http://www.relativitybook.com/w/api.php?action=feedcontributions&user=Eric+Baird&feedformat=atomRelativity - User contributions [en]2022-11-29T17:13:24ZUser contributionsMediaWiki 1.26.3http://www.relativitybook.com/w/index.php?title=MediaWiki:Common.css&diff=605MediaWiki:Common.css2016-07-28T00:11:29Z<p>Eric Baird: </p>
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<div>{{#seo:<br />
|title=Albert Einstein (1879 – 1955), and relativity theory<br />
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'''Albert Einstein (1879 – 1955)''' is the person most popularly associated with the idea of relativity theory. <br />
<br />
Born in Germany in the latter half of the Nineteenth Century, Einstein was an independent-minded student who earned the ire of his professors by not treating them what they considered to be adequate respect – when they proclaimed that a thing was true, instead of takign their word for it, Einstein would sometimes have the effrontery to ask how it was that we ''knew'' that such a thing was true. Disgraceful behaviour for a young scientist! His professors were also not amused by Einstein's apparent disdain for lab work, and his habit of not turning up to lectures to hear his professors speak.<br />
<br />
Someone with such a disrespectful attitude clearly had no place in physics – Einstein, said his professor [[Hermann Minkowski]], was a lazy dog who would never amount to anything. Although Einstein graduated, his professors wrote such bad references for him that he considered himself unemployable with respect to university work, and Einstein is supposed to have applied to every university in Europe for a position, and been rejected or ignored. At one point his father even resorted to writing begging letters on his behalf, pleading for his son to be considered for a position. <br />
<br />
After a succession of tutoring and miscellaneous jobs, Einstein managed to get long-term employment at the Swiss Patent office as a patent examiner. He reputedly liked the work, and how it exposed his to a wide range of ideas that needed assessment, and used the stability and isolation to work on his own ideas. During this time he was separated from his wife and child, and living alone - this may have been partly because Swiss governmental departments took a dim view of children born out of wedlock and Einstein might have been less than completely honest about his domestic arrangements, but also partly because it allowed him to work without interruption.<br />
<br />
==1905, the Wonder Year: Special relativity==<br />
<br />
By 1905, Einstein had assembled enough ammunition to make an assault on the scientific community and claw his way into paid academia. He did this with a series of papers published in the German journal '''Annalen der Physik''', which apparently had a policy that once an author had published in the journal once, further submissions tended to be nodded though unless there was something badly wrong with them. Having "opened the door" with his first accepted paper, Einstein fired a series of followup papers though the gap, and during 1905 published papers on the quantised nature of light and the photoelectric effect (a arguably the birth of quantum theory), a rederivation of the equations of Lorentzian aether theory (published in the same journal in 1904), which derived the relationships form more abstract principles with a set of relativistic arguments that later became known as special relativity, and a quick followup paper that showed that if the Lorentz-Einstein equations were correct, they led to the relationship E=mc^2.<br />
<br />
This sudden body of published work got Einstein a full-time university position in 1909, at which point he quit his patent office job, and set to work developing further arguments and extensions of the 1905 work.<br />
<br />
==1911: Gravitational time dilation==<br />
In Einstein's 1911 "on the effect of gravitation on light", he argued that a gravitational gradient ought to shift the frequency and wavelength of any light crossing it. While the effect had been proposed before (and forgotten), by John Michell in 1783, Einstein went further and pointed out that the frequency-shifting of light-signals led to logical absurdities unless the rate of timeflow was physically different in different gravitational environments.<br />
<br />
==1911-1916==<br />
In 1916, Einstein published the finalised from of his theory of general relativity. GR was a curved-spacetime geometrical theory of gravitation, and while brilliant mathematicians had previously tried and failed to describe gravity in terms of curved-space geometry, Einstein's earlier trivial result that gravity also warped time coordinates meant that he had the secret to to solving the problem, which was to apply curvature in four dimensions rather than three, and obtain a description not of curved space, but curved space''time''.<br />
<br />
Since he'd already published the critical piece of information in 1911, Einstein knew that he had competition many of whom were much better mathematicians than he was, and in an attempt to be the first to present a working theory, drove himself almost to the point of a breakdown. A major breakthrough was Einstein's realisation that a falling body feels "weightless" – if one dropped a small self-contained freefalling laboratory towards the Earth, then the earth's gravitational field would not obviously be detectable inside the lab. Einstein used this argument to say that gravitational physics needed to reduce over small free-falling regions to non-gravitational physics ("the happiest thought of my life"), declared that his general theory therefore should reduce to the existing physics of his special theory, and went on to complete a formulation. <br />
<br />
===1914-1918: World War One===<br />
One of the factors working in Einstein's favour was the outbreak of World War One (1914-1918). With many of his colleagues joining the military having their research diverted towards war work, Einstein (as a pacifist) was able to continue with his research with minimal interference or criticism from colleagues. <span class="PERSON">[[Karl Schwarzchild]] (1873 – 1916)</span>, who might have been expected to provide Einstein with some competition had patriotically joined the army and died on the Eastern Front toward the end of the war.<br />
<br />
===Perihelion shift of Mercury===<br />
Einstein was aware that the highly-elliptical orbit of the planet Mercury constantly shifted its alignment, and that existing theory could only account for part of the effect. Keen to use the perihelion shift as a test of the theory, Einstein found that the correct amount of shift did in fact show up under the new general theory, and once all the remaining bugs were worked out of the mathematics, and the perihelion result was still present, Einstein declared the theory finished. <br />
<br />
==1919: Eddington==<br />
A new result of the 1916 theory was that light ought to be deflected by a gravitational field by roughly twice as much as had been predicted by Newtonian arguments. While Newton's system predicted light-bending analogous to curved space, and Einstein's 1911 arguments had led to essentially the same result as a result of "refractive index" arguments based on a variation on lightspeeds due to curved time, the combination of the two effects meant that according to the new general theory, light ought to be deflected by around twice as much by a gravitational field as had previously been predicted.<br />
<br />
<span class="PERSON">[[Arthur Eddington]]</span> set out to mount an expedition to measure the apparent deflection of starlight during an eclipse, and reported agreement with the 1916 prediction. To a world deeply depressed by the carnage of WW1 and the loss of faith in existing political systems, the idea that a German and an Englishman had devised a new system of the world and demonstrated it correct was embraced by the public as a reason to be optimistic about the future, and Einstein became a celebrity.<br />
<br />
With the rise to power of the Nazi party, Einstein left Germany for the United States, and took a position at the new Institute of Advanced Study, in Princeton.<br />
<br />
==1939: The A-Bomb letter==<br />
Einstein had originally argued that the idea of using nuclear power for anything useful was unworkable, since the only suitable element isotopes were vanishingy rare. Uranium 235 was a candidate, but uranium ore was only found in limited quantities, and more than 99% of ''that'' was in the form of U238. The discovery of large quantities of uranium ore in the Belgian Congo changed things, and when Einstein heard through his contacts with the Belgian Royal Family that Nazi Germany had taken control of the Congo and that its agents were interested in uranium, he deduced (correctly) that Germany was interested in exploring the idea of building a nuclear weapon, and wrote to President Franklin Roosevelt warning him of Germany's apparent intentions, and urging action by the United States.<br />
<br />
==External links==<br />
* [http://www.atomicarchive.com/Docs/Hiroshima/EinsteinResponse.shtml On My Participation In The Atom Bomb Project, Albert Einstein, 1952 (atomicarchive.com)]<br />
<br />
{{People}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:Acoustic_metrics&diff=591Category:Acoustic metrics2016-07-27T20:52:31Z<p>Eric Baird: </p>
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|description=Acoustic metrics describe the properties of regions in which signal-propagation is significantly nonlinear. They are interestign to quantum gravity researchers since they support Hawking radiation within a classical system.<br />
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A '''metric''' describes the apparent geometry of a region when probed using signals or test bodies – an '''acoustic metric''' describes a region in which the presence and properties of those signals is nonlinear, and physically changes the geometry. <br />
<br />
==In acoustics==<br />
In acoustics, an acoustic wave is caused by the transmission of density-waves in a particulate medium. This requires particles to shift their positions and briefly have forward-and-backward velocities as the wave passes through their location. If we imagine that a "loud" low-frequency wave is "rocking" the atoms back and forth in a region, and we then send a higher-frequency wave through the same region in a different direction, the waveshapes do not simply superimpose "additively" in a linear manner - the high-frequency signal experiences the low-frequency signal as a series of regions in which the medium is moving, and this makes the second signal transmit faster or slower through the zones as a result of the different pressures and different averaged background velocities of the medium in those zones – the initial low-frequency signal is not simply propagating through the metric, it is also modifying the shape of the metric, in such a way that the map of apparent distances and geometrical properties of the region when a signal is present is no longer the same as the map for when the region was "quiet".<br />
<br />
====Self-interaction====<br />
