Paolo Pasqualucci : 'Warped Space' : a Notion in Question

  

Paolo  Pasqualucci

‘Warped Space’ :  a Notion in Question

 

Summary :  1. Eddington’s denial as metaphysical of the distinction between space itself and the physical objects which define space.  2.  Dismissal of the “closed universe” hypothesis.  3.  Light always traveling on a straight line in the cosmos, as if it were always rushing ahead in a vacuum:  i. personal experience; ii. Einstein rings;  iii. Experiments showing light never scatters, no matter how wide the space run across.  4. Cosmic space now revealed as interspersed with cosmic voids, making smoothness and continuity of space  problematic notions.  5. Interstellar space not shaped by masses.  5.1  A massive, empty interstellar space between any two stars.   6. A reply to Eddington:  stellar gravitational fields “warp” physical objects in space not space as such.   

 

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How do we answer the following question, today:  

“What is “warped” by the Sun’s gravitational field, is it space itself or “the physical objects which define space””?

1.  Eddington’s denial of the distinction as “metaphysical”.  

Such a question is considered abstruse and therefore uninteresting by the majority of Physicists, dismissed as merely philosophical, in the sense of the old, discredited “metaphysics”.  Eddington himself, in replying to his critics, simply discarded it.

“These experimental proofs, that space in the gravitational field of the sun is non-Euclidean or curved, have appeared puzzling to those unfamiliar with the theory.  It is pointed out that the experiments show that physical objects or loci are “warped” in the sun’s fields;  but it is suggested that there is nothing to show that the space in which they exist is warped.  The answer is that it does not seem possible to draw any distinction between the warping of physical space and the warping of physical objects which define space.  If our purpose were merely to call attention to these phenomena of the gravitational field as curiosities, it would, no doubt, be preferable to avoid using words which are liable to be misconstrued.  But if we wish to arrive at an understanding of the conditions of the gravitational field, we cannot throw over the vocabulary appropriate for that purpose, merely because there may be some who insist on investing the words with a metaphysical meaning which is clearly inappropriate to the discussion”.[1]

In his reply, Eddington assumes, as if it were obvious, that it is impossible to draw any distinction between space and the “physical objects” that occupy it or “that define it”.  In other words:  void does not exist, therefore the warping of spacially existing physical objects is the warping of the space they “define” (a term perhaps not overwhelmingly clear, though traditional).  

 Eddington seems to share the opinion of all those who have denied any distinction between space and what occupies it, whether moving in it or not (from Aristotle to Einstein, via Descartes, Leibniz and others).  But Newton, if I am not mistaken, shared the opposite view and his opinion we surely cannot qualify nor dismiss as “metaphysical”.  I mean, when he thought of  ether  as a medium existing other than in bodies also “in the void celestial space” extended among the sun, the stars, the planets, the comets:  “Qu. 21. Is not this Medium much rarer within the dense Bodies of the Sun, Stars, Planets and Comets, than in the empty celestial Space between them?”[2]

    The effective “shape of space” seems to have its importance  for an exact knowledge of the physical world.

2.  Dismissal of the “closed universe” hypothesis.  

Briefly resuming for the larger public the theory on the existence of “dark matter”, the astrophysicist, prof. Russell Stannard, wrote:  “Most of the matter we see around us today did not, in fact, originate at the instant of the Big Bang;  it was created a fraction of a second later during inflation.  Moreover, the amount produced is such that the overall density should end up with exactly the critical value.  The agreement between this requirement and the experimentally measured value for the mean density of the universe, provides powerful evidence in favour of the inflation theory.  So what does this mean in terms of the size of the universe? Because the density is critical -  and does not exceed that value – three-dimensional space does not curve back on itself.  So the closed universe hypothesis – attractive though it might be – is dead […]  This means that we are left with the answer that the universe is infinite.  But what kind of answer is that?  What do we actually mean by saying it is infinite?”[3]

