Abstract
Gravity bends a light beam more than a particle beam.  We show how elevator occupants can use that fact to determine whether the forces they feel are caused by a gravitational or non-gravitational acceleration. I.e., although that capability apparently violates the ‘Equivalence principle’ in ‘General Relativity’. Einstein imagined ‘the experiences of occupants in a windowless chamber, in deep, isolated space’ as it was ‘accelerated upward’ by a pulling.  And claimed ‘Equivalent’ (identical) feelings and test results would arise for occupants in a non-moving elevator on our gravitational earth.[1]   Yet, below, we will imagine that a photon and an ultra-high-speed particle are launched at the same time from an internal wall of an elevator; then they go through two adjacent pin-holes, and finally hit the opposite wall.  But surprisingly, they do not hit the same spot - because the gravity bends photons twice as much as a particle beam.[2]  But the outcome would have been different, had the chamber been in far outer space and its rocket engines caused a non-gravitational acceleration!  So we discuss that violation of ‘Equivalence in Relativity’ and its broad implications, below.

Introduction 
It might seem, at first, that our ‘windowless’ elevator occupants can’t overcome the limitations imposed by the “Gravitation-Acceleration Equivalence Principle’ – as Einstein argued.  I.e., that an astronaut in a windowless accelerating rocket far from earth – could not tell that from his being in an unmoving elevator on earth, with earth’s gravity.  But we show that in principle, such occupants can run a test to tell them the difference.  I.e., By performing a test based on the results and implications of the great “Einstein-Eddington Gravitational ‘light-bending’ observation.” Because that would successfully discern subtle distinctions between ‘gravity’ and ‘other causes’ of acceleration.  Many scientists believe that that ‘Einstein-Eddington light-bending experiment’ was among the top-few most important experiments and results ever accomplished, and perhaps the greatest.[3]  And that experiment has been performed by experts more than once, with the same results, and so seems to ‘hold good’. So, let’s use it!

Discussion and Details
To help grasp some of its implications, let us compare two situations, as follows:

Suppose we were to launch a particle in a straight horizontal path at a high-speed almost exactly equal to the speed of light ‘c’, as previously mentioned. That would mean that the particle mass, (somewhat like the protons in the ‘super-collider’ Higgs research), would reach speeds of nearly ‘c’, i.e., 99.9999991% of the speed of light. In fact, we can imagine even a pinch faster, if helpful in our ‘Thought-Experiment”, in this article

So our imagined particles would have such great relativistic mass and energies as to be very comparable to the very massive Higgs Boson. [4]  And we can even imagine a pinch greater mass, if that enhances our ‘thought-experiment. But, here, to make our point with simplicity, we can, at first, imagine a high-speed race between such proton and photon, i.e., ‘racing’ from one internal elevator wall to the opposite wall.  And importantly, that they would hit the target wall at almost exactly the same time, i.e., ideally, both hitting so close to ‘the same instant’ that any time difference would be indistinguishable.  And that would simplify our seeing the correctness of our conclusions -- the different bending resulting from gravitational vs. non-gravitational accelerations.

(Although there is a so-called ‘large relativistic increase’ in the mass of the ‘gross particle’, when traveling at nearly speed ‘c’, compared to it ‘rest mass’, we also note this:  The gravitational force on the great ‘relativistic mass’ is also proportionally increased.  So the resultant ‘downward-acceleration’ on our imagined mass particle is not increased by its velocity-related increased ‘relativistic mass’ compared to its lesser ‘rest mass’ or ‘slow-moving’ mass.)

Also, to more easily grasp my point, imagine that our elevator was speedily traveling parallel to the surface of a super-massive neutron star, say, 30 miles above the neutron star’s surface.  The ‘downward pull’ of gravity on it would be great, indeed. And quite enough to cause a very clear and great difference in the bending of the photon’s path vs. the fast-speeding particle’s path.  And thus that difference could be easily imagined and measured.[5]  (I.e.,  even an 8-degree difference in bending outcomes for a ‘near surface-scraping’ extreme case.) 

So by comparison, that difference in paths, between the photon and gross particle would be so clear and great as to dwarf, in magnitude, the minor secondary effect.  I.e., the extremely small effect, arising from our “flying particle’s speed”, being a virtually ‘undetectable’ pinch less than the photon’s speed, ‘c’.  I.e., even though the particle hit the ‘target wall’ a pinch after the photon.  Thus, we can validly imagine that, as our basic laboratory equipment came closer and closer to super-capability and ‘ideal perfection,’  -- that our experimental outcome and its description would become more and more easily visible, clear, and irrefutable! 

So, we imagine that the particle and photon are simultaneously emitted from a point of the chamber wall.  And then pass through a rather nearby vertical strip having ‘side-by-side’ adjacent ‘pinholes’ in it, those pinholes extremely close together, and at the same horizontal level.  Then, shortly later, at the opposite chamber wall (target), there would be noted a very great difference between where the photon hit the wall, vs. where the gross particle hit the wall.  I.e., the ‘photon would hit the wall well-below the gross particle’. And that, for close distances to a massive neutron star, a great landing difference would clearly reveal that a ‘gravitational acceleration’ was in action, here.  And not a ‘non-gravitational acceleration’.  And thus, the General Relativity alleged Equivalency Principle is, here, violated!   

Optionally, we might note that, in all of the above, we are NOT seeking some ‘superficial factor’ or ‘frivolous artifact’ as a cause of producing a different experimental result than as predicted by the ‘Relativistic Equivalence Principle’  For example, the superficial ‘very slight difference in gravity’ existing between the upper and lower regions of our elevator.  Those ‘superficial imperfections’ only distract us away from our far more important fundamental, subtle basic inherent factors and considerations, even though our effects may be small.  I.e., the factors and considerations that we considered would, indeed, cause the ‘Elevator-gravity-acceleration equivalence’ principle to clearly fail -- under the special and important circumstances which we described.  I.e., even though our special circumstances would be a rarity.  And, of course, the finer our equipment and instruments -- the clearer our results, instead of ‘less-clear’ – because our considerations are so basic, not ‘superficial.

OPTIONAL, Additional Related Discussion and Miscellaneous:

I do NOT think that there is only one major exception to what is generally held to be ‘the 100% flawless’ aspects of ‘General Relativity Theory’.  But, rather, I think that several aspects of ‘General Relativity Theory’ are occasionally violated by special ‘exceptional circumstances and considerations.’  And the ‘Special’ and the ‘General’ Relativity Theories also have some ‘ambiguities’, that thus invite and receive differing interpretations from experts.  But I still think many aspects of General Relativity ‘hold good’, and remain helpful, useful, and admirable. 

And there is not enough space in this intendedly short paper to discuss nearly all aspects of General Relativity for which exceptions arise, nor the details of the exceptions.  Nor space to discuss some other fine scientists, who sometimes step out of the ‘mainstream’, by having their own ‘list of exceptions’ to General Relativity Theory.  (And, incidentally, even as of my paper’s date, there are also a few other scientists, ‘on-the-net’, who also believe that Einstein’s Equivalence Principle does have some minor exceptions, but I think my examples are more serious.)

So I will try, here, to just outline what I regard as a few more ‘exceptions – important exceptions, at least to some aspects or implications of General Relativity.  Although one will be a sort of ‘statistical-based’ criticism, in nature. (And after that and separately – I’ll also describe some ambiguities arising in Special and General Relativities.)

1… Let us suppose an observer in a rocket was travelling, say, at half the speed of light, ‘c’, and viewed every major star, both in front and in back of him.  And with a good telescope.  He would see the light from the stars in front of him clearly shifted ‘more-toward the blue’, (ultra-violet).  And the light from stars in back of him – clearly shifted more to the ‘red’, (infra-red).  And he would conclude, invariably or almost invariably, correctly -- that he was very likely ‘absolutely’ travelling in the ‘blue-shifted’ direction, relative to the massive universe.  And thus, I think he would correctly dispute the position held by most scientists, regarding ‘Relativity’ – i.e., that no one can correctly claim that they are the ones who are stationary or nearly stationary, and that it is the others that are ‘linearly’ traveling.  I.e.,  Rather, I think that sometimes one can rightly claim that “they are the more likely ones that are ‘absolutely moving’.”

2… And somewhat similar to the example above, let us suppose that our ultra-fast travelling rocketeer held up a double-faced ‘scoop or particle gatherer’ – after initially aiming his rocket route away from any star.  He would likely discover over an extremely long time-span and distance travelled – that he had ‘scooped-up’ (detected) more particles (such as ‘cosmic-rays’ and noted them hitting harder), in the direction that he was travelling at his ultra-high speed.  That is -- compared to ‘from the opposite direction’, where the hits were less often and gentler.  And thus, he would conclude (correctly) that he had a high probability of being correct in his claim about his ‘absolute’ direction of travel, i.e., in the direction that the greater number of particles were ‘scooped up’.  And so this example is somewhat similar to the ‘previous example’.

3…Regarding ambiguities and other ‘criticisms’, I think the entire ‘thesis’ about ‘fast moving rods shortening’ – makes ridiculous simplifications, regarding the behavior of complicated bonds between atoms and molecules.  For example – the assertion, that even for a rod, moving just a below light’s speed – that the extension of its matter, (its length) would become virtually Zero. I.e., thus, that ‘dubious’ assertion, in effect, asserts that mass has no inherent significant extension.  (In fact, I know of no rod, that was ever found intact, after it had been detected flying at super-speeds, i.e., almost undetectably less than the speed of light -- like some very fast cosmic rays travel.)

4…Suppose a scientist used an ‘at rest’, small detector, which used ‘touch or feel’, (instead of visual light), to detect the presence of any small portion of a typical rod – the typical rod being ‘at rest’ or almost ‘at rest’.  And he initially used a (great quality) ‘standard’ rod -- to measure and confirm that his typical, ‘at rest’ rod, was also, fortunately, a ‘one-meter-long’ rod.  And then he ‘used a huge amount of fuel’ to accelerate that typical long rod and cause it to pass by, (slide-by), at very fast speed, his ‘touch-sensing’, ‘at rest’, ’point’ detector.  I.e., to pass by his detector, presumably and reasonably, at nearly ‘the speed of light’.

Even assuming that the rod ‘held together intact’, in such ‘thought-experiment’ – experts seem to differ so basically about the answer to the following simple question:  As to the time-span required (as measured by the time-clock at the point sensing the rod’s material) – for the entire rod -- to have entirely passed the ‘touch-sensing point’!  In other words, whether that time duration was virtually ‘zero’, i.e., because, supposedly, the fast-travelling rod had actually shrunk to virtually ‘zero’ length?  Or whether the rod’s length had not appreciably changed in length, during its fast ‘fly-by, -- and thus the timer-clock would have indicated a quite definite amount of time, although brief, for that one-meter-long rod to have entirely passed by the touch-sensing timer.  I.e., such definite time-span -- that the outcome would be quite duplicatable with repeated tests!  (A pretty embarrassing ‘experimental outcome’ to find ‘experts’ disagreeing about such outcome, I think!)

And somewhat similarly, for a wheel with circular rim, spinning but without traveling, in space.  And that rim’s speed at nearly ‘the speed of light’.  Does its circular perimeter shorten (per common interpretation of famous ‘MM’ experimental results).  But, yet, the wheel’s spokes remaining unshortened – (also, per common interpretation of that ‘MM’ experimental result).  If so, quite a ‘jamming’ and ‘breakage’ would seem to result!  That  ‘thought-experiment’ illustrates a long-known paradox -- known as the “Ehrenfest paradox”; and further details can thus be readily obtained by ‘surfing the net’, using the words, ‘Ehrenfest paradox’.

So the point is, again, that there are some very basic ambiguities even among experts, regarding interpreting and applying some aspects of the ‘General’ and the ‘Special’ Theories of Relativity.  And, I think, in principle, it is very serious, non-trivial, and in fact, embarrassing!  (I.e., even though, so many such ‘thought experiments’, involving how actual ‘contraptions’ would behave near the speed-of-light, – are not really ‘practical’ experiments that can be carried out.)

Also, it seems to me that many theoretical physicists and some other scientists too, sometimes remain rather oblivious to observed realities and the reasons for those realities, when trying to make a point.  I.e., for example, realities like, “we just don’t seem to see or detect typical rods, clocks, etc., flying around the universe at speeds of nearly ‘c’, to ‘meet the conveniences’ of our ‘thought-experiments’.”  That is, despite ‘our wish to the contrary’, when trying to ‘freely make our point.’!  (Again, chemical bonds are complicated, and I think mass does occupy non-zero volume.  And we should occasionally remind ourselves of Bacon’s cautions, as described in a footnote below, when perhaps being over-presumptuous, as we try to make a point.)

Conclusions and Summary

For some physics experts, our ‘Abstract’ is sufficient, by itself, to also serve as our ‘Summary and main Conclusion’.  (See beginning of article.)

We assumed the following reasonable assumption throughout this article:  That suppose  a very low-mass elevator was in deep, isolated, outer space, and we suddenly began accelerating that elevator?  We assume that the previously discussed “launched super-fast ‘gross particle’ and the ‘flying photon’ would hit the opposite elevator wall at almost the same time, i.e., a virtually undetectable time-difference.”  In-other-words, we assume Newton’s first law holds good, regarding ‘inertia’.  And that all basic relevant laws and behaviors, as described in good, rather modern Physics textbooks, are correct and highly accurate.