This non-linear behaviour also appears even if we only have a single signal - producing the apparently paradoxical result that our map of how signals propagate through a region is only technically correct if no such signals are present(!). In practice, the linear approach is usually "good enough" to describe signals that are of reasonably low amplitude - if we clap our hands once, the shockwave will travel at the standard speed of sound <math>s</math> calculated from the normal density and composition of the air. However, if we create a more extreme shockwave using high explosives, the wave can propagate at more than the background speed of sound, as the extreme physics taking place at the shockwave invalidates the usual assumptions that we used to calculate <math>s</math> (air molecules being flung forwards at more than <math>s</math>, condensation of water vapor behind the shockwave, and so on). If we try to use a linear approach in these situation, we can appear to get apparently nonsensical results, with signals propagating at speeds other than the "official" propagation speed of the medium.<br />
<br />
==Examples of nonlinearity==<br />
<br />
* '''When an extremely high-energy EM wave''' passes through a region, energy-densities may be high enough for the creation of particle-pairs, which ... even if the pairs then self-annihilate ''almost'' immediately ... can affect how the signal propagates.<br />
* '''Gravitational waves''' – gravity-waves are generally assumed to travel at the same speed as light, <math>c</math>. But since a variation in gravitational properties ''changes'' the speed of light, how fast should a gravity-wave propagate in practice? (see: the ''[[gravity-wave problem]]''').<br />
* In gravitational theory, we might also consider '''a moving gravitational mass''' to count as type of gravitational signal (as it carries a gravitational payload from place to place). Given that he speed of the body is a function of it's momentum and energy divided by its inertia, along with the background properties of the region that it passes through, then if its presence changes those background properties, how fast does the object move?<br />
<br />
==See also:==<br />
* [[Acoustic horizon]]<br />
<br />
{{Links}}<br />
* [https://en.wikipedia.org/wiki/Acoustic_metric Acoustic metric (Wikipedia.org)]]<br />
<br />
{{GEM}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Spin-spin_interaction&diff=590Spin-spin interaction2016-07-26T23:37:54Z<p>Eric Baird: creation</p>
<hr />
<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 />
<br />
==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 />
<br />
==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 />
<br />
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 />
<br />
==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/w/index.php?title=Accelerational_gravitoelectromagnetism&diff=589Accelerational gravitoelectromagnetism2016-07-26T22:49:13Z<p>Eric Baird: </p>
<hr />
<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 />
<br />
==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 />
<br />
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 />
<br />
==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 />
<br />
==Further reading==<br />
* ''Albert Einstein'', '''The Meaning of Relativity''' (1922)<br />
<br />
{{GEM}}<br />
{{Motion}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:Gravitoelectromagnetism_(GEM)&diff=588Category:Gravitoelectromagnetism (GEM)2016-07-26T22:47:56Z<p>Eric Baird: a couple of references, quotebox</p>
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<div>{{#seo:<br />
|title=Gravitoelectromagnetism (GEM) / Gravitomagnetism (GM)<br />
|titlemode=replace<br />
|keywords=gravitoelectromagnetism, gravitomagnetism, GEM, GM, general relativity, Albert Einstein, Mach's Principle, frame-dragging, rotation, Kerr black hole<br />
|description=Gravitoelectromagnetism (GEM) <br />
}}<br />
{{NoRefs}}{{NOQUOTES}}{{GEMBox}}{{Motion}}<br />
The subject of '''Gravitoelectromagnetism (GEM)''' deals with the effects that moving masses have on the shape of spacetime. Textbooks often prefer to talk about '''gravitomagnetism (GM)''' which is a slightly shorter word, and is less likely to be mistaken for something that involves ''actual'' electric fields (which GEM/GM doesn't).<br />
__TOC__<br />
=="EM" vs "GEM"==<br />
The GEM name is based on an analogy with '''electromagnetism (EM)''' – where the subject of ''EM'' deals (in part) with the effects due to a moving ''electrical'' charge, ''GEM'' effects are the analogous behaviours caused by a moving ''gravitational'' charge (a moving mass). <br />
<br />
The analogy is not exact (electrical charges can be positive or negative, gravitational charges can only be positive), but since both types of field are bound by the same general constraints of classical field theory, and both have a finite propagation speed (defined as "<math>c</math>" for EM, and generally assumed to nominally be "<math>c</math>" for GEM), the two classes of problem can't help but share some basic behaviours. <br />
{{PullQuote|content=<br />
Frame dragging is a direct manifestation of gravitomagnetism. Its consequences have found important astrophysical application in, for example, models of relativistic jets ...|author=National Research Council|source=Review of Gravity Probe B|date=1995}}<br />
<br />
==Categories==<br />
GEM effects cause a deflection of light and a deflection of the paths of objects passing through a region, and can be modelled as spacetime distortion effects, or as the result of nontraditional gravitational fields.<br />
<br />
We can define three main classes of GEM effect:<br />
<ul><br />
<li> '''[[Rotational gravitoelectromagnetism|Rotational GEM]]''' – creates a radial attraction at right angles to the rotation axis, and also a rotational dragging around the rotation axis, in the direction of rotation. <br> &nbsp;&nbsp;&nbsp; These two effects are "Machian", and appear in C20th GR. </li><br />
<li> '''[[Accelerational gravitoelectromagnetism|Accelerational GEM]]''' – creates a dragging effect around the accelerated body, in the direction of forced acceleration. <br> &nbsp;&nbsp;&nbsp; This effect is "Machian", and appears in C20th GR.</li><br />
<li style="color: darkred;"> '''[[Velocity-dependent gravitoelectromagnetism|Velocity-based GEM]]''' – creates a dragging effect around a moving body, in the direction of motion. <br> &nbsp;&nbsp;&nbsp; <span style=" background-color: #ffffef">This effect is derivable from the rotational effect or from general gravitational arguments, but is at odds with special relativity. Its status under C20th GR is problematic.</span></li><br />
</ul><br />
<br />
==Multiple paths to GEM==<br />
;GEM effects considered as the result of "smudging"<br />
: If the properties of physics, including the properties of spacetime ''and the properties of bodies'' can be described using field theory, then the condition that classical field theory has "no sharp edges" means that our descriptions of how matter interacts with spacetime and with other matter end up with a certain degree of "blurring". If the mass of a moving particle, idealised as a point, is not allowed to be described as a point, but has to be smudged out into the surrounding region, then the mass becomes a field whose strength dies away with distance, and since a field carrying the property of mass is a gravitational field (or an inertial field), smudging or blurring turns a description of particulate matter physics into a description in which each particle has its own gravity-well.<br />
: If we now consider a situation in which particles are moving, the smudging of a particle's rotational momentum, accelerational forces or linear momentum produces a field description in terms of rotational GEM, accelerational GEM, and velocity-based GEM.<br />
<br />
;GEM effects considered as the result of statistical mechanics<br />
: If two bodies with relative acceleration, rotation or velocity are placed in a particulate medium, the intermediate particles will acquire the "imprint" of those bodies by collision, and then by colliding with each other, create an interaction between the two bodies at a distance ("indirect collision"). The smoothed and averaged statistical behaviour of these interactions can then be modelled in an abstract way without knowing the positions or velocities of the intermediate particles as a field, which then gives GEM behaviour.<br />
<br />
;GEM analogues under aether theory<br />
: While GEM is not derived as an "aether theory" effect, GEM classes typically have easily-visualisable aether-theory counterparts – for instance, the rotational GEM effects are broadly similar to the effects expected from a dragged-aether theory. This is partly because aether models tend to have a "statistical mechanical" component, and partly because their dragging effects are usually expressable in idealised form as fields, making them subject to the same "classical field theory" limitations and restrictions as GEM fields ("smudging").<br />
<br />
;GEM as the result of Quantum Mechanics<br />
: The statistical route to GEM seems to mesh well with quantum theory. if we fire photons or other small particles at a moving target particle, the target's position will have a certain degree of uncertainty, meaning that our pattern of potential "hits" will be scattered over the region, and can be idealised as a probability field, with the attributes of mass and momentum of the original particle. This then takes us back to the earlier description of the moving particle having effective static and GEM gravitational field components, which describe its rest properties and state of motion. We can also statistically model the interaction of bodies via [[virtual particle]]s and arrive at the same basic patterns of behaviour as before.<br />
<br />
==Status of GEM effects==<br />
The status of GEM effects under C20th General relativity is somewhat elusive – the general principle of relativity requires that the rotational and accelerational effects must be real, and general gravitational arguments and extrapolations from GEM-r then seem to say that the velocity-dependent effects also have to exist, too. A full logically-consistent description of GEM seems to require all three classes of effect.<br />
<br />
However, special relativity is derived from the assumption that there are no distortion effects associated with relative motion, so the "SR" side of GR1960 requires GEM-v ''not'' to exist. The other two effects were described by Einstein as appearing in general relativity, but were found in 1960 to also conflict with SR. The apparent absence of a full peer-reviewed study of GEM/GM effects seems to be down to implicit and explicit conflicts with special relativity.<br />
<br />
==Not to be confused with:==<br />
* ''Electrogravity'' ... GEM/GM describes gravitational field-effects that ''mimic'' some EM field behaviours, "electrogravity" is a concept that deals with possible interactions between the two types of field.<br />
<br />
==Further reading==<br />
* ''Albert Einstein'', '''Is There a Gravitational Effect Which Is Analogous to Electrodynamic Induction? ''' [http://mc1soft.com/papers/1912-Einstein_Inertia.pdf Vierteljahrsschrift für gerichtliche Medizin und öffentliches Sanitätswesen 44 (1912): 37-40] – ''pdf''<br />
* ''Herbert Pfister'' and ''Markus King'', '''Inertia and Gravitation: The Fundamental Nature and Structure of Space-Time''' 4: Mach's Principle, Dragging phenomena, and Gravitomagnetism<br />
By <br />
<br />