In my opinion, one important consequence of the rediscovery of the Infinite (also from a purely philosophical point of view) might be the splitting of the two notions of space and universe, so far unified in the image of the universe as a tridimensional space “curved back on itself”; that is, unum et identicum with the matter and the energy that “define” it, supposedly “bending” it on itself.   We might consider the observable Universe or Cosmos as the system of multiple and complex combinations of matter and energy observed, discovered and analized by scientists:  from the Planck scale (10^-35 m) to the cosmic horizon (10²⁷ m)[4].  But matter and energy are finite physical realities:  their continual renewal does not make them infinite.  Therefore, they cannot possess the open and infinite dimension we believe should now be attributed to space as such; a reality which is now considered almost completely “flat”, a property which means first of all: “not curved”[5].   So, are we  seemingly compelled to revert to the old traditional distinction between space in itself – an open, infinite, isotropic, tridimensional reality in its own right– and the  

This differentiation might seem “metaphysical”, i.e., abstract and irrelevant, to the scholars who share Eddington’s view on space (see above, § 1).  But it was instead considered “realistic” by philosophers of science like Nehrlich:  “…space is a real, concrete thing, which, though intimately linked to material objects by containing them all, is not dependent on them for its existence […]  I call this answer realism”.  We must realistically admit that “space is an entity in its own right”.[6]   

  To say the truth, the recently proclaimed death of the “closed universe hypothesis” seems to have been of no consequence for the prevailing Image of the World.  The “closed universe hypothesis”, that shapes the universe as the continuous, unlimited  though finite “curved space” of a smooth spheroid,  is still taught in the Universities and seems to be still predominant with the larger public.  Yet, we know that an open, flat, tridimensional, infinite space was never effectively eliminated from physical theory: it is still alive as the only “shape of space” suitable for quantum mechanics.  In his best-selling booklet, prof. Carlo Rovelli  has reminded us of the ambivalent vision of space still haunting contemporary Physics.  “In the morning, when lectured on general relativity, the students are taught that the world is a curved space where everything is continuous;  in the afternoon, when lectured on quantum mechanics, they are confronted with a flat space in which quanta of energy jump all over”.  The overcoming of this “schizofrenic” dualism, he points out, may succeed only if a new vision of the physical world appears, capable of unifying quanta and gravity in a new concept of gravity (quantum gravity), so far not yet attained.[7]

In the Oxford Dictionary of Astronomy we read that Eddington “obtained observational proof that gravity bends light, as predicted by the general theory of relativity, when he measured slight apparent changes in the position of stars seen near the sun during the total solar eclipse of 1919; the accuracy of his results has since been questioned, but their announcement influenced the acceptance of general relativity.”[8]  Notwithstanding a possible lack of accuracy on the part of Eddington, we know that subsequent and repeated “astrometric” measurements of cosmic radiowaves using very sophisticated instruments  (Hubble Space Telescope, ESA Hipparcus Satellite), have confirmed the apparent changes.  “Even for stars in line with the Sun, the shift in apparent position is less than two seconds of arc, or a few ten-thousands of a degree.”[9]    

 These figures have been interpreted as evidence of the curvature of the whole cosmic space, too big to be perceived at the small scale to which our normal point of view belongs.  In my opinion, such an evidence seems today difficult if not impossible to maintain.  Since the now prevailing calculations implies that space  i s  on the large scale “almost perfectly flat” and “warped” on the small scale only, this means that the “flatness” of cosmic space is not an illusion provoked in our vision by the enormous extention revealed by the supposed cosmic spheroid[10].  The reaffirmed, intrinsic, objective Euclidean “flatness” of space might also explain, perhaps, why light seems to be traveling always in a straight line, as if it were always traveling in a vacuum.    Let’s consider this important property of light through evidence offered by experience.    

3.  Light always traveling on a straight line, as if it were always rushing ahead in a vacuum.   

Explaining in a drawing the meaning of the famous Isle of Prince observations of 29 May 1919, Eddington wrote:  “The main part of the bending of the ray [of light] occurs as it passes the sun S; and the initial course PQ and the final course FE are practically straight.”[11]  The “initial course” PQ is the course of light from its source, located in the  Hyades cluster, to the Sun;  the “final course” FE is the distance from the Sun to the Earth.  Given the “deflection” suffered in the proximity of the Sun by the beam of light coming from the Hyades, the position of some of these stars, as seen from the Earth, must appear slightly different than it normally does, as confronted with background stars of the same cluster[12].  This apparent change in the position of the stars is caused by a deviation or deflection from a  course of  light that must necessarily be straight, given the fact that we become aware of it only when a total solar eclipse reveals that the light beams are running on a tangent aligning the Earth, the Moon and the Sun; and straight must also be the course of the slightly deflected light from the periphery of the Sun to us, otherwise we would not be able to see it as a luminous point on that same tangent. Looking at the way light travels in our solar system, maybe we can say that it shows a “warping” of the space immediately around the Sun but not of the space between us on the Earth and the Sun?

  The Hyades cluster is calculated to be at 153 light years from the solar system.  In one year, as we know, light covers 9,463 billion kilometers. [13]  9,463 times 153 = 1, 447,839.  This means :  one million 447,839 thousand billions kilometers, if I am not mistaken.  This enormous distance is the “initial course” mentioned by Eddington, while the last jump of “only” 150 million km, from the Sun to us, is its “final course”.  This “initial course” is seemingly run across by light always in a rectilinear motion, as if it were always advancing in a vacuum. Looking at the way light travels in our solar system, maybe we can say that it shows a “warping” of the space immediately surrounding the Sun but not of the space between us and the Sun.  

Eddington’s statement is supported by the visual evidence offered to us by the geometry of lines and solids belonging to reality outside us. Such an evidence seems to be a multiple one.

i. Personal experience.  During Spring 2007, on the 29^th of March, I witnessed an extraordinary astronomical event.  A lunar eclipse took place exactly when, by a rare coincidence, Saturn, the Moon and the Earth were all aligned on the same straight line:  the Earth and Saturn were simultaneously on the tangent of the Moon.  The night was clear, my wife Sandra Anne and I, alerted by the Media, looking from the tarmac in front of our bungalow, located in the South-East of Ireland, were able to see with our naked eye a minuscule but very bright point that appeared to be attached to the small crescent of sun light left by the umbra projected by the Earth  on the Moon.  That implied, if I am correct, that the sunbeams exposing Saturn had travelled in a straight line for about 1.434 billion kilometers, which is Saturn’s mean distance from the Sun.  This experience confirms, in my opinion, that light travels in a straight line and practically so in the whole solar system, not only within the limited space between the Sun and the Earth.

ii.  Einstein Rings.  We could say, I think, that the same occurs in the case of the so called Einstein rings.  In this case, the gravitational lensing effect is produced, as we know, when a galaxy “bends the light emanating from a galaxy that is directly behind it”, creating a “ring of light warped by the gravitational pull of the galaxy on the forefront.”  We can observe this phenomenon only when there is “ exact alignment of the source [the galaxy behind], lens [the galaxy on the forefront] & observer [the Earth or the Hubble Space Telescope]”.[14]     

Exact alignment means a display of objects all placed exactly on the same straight line.   But how far are these  “rings” from one another and from the Earth?   “The thin blue bull’s-eye pattern in these eight Hubble Space Telescope images appears like neon signs floating over reddish-white blobs.  The blobs are giant elliptical galaxies roughly 2 to 4 billion light-years away.  The bull’s-eye patterns are created as the light from galaxies twice as far away is distorted into circular shapes by the gravity of the giant elliptical galaxies.”[15]

Two to four billion light-years away from the Earth but “twice as far away” from one another, that is:  4 to 8 billion light-years away from one another.  Therefore, the galaxy providing the “source” can be 10 to 12 billion light-years away from the Earth. Indeed, the first Einstein-ring to be discovered was “10 billion light-years away from Earth (or a redshift of z = 1.849).”[16]   This means that, in this case, the galaxy acting here as “source” might be 14 to 18 billion light-years away from the Earth.  This implies, in my opinion, that we have solid evidence of the fact that light can travel on a straight line to our retinas all along these monstrous distances: two to four to ten or more billion light-years for the image of the “Einstein ring”!

    iii. Experiments showing light never scatters, no matter how wide the space run across.   The man-on-the-street  can’t but marvel at all this.  How is it possible that light can travel such distances (in our case, around 1/3  of the alledged radius of the visible Universe) always maintaining the same velocity and a rectilinear path, always immediately resumed once it is (slightly) deflected by the gravitational field of a massive celestial body?  How is it possible that light never seems to scatter, during such an immense intergalactic voyage?  If space is “bent”, as a result  of the density of matter and energy everywhere superior to 0, a density furthermore “warped” by the gravitational fields of massive stellar bodies, how could the straightlinear course of light not be significantly affected by this all pervading, bent and locally warped density?  And yet light does not seem to be affected at all, in its cosmic traveling:  when deflected, it resumes immediately its straight thrust forward.  This peculiarity is perhaps best understood  from the standpoint of quantum physics.  The late prof. Steven Weinberg, Nobel laureate,  explained it this way:

“An ordinary light wave contains a huge number of photons traveling along together, but if we were to measure the energy carried by the train of waves very precisely, we would find that it is always some multiple of a definite quantity, which we identify as the energy of a single photon.  As we shall see, photon energies are generally quite small, so that for most practical purposes it appears as if an electromagnetic wave could have any energy whatever.  However, the interaction of radiation with atoms or atomic nuclei usually takes place one photon at a time, and in studying such processes it is necessary to adopt a photon rather than a wave description.  Photons have zero mass and zero electrical charge, but they are real nonetheless – each one carries a definite energy and momentum, and even has a definite spin around its direction of motion.

What happens to an individual photon as it travels along through the universe?  Not much, as far as the present universe is concerned.  The light from objects some 10,000 million light years away seems to reach us perfectly well.  Thus whatever matter may be present in intergalactic space must be sufficiently transparent so that photons can travel for an appreciable fraction of the age of the universe without being scattered or absorbed.”[17]

There is, then, a precise relationship between the energy of the single photon and the energy of the wave in which it is traveling.  Applying the quantum theory, Einstein has formulated the correct explanation, according to which, “the energy of any photon is inversely proportional to the wavelength”.[18]  Therefore, light bolts forward in a continuous straight path and never gets lost along the road, so to say: “never scatters nor is absorbed.”   There seems to be an experimental confirmation to this from a thirteen years old research on the possibility of diffraction of light in space.

“In a crystal, the rows and columns of atoms create countless apertures.  Sending waves of a comparable wavelength through these gaps makes a diffraction pattern that can be measured, so we can work out the structure of the crystal.  Observing how light scatters can also reveal the structure of empty space.  If space is perfectly smooth, it won’t scatter light.  If it is constructed from minuscule building blocks, as many physicists suspect, it should scatter different wavelengths of light by different amounts – albeit tiny amounts, since the structure is much smaller than any observable wavelenghts, blurring out the effects of the scattering.  Last year [2012] scientists using NASA’s Fermi Gamma-ray Space Telescope observed three photons with different wavelenghts arriving at Earth simultaneously.  The photons emanated from a gamma-ray burst seven billion years ago – enough time to accumulate a noticeable difference in arrival times if one wavelength takes a slightly more wiggly path than another due to scattering.  The observed simultaneity puts a limit on the size of any fundamental unit of space, if they exist at all.”       [19]

   So, no “wiggly path”, no diffraction, for the three photons which traveled in a parallel route for 7 billion  years!  The “observed simultaneity” of their arrival makes the size of any possible “minuscule building block” so minuscule as to disappear completely from space.  This experiment seems to demonstrate  that space does not have a material “structure” of its own. 

A path that does not “wiggle”, is generally considered a straight one.  Since it seems evident that, in the above quoted experiences and experiment, light is effectively traveling in a straight line,  maybe we have here reliable evidence of the fact that light has effectively traveled in an open tridimensional space, intrinsically as flat as it appears  in Euclid’s geometry?

 Other aspects of the complex nature of cosmic space revealed by recent research (both relevant, in my opinion, for the “shape of space”), must be taken into consideration too.

4.  Cosmic Space now revealed as interspersed with “cosmic voids”, making smoothness and continuity of space problematic notions.

From the experiments just quoted one could assume that “smoothness” plays a decisive role in the rectlinear cosmic traveling of light. Yet, more recents studies have demonstrated that cosmic space cannot be considered “smooth”, i.e.  globally smooth and continuous, as requested for instance by the general theory of relativity.     

From the results of the experiment commented by dr. Evans it appears that space should be considered “perfectly smooth” or sufficiently “smooth” so as to allow light to travel in it without ever scattering.  Smoothness implies continuity:  curved space must be continuous, being alledgedly the surface of an unlimited cosmic spheroid.  So smothness qualifies especially curved space[20].  One is reminded here of the ancient Parmenidean verse: the Being is everywhere accomplished / similar to a well rounded sphere / from its centre onwards everywhere the same…”[21]

But smoothness qualifies also the energy that together with matter fills the space that seems void to us: the quantum field.  This energy is made of particles but “it is important to remember that “particle” here really describes a particular kind of configuration of a quantum field.  The reason it is important is that the idea of a world of particles strongly suggests that there are stretches of empty space between particles.  But quantum field theory allows no such thing”[22].  From the standpoint of particle physics, which explains the dynamic of the three “fundamental forces” (strong force, electromagnetism, weak force) with the “largely unified theoretical framework of quantum field theory”, there cannot be a real void, “in a region of space and time.  Nothing is not the absence of stuff; instead it is just one possible configuration of stuff”[23].   In other words:  “nothing means the quantum field theoretic vacuum – replete with fluctuations and creation/annihilation of many different kinds”[24].

So we have vacuum, that is void space, but only theoretically since it is always  occupied by the manifold fluctuations of “stuff” replening it without interruption.  Yet it seems to me that, wether full of fields of energy or pro tempore partially empty,  v o i d  remains always an entity in its own right: void, i.e. flat, tridimensional space, extended in all directions.   In any case, the continuous fluctuations of matter and energy must be sufficiently transparent, as underlined by prof. Weinberg, as to allow light to pass through undisturbed in its (rectlinear) motion.  Indeed, we can say that whether full of fluctuating matter and energy or empty, space always allows light to travel on a straight line, as if always traveling in a vacuum, no matter how big the distance covered. Further studies have so far confirmed that space can’t be considered  “chunky” or “grained” or “pixelated”, as implied by the Quest for the Graviton[25].

Furthermore, the existence of “cosmic voids” has been accurately mapped:  “voids, which can stretch from tens to hundreds of millions of light years across”.  These voids “shake the presumption that the universe is smooth”.  Instead, “galaxies and clusters of galaxies are themselves concentrated into a gigantic web of concentrated regions of matter connected by streaming filaments with gargantuan voids inbetween”.  The study of these voids can alledgedly help to understand the action of (so far elusive) dark matter & dark energy.  Nonetheless, they represent “a danger” for general relativity, which remains  “our best theory of gravity”.  General relativity could “break down somehow over very large distances”.  The author does not elaborate further but it seems inevitable to infer that, if these “very large distances” are intermingled with large swaths of void spaces, space could not be conceived of as a continuum, the structure of which is determined by the stellar masses it contains in the form of “quantum fields” that supposedly configure it, as requested by the theory of general relativity.[26]

But a “danger” for Einstein’s theory of general relativity appears, in my opinion, also from another quarter, involving the “shape of space” too.  General relativity aims towards eliminating the notion of the instantaneous “action at distance”, admitted by Newton and rejected as “irrational” by Einstein[27].  But the “spooky” action at distance should perhaps be taken again into consideration, as demonstrated by the many experiments aiming at solving the misteries of the ”quantum entanglement”, when particles, as we know, “seem to be in two or more places or status at once” – a resurrection that seems to threaten the foundations of the theory of special (but, it seems to me, also general) relativity[28].

Against Einstein’s opinion, our world seems to have become Euclidean again.       

5.  Interstellar space not shaped by masses.  

In fact, Alfred Einstein and Leopold Infeld have written, in their classic Development of Modern Physics:  “Our world is not Euclidean.  The geometrical nature of our world is shaped by masses and their velocity.  The gravitational equations of the general relativity theory try to disclose  the geometrical properties of our world.”[29]

Which world is meant, here, by the two Authors?  The solar system or the whole universe?  We know that for Einstein the whole space (space-time) is a field of electromagnetic “geodetics”, bent in a spheroidal continuum of matter and energy, irregularly shaped by the cosmic gravitational fields of the celestial “masses” in perpetual motion.  Therefore, the “warping of space” in the gravitational field or heliosphere of a star like the Sun, is the local “warping” of a “fabric” that is already curved in itself.

If the heliosphere made of hot, ionized, gaseous fluid called plasma by Physicists identifies the space warped by the gravitational field of the Sun, it is perfectly logical to consider this space as embedded, so to say, in a continuum made of an infinite number of plasmata, emanating by the infinite number of stars that populate the universe.   Prof. Ester Antonucci, a renown specialist in Sun studies, stated, as if it were not only a common opinion but also an established truth, that:  “The universe is mainly made of plasmata, like our solar system, where the prevailing matter is plasma, at least because almost all the mