodies. If you think hard about accelerating by rocketry, you will conclude that a light beam crossing your path would appear to bend some – and in the same direction that everything else is being tugged. This fact goes to further reinforce the equivalence of gravity and acceleration.
    
    

    
    

  • Such decorum   And by virtue of this equivalence, wouldn’t you know – again, each and every observer’s frame can rightly claim to be stock still, however jerky it’s motion may seem to others. Even though lurches are felt, they are no indication of movement; no, those are pulls from some unusual ‘passing’ gravitational fields. And truly, no study of the behavior of light would reveal any different.
    
    

  
  

• The Spin Proviso   Relativity is the absence of a preferred reference frame, and this scheme works fine, as we see it confirmed by the behavior of light signals. But relativity does not actually extend unqualified to rotating frames of reference, as was implied earlier. If you sit in your easy chair atop the North Pole, you will see the same heavens pass by, again and again repeatedly, each 24-hour period. That’s a pretty fair indication that you are spinning. The alternative is: you are still and the world spins. But if that were the case, then you would have the very personal distinction of being situated right on the central axis of cosmological spin – and that can’t be, because it unjustly excludes other spinning bodies from sharing the distinction. There are too many other clues as well; hold a bicycle wheel by the axle ends and you can freely orient it to face any direction, but NOT if the wheel is spinning. When it’s spinning, forces resist such reorienting. The fact is, spinning objects are so righteously unequivocal in this world that gyroscopes are used to help navigate and orient us.
  
  

  
  

• Relativity Mastered   It is still true that a Westbound and an Eastbound light signal take the same time to cross a given local span (all other things being equal – even the Moon’s proximity overhead skews local time infinitesimally); and this phenomenon serves ideally to spark illumination of the subject, relativity. Yet truly, the metric of rotating frames is not so simple overall: in them, some skewing of clocks and measures is implicit. Similarly, an object hurtling through space in freefall may be mathematically very close to a so-called inertial frame, but never completely so. Yes, every such object rightly lays claim to its own proprietary space/time continuum – locally regular and consistent – but as always, accelerations and heavenly bodies contribute some skew. “General Relativity” is a generalized mathematical model for mapping the time/space coordinates of one dynamic system onto any other; it takes every factor into account, and may evidence specific length distortions, time flow distortions and clock dissynchronicities. When you probe deep the math gets thorny, but all the formulations bear out the uniformity of light’s speed and behavior, per any (presumed still) vantage – that’s the crux.
  
  
  

  
  

• Epilogue   One might well ask, “Are the time and distance distortions of relativity real?” Answer: they are real to the observer, yes. They are not uncategorically real, like the hot kiss at the end of a hard fist; but rather they are a function of perspective. We run across perspective a lot in life and usually take it for granted. Mankind supposedly went a very long time before noticing the effects of relativistic space-time distortions, because the effects are downright minuscule in all but the most extreme cases. Think about the perspective-based mutual voice distortions cited in an earlier paragraph, when two shouters are far separated. The muffling of the voices is not real... certainly not to each shouter himself; yet the effect on the listener is no illusion. So like any effect of perspective, relativistic distortion is “subjectively real”, and as such, it must enter into our plans and computations. A main key to understanding relativity is this subjectivity: time and space measurements cited of a moving/alien frame are flawed unless transformed, but you can employ data collected in your native frame all the day long, without a hitch.
  
  

– by KJS       (The Uncredentialed)

Feedback, to the author

For a tad more reinforcement, read also
Addendum I, The Number Line Argument
Addendum II, The Perspective Analogy
Addendum III, Intriguing Posers in Quantum Physics & Relativity
Addendum IV, Twin Paradox Without Accelerations
Glossary of Terms
And see this animation illustrating just how fast lightspeed is.

In the event that your system displays the following diagrams and accompanying text too small, click right here to load scaled-up diagrams.

In the event that your system displays the following diagram and accompanying text too small, click right here to load scaled-up diagram.

Copyright © 2001 - 2005 KJS. All rights reserved

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