{{Notes|* It has been accepted since around 1960 that the GPoR and special relativity are mutually incompatible (Schild) – the logical inconsistency of C20th GR, even after 1960, can be expressed in terms of the 1960 theory's inability to properly process questions related to GEM. |* C20th textbook theory appears to deal with the subject of GEM and its associated contradictions ("Gravity and the GPoR requires GEM to exist" / "SR requires GEM not to exist") in the manner of a '''disassociative identity disorder ("DID")''' – by compartmentalising information and descriptions that would otherwise conflict, and "blanking" subjects that would reveal logical inconsistencies. |* If we embrace full-range GEM (which seems necessary for compatibility with QM and with a range of other principles), the result seems to be a [[Cliffordian universe]], a [[relativistic acoustic metric]], and a [[AGR|''fully-general'' general theory of relativity]].}}<br />
<br />
{{AGR}}<br />
{{GravitationalStuff}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:Noindexed_pages&diff=587Category:Noindexed pages2016-07-26T22:43:37Z<p>Eric Baird: Created page with "{{Site}}"</p>
<hr />
<div>{{Site}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:Gravitoelectromagnetism_(GEM)&diff=586Category:Gravitoelectromagnetism (GEM)2016-07-26T22:10:59Z<p>Eric Baird: +seo, tweaks</p>
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<div>{{#seo:<br />
|title=Gravitoelectromagnetism (GEM) / Gravitomagnetism (GM)<br />
|titlemode=replace<br />
|keywords=gravitoelectromagnetism, gravitomagnetism, GEM, GM, general relativity, Albert Einstein, Mach's Principle, frame-dragging, rotation, Kerr black hole<br />
|description=Gravitoelectromagnetism (GEM) <br />
}}<br />
{{NoRefs}}{{GEMBox}}{{Motion}}<br />
The subject of '''Gravitoelectromagnetism (GEM)''' deals with the effects that moving masses have on the shape of spacetime. The subject is also sometimes referred to as '''gravitomagnetism (GM)''' which is arguably less correct, but has the advantage of being shorter, and is less likely to be mistaken for something that involves ''actual'' electric fields (which GEM/GM doesn't).<br />
__TOC__<br />
=="EM" vs "GEM"==<br />
The GEM name is based on an analogy with '''electromagnetism (EM)''' – where the subject of ''EM'' deals (in part) with the effects due to a moving ''electrical'' charge, ''GEM'' effects are the analogous behaviours caused by a moving ''gravitational'' charge (a moving mass). <br />
<br />
The analogy is not exact (electrical charges can be positive or negative, gravitational charges can only be positive), but since both types of field are bound by the same general constraints of classical field theory, and both have a finite propagation speed (defined as "<math>c</math>" for EM, and generally assumed to nominally be "<math>c</math>" for GEM), the two classes of problem can't help but share some basic behaviours.<br />
<br />
==Categories==<br />
GEM effects cause a deflection of light and a deflection of the paths of objects passing through a region, and can be modelled as spacetime distortion effects, or as the result of nontraditional gravitational fields.<br />
<br />
We can define three main classes of GEM effect:<br />
<ul><br />
<li> '''[[Rotational gravitoelectromagnetism|Rotational GEM]]''' – creates a radial attraction at right angles to the rotation axis, and also a rotational dragging around the rotation axis, in the direction of rotation. <br> &nbsp;&nbsp;&nbsp; These two effects are "Machian", and appear in C20th GR. </li><br />
<li> '''[[Accelerational gravitoelectromagnetism|Accelerational GEM]]''' – creates a dragging effect around the accelerated body, in the direction of forced acceleration. <br> &nbsp;&nbsp;&nbsp; This effect is "Machian", and appears in C20th GR.</li><br />
<li style="color: darkred;"> '''[[Velocity-dependent gravitoelectromagnetism|Velocity-based GEM]]''' – creates a dragging effect around a moving body, in the direction of motion. <br> &nbsp;&nbsp;&nbsp; <span style=" background-color: #ffffef">This effect is derivable from the rotational effect or from general gravitational arguments, but is at odds with special relativity. Its status under C20th GR is problematic.</span></li><br />
</ul><br />
<br />
==Multiple paths to GEM==<br />
;GEM effects considered as the result of "smudging"<br />
: If the properties of physics, including the properties of spacetime ''and the properties of bodies'' can be described using field theory, then the condition that classical field theory has "no sharp edges" means that our descriptions of how matter interacts with spacetime and with other matter end up with a certain degree of "blurring". If the mass of a moving particle, idealised as a point, is not allowed to be described as a point, but has to be smudged out into the surrounding region, then the mass becomes a field whose strength dies away with distance, and since a field carrying the property of mass is a gravitational field (or an inertial field), smudging or blurring turns a description of particulate matter physics into a description in which each particle has its own gravity-well.<br />
: If we now consider a situation in which particles are moving, the smudging of a particle's rotational momentum, accelerational forces or linear momentum produces a field description in terms of rotational GEM, accelerational GEM, and velocity-based GEM.<br />
<br />
;GEM effects considered as the result of statistical mechanics<br />
: If two bodies with relative acceleration, rotation or velocity are placed in a particulate medium, the intermediate particles will acquire the "imprint" of those bodies by collision, and then by colliding with each other, create an interaction between the two bodies at a distance ("indirect collision"). The smoothed and averaged statistical behaviour of these interactions can then be modelled in an abstract way without knowing the positions or velocities of the intermediate particles as a field, which then gives GEM behaviour.<br />
<br />
;GEM analogues under aether theory<br />
: While GEM is not derived as an "aether theory" effect, GEM classes typically have easily-visualisable aether-theory counterparts – for instance, the rotational GEM effects are broadly similar to the effects expected from a dragged-aether theory. This is partly because aether models tend to have a "statistical mechanical" component, and partly because their dragging effects are usually expressable in idealised form as fields, making them subject to the same "classical field theory" limitations and restrictions as GEM fields ("smudging").<br />
<br />
;GEM as the result of Quantum Mechanics<br />
: The statistical route to GEM seems to mesh well with quantum theory. if we fire photons or other small particles at a moving target particle, the target's position will have a certain degree of uncertainty, meaning that our pattern of potential "hits" will be scattered over the region, and can be idealised as a probability field, with the attributes of mass and momentum of the original particle. This then takes us back to the earlier description of the moving particle having effective static and GEM gravitational field components, which describe its rest properties and state of motion. We can also statistically model the interaction of bodies via [[virtual particle]]s and arrive at the same basic patterns of behaviour as before.<br />
<br />
==Status of GEM effects==<br />
The status of GEM effects under C20th General relativity is somewhat elusive – the general principle of relativity requires that the rotational and accelerational effects must be real, and general gravitational arguments and extrapolations from GEM-r then seem to say that the velocity-dependent effects also have to exist, too. A full logically-consistent description of GEM seems to require all three classes of effect.<br />
<br />
However, special relativity is derived from the assumption that there are no distortion effects associated with relative motion, so the "SR" side of GR1960 requires GEM-v ''not'' to exist. The other two effects were described by Einstein as appearing in general relativity, but were found in 1960 to also conflict with SR. The apparent absence of a full peer-reviewed study of GEM/GM effects seems to be down to implicit and explicit conflicts with special relativity.<br />
<br />
==Not to be confused with:==<br />
* ''Electrogravity'' ... GEM/GM describes gravitational field-effects that ''mimic'' some EM field behaviours, "electrogravity" is a concept that deals with possible interactions between the two types of field.<br />
<br />
{{Notes|* It has been accepted since around 1960 that the GPoR and special relativity are mutually incompatible (Schild) – the logical inconsistency of C20th GR, even after 1960, can be expressed in terms of the 1960 theory's inability to properly process questions related to GEM. |* C20th textbook theory appears to deal with the subject of GEM and its associated contradictions ("Gravity and the GPoR requires GEM to exist" / "SR requires GEM not to exist") in the manner of a '''disassociative identity disorder ("DID")''' – by compartmentalising information and descriptions that would otherwise conflict, and "blanking" subjects that would reveal logical inconsistencies. |* If we embrace full-range GEM (which seems necessary for compatibility with QM and with a range of other principles), the result seems to be a [[Cliffordian universe]], a [[relativistic acoustic metric]], and a [[AGR|''fully-general'' general theory of relativity]].}}<br />
<br />
{{AGR}}<br />
{{GravitationalStuff}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:Advanced_General_Relativity_(AGR)&diff=585Category:Advanced General Relativity (AGR)2016-07-26T21:14:23Z<p>Eric Baird: +seo</p>
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<div>{{#seo:<br />
|title=Advanced General Relativity (AGR)<br />
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|description=Advanced General Relativity (AGR) is a "purist" reimplementation of Einstein's concept that aims to fix the bugs, add additional equivalence principles, integrate the theory with quantum mechanics, and generally take the concept to the next level.<br />
}}<br />
{{GRBox|Date1=C21st}}<br />
'''Advanced General Relativity''' (or '''Acoustic General Relativity''', '''AGR''', '''GR(a)''', etc.) is a purist reimplementation of the general theory of relativity that avoids the compromises introduced into "textbook GR" from 1960 onwards. It is a “top down” theory – it starts with the General Principle of Relativity (GPoR), and rederives the rest of classical physics to suit, without assuming that all existing “legacy” theories have to live on in the new theory as perfect limiting cases. It can also be considered as an implementation of Einstein’s declaration in 1950 that nothing should be accepted as part of general relativity until it can be shown to conform to the GPoR. <br />
<br />
An accidental side-effect of taking this purist approach is that the result appears to be in agreement with quantum mechanics, and would therefore seem to be not just a “more general” general theory, but technically also a theory of quantum gravity.<br />
<br />
==GR: "Top-down" vs "bottom-up"==<br />
{{PullQuote|content=... all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning.|author=[[Albert Einstein]]|source=Scientific American, April 1950}}<br />
We can characterise a "top down" theory as being principle-based, and working from a set of higher rules (which then require underlying mathematical machinery to be constructed to suit), and a "bottom-up" theory as being "constructional", and assembled pragmatically and incrementally from available components.<br />
<dl><br />
<dt> '''[[GR1916]]:''' <br />
<dd><br />
Einstein's original general theory combined “top-down” and “bottom-up” approaches, with the hope that the two approaches would meet and mesh somewhere in the middle – the “top-down” component was the General Principle of Relativity (GPoR), the “bottom up” component was special relativity. Unfortunately, in 1960 it was realised that the two components did not mesh, and were in fact geometrically incompatible. The theory was logically inconsistent.<br />
<br />
<dt> '''[[GR1960]]:''' <br />
<dd>After the 1960 crisis, “textbook GR” was modified to make SR-compatibility a fundamental rule of the theory, with the GPoR having secondary importance. Whenever the GPoR and SR were in conflict, the GPoR was to be suspended in favour of SR, converting the “hard crash” of GR1916 into a “soft crash”, with guidance for how users were to proceed. * While the incorporation of a “fail protocol” into the theory imposed a [[theological consistency]], the resulting system was no longer a fully principle-based theory, and … as it no longer treated the GPoR as an unbreakable law … was technically no longer a full, general implementation of the concept of relativity. * It was “more general” than special relativity, but not completely general.<br />
<br />
<dt> '''Advanced GR:'''<br />
<dd>A "purist" approach to general relativity is instead “top-heavy” – it is required to make the GPoR inviolable, and while special relativity can still be used as a convenient approximation or engineering theory, SR physics cannot be a perfect subset of a “proper” general theory’s physical predictions. With “Advanced GR” we obtain most of the same experimental proofs and behaviours of SR, but using a different Lorentzlike relationship, and a relativistic acoustic metric. The main divergences from current classical theory relate to horizon behaviour, which under AGR appears to correspond well to the behaviours of quantum mechanics.<br />
</dl><br />
{{PullQuote|content= I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified.|author=[[Albert Einstein]]|source=Scientific American, 1950}}<br />
==Naming==<br />
It would seem that if SR and the GPoR cannot both coexist in a single larger logical system[], any theory that includes special relativity as a perfect physical limiting case cannot logically be ''fully'' compliant with the GPoR.<br />
<br />
Since all gravitational models currently accepted as credible by C20th criteria are currently required to incorporate SR physics as a perfect subset[], it would follow that none of these theories can be truly GPoR-compliant, and that none of these can in principle be considered truly ''100% general'' general theories of relativity. <br />
<br />
As a result, although it is practical to refer to the "advanced" general theory with some form of qualifying prefix to distinguish it from GR1960 ("advanced" / "acoustic" / "purist" / Cliffordian / "truly general" , ''etc.''), the ''technically correct'' characterisation of the theory would be that it is simply "general relativity". <br />
<br />
{{Notes<br />
|* It has been suggested that perhaps a more accurate name for GR1960 would be "theory of covariance" []}}{{GR}}<br />
{{PullQuote|content=For the time being we have to admit that we do not possess any general theoretical basis for physics, which can be regarded as its logical foundation.|author=[[Albert Einstein]]|source="The Fundaments of Theoretical Physics", Science, 1940}}<br />
<br />
{{Theory}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Stratification_problem&diff=584Stratification problem2016-07-26T20:42:15Z<p>Eric Baird: /* Summary of scale-stratification */</p>
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<div>The '''stratification problem''' refers to the way that C20th physics has different operating rules over three or four different scale ranges. The result is a layered system of physics in which different rules and laws apply at different scales, with the transitions between scales decided pragamtically.<br />
<br />
==Stratification across different physical scales==<br />
;Large-scale – Cosmology:<br />
:Cosmological horizons appear to function as acoustic horizons (which seems ot make their bulk behaviour statistically compatible with quantum mechanics), and their recession-velocity/redshift relationship is different to that of special relativity.<br />
;Mid-scale – Gravity, GR:<br />
: [[GR1960]]'s gravitational velocity-shift relationship is inherited from special relativity. This disagrees with the cosmologically-derived relationship, and generates different horizon behaviour – while cosmological horizons fluctuate and radiate in accordance with QM, GR1960 horizons don't, and [[are not QM-compatible]].<br />
; Human-scale - Simple mechanics<br />
: [[Special relativity]] is assumed to operate over scales where the gravitational fields effects of bodies are not obvious. It shares shift relationships with Einstein's general theory, but has very different founding principles. Where Einstein's GR makes inertial and gravitational descriptions interchangeable – no inertial mass without gravitational mass – special relativity assumes that arbitrarily-high concentrations of energy have zero effect on spacetime curvature. as well as being logically incompatible, SR and the [[GPoR]] also turn out to be [[geometrically incompatible]].<br />
; Small-scale - Quantum mechanics<br />
:Quantum mechanics describes the statistical behaviour of atomic and subatomic-scale physics, in which signal absorption and emission is quantised. This description is obviously very different to that of SR and C20th textbook GR, and according to the [[Copenhagen interpretation]], Quantum and classical physics are simply different beasts with different rules. However, the statistical laws of QM can be used to derive a hypothetical underlying layer of classical physics, which is then quantised to produced QM. The properties of this QM-compatible classical model are not those of SR, but do seem to be those of an "acoustic" general theory, which would seem to agree with cosmological horizon behaviour, but not with SR/GR1960.<br />
<br />
==Summary of scale-stratification==<br />
If we label these four scales '''1-4''', with '''1''' being QM and '''4''' being cosmology, then the adjacent '''2&3''' share a shift relationship that disagrees with '''4''' (and possibly '''1'''). '''1''' and '''4''' are compatible with an acoustic model, which then conflicts with '''2''' (SR), and with '''3''' (SR-based GR). '''3''' and '''1''' make different predictions for black hole radiation.<br />
<br />
==Theoretical stratification==<br />
{{PullQuote|content=The multitude of layers discussed above corresponds to the several stages of progress which have resulted from the struggle for unity in the course of development. As regards the final aim, intermediary layers are only of temporary nature. They must eventually disappear as irrelevant. |author=[[Albert Einstein]]|source="Stratification of the scientific system", in "Physics and Reality", 1936|note=p295}}<br />
<br />
C20th theoretical physics also has a degree of theoretical stratification. Newtonian theory is derived for simple mechanics, but is not compatible with flat spacetime. Special relativity is derived for flat spacetime, and modifies the equations of NM with a Lorentz factor - for low velocities this gives "effective" NM behaviour as a physical limiting case. Since gravitation and relative acceleration involve curvature, which requires an additional layer of theory on top of SR, GR(C20th). <br />
<br />
Since GR(C20th) is then incompatible with quantum mechanics, we then require an additional layer of theory, quantum gravity, which is expected to somehow include both QM and GR1960 inside a larger structure without amending either.<br />
<br />
Although theoretical stratification is useful in that it allows an incremental approach to physics, a total theory with more layers appears more arbitrary and less minimalistic – and therefore less fundamental – than one with fewer layers.<br />
<br />
==De-stratification==<br />
Advanced general relativity replaces the C20th system's four scale-dependent layers with a single-layer theory, plus quantisation. Eliminating the SR layer reduces the total number of levels from four to three, "GR without SR" then ends up using a relativistic acoustic metric, which then merges the gravitational and cosmological behaviours and equations (giving only two layers), and the resulting "rewritten" GR, with fluctuating and radiating horizons, then also appears to be compatible with QM statistics, opening the door to a single-layer classical theory, which, with quantisation, appears to generate QM.<br />
<br />
{{AGR}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Fourth-generation_relativity_theory&diff=583Fourth-generation relativity theory2016-07-26T20:40:16Z<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 />
<br />
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 />
<br />
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 />
<br />
{{AGR}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=User:Eric_Baird&diff=582User:Eric Baird2016-07-26T20:37:41Z<p>Eric Baird: creation</p>
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<div>I specialise in next-generation relativity theory (specifically fourth-generation theory). 4-Gen represents the stage after C20th general relativity, where Galileo-Newton is first-generation theory, [[special relativity]] is second-generation, and [[GR1916]]/[[GR1960]] is third-generation. 4-Gen is the next major iteration.<br />
<br />
The aim of fourth-generation theory is to fix all the bugs in GR1916 and redesign the system around [[Einstein]]'s revised 1950 view "No physics without gravitation" (which echoes W.K. Clifford's C19th "No physics without curvature"). Fixing the incompatibility between the GPoR and SR means jettisoning special relativity and the concept of flat-spacetime physics, and embracing relativistic acoustic metrics, increased non-linearity, a spatially "closed" cosmology, a range of additional equivalence principles, and compatibility with quantum mechanics.<br />
<br />
===''Books:''===<br />
I put out a ~400-page book in 2007:<br />
* '''Relativity in Curved Spacetime''' ISBN 0955706806 <br />
and a fun graphics-heavy book on fractals in 2011<br />
* '''Alt.Fractals: A Visual Guide to Fractal Geometry and Design''' ISBN 0955706831 <br />
<br />
===''Other things:''===<br />
Back in the Nineties, I ran what was probably the internet's most popular physics website, and while creating the Fractals book, I produced the first proper three-dimensional extrapolation of a Koch Curve (the "Delta"), and also devised the [https://fr.wikipedia.org/wiki/Cube_de_J%C3%A9rusalem Jerusalem Cube] fractal and did some background work on the subject of atomistic fractals.</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:Advanced_General_Relativity_(AGR)&diff=581Category:Advanced General Relativity (AGR)2016-07-26T20:37:07Z<p>Eric Baird: tweaked</p>
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<div>{{GRBox|Date1=C21st}}<br />
'''Advanced General Relativity''' (or '''Acoustic General Relativity''', '''AGR''', '''GR(a)''', etc.) is a purist reimplementation of the general theory of relativity that avoids the compromises introduced into "textbook GR" from 1960 onwards. It is a “top down” theory – it starts with the General Principle of Relativity (GPoR), and rederives the rest of classical physics to suit, without assuming that all existing “legacy” theories have to live on in the new theory as perfect limiting cases. It can also be considered as an implementation of Einstein’s declaration in 1950 that nothing should be accepted as part of general relativity until it can be shown to conform to the GPoR. <br />
<br />
An accidental side-effect of taking this purist approach is that the result appears to be in agreement with quantum mechanics, and would therefore seem to be not just a “more general” general theory, but technically also a theory of quantum gravity.<br />
<br />
==GR: "Top-down" vs "bottom-up"==<br />
{{PullQuote|content=... all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning.|author=[[Albert Einstein]]|source=Scientific American, April 1950}}<br />
We can characterise a "top down" theory as being principle-based, and working from a set of higher rules (which then require underlying mathematical machinery to be constructed to suit), and a "bottom-up" theory as being "constructional", and assembled pragmatically and incrementally from available components.<br />
<dl><br />
<dt> '''[[GR1916]]:''' <br />
<dd><br />
Einstein's original general theory combined “top-down” and “bottom-up” approaches, with the hope that the two approaches would meet and mesh somewhere in the middle – the “top-down” component was the General Principle of Relativity (GPoR), the “bottom up” component was special relativity. Unfortunately, in 1960 it was realised that the two components did not mesh, and were in fact geometrically incompatible. The theory was logically inconsistent.<br />
<br />
<dt> '''[[GR1960]]:''' <br />
<dd>After the 1960 crisis, “textbook GR” was modified to make SR-compatibility a fundamental rule of the theory, with the GPoR having secondary importance. Whenever the GPoR and SR were in conflict, the GPoR was to be suspended in favour of SR, converting the “hard crash” of GR1916 into a “soft crash”, with guidance for how users were to proceed. * While the incorporation of a “fail protocol” into the theory imposed a [[theological consistency]], the resulting system was no longer a fully principle-based theory, and … as it no longer treated the GPoR as an unbreakable law … was technically no longer a full, general implementation of the concept of relativity. * It was “more general” than special relativity, but not completely general.<br />
<br />
<dt> '''Advanced GR:'''<br />
<dd>A "purist" approach to general relativity is instead “top-heavy” – it is required to make the GPoR inviolable, and while special relativity can still be used as a convenient approximation or engineering theory, SR physics cannot be a perfect subset of a “proper” general theory’s physical predictions. With “Advanced GR” we obtain most of the same experimental proofs and behaviours of SR, but using a different Lorentzlike relationship, and a relativistic acoustic metric. The main divergences from current classical theory relate to horizon behaviour, which under AGR appears to correspond well to the behaviours of quantum mechanics.<br />
</dl><br />
{{PullQuote|content= I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified.|author=[[Albert Einstein]]|source=Scientific American, 1950}}<br />
==Naming==<br />
It would seem that if SR and the GPoR cannot both coexist in a single larger logical system[], any theory that includes special relativity as a perfect physical limiting case cannot logically be ''fully'' compliant with the GPoR.<br />
<br />
Since all gravitational models currently accepted as credible by C20th criteria are currently required to incorporate SR physics as a perfect subset[], it would follow that none of these theories can be truly GPoR-compliant, and that none of these can in principle be considered truly ''100% general'' general theories of relativity. <br />
<br />
As a result, although it is practical to refer to the "advanced" general theory with some form of qualifying prefix to distinguish it from GR1960 ("advanced" / "acoustic" / "purist" / Cliffordian / "truly general" , ''etc.''), the ''technically correct'' characterisation of the theory would be that it is simply "general relativity". <br />
<br />
{{Notes<br />
|* It has been suggested that perhaps a more accurate name for GR1960 would be "theory of covariance" []}}{{GR}}<br />
{{PullQuote|content=For the time being we have to admit that we do not possess any general theoretical basis for physics, which can be regarded as its logical foundation.|author=[[Albert Einstein]]|source="The Fundaments of Theoretical Physics", Science, 1940}}<br />
<br />
{{Theory}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:ToDo&diff=580Category:ToDo2016-07-26T20:30:48Z<p>Eric Baird: </p>
<hr />
<div>__NOINDEX__<br />
==Sections needed:==<br />
<br />
==[[Relativity]]==<br />
: [[Relativity of Rotation]]<br />
: [[Relativity of acceleration]]<br />
: [[Einstein on Mach's Principle]]<br />
<br />
==[[People]]==<br />
: [[W.K. Clifford]]<br />
: [[John Archibald Wheeler]]<br />
: [[John Michell]]<br />
<br />
==[[Crises and Catastrophes]]==<br />
: [[The Newtonian Catastrophe]]<br />
: [[The Utraviolet catastrophe]]<br />
: [[1960|The 1960 Crisis]]<br />
<br />
: [[The Harwell paper]]<br />
: [[Schild, 1960]]<br />
: [[Hasselkemp Transverse Test]]<br />
<br />
==[[Gravitoelectromagnetism (GEM)]]==<br />
: [[Rotational gravitoelectromagnetism (GEM-r)]]<br />
: [[Accelerational gravitoelectromagnetism (GEM-a)]]<br />
: [[Velocity-based gravitoelectromagnetism (GEM-v)]]<br />
<br />
==[[Einstein]]==<br />
: [[Einstein: Mach's Principle and GR]]<br />
: [[Einstein: Principle of equivalence ()]]<br />
: [[Einstein: General Principle of Relativity]]<br />
: [[Einstein: SR plus GR (1950)]]<br />
: [[Einstein: GR as aether theory ()]]<br />
: [[Einstein: Causality]]<br />
<br />
: [[K H Namsrai and Stochastic QM]]<br />
<br />
==GEM-v==<br />
: [[GEM-v: Ring argument]]<br />
: [[GEM-v: Dumbbell argument]]<br />
: [[GEM-v: Horizon argument]]<br />
: [[GEM-v: Gravitational aberration argument]]<br />
: [[GEM-v: GEM unification argument]]<br />
: [[GEM-v: Stochastic QM argument]]<br />
: [[GEM-v: Domain-shifting argument]]<br />
: [[GEM-v: Shift unification argument]]<br />
: [[GEM-v: Time-domain argument]]<br />
<br />
: [[-v: Particle physics arguments]]<br />
<br />
==[[Principles]]==<br />
===[[Equivalence Principles]]===<br />
: [[Equivalence Principle]]<br />
: [[Shift Equivalence Principle (SEP)]]<br />
: [[Horizon Equivalence Principle (HEP)]]<br />
: [[Universal Shift Equivalence Principle (USEP)]]<br />
: [[Observerspace]]<br />
: [[Wave-particle equivalence]]<br />
<br />
==[[Acoustic metrics]]==<br />
: [[Acoustic metrics: Quantum gravity]]<br />
: [[Acoustic metrics: Definitional exclusion]]<br />
: [[Acoustic metrics: Cosmological inevitability]]<br />
: [[Acoustic horizons: incompleteness]]<br />
: [[Acoustic horizons: radiation]]<br />
: [[Acoustic horizons: particle-pair production]]<br />
<br />
{{Site}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Template:Site&diff=579Template:Site2016-07-26T20:26:27Z<p>Eric Baird: </p>
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<div>__NOINDEX__<br />
[[Category: Site management pages]]</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Template:StatementI&diff=578Template:StatementI2016-07-25T19:19:54Z<p>Eric Baird: Inline Statement</p>
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<div><span class=statement><strong>{{{1|Lorem Ipsum}}}</strong></span></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Template:StatementL&diff=577Template:StatementL2016-07-25T19:18:07Z<p>Eric Baird: Created page with ":::<div class=statement><strong>{{{1|Lorem Ipsum}}}</strong></div>"</p>
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<div>:::<div class=statement><strong>{{{1|Lorem Ipsum}}}</strong></div></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Special_relativity_as_a_uniquely_flat_solution&diff=576Special relativity as a uniquely flat solution2016-07-25T19:15:50Z<p>Eric Baird: /* Results */ +result</p>
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<div>{{NOPIC}}{{SRBox}}<br />
The relativistic equations of [[special relativity]] '''are the only set that allow a flat-spacetime solution'''.<br />
<br />
{{StatementC| '''SR = relativity plus flat spacetime'''}}<br />
<br />
==Defining a range==<br />
In the [[relativistic ellipse]] exercise, the principle of relativity generates a spectrum of potential relativistic equations, given by the relationship <math>CT × {(1 - \frac{v^2}{c^2})}^x</math>, where the exponent, <math>x</math> has a value between <math>0</math> and <math>1</math><br />
<br />
==Logical possibilities==<br />
====x equals 0.5====<br />
: '''If x=0.5 ''exactly''''', the relativistic ellipse has the same width for any value of <math>v</math>, and simply elongates by the Lorentz factor – its internal wavelength distances can be fitted back into the original spherical outline by a simple Lorentz contraction without introducing any intrinsic curvature. Although this contraction is arguably a form of distortion, it is a '"flat"' distortion – angles certainly change, but every line that is “straight” before the contraction is still straight afterwards. <br />
<br />
: All other values of <math>x</math> require more complex distortions that involve curvature:<br />
<br />
====x is greater than 0.5====<br />
: '''If x is any greater than 0.5''', then wavelengths and wavelength-distances inside the ellipse diagram are correspondingly longer, and a simple uniform contraction is not sufficient to cram everything back inside a circle of the original radius – a normalised map of the internal distances has to curve out of the plane. For values of <math>0.5 < x <= 1</math>, the region around a moving body appears to be associated with an effective tilted gravity-well, or the deepening and tilting of the body’s existing gravity-well. Solutions in this range are [[gravitoelectromagnetic]], and associate the relative motion of masses with non-Euclidean (non-flat) distortions of the lightbeam grid. <br />
<br />
: – In other words, they associate positive recoverable kinetic energy with positive curvature.<br />
<br />
====x is less than 0.5====<br />
: By contrast, '''if x is any less than 0.5''', the wavelengths at any given nominal positive velocity will all be shorter than the <math>x=0.5</math> solution. If <math>x=0.5</math> represents zero curvature with relative velocity, then <math>0 =< x < 0.5</math> represents solutions that associate ''positive'' recoverable kinetic energy with ''negative'' curvature – a situation that doesn’t seem credible in a physical model.<br />
<br />
==Results==<br />
This exercise suggest five main conclusions:<br />
<br />
;SR has the unique relativistic solution for flat spacetime<br />
:The assumptions of the principle of relativity and perfectly flat spacetime are enough to let us derive the equations of special relativity as the only possible solution. Pages and pages of unnecessary calculations and overly-complicated proofs are not required.<br />
