http://www.relativitybook.com/w/index.php?title=Special:NewPages&feed=atom&hideredirs=1&limit=50&offset=&namespace=0&username=&tagfilter=Relativity - New pages [en]2019-10-17T08:50:49ZFrom RelativityMediaWiki 1.26.3http://www.relativitybook.com/wiki/Spin-spin_interactionSpin-spin interaction2016-07-26T23:37:54Z<p>Eric Baird: creation</p>
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<div>{{GEMBox}}<br />
'''Spin-spin interaction''' is a fascinating class of gravitoelectromagnetic effect in which positive masses can interact in ways that appear to show an analogue of polarisation.<br />
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==The effect==<br />
If we take two parallel discs and spin them on a common axis at the same speed (wrt the background stars), then they will be more strongly attracted to each other if they rotate in opposite directions than if they rotate in the same direction. This creates an analogue of the rule with electric charges or magnetic poles, that "opposite charges attract, like charges repel" but in this case, we have "Opposite spins attract, like spins repel". The analogy is stronger with magnetism, since each spinning body has to have two poles with opposite nominal polarity.<br />
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==Justification for the effect== <br />
<br />
* '''If only one disc rotates''', then it will feel a rotational GEM effect to both the background stars and to the parallel disc, which both have relative rotation. <br />
* '''If the second disc rotates in lock-step with the first''', there is then no relative rotation between the two, and the additional gravitomagnetic attraction that existed in the first situation disappears. (arguably, expressable as a repulsive effect compared to the first situation).<br />
* '''If both disks rotate in opposite directions''', then the rotational GEM attraction between them is stronger than if only one rotates, because the relative rotation is now even faster.<br />
<br />
==More advanced effects==<br />
In the previous section, the repulsive component between two parallel-rotating discs is "relative" to the case in which only one disc rotates. However, in a more nonlinear theory, we can imagine a scenario in which this repulsive antigravitational effect is real. If we visualise these situations in terms of twisted gravitational fieldlines, where the greater the twist, the more strongly intersected the region, and the stronger the attraction, then we can imagine the attraction between the contra-rotating discs as being due to the spatial linkages between atoms in the two discs being twisted up by the relative rotation creating a region with a more intense field, even though it contains the same number of fieldlines.<br />
<br />
If we now consider the case of the pair of co-rotating discs, we can introduce the question of what might be called "gravitational transparency". For disc A, disc B seems to show an apparent outward radial gravitational field, and in a strongly nonlinear model, this field can deflect other gravitational fieldlines passing through the region, outwards, so that the background starfield seen by A through co-rotating disc B appears to show lensing effects.<br />
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Whether these further-generation effects are real or not, and whether they can be built on for practical [[metric engineering]] purposes, will require a more advanced theory than C20th GR. <br />
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==Further reading==<br />
* ''Robert Wald'', '''Gravitational Spin Interaction''' Phys. Rev. D 6, 406, 15 July 1972 [http://dx.doi.org/10.1103/PhysRevD.6.406 doi:10.1103/PhysRevD.6.406]<br />
{{GEM}}<br />
{{Motion}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/BoogeymanBoogeyman2016-07-13T21:10:56Z<p>Eric Baird: +"Mandelbrot Set" lyrics quote, Jonathan Coulson</p>
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<div>In theoretical physics, a "'''Boogeyman'''" is a "monstrous" theory, model or idea – a hypothetical or notional model defined by its theoretical ability to "kill and eat" a popular theory. A boogeyman can be considered as a "what if" scenario - the Boogeyman is not guaranteed to exist, and its existence may even be considered vanishingly unlikely ... however the more unlikely a Boogeyman appears to be, the more constraints there are on its existence, and the more specific we can be about its potential properties. <br />
<br />
If the Boogeyman's constraints are sufficiently severe, then so such theory may be possible. However, the point of the Boogeyman exercise is to test our own preconceptions and try to deliberately design a "nightmare scenario" for a popular theory ... it is less about arguing that the Boogeyman cannot exist, and more about deriving the characteristics (however unlikely) that it would need to have in order to exist, so that we can then assess probabilities.<br />
<br />
==Properties of a Boogeyman==<br />
In common with the "Boogeyman" in children's stories, a scientific Boogeyman is (a) a threat, (b) scary, (c) indistinctly defined (at least, at first), and (d) not believed-in by experienced adults. As a scientific theory, a Boogeyman also has to have "stealth" properties – in order to be "lurking in the background", there needs to be some reason why the theory has not previously been thoroughly examined, either because it sidesteps existing definitions, contravenes assumed behaviours, or if its validity would have terrible consequences or would require us to rethink our belief systems in ways that are so repugnant as to make the very idea unthinkable, or ... ideally ... all of the above. <br />
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==The value of the Boogeymen exercise==<br />
The Boogeyman approach lets us short-circuit our existing beliefs and explore possibilities which, if correct, might overturn existing thinking. <br />
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====Potential past "Boogeyman" candidates:==== <br />
{{PullQuote|content=Pathological monsters! cried the terrified mathematician / Every one of them a splinter in my eye / I hate the Peano Space and the Koch Curve / I fear the Cantor Ternary Set / The Sierpinski Gasket makes me wanna cry ... |author=Jonathan Coulton|source=[http://www.jonathancoulton.com/wiki/Mandelbrot_Set/Lyrics Mandelbrot Set (song)]}}<br />
* For the '''Pythagorean Brotherhood''', whose core project was the construction of a logical system of the universe in which all reality was based on integers and integer ratios, '''Hippasus'''' suggestion of the existence of numbers which did ''not'' represent integer ratios – the so-called '''"irrational" numbers''' – challenged core beliefs and required a revolution in thinking. Legend has it that Hippasus was put to death for mathematical heresy before the validity of his argument was accepted.<br />
* In '''geometry''', the early subject of '''fractals''' (before it acquired the name) was originally rejected as aberrant and pathological, with fractal shapes dismissed as "monsters". Supposedly, an early argument against the validity of the '''Mandelbrot Set''' as a legitimate field of mathematical study was that the shape had to be an artefact of the computer systems that generated it, perhaps caused by rounding errors or bad coding.<br />
* In '''C18th English physics''', '''Isaac Newton''''s status was regarded as almost godlike, and the idea that he had almost single-handedly rescued the reputation of English natural philosophy against the predations of the Continentals meant that Newton's system was then considered "too big to fail". When Continental scientists started using wave theory to suggest different energy/wavelength relationships to Newton's, the English response was to dismiss wave theory as obviously wrong, and its proponents as foolish and ignorant. In this context, the "Boogeyman" for C18th Newtonian theory could stem from the question, "What if the continentals are right, and Newton's system contains a terrible mistake?". Studying this question could have allowed English scientists to construct a corrected version of Newton's system, in advance of the experimental results from ~1800 onwards that showed that the original Newtonian system – unthinkably – was wrong.<br />
<br />
{{links}} <br />
* [https://en.wikipedia.org/wiki/Bogeyman Bogeyman (wikipedia.org)] – ''see also "Bogie", an unidentified radar signal requiring investigation''<br />
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{{theory}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/Velocity-dependent_gravitoelectromagnetismVelocity-dependent gravitoelectromagnetism2016-07-12T21:49:50Z<p>Eric Baird: spellcheck! :)</p>
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<div>{{GEMBox}}<br />
'' Velocity-dependent [[gravitoelectromagnetic]] effects'' are the dragging effects (or spacetime distortion effects) that are expected to appear between relatively-moving bodies.<br />
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The status of GEM-v effects is difficult to establish – <br />
* On the one hand, these effects were assumed not to exist in Einstein's 1905 theory, as a way of simplifying the geometry ... since SR assumes of flat spacetime, a curved-spacetime description invalidates the SR proofs. In GEM-v effects exist, then special relativity is the wrong theory of relativity – this is enough to convince many physicists that GEM-v effects cannot be real.<br />
* On the other hand, GEM-v effects appear to agree with the available experimental evidence, and general gravitational arguments and the general principle of relativity, appear to insist that GEM-v effects '''must''' exist in order for gravitational theory to be logically consistent.<br />
<br />
This leaves us in an awkward situation, where SR requires the effects not to exist, and the GPoR requires the opposite. Assuming that we can take special relativity's side and suspend the GPoR, more fundamental gravitational arguments also seem to require GEM-v, and so apparently, does compatibility with quantum mechanics.<br />
<br />
==GPoR-based arguments for GEM-v==<br />
If we assume that rotational GEM dragging effects are real (Mach, Einstein 1921, Gravity Probe B), then:<br />
* '''The dumb-bell argument''' copies an argument by Galileo and says that if we change the shape of a rotating gravitational body until it takes the shape of a dumb-bell, and have the two parts of the dumb-bell rotate at exactly the right speed to co-orbit, so that we can remove the central connecting bar without obviously affecting the physics, then since the original body drags light, each of the two resulting circling bodies should also drag light, even for short sections of path that appear indistinguishable from a straight line, apparently giving a description of GEM-v.<br />
* '''The ring argument''' similarly says that if we mould a rotating spherical gravitational mass into the form of a ring or torus, gravitational dragging ought to occur alongside the rotating limb – both inside and outside the ring, and also above and below it. If the ring's orbital speed matches the speed required for self-orbiting (if there are no significant stresses within the ring), we can compact the ring until it is arbitrarily thin, and then break it into segments which follow the same path as before, orbiting a common centre. Each of these small pieces should still exert a dragging effects on nearby matter, even though, if we zoom in far enough, they may each ''appear'' to be moving in a straight line at constant velocity.<br />
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'''More generally''', while SR requires the absence of velocity-dependent gravitoelectromagnetism, rotational GEM, which is considered to be an accepted and experimentally verified part of mainstream physics, does include a GEM velocity component.<br />
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==Frame-dragging and gravitational aberration arguments==<br />
We can argue that, regardless of theory, the absence of GEM-v effects is known as an ''empirical fact'', due to the operation of Newton's First Law ("N1L"). If moving masses drag light and matter, then a body moving at speed wrt its background environment ought to be attracted more strongly by the receding stars behind it than the approaching stars before it. Bodies moving wrt the background starfield would then be expected to slow until their average speed wrt the starfield approached zero. This does not happen, therefore GEM-v effects do not exist.<br />
<br />
A parallel argument applies to gravitational aberration effects. Theory suggests that the gravitationally-sensed position of a star ought to correspond to its optically-observed position ... but if stars exerted an attraction to their apparent locations, then the aberrated starfield seen by a moving observer would appear more concentrated in the forwards direction, and a moving body would accelerate. This does not happen, therefore the effect cannot exist.<br />
<br />
HOWEVER, both the first decelerative effect and the second accelerative effect seem to have the same magnitude but different polarities. This suggests that rather than our manually overriding both effects sequentially on the basis of empirical evidence, if we ''allow'' both effects, they appear to cancel out. If we accept this, then N1L and apparent background flatness in inertial physics is not something that we have to force onto relativity theory, they are emergent effects that appear from deeper curved-spacetime principles as a special case of cancellation in 3+1 dimensions.<br />
<br />
Rather than saying that GEM-v cannot be correct because of N1L, we are then saying that GEM-v is a ''necessary compensating mechanism'' required for the emergence of N1L, and that without it, gravitational physics doesn't work. *<br />
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==General gravitational arguments for GEM-v===<br />
* '''Time-domain argument''' – If we define the effective gravitational differential between an initial position and the surface of an attracting body "pragmatically", by the change in velocity that a test particle undergoes as it falls to the surface, then this change in velocity is greater if the gravitational source recedes and smaller if it approaches. While we can argue that this is a trivial time-domain effect (the receding mass creates a greater delta-vee, because it gets to act on the test mass for longer), the uninterpreted result is that the receding mass creates a greater delta-vee than the approaching mass. If we take this outcome and describe it in the gravitational domain rather than in the time domain, we obtain a description in which a moving gravitational field includes a velocity component that attracts in the direction of motion (GEM-v).<br />
* '''black hole horizon argument''' – The r=2m radius of a stationary black hole represents an '''effective horizon''', and also (under GR1960) an '''absolute horizon'''. Light-rays originating at r=2M and aimed outwards, remain at 2M. <br> If we now consider the same black hole from the point of view of an observer for whom it is receding, we require these "critical" rays to recede at the same speed as the hole. This means that they now point ''away'' from the observer (parallel to the hole's worldline), meaning that if the angle of observer-aimed rays is a function of distance from the hole ([[tipped light-cones]]), the critical surface at which rays aimed at the observer appear "frozen" (pointing only in the observer's time direction) is some distance ''outside'' r=2M. The effective horizon surface is further from the hole's nominal centre of gravity if the hole recedes than if it approaches (corresponding to an apparent stronger pull by the hole if it moves away rather than towards the observer).<br />
<br />
Since this apparent gravitational velocity component ought to shift the energy of light, we find that:<br />
* If the motion shift of a gravitational body nominally obeys special relativity, then when the additional curvature effects are taken into account, the equations of motion have to diverge from special relativity ... <br />
* * ... but if the shift relationships for a ''gravitational'' body diverge from SR, then since we require lightsignals to obey the same velocity-shift relationship when passed between a "gravitational" and a "non-gravitational" body regardless of which is supposed to be "really" moving, the same divergence must then appear for nominally non-gravitational bodies. If we start by assuming the correctness of SR and its flat-spacetime derivation, we conclude that all signals sent between moving masses must obey a different, modified set of equations ("SR is nominally correct, but does not describe reality").<br />
* On the other hand, we may like to argue that the "gravitational" velocity component does not act in ''addition'' to the conventonal motion shift, but actually ''is'' the conventional motion shift, described within the gravitational domain.<br />
** This would mean that our equations of motion would not need to be modified by an additional GEM-v effect, since it would already be built into the equations. However, we would then need to derive those equations of motion by assuming that velocity-dependent curvature was an intrinsic part of inertial physics ([[Cliffordian universe]]). Since SR and Minkowski spacetime depend so critically on the assumption of flatness, it would seem that a relativistic derivation that assumes curvature must arrive at a different set of relativistic equations to those of SR. <br />
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==Experimental evidence for GEM-v==<br />
If velocity-dependent dragging effects are real but cancel with gravitational aberration effects for a uniform background, we should still expect to see physical dragging effects when the distribution of matter is not uniform<br />
# We should expect a body skimming a moving star or planet to be dragged (to "undergo momentum exchange") with that larger moving body, and<br />
# We should expect light-signals skimming atoms to be influenced by the atoms' motion.<br />
<br />
In reality we find that:<br />
<ol><br />
<li> If we throw a space probe at the rear edge of a moving planet, the probe emerges from the encounter with a deflection in the direction of the planet's motion, having acquired some of the planet's momentum (indirect collision, via the field). This is the basis of the '''slingshot effect''' used by NASA to accelerate probes across the solar system. <br />
<br>Although we can describe this effect in terms of the planet's velocity-dependent gravitoelectromagnetic field component accelerating the probe, we find it more convenient to carry out slingshot calculations using Newtonian gravitational theory, in the time domain (tracking how locations vary with time). <br />
<li> If we try to magnify the measurable effect of a single moving atom on light, by shining light through a region containing a co-moving ''body'' of atoms (water flowing in a tube, a spinning glass or perspex block, ''etc.''), we find that the velocity of light passing through the moving particulate medium does appear to be dragged – light crosses the distance more quickly when it is travelling in the same direction as the particles, than when it is moving the other way - the GEM-v light-dragging behavior appears to be real.<br />
<br>Proponents of SR can counter that:<br />
<ol type="a"><br />
<li>Special relativity does not claim validity in particulate media, only in "empty space", and, <br />
<li>Special relativity's velocity-addition formula can be used to model light-dragging, with light within the media treated as operating under a different set of rules, and ''not'' required to have a speed of <math>c</math> for all onlookers. <br />
</ol><br />
However, the first argument says that special relativity, which is supposed to be a theory that predicts how observers and masses interact, is allowed to be wrong if the observers or masses are particulate – which they pretty much always are. This weakens the special theory's experimental falsifiability ("disproofs don't count if they involve particles").<br />
<br />
The second argument includes an ''ad hoc'' rule added from experience ("lightspeed is not c or isotropic when significant numbers of particles are present, not because we derive this from SR, but because we already know it to be true, and override SR's "vacuum" behaviour accordingly"). Einstein's relativity book suggests that the Fizeau experiment physics provides compelling evidence for SR's model, thanks to the SR velocity addition formula applied to light as if it was a non-luminal velocity. However, the simplified SR equation provided by Einstein as having been verified turns out to be the exact equation already derived by Fresnel in the early C18th, derived from a dragged-light model. <br />
</ol><br />
<br />
The experimental effects that we would expect to see if moving matter dragged light, both at the lab scale and at astronomical scales, appear to be real. On the other hand, there seem to be no experimental confirmation for the ''absence'' of short-range dragging effects around matter, to support SR's geometry. Given that GEM-v can be regarded as a classical field theory implementation of statistical mechanics (the "smudging" of a body's mass and momentum, implemented as a field), it might even be ''impossible'' for counter-evidence to exist.<br />
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{{Notes<br />
|* While SR and GEM-v effects do seem to be incompatible, the fact that we live in a universe that includes gravitation and allows relative motion between gravity-sources suggests that if we have to choose between SR and GEM-v for "expulsion" from physics, SR seems to be the weaker of the two. General arguments seem to require the existence of GEM-v, but no corresponding arguments seem to require that relative motion needs to be a "flat" problem. **<br />
| ** SR's assumption of flatness seems to have been made to obtain the simplest possible solution to inertial physics in the context of a theory that did not address gravitation or assume that the principle of relativity applied generally. However, the simplest solution for a restricted range of phenomena is not necessarily the simplest solution for a wider range. A general theory does not have to reduce perfectly to a more limited theory, if the founding principles of the two theories aren't compatible. <br />
}}<br />
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{{GEM}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/Accelerational_gravitoelectromagnetismAccelerational gravitoelectromagnetism2016-07-11T03:47:59Z<p>Eric Baird: </p>
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<div>{{GEMBox}}<br />
'''Accelerational [[gravitoelectromagnetic]] effects''' are the dragging effects (or spacetime distortion effects) that are expected to appear when a body is forcibly accelerated (forced to change speed by anything other than gravitation). The effect creates a distortion around the accelerated body.<br />
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==Machian derivation of acceleration effects==<br />
{{PullQuote|content=Mach ... A body must experience an accelerating force when neighbouring masses are accelerated, and, in fact, the force must be in the same direction as that acceleration.<br />
...<br />
There is an inductive action of accelerated masses, of the same sign, upon the test body. ... |author=[[Albert Einstein]]| source=Princeton Lectures|date=1921}}<br />
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Suppose that we sit in the cockpit of a rocket-ship and ignite the engines. As the ship accelerates, the gee-forces push us back into our chair.<br />
<br />
* '''Under Eighteenth-Century Newtonian physics''', we say that the existence of these gee-forces shows that our acceleration is not just a matter of relative physics which can be transformed away by mathematics and a choice of coordinate system: there is a physical consequence to our acceleration wrt the background stars, which entitles us to refer to the change in motion as "real", or "absolute". It is a case of "absolute" motion referred to in Newton's <cite>Principia</cite>. <br />
* '''Under a Mach-Einstein model''', we are entitled to say that the apparent gravitational effects that we feel are, for us, ''real'' gravitational effects. We are entitled to argue that, according to what we ''see'', the universe appears to permeated by an ''actual'' gravitational field, whose reality can be demonstrated by the fact that the rest of the universe is "falling" in this field, and undergoing free-fall acceleration in the direction pointed to by the tail of our spaceship. Outside observers are not able to feel this field because they are all in freefall, we are able to sense the field because we are ''not'' in freefall – we are able to remain stationary and maintain our position, resisting the field, only by firing our rocket engines.<br />
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==Results==<br />
The immediate objection to the Machian interpretation of acceleration is that it is merely an empty ''re''interpretation of existing known physics. <br />
<br />
However, if we argue that the result is not a "special" one, and must be generalisable, we can start to derive new results from it. For instance, if the relative acceleration of the stars wrt our spaceship causes a dragging effect on the ''ship'', then the relative acceleration of the ship wrt the stars, must also cause a (correspondingly smaller) dragging effect on the ''stars''.<br />
<br />
When we forcibly accelerate a mass, the region around that mass should feel a gravitoelectromagnetic effect pulling in the direction that the mass is being forcibly accelerated in. The region around the mass is distorted by a ''real'' gravitational field. Since this induced curvature is ''intrinsic'' curvature, the (agreed for all observers) forced acceleration of the mass is accompanied by an (agreed for all observers) distortion of the region's spacetime. <br />
<br />
This is an important result for a geometrical theory of gravity - where we might be tempted to say that since different motions of the observer can result in the apparent appearance of non-appearance of a field, all such fieldsmust be unphysical, in fact, the opposite is true: this is a situation where changing the observer's state of motion does not merely translate the same physics and the same geometry between different projections, obtained with a mathematical transform ("accelerated frame" vs "inertial frame") – changing the way that the observer moves can physically change the geometry of spacetime around the observer's position. <br />
<br />
So ... a forcibly-accelerated mass causes deviations from flat spacetime.<br />
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==Further reading==<br />
* ''Albert Einstein'', '''The Meaning of Relativity''' (1922)<br />
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{{GEM}}<br />
{{Motion}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/Rotational_gravitoelectromagnetismRotational gravitoelectromagnetism2016-07-10T22:06:29Z<p>Eric Baird: </p>
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<div>{{GEMBox}}<br />
'''Rotational [[gravitoelectromagnetic]] effects''' are the dragging effects (or spacetime distortion effects) that are expected to appear when a body rotates with respect to its environment.<br />
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==Effects==<br />
There are two main classes of GEM effect associated with rotation:<br />
* '''sideways dragging effect''', and<br />
* '''a radial effect'''. <br />
<br />
Both appear in Twentieth Century gravitational theory, and can be derived from [[Mach's principle]].<br />
<br />
==Machian derivation of the transverse GEM effect==<br />
{{PullQuote|content=Mach ... A rotating hollow body must generate inside of itself a 'Coriolis field' , which deflects moving bodies in the sense of the rotation, and a radial centrifugal field as well. |author=[[Albert Einstein]]| source=Princeton Lectures|date=1921}}<br />
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Suppose that we stand at the Earth's equator, and launch a space-rocket, straight up. <br />
<br />
after it has left the Earth's influence, an observer drifting in deep space should see the rocket appear to be travelling in practically a straight line with respect to the background stars .<br />
<br />
However, to ''us'' standing on the equator, the reference system provided by the background starfield appears to rotate around us once every 24 hours, moving from East to West. If our rocket eventually moves in a straight line wrt this starfield, then we must see it appearing to veer Westward after it has been launched , so that we end up seeing it passing overhead once every 24 hours, in lockstep with the starfield.<br />
<br />
While there is no difficulty explaining the rocket's behaviour from the viewpoint of view of the deep-space observer, the Machian explanation of what ''we'' see is that, for us, the rocket is being deflected westwards by a gravitational effect associated with the rotation of the surrounding starfield.<br />
<br />
If there is nothing special or unique about the matter making up these stars, we can extrapolate from the Machian observation to make a more general prediction:<br />
* '''A hollow rotating massed shell should create dragging forces within it that pull contained matter and light around in the direction of rotation.'''<br />
<br />
This may seem like not a very useful prediction to make, as we are not in the habit of constructing giant hollow spheres from quantities of matter measured in solar masses. However, we can use topological arguments to "turn the experiment inside out" – we normally think of the Earth' surface as being contained within the universe and pointing outwards, and the background stars as being equivalent to a hollow spherical shell facing inwards. we can, though, create an artificial geometrical remapping that describes the Earth on the outside facing in, and the starfield as an outward-facing rotating ball of matter. In this artificial description, a central rotating mass is associated with a sideways gravitational dragging effect, and if the same basic laws of physics apply in all systems, then this sideways dragging around a rotating mass should also apply in more sane coordinate systems, when we look at the physics of a rotating star or planet.<br />
<br />
We can also apply the principle of mutuality - if the rotating background universe exerts a drag on the Earth, then the rotating Earth should also apply a (far weaker!) drag on the distant stars. This gives us a second behaviour:<br />
<br />
* '''A solid rotating mass should create dragging forces around it that pull contained matter and light around in the direction of rotation.'''<br />
<br />
==Experimental verification==<br />
<br />
To test the dragging prediction, NASA funded the '''Gravity Probe B''' experiment, which launched in 2004. GP-B placed four exquisitely-engineered gyroscopes in polar orbit, to measure the variation in alignment as the satellites orbited. In "old" Newtonian physics, the satellites should align based purely on their motion relative to the background stars ... in the GP-B result, the satellites' sense of what constituted "a non-rotating frame" was dominated by the influence of the background starfield, but the rotation of the Earth's mass beneath the gyroscopes also had an effect (''see:'' [[Democratic principle]]).<br />
<br />
==Radial effect==<br />
In our "rocket" example, the Earth's rotation helps to "hurl" the rocket free of the Earth's gravitational field, so the the rocket needs less fuel to escape Earth-gravity (this is why rocket-launching sits tend to be situated as near as possible to the equator).<br />
<br />
In the Machian description, physics as seen by an observer standing at the equator reveals the rocket managing to get into space more easily because of an outward-pointing gravitational field associated with the rotation of the starfield:<br />
* '''A hollow rotating massed shell should create a gravitational effect pulling light and matter directly away form the rotation axis, and increasing in strength roughly as a function of the distance from the axis.'''<br />
<br />
Once again, the initial prediction does not seem particularly useful, and just seems to give a more complicated way of describing the effects that we already know. <br />
<br />
But once again, we can apply topology and/or the principle of mutuality to obtain a more useful effect:<br />
* '''A solid rotating mass should create an additional inward attraction, acting at right angles to its rotation axis.''' *<br />
<br />
So, a spinning star creates a twist in the paths of nearby moving matter and light, and also has an enhanced attraction due to its rotation (which can be thought of as the gravitational effect of the star's kinetic energy). <br />
<br />
{{links}}<br />
* [http://www.scientificamerican.com/article/space-shuttle-weather-florida/ Why Does NASA Launch Space Shuttles from Such a Weather-Beaten Place? (Florida) (scientificamerican.com)]<br />
* [http://www.nasa.gov/vision/earth/lookingatearth/earth_drag.html As World Turns it Drags Time and Space 21-Oct-2004 (nasa.gov)]<br />
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{{Notes<br />
|* The combination of the radial and transverse effects means that small surrounding objects aren't attracted towards the star's ''exact'' centre, or to the ''exact'' position of its rotation axis, but to positions offset sideways from the central axis, in the direction of motion of the star's nearest parts (''see:'' [[Kerr singularity]]).}}<br />
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{{GEM}}<br />
{{Motion}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/Equivalence_PrincipleEquivalence Principle2016-07-08T21:35:03Z<p>Eric Baird: </p>
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<div>The Principle of Equivalence is generally defined as being the principle that a body's inertial mass and gravitational mass are different aspects of the same underlying property. A weaker version of the principle is that a body's inertial and gravitational masses are proportional.<br />
<br />
The immediate result of the principle of equivalence is that if the gravitational mass of a body (which persuades it to change its motion in a gravitational field) and the body's inertial mass (which resists that change in motion) always have exactly the same proportion, then all bodies immersed in the same simple background gravitational field should fall at the same rate, giving [[Eotvos' Principle]].<br />
<br />
A further assumption that gravitational and inertial ''effects'' are interchangeable then leads to the idea that inertial and gravitational descriptions are fully interchangeable, giving [[Mach's Principle]] and a [[general theory of relativity]].<br />
<br />
==Duality of gravitation and inertia==<br />
In the "bucket" thought-experiment in Newton's Principia, we are invited to consider the case of a spinning bucketful of water that has reached equilibrium. <br />
<br />
: '''Considered in the frame in which the background stars are fixed''', we see that the surface of the water is curved – the components of the rotating body of water are attempting to travel in inertial straight lines, but are being prevented by the walls of the bucket, causing the water to ride up the bucket sides. According to Newton, we can take this identifiable curvature of the water's surface as demonstrating that the bucket is "really" rotating, in the sense that the consequences of it motion are real for all observers, and cannot be transformed away with an arbitrary choice of coordinate systems. <br>We can say that within this interpretation, the curve of the water surface is due to its '''inertial mass'''. <br />
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However, Mach pointed out an alternative explanation:<br />
: '''Considered in the frame in which the bucket is stationary and the background stars rotate''', we are forced to agree that the surface of the water is curved, but we can no longer blame the effect on inertia, as nothing in the immediate vicinity of the experiment is moving. The inertial explanation can only be used here is we say that our own experiences are invalid, and that the experiences and interpretation of a different ("nonrotating") observer, with a different state of motion, override ours. However, if we require that physics be seen to be consistent in our own frame ("[[observerspace]]"), we can point out that our instruments seem to report the existence of an outward-pointing radial gravitational field associated with the rotation of the background shell of surrounding stars - the outward force increases if the star-shell seems to rotate faster, and the field is aligned to point directly away from the central axis around which the shell rotates. It is this field which pulls the water away from the centre of the bucket and causes it to press harder "downhill" against the surrounding bucket walls. <br> We can say that within this interpretation, the curve of the water surface is due to its '''gravitational mass'''.<br />
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==The 1960 breakdown==<br />
The realisation [[1960|in 1960]] that the general principle of relativity conflicted with the geometry of [[special relativity]] led to the difficult conclusion that SR physics seemed to require a universe in which the Equivalence Principle was not a law. The EP, if taken as a founding principle, led to the invalidation of special relativity. <br />
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Since we had been taught that the EP was one of the soundest principles in gravitational physics, to now suggest that it was wrong would be unfortunate. However, to suggest that the EP was correct and that SR was wrong would ''also'' be unfortunate. Modern textbooks get around this awkwardness by defining a new principle with the same name – "Principle of Equivalence" – which is no longer defined by the assumed equivalence of inertial and gravitational mass, or the equivalence of inertial or gravitational effects, but is instead the principle that all physics must reduce to SR. With this redefinition, the "new PoE" no longer invalidates SR, but enforces it. <br />
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==See also:==<br />
* [[Inertial field]]<br />
* [[Mach's Principle]]<br />
* [[PPN|PPN criteria]]<br />
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{{Notes<br />
|* The use of the same name for two different opposing principles is unfortunate. <br />
|* The first "PoE" makes it impossible for us to fully incorporate SR into a valid gravitational model, the second makes it compulsory.<br />
}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/Fourth-generation_relativity_theoryFourth-generation relativity theory2016-07-08T21:04:03Z<p>Eric Baird: </p>
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<div>A '''Fourth-generation theory of relativity''' would be a theory representing a further iteration of relativity beyond '''Galilean-Newtonian theory''' ("first generation"), '''[[SR|Einstein's Special Theory]]''' ("second generation"), and '''[[GR1916|Einstein's General Theory]]''' ("third generation"). <br />
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The "'''[[AGR|advanced GR]]'''" described in these pages can be classed as a fourth-generation theory, as it introduces new concepts and principles, is structurally different from the previous iteration (no perfect reduction to SR), makes some identifiably different physical predictions, and incorporates different classes of behaviour (cosmological theory, quantum mechanics).<br />
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Other possible theories of Quantum Gravity may also count as being "fourth generation", if they can be shown to apply the principle of relativity more strongly, thoroughly and/or widely than the C20th third-generation theories.<br />
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{{AGR}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/Flat-moon_theoryFlat-moon theory2016-07-06T21:47:45Z<p>Eric Baird: minor word tweak, +"assessment"</p>
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<div>'''Flat Moon Theory''' is a deliberately-perverse demonstration that it is possibel to star from a bad starting-point derive a bad theory, and still end up with the Lorentz relationships – the appearance of Lorentz relationships in a theory is therefore not proof that the theory is not a bad one (no matter how mathematically profound these relationships may appear to be).<br />
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==Results of assuming a flat moon==<br />
Since the orbit of the Earth's Moon is [[tidally locked]] and always presents the same face to us, one can imagine a particularly obstinate computer program analysing the data and deciding that due to the statistical improbability of every picture of the moon showing exactly the same details, that it is simpler to assume that the moon is not a sphere, but a flat disc.<br />
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Examining photographs of the disc, we see that its surface features show an apparent distortion effect - while the surface craters appear almost perfectly circular near the disc's centre, craters closer to the rim appear progressively flattened into ellipses as their distance from the centre increases – they appear contracted along the disc's radii. If we analyse pictures of the Moon, we find that for a smallish crater placed at a radial distance <math>r</math> from the disc centre, with the disc radius beind <math>R</math>, the radial contraction effect is <br />
::: <math>{diameter}'/{diameter} = {\left( 1 - \frac{r^2}{R^2} \right)}^\frac{1}{2}</math><br />
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This is somewhat reminiscent of the Lorentz length-contraction or velocity-rescaling effect of special relativity, <br />
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::: <math>{value}'/{value} = {\left( 1 - \frac{v^2}{c^2} \right)}^\frac{1}{2}</math><br />
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, up to and including the existence of a horizon with attendant infinities at <math>r=R</math>. Since events happening beyond the real spherical horizon could result in visible effects within the disc (an unseen astronaut over the horizon could throw a ball that could land in the visible area), it even includes a sort of counterpart to [[Hawking radiation]].<br />
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==The cautionary example of "flat moon" theory==<br />
In this case a physically-bad assumption (the "flat moon") generates SR-like Lorentz interrelationships that have similar mathematical profundity to those of the special theory. <br />
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No matter how deep these relationships appear, and how absorbing the implications might be for group theory or other fields of higher mathematics, the appearance of this relationship in a theory does not mean that the theory is not still fundamentally wrong in its founding assumptions, or that its ability to reproduce first-degree behaviour means that we "got it right". The appearance of the Lorentz relationship in a theory is no guarantee that the theory is "true". It ''might'' be, it might ''not'' be. To find out which, we need to apply different assesment criteria.<br />
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{{Notes<br />
|* The aesthetics of the mathematician and that of the theoretical physicist can be very different. An operation that generates cascading series of correction factors (such as the infinite stream of digits that appears in Pi when we try to compare the diameter and circumference of a circle using integer math) is beautiful and magical, spawns new realms of mathematics and offers deep insights into the nature of the universe. To a physicist, it means that we probably just did something really stupid. <br />
|* Where the mathematician is enthralled by mathematical sophistication, the physicist prefers systems and descriptions that are as mundane and uninteresting as possible. They ideally like things to equal "one" ... or perhaps, at a stretch, "two". <br />
}}</div>Eric Bairdhttp://www.relativitybook.com/wiki/Main_PageMain Page2016-07-04T11:33:44Z<p>Eric Baird: </p>
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<h2 style="margin: 3px; padding: 0.8em; font-family: Verdana, Geneva, sans-serif;" ><br />
WELCOME TO RELATIVITY </h2><br />
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These pages started to come online from July 2016 onwards - expect references and cross-linking to improve, as more material appears. <br />
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The aim of these pages is to try to explain a range of advanced concepts in relativity theory with the minimum of mathematics, so that most people with a very basic grounding or interest in science should be able to understand them. <br />
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'''EB'''<br />
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<h3 style="margin: 3px; padding: 0.4em; background: #cef2e0; border: 1px solid #c0c0c0; font-family: Verdana, Geneva, sans-serif;" >Sections under preparation:</h3><br />
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;[[Albert Einstein]]<br />
: ... A range of texts by Einstein on his 1905 and 1916 theories, on relativity in general, and on the fundamental character of theoretical physics. Much more material to come.<br />
; [[General Relativity]]<br />
: ... The General Principle of Relativity (GPoR). Mach and Einstein. How GR1916 was ''supposed'' to work. How a general theory is supposed to work ''in general''. The 1960 destruction of the original general theory. <br />
; [[Advanced General Relativity]]<br />
: ... How general relativity looks if we keep the GPoR as a fundamental principle, and don't insist on "perfect" agreement with SR. A [[Cliffordian universe|"Cliffordian" universe]] as a counter-example to the notion that curved-spacetime theories must reduce to flat-spacetime physics. New principles, behaviors and equivalences. Compaction of the current stratified system and increased data-redundancy. Curvature as geometrical "memory". Time-domain vs gravitational domain descriptions. Holographic principles and duality. Observerspace logic. Relativistic acoustic metric behavior derived from stochastic QM. Multiple converging arguments for an extension of current gravitoelectromagnetic theory. Relativistic energy-losses predicted and discovered. The cancellation of GEM and gravitational aberration effects. Necessity of velocity-dependent GEM effects. AGR as the logical endpoint of John Archibald Wheeler's "Geometrodynamics" project. Trans-horizon physics and classical indirect radiation. Convergence with quantum mechanics. Unification of horizon physics. Acoustic metrics. Alternative "Lorentzlike" factors. Changing the equations of motion. Significance and lack of significance in C20th testing procedures. Conceptual filters and "forbidden" concepts in C20th GR. Testing the new system.<br />
; [[Special Relativity]]<br />
: ... SR as the perfect answer to an over-idealised question. [[Special relativity considered as an average|SR considered as an average]]. SR as a first approximation of curved-spacetime physics. Limitations of Minkowski spacetime. Einstein on SR's causality. The relativistic ellipse and the generalised relativistic equations of motion. SR as the unique solution for flat spacetime. Rejection of non-SR solutions. The Lorentz factor and the "[[Flat-moon theory|flat moon]]". Constructing a "Boogeyman" theory. <br />
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<h3 style="margin: 3px; padding: 0.4em; background: #cedff2; border: 1px solid #c0c0c0; font-family: Verdana, Geneva, sans-serif;" >The "social problem" in physics</h3><br />
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The purpose of most relativity textbooks is to teach students to use, understand and embrace current theory, in order that they can become fully-qualified practitioners. It is considered in the interest of the students not to confuse their minds with the more troubling issues in current theory, lest by failing to "believe", they become sidetracked by troubling inconsistencies in the theory, and become distracted from their studies. Students are taught that special relativity is correct beyond a shadow of a doubt and is to be regarded as fact, that SR testing was carried out to the highest standards, that general relativity is one of the greatest theories of all time, that there are no cracks or flaws in the system, and that everything in the relativistic garden smells lovely.<br />
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Unfortunately, none of this is true. <br />
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Einstein called the design of his own 1916 general theory "unjustifiable", and the theory was then found to be ''logically inconsistent'' in 1960. In short, it was a bad theory. The principles of the relativity of rotation and acceleration are now known to be fundamentally incompatible with the geometry and equations of special relativity (1960), so although Einstein's 1916 theory was designed to ''incorporate'' SR, its SR component essentially makes the rest of the theory self-destruct. GR was "fudged" in 1960 as a workaround, and is technically no longer a ''general'' theory of relativity, or a "principle theory". Then, in the 1970s, we found that the "fudge" also made the resulting system incompatible with quantum mechanics, making GR1960 incompatible with information theory and thermodynamics. Black hole horizons and cosmological horizons currently operate according to different laws of physics, GR can't derive its own equations of motion for particles with gravitational fields, we have no proper relativistic theory that describes the distortions due to moving particulate matter, we've had to suspend the principle of the equivalence of inertial and gravitational mass, and GR1960 breaks down for the simple case of a black hole moving at constant speed in a straight line. A great deal of the theory appears to be broken. Redesigning GR to work properly results in increased nonlinearity, the effects of which now seem to have been measured, but we prefer to explain these using the ''ad hoc'' hypothesis of dark matter.<br />
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Other relativistic solutions were rejected without public study, testing procedures were compromised, the significance of evidence was misrepresented, and research into ''full'' general relativity was blocked. We were told that a theory of quantum gravity would come along soon that could incorporate GR1960 and QM "as-is", but we've been waiting for half a century for it, and it still hasn't arrived. It may never appear. <br />
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In short, the current system of inertial and gravitational physics somewhat resembles the aftermath of a plane crash.<br />
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On the plus side, if we don't ''need'' relativity theory to correspond to the mathematical mess in the current textbooks, the concepts become a lot simpler, and the way forward is not so difficult.<br />
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So, welcome to the Twenty-First Century, and congratulations for coming along at the right time. Physics is about to change. <br />
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