So, I think that, in trying to broadly and simply apply ‘Relativity’; the scientific mainstream has over-extended themselves and somewhat failed.  I.e., as regards to, in this case, the flawed, “Relativity’s Equivalence principle” (as applied to ‘gravitation and non-gravitational accelerations’).  As F. Bacon cautioned, "The subtlety of nature is greater many times over than the subtlety of the senses…” [6]

So, basically, we have studied Einstein’s famous ‘Equivalence Assertion’ in ‘General Relativity’.  (That is -- as it is understood and explained by Einstein himself, and by most scientists).  And we have shown that, regarding ‘Equivalence’, it does NOT always ‘hold good’.  I.e., contrary to what is generally believed!  And we have described conditions under which that Relativity Principle FAILS.  And we used the alleged “Equivalency of ‘gravity pulling downward on a stationary, earthly Elevator’ compared to the ‘Accelerating Rocket’ deep in space ” -- as an example of a ‘failed equivalency’!  So, there is a basic internal difference inside a chamber between some results -- depending on whether the chamber  is ‘being accelerated by someone pulling it’ or ‘gravity pulling it’  We even used Einstein’s own prediction (maybe the greatest in history) -- that Gravity bends light twice as much as Newton predicted – to illustrate why General Relativity failed.  I.e., Why the failure of Einstein’s own famous principle of “Gravity Equivalence to spaceship acceleration”!

And some other subtle aspects of violations of the General Theory of Relativity, and related subjects – were also discussed.  (In fact, it has occasionally bothered me that certain aspects of ‘Relativity’ and earlier ideas of Ernst Mach, seem slightly to promote a return the “Ptolemaic System or the like.”  But further discussion of that is beyond the scope of this article.)

But the rather few violations or exceptions to ‘General Relativity’ discussed, although interesting and non-trivial, -- are rare.  And General Relativity almost always ‘holds good’, and is helpful.  And its likely greatest prediction, (that gravitational light bending is twice that which Newton predicted), – should continue to be regarded is a super-human achievement.  I.e., as long as it continues to stand unviolated by experiments.

References, footnotes

[1]…Albert Einstein, Relativity : the Special and General Theory. (London, Methuen & Co Ltd, 1920), section XX, “The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity.”, (Authorized Translation by Robert W. Lawson, D.Sc. University of Sheffield 1916), and apparently available free by online searching, using its title, or perhaps inserting or clicking  Project Gutenberg

[2]… NASA’s Cosmic Times (brought to you by “Imagine the Universe!”, National Aeronautics and Space Administration Goddard Space Flight Center, A service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Andy Ptak (Director), Page last Updated: Fri, Dec 08, 2017.  An old article, more recently made available by NASA,  and that old article appearing in “Cosmic Times”, 1919, in a series of articles, entitled, “Age of the Universe: Infinite”, and entitled, “Sun's Gravity Bends Starlight Einstein's Theory Triumphs”

[3]…Apparently, regarding Einstein’s prediction of light bending (being twice that predicted by Newton) -- Sir. Joseph Thompson said this: "The greatest achievement in the history of human thought was a prediction made by Dr. Albert Einstein. Dr. Einstein's prediction was proven true during the total eclipse of the sun on May 29, 1919.”  ((Apparently, Sir Joseph made this pronouncement at a joint meeting of ‘the Royal Society’ and ‘the royal Astronomical Society’ in London on November 6, 1919.  Dr. Einstein was then a Professor of Physics at the University of Berlin and Director of the Kaiser Wilhelm Physical Institute.))

[4]… Wikipedia -- There, we noted on 5-7-2026 -- the article available under topic, “Large Hadron Collider”. (In scanning that Wikipedia article, keep in mind that a single ‘at rest’ Proton has an ‘energy equivalent’ mass of very roughly 1’Gev’, and that a 1000 ‘Gev’ equals 1’Tev’.) 

[5]…Light deflection from a neutron star, AAPT – American Association of Physics Teachers, https://www.aapt.org > January 1984-Problem3  PDF  (And similar descriptions in other good posts on the topic).  ((This article indicates that if a photon passed by a neutron star very close to that star’s surface, the photon would be deflected by roughly 17 Deg.  And, thus I think that since a typical neutron star is less than about 15 miles in diameter -- that even a photon passing 50 miles above the neutron star’s surface would obviously gravitationally deflect a very detectable distance, in our ‘thought-experiment’.))

[6]… F. Bacon, , in Book I, Novum Organum (The New Organon), Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man, Aphorism X, (1620). (Translated by James Spedding)

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