<br />
;In SR, it's relativity and flat spacetime that are important<br />
:Although Einstein quoted his two postulates as "relativity" and "constant lightspeed", we can have relativity and ''locally'' constant lightspeed in a curved model, without getting the SR equations. For SR, Einstein took c-constancy to mean ''global'' c-constancy, which is another way of saying that the lightbeam geometry of the region is flat (SR's implicit [[third postulate]]).<br />
<br />
;Newtonian mechanics was never really a flat-spacetime theory<br />
:Since C19th Newtonian optics generates the shift equations of x=1, this tells us that Newtonian physics does not "fit" flat spacetime. To be geometrically consistent, a Newtonian system has to involve velocity-dependent curvature, and any geometrical implementation of NM has to be more sophisticated than special relativity,'s flat [[Minkowski spacetime]].<br />
<br />
;Any relativistic alternative to SR must involve curved spacetime<br />
:If SR "owns" the flat-spacetime solution, any competing relativistic model must occupy part of the (positive) curved-spacetime range, <math>x>0.5</math>.<br />
<br />
;Much of the C20th testing was pretty badly thought-out<br />
:If we want to test whether special relativity is the ''correct'' theory of relativity, we need to test where the shift equations fall in the range <math>0.5<=x<=1</math>. We need to test SR against ''redder'' predictions, but C20th testing typically only compared SR against bluer predictions, which were never particularly credible in the first place. <br />
<br />
{{Notes|It was typical in the C20th for texts to give the impression that SR's were the only possible set of relativistic equations. While technically wrong, this worldview was encouraged by using the word "relativistic Doppler" for the SR Doppler predictions (implying that there were only one set of relativistic Doppler equations), and using the word "relativistic" more generally as meaning "SR-compatible". For instance we see Newtonian relationships <math>x=1</math> referred to as "non-relativistic", when in fact they are relativistic ... just not compatible with flat spacetime.}}<br />
<br />
{{SR}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=MediaWiki:Common.css&diff=575MediaWiki:Common.css2016-07-25T19:13:00Z<p>Eric Baird: tweak</p>
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<div>/* CSS placed here will be applied to all skins */<br />
<br />
#PAGEBLOCK {<br />
margin: 1em 0;<br />
padding: 20px 40px;<br />
box-shadow: 10px 5px 5px black;<br />
text-indent: 1em;<br />
background-color:#ffffef;<br />
border: 1px;<br />
border-color: black;<br />
}<br />
#PAGEBLOCK i { <br />
color: darkred; <br />
}<br />
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.NOINDENT {<br />
text-indent: 0px;<br />
}<br />
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math { <br />
color: darkred; <br />
}<br />
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.person {<br />
color: darkblue;<br />
}<br />
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.statement {<br />
font-weight: heavy;<br />
font-size: 110%;<br />
font-color: darkred;<br />
background-color: rgb(240,255,255);<br />
}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=MediaWiki:Common.css&diff=574MediaWiki:Common.css2016-07-25T19:11:04Z<p>Eric Baird: +.Statement</p>
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<div>/* CSS placed here will be applied to all skins */<br />
<br />
#PAGEBLOCK {<br />
margin: 1em 0;<br />
padding: 20px 40px;<br />
box-shadow: 10px 5px 5px black;<br />
text-indent: 1em;<br />
background-color:#ffffef;<br />
border: 1px;<br />
border-color: black;<br />
}<br />
#PAGEBLOCK i { <br />
color: darkred; <br />
}<br />
<br />
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.NOINDENT {<br />
text-indent: 0px;<br />
}<br />
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math { <br />
color: darkred; <br />
}<br />
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.person {<br />
color: darkblue;<br />
}<br />
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.Statement {<br />
font-weight: heavy;<br />
font-size: 110%;<br />
font-color: darkred;<br />
background-color: rgb(255,0,0);<br />
}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=MediaWiki:Sidebar&diff=573MediaWiki:Sidebar2016-07-25T19:01:01Z<p>Eric Baird: +links</p>
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* Outside links:<br />
** https://www.researchgate.net/profile/Eric_Baird|Researchgate<br />
** http://erkdemon.blogspot.co.uk/|ErkDemon Blog<br />
** https://books.google.co.uk/books?id=SJRNoOaXs2wC|Alt.Fractals<br />
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* LANGUAGES</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Template:StatementC&diff=570Template:StatementC2016-07-25T10:50:40Z<p>Eric Baird: Created page with "<center><div class=statement style="text-align: centre;"><strong>{{{1|Lorem Ipsum}}}</strong></div></center>"</p>
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<div><center><div class=statement style="text-align: centre;"><strong>{{{1|Lorem Ipsum}}}</strong></div></center></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Template:NOPIC&diff=569Template:NOPIC2016-07-25T10:39:14Z<p>Eric Baird: Created page with "<includeonly> Category: Pages requiring pictures </includeonly>"</p>
<hr />
<div><includeonly><br />
[[Category: Pages requiring pictures]]<br />
</includeonly></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Special_relativity_as_a_uniquely_flat_solution&diff=568Special relativity as a uniquely flat solution2016-07-25T10:38:13Z<p>Eric Baird: tidied a little</p>
<hr />
<div>{{NOPIC}}{{SRBox}}<br />
The relativistic equations of [[special relativity]] '''are the only set that allow a flat-spacetime solution'''.<br />
<br />
{{StatementC| '''SR = relativity plus flat spacetime'''}}<br />
<br />
==Defining a range==<br />
In the [[relativistic ellipse]] exercise, the principle of relativity generates a spectrum of potential relativistic equations, given by the relationship <math>CT × {(1 - \frac{v^2}{c^2})}^x</math>, where the exponent, <math>x</math> has a value between <math>0</math> and <math>1</math><br />
<br />
==Logical possibilities==<br />
====x equals 0.5====<br />
: '''If x=0.5 ''exactly''''', the relativistic ellipse has the same width for any value of <math>v</math>, and simply elongates by the Lorentz factor – its internal wavelength distances can be fitted back into the original spherical outline by a simple Lorentz contraction without introducing any intrinsic curvature. Although this contraction is arguably a form of distortion, it is a '"flat"' distortion – angles certainly change, but every line that is “straight” before the contraction is still straight afterwards. <br />
<br />
: All other values of <math>x</math> require more complex distortions that involve curvature:<br />
<br />
====x is greater than 0.5====<br />
: '''If x is any greater than 0.5''', then wavelengths and wavelength-distances inside the ellipse diagram are correspondingly longer, and a simple uniform contraction is not sufficient to cram everything back inside a circle of the original radius – a normalised map of the internal distances has to curve out of the plane. For values of <math>0.5 < x <= 1</math>, the region around a moving body appears to be associated with an effective tilted gravity-well, or the deepening and tilting of the body’s existing gravity-well. Solutions in this range are [[gravitoelectromagnetic]], and associate the relative motion of masses with non-Euclidean (non-flat) distortions of the lightbeam grid. <br />
<br />
: – In other words, they associate positive recoverable kinetic energy with positive curvature.<br />
<br />
====x is less than 0.5====<br />
: By contrast, '''if x is any less than 0.5''', the wavelengths at any given nominal positive velocity will all be shorter than the <math>x=0.5</math> solution. If <math>x=0.5</math> represents zero curvature with relative velocity, then <math>0 =< x < 0.5</math> represents solutions that associate ''positive'' recoverable kinetic energy with ''negative'' curvature – a situation that doesn’t seem credible in a physical model.<br />
<br />
==Results==<br />
This exercise suggest four main conclusions:<br />
<br />
;SR has the unique relativistic solution for flat spacetime<br />
:The assumptions of the principle of relativity and perfectly flat spacetime are enough to let us derive the equations of special relativity as the only possible solution. Pages and pages of unnecessary calculations and overly-complicated proofs are not required.<br />
<br />
;In SR, it's relativity and flat spacetime that are important<br />
:Although Einstein quoted his two postulates as "relativity" and "constant lightspeed", we can have relativity and ''locally'' constant lightspeed in a curved model, without getting the SR equations. For SR, Einstein took c-constancy to mean ''global'' c-constancy, which is another way of saying that the lightbeam geometry of the region is flat (SR's implicit [[third postulate]]).<br />
<br />
;Newtonian mechanics was never really a flat-spacetime theory<br />
:Since C19th Newtonian optics generates the shift equations of x=1, this tells us that Newtonian physics does not "fit" flat spacetime. To be geometrically consistent, a Newtonian system has to involve velocity-dependent curvature, and any geometrical implementation of NM has to be more sophisticated than special relativity,'s flat [[Minkowski spacetime]].<br />
<br />
;Much of the C20th testing was pretty badly thought-out<br />
:If we want to test whether special relativity is the correct theory of relativity, we need to test where the shift equations fall in the range <math>0.5<=x<=1</math> . However, most testing seems to have assumed that the only important range was <math>0<=x<=0.5</math> . We needed to test SR against redder theories, but we actually tested SR against bluer theories. Until we fix this, we cant yet claim (scientifically) that we know that SR is valid foundation theory.<br />
<br />
PIC<br />
<br />
{{Notes|It was typical in the C20th for texts to give the impression that SR's were the only possible set of relativistic equations. While technically wrong, this worldview was encouraged by using the word "relativistic Doppler" for the SR Doppler predictions (implying that there were only one set of relativistic Doppler equations), and using the word "relativistic" more generally as meaning "SR-compatible". For instance we see Newtonian relationships <math>x=1</math> referred to as "non-relativistic", when in fact they are relativistic ... just not compatible with flat spacetime.}}<br />
<br />
{{SR}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=File:Relativity.pdf&diff=567File:Relativity.pdf2016-07-18T02:39:43Z<p>Eric Baird: </p>
<hr />
<div>[[Albert Einstein]]'s book, '''"[[:Category: Relativity - The Special and the General Theory|Relativity: The Special and the General Theory]]"''', transcribed and converted to PDF format.<br />
<br />
{{Einstein}}<br />
[[Category: Relativity - The Special and the General Theory]]</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=File:Relativity.pdf&diff=566File:Relativity.pdf2016-07-18T02:29:00Z<p>Eric Baird: '''Albert Einstein's book, "Relativity: The Special and the General Theory"''', transcribed and converted to PDF format.
{{Einstein}}</p>
<hr />
<div>'''[[Albert Einstein]]'s book, "Relativity: The Special and the General Theory"''', transcribed and converted to PDF format.<br />
<br />
{{Einstein}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=MediaWiki:Sidebar&diff=565MediaWiki:Sidebar2016-07-18T01:43:13Z<p>Eric Baird: </p>
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* LANGUAGES</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Category:Relativity_-_The_Special_and_the_General_Theory&diff=564Category:Relativity - The Special and the General Theory2016-07-18T01:38:41Z<p>Eric Baird: Created page with "{{Einstein}}"</p>
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<div>{{Einstein}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Template:Bookblock&diff=563Template:Bookblock2016-07-18T01:36:26Z<p>Eric Baird: </p>
<hr />
<div>[[Albert Einstein]]: '''<cite>Relativity: The Special and the General Theory</cite>''' <br><br />
<small><b><br />
[[Einstein:Book chapter 00|00]] <br />
[[Einstein:Book chapter 01|01]] <br />
[[Einstein:Book chapter 02|02]] <br />
[[Einstein:Book chapter 03|03]] <br />
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[[Einstein:Book chapter 15|15]] <br />
[[Einstein:Book chapter 16|16]] <br />
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[[Einstein:Book chapter29|29]] - - <br />
[[Einstein:Book chapter30|30]] <br />
[[Einstein:Book chapter31|31]] <br />
[[Einstein:Book chapter32|32]]<br />
</b></small><br />
<includeonly><br />
{{Einstein}}<br />
[[Category: Relativity - The Special and the General Theory]]<br />
</includeonly></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Template:Bookblock&diff=562Template:Bookblock2016-07-18T01:35:49Z<p>Eric Baird: </p>
<hr />
<div>[[Albert Einstein]]: '''<cite>Relativity: The Special and the General Theory</cite>''' <br><br />
<small><b><br />
[[Einstein:Book chapter 00|00]] <br />
[[Einstein:Book chapter 01|01]] <br />
[[Einstein:Book chapter 02|02]] <br />
[[Einstein:Book chapter 03|03]] <br />
[[Einstein:Book chapter 04|04]] <br />
[[Einstein:Book chapter 05|05]] <br />
[[Einstein:Book chapter 06|06]] <br />
[[Einstein:Book chapter 07|07]] <br />
[[Einstein:Book chapter 08|08]] <br />
[[Einstein:Book chapter 09|09]] <br />
[[Einstein:Book chapter 10|10]] <br />
[[Einstein:Book chapter 11|11]] <br />
[[Einstein:Book chapter 12|12]] <br />
[[Einstein:Book chapter 13|13]] <br />
[[Einstein:Book chapter 14|14]] <br />
[[Einstein:Book chapter 15|15]] <br />
[[Einstein:Book chapter 16|16]] <br />
[[Einstein:Book chapter 17|17]] - - <br />
[[Einstein:Book chapter 18|18]] <br />
[[Einstein:Book chapter 19|19]] <br />
[[Einstein:Book chapter20|20]] <br />
[[Einstein:Book chapter21|21]] <br />
[[Einstein:Book chapter22|22]] <br />
[[Einstein:Book chapter23|23]] <br />
[[Einstein:Book chapter24|24]] <br />
[[Einstein:Book chapter25|25]] <br />
[[Einstein:Book chapter26|26]] <br />
[[Einstein:Book chapter27|27]] <br />
[[Einstein:Book chapter28|28]] <br />
[[Einstein:Book chapter29|29]] - - <br />
[[Einstein:Book chapter30|30]] <br />
[[Einstein:Book chapter31|31]] <br />
[[Einstein:Book chapter32|32]]<br />
</b></small><br />
<noinclude><br />
{{Einstein}}<br />
[[Category: Relativity - The Special and the General Theory]]<br />
</noinclude></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Einstein:GR1916_chapter_02_-_Physical_Meaning_of_Geometrical_Propositions&diff=560Einstein:GR1916 chapter 02 - Physical Meaning of Geometrical Propositions2016-07-18T01:31:51Z<p>Eric Baird: Eric Baird moved page Einstein:GR1916 chapter 02 to Einstein:GR1916 chapter 02 - Physical Meaning of Geometrical Propositions</p>
<hr />
<div><div id="PAGEBLOCK" ><br />
<cite>Die Grundlage der allgemeinen Relativitätstheorie</cite> / <cite>The Foundation of the General Theory of Relativity</cite>, ''Annalen der Physik'' '''49''' (1950)<br />
==2: Physical Meaning of Geometrical Propositions==<br />
<p class="NOINDENT">{{Boldword|I|N}} classical mechanics, and no less in the special theory of relativity, there is an inherent epistemological defect which was, perhaps for the first time, clearly pointed out by [[Ernst Mach]]. We will elucidate it by the following example:– two fluid bodies of the same size and nature hover freely in space at so great a distance from each other and from all other masses that only those gravitational forces need be taken into account which arise from the interaction of different parts of the same body. Let the distance between the two bodies be invariable, and in neither of the bodies let there be any relative movements of the parts with respect to one another.<br />
But let either mass, as judged by an observer at rest relatively to the other mass, rotate with constant angular velocity about the line joining the masses. This is a verifiable relative motion of the two bodies. Now let us imagine that each of the bodies has been surveyed by means of measuring instruments at rest relatively to itself, and let the surface of <math>S_1</math> prove to be a sphere, and that of <math>S_2</math> an ellipsoid of revolution. Thereupon we put the question – What is the reason for this difference in the two bodies? No answer can be admitted as epistemologically satisfactory,<sup>1</sup> unless the reason given is an ''observable fact of experience''. The law of causality has not the significance of a statement as to the world of experience, except when ''observable facts'' ultimately appear as causes and effects.</p><br />
<br />
Newtonian mechanics does not give a satisfactory answer to this question. It pronounces as follows:– The laws of mechanics apply to the space <math>R_1</math>, in respect to which the body <math>S_1</math> is at rest, but not to the space <math>R_2</math>, in respect to which the body <math>S_2</math> is at rest. But the privileged space <math>R_1</math> of [[Galileo]], thus introduced, is a merely ''fictitious'' case, and not a thing that can be observed. It is therefore clear that Newton's mechanics does not really satisfy the requirement of causality in the case under consideration , but only apparently does so, since it makes the fictitious cause <math>R_1</math> responsible for the observable difference in the bodies <math>S_1</math> and <math>S_2</math>.<br />
<br />
The only satisfactory answer must be that the physical system consisting of <math>S_1</math> and <math>S_2</math> reveals within itself no imaginable cause to which the differing behaviour of <math>S_1</math> and <math>S_2</math> can be referred. The cause must therefor else ''outside'' this system. We have to take it that the general laws of motion, which in particular determine the shapes of <math>S_1</math> and <math>S_2</math>, must be such that the mechanical behaviour of <math>S_1</math> and <math>S_2</math> is partly conditioned, in quite essential respects, by distant masses which we have not included in the system under consideration. These distant masses and their motion relative to <math>S_1</math> and <math>S_2</math>must then be regarded as the seat of the causes (which must be susceptible to observation) of the different behaviour of our two bodies <math>S_1</math> and <math>S_2</math>. They take over the role of the fictitious cause <math>R_1</math>. of all imaginable spaces <math>R_1</math>, <math>R_2</math>, etc., in any kind of motion relatively to one another, there is none which we may look upon as privileged ''a priori'' without reviving the above-mentioned epistemological objection. '''''The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion.''''' Along this road we arrive at an extension of the postulate of relativity.<br />
<br />
In addition to this weighty argument from the theory of knowledge, there is a well-known physical fact which favours an extension of the theory of relativity. Let <math>K</math> be a Galilean system of reference, i.e. a system relatively to which (at least in the four-dimensional region under consideration), a mass, sufficiently distant from all other masses, is moving with uniform motion in a straight line. Let <math>K'</math> be a second system of reference which is moving relatively to <math>K</math> in ''uniformly accelerated'' translation.Then, relatively to <math>K'/math>, a mass sufficiently distant from other masses would have an accelerated motion such that its acceleration and direction of acceleration are independent of the material composition and physical state of the mass.<br />
<br />
Does this permit an observer at rest relatively to <math>K'/math> to infer that he is on a "really" accelerated frame of reference? The answer is in the negative:; for the above-mentioned relation of freely movable masses to <math>K'</math>may be interpreted equally well in the following way. The system of reference <math>K'</math> is unaccelerated, but the space-time territory in question is under the sway of a gravitational field, which generates the accelerated motion of the bodies relatively to <math>K'</math>.<br />
<br />
This view is made possible for us by the teaching of experience as to the existence of a field of force, namely, the gravitational field, which possesses the remarkable property of imparting the same acceleration to all bodies. <sup>2</sup> The mechanical behaviour of bodies relatively to <math>K'</math> is the same as presents itself to experience in the case of systems which we are wont to regard as "stationary" or as "privileged". Therefore, from the physical standpoint, the assumption readily suggests itself that the systems <math>K</math> and <math>K'</math> may both with equal right be looked upon as "stationary," that is to say, they have an equal title as systems of reference for the physical description of phenomena.<br />
<br />
It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to "produce" a gravitational field merely by changing the system of coordinates. It will also be obvious that the principle of the constancy of the velocity of light ''in vacuo'' must be modified, since we easily recognize that the path of a ray of light with respect to <math>K'</math> must be in general curvilinear, if with respect to <math>K</math> light is propagated in a straight line with a definite constant velocity.<br />
<br />
{{BookNotes<br />
|# Of course an answer may be satisfactory from the point of view of epistemology, and yet be unsound physically, if it i in conflict with other experiences.<br />
|# [[Eötvös]] has proved experimentally that the gravitational field has this property in great accuracy.<br />
|* I've changed the original translator's use of the word "facticious" to "fictitious" throughout. '''EB 2016'''}}<br />
</div><br />
<br />
{{Einstein}}<br />
{{Observerspace}}</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Einstein:GR1916_chapter_02&diff=561Einstein:GR1916 chapter 022016-07-18T01:31:51Z<p>Eric Baird: Eric Baird moved page Einstein:GR1916 chapter 02 to Einstein:GR1916 chapter 02 - Physical Meaning of Geometrical Propositions</p>
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<div>#REDIRECT [[Einstein:GR1916 chapter 02 - Physical Meaning of Geometrical Propositions]]</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Einstein:Book_chapter21_-_In_What_Aspects_are_the_Foundations_of_Classical_Mechanics_and_of_the_Special_Theory_of_Relativity_Unsatisfactory&diff=558Einstein:Book chapter21 - In What Aspects are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory2016-07-18T01:30:31Z<p>Eric Baird: Eric Baird moved page Einstein:Book chapter21 to Einstein:Book chapter21 - In What Aspects are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory</p>
<hr />
<div>{{Bookblock|21}}<br />
<div id="PAGEBLOCK" ><br />
==21: In What Aspects are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory?==<br />
<p class="NOINDENT">{{Boldword|W|E}} have already stated several times that classical mechanics starts out from the<br />
following law: Material particles sufficiently far removed from other material particles<br />
continue to move uniformly in a straight line or continue in a state of rest. We have<br />
also repeatedly emphasised that this fundamental law can only be valid for bodies of<br />
reference <math>K</math> which possess certain unique states of motion, and which are in uniform<br />
translational motion relative to each other. Relative to other reference-bodies <math>K'</math> the law is not<br />
valid. Both in classical mechanics and in the special theory of relativity we therefore<br />
differentiate between reference-bodies <math>K</math> relative to which the recognised "laws of nature" can<br />
be said to hold, and reference-bodies <math>K'</math> relative to which these laws do not hold. </p><br />
<br />
But no person whose mode of thought is logical can rest satisfied with this condition of<br />
things. He asks: "How does it come that certain reference-bodies (or their states of motion)<br />
are given priority over other reference-bodies (or their states of motion)? ''What is the reason<br />
for this preference?''" In order to show clearly what I mean by this question, I shall make use of<br />
a comparison.<br />
<br />
I am standing in front of a gas range. standing alongside of each other on the range are<br />
two pans so much alike that one may be mistaken for the other.<br />
<br />
Both are half full of water. I notice that steam is being emitted continuously from the one<br />
pan, but not from the other. I am surprised at this, even if I have never seen either a gas<br />
range or a pan before. But if I now notice a luminous something of bluish colour under the first<br />
pan but not under the other, I cease to be astonished, even if I have never before seen a gas<br />
flame. For I can only say that this bluish something will cause the emission of the steam, or at<br />
least possibly it may do so.<br />
<br />
If, however, I notice the bluish something in neither case, and if I observe that the one<br />
continuously emits steam whilst the other does not, then I shall remain astonished and<br />
dissatisfied until I have discovered some circumstance to which I can attribute the different<br />
behaviour of the two pans.<br />
<br />
Analogously, I seek in vain for a real something in classical mechanics (or in the special<br />
theory of relativity) to which I can attribute the different behaviour of bodies considered with<br />
respect to the reference-systems <math>K</math> and <math>K'</math>. <sup>NOTE</sup> Newton saw this objection and attempted to<br />
invalidate it, but without success. But E. Mach recognised it most clearly of all, and because<br />
of this objection he claimed that mechanics must be placed on. a new basis. It can only be got<br />
rid of by means of a physics which is conformable to the general principle of relativity, since<br />
the equations of such a theory hold for every body of reference, whatever may be its state of<br />
motion. <br />
<br />
{{BookNotes<br />
|# The objection is of importance more especially when the state of motion of the reference-body is of such a nature that it does not require any external agency for its maintenance, ''e.g.'' in the case when the reference-body is rotating uniformly.}}<br />
<br />
</div></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Einstein:Book_chapter21&diff=559Einstein:Book chapter212016-07-18T01:30:31Z<p>Eric Baird: Eric Baird moved page Einstein:Book chapter21 to Einstein:Book chapter21 - In What Aspects are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory</p>
<hr />
<div>#REDIRECT [[Einstein:Book chapter21 - In What Aspects are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory]]</div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Einstein:Book_chapter_19_-_Physical_Meaning_of_Geometrical_Propositions&diff=556Einstein:Book chapter 19 - Physical Meaning of Geometrical Propositions2016-07-18T01:29:36Z<p>Eric Baird: Eric Baird moved page Einstein:Book chapter 19 to Einstein:Book chapter 19 - Physical Meaning of Geometrical Propositions</p>
<hr />
<div>{{Bookblock|19}}<br />
<div id="PAGEBLOCK" ><br />
==19: Physical Meaning of Geometrical Propositions==<br />
<p class="NOINDENT">{{Boldword|"I|F}} we pick up a stone and then let it go, why does it fall to the ground?" The usual<br />
answer to this question is: "Because it is attracted by the earth." </p><br />
<br />
Modern physics formulates the answer rather differently for the following reason. As a<br />
result of the more careful study of electromagnetic phenomena, we have come to regard<br />
action at a distance as a process impossible without the intervention of some intermediary<br />
medium.<br />
<br />
If, for instance, a magnet attracts a piece of iron, we cannot be content to regard this as<br />
meaning that the magnet acts directly on the iron through the intermediate empty space, but<br />
we are constrained to imagine — after the manner of Faraday — that the magnet always calls<br />
into being something physically real in the space around it, that something being what we call<br />
a "magnetic field." In its turn this magnetic field operates on the piece of iron, so that the latter<br />
strives to move towards the magnet. We shall not discuss here the justification for this<br />
incidental conception, which is indeed a somewhat arbitrary one. We shall only mention that<br />
with its aid electromagnetic phenomena can be theoretically represented much more<br />
satisfactorily than without it, and this applies particularly to the transmission of<br />
electromagnetic waves.<br />
<br />
The effects of gravitation also are regarded in an analogous manner.<br />
<br />
The action of the earth on the stone takes place indirectly. The earth produces in its<br />
surroundings a gravitational field, which acts on the stone and produces its motion of fall. As<br />
we know from experience, the intensity of the action on a body diminishes according to a<br />
quite definite law, as we proceed farther and farther away from the earth. From our point of<br />
view this means: The law governing the properties of the gravitational field in space must be a<br />
perfectly definite one, in order correctly to represent the diminution of gravitational action with<br />
the distance from operative bodies.<br />
<br />
It is something like this: The body (''e.g.'' the earth) produces a field in its immediate<br />
neighbourhood directly; the intensity and direction of the field at points farther removed from<br />
the body are thence determined by the law which governs the properties in space of the<br />
gravitational fields themselves.<br />
<br />
In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable property, which is of fundamental importance for what follows. Bodies which are moving<br />
under the sole influence of a gravitational field receive an acceleration, ''which does not in the least depend either on the material or on the physical state of the body''. For instance, a piece<br />
of lead and a piece of wood fall in exactly the same manner in a gravitational field (''in vacuo''), when they start off from rest or with the same initial velocity. This law, which holds most<br />
accurately, can be expressed in a different form in the light of the following consideration.<br />
<br />
According to Newton's law of motion, we have<br />
<br />
<math>Force = ( inertial mass ) × ( acceleration ) </math>,<br />
<br />
where the "inertial mass" is a characteristic constant of the accelerated body. If now<br />
gravitation is the cause of the acceleration, we then have<br />
<br />
<math>Force = ( gravitational mass ) × ( intensity of the gravitational field ) </math>,<br />
<br />
where the "gravitational mass" is likewise a characteristic constant for the body. From these<br />
two relations follows: <br />
<br />
<math>acceleration = \frac{( gravitational mass )}{( inertial mass )} × ( intensity of the gravitational field )</math> .<br />
<br />
If now, as we find from experience, the acceleration is to be independent of the nature and<br />
the condition of the body and always the same for a given gravitational field, then the ratio of<br />
the gravitational to the inertial mass must likewise be the same for all bodies. By a suitable<br />
choice of units we can thus make this ratio equal to unity. We then have the following law:<br />
<br />
: '''The ''gravitational'' mass of a body is equal to its ''inertial'' mass.'''<br />
<br />
It is true that this important law had hitherto been recorded in mechanics, but it had not been<br />
''interpreted''.<br />
<br />
A satisfactory interpretation can be obtained only if we recognise the following fact:<br />
''The same'' quality of a body manifests itself according to circumstances as "inertia" or as<br />
"weight" (lit. "heaviness"). In the following section we shall show to what extent this is actually<br />
the case, and how this question is connected with the general postulate of relativity.<br />
<br />
</div></div>Eric Bairdhttp://www.relativitybook.com/w/index.php?title=Einstein:Book_chapter_19&diff=557Einstein:Book chapter 192016-07-18T01:29:36Z<p>Eric Baird: Eric Baird moved page Einstein:Book chapter 19 to Einstein:Book chapter 19 - Physical Meaning of Geometrical Propositions</p>
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<div>#REDIRECT [[Einstein:Book chapter 19 - Physical Meaning of Geometrical Propositions]]</div>Eric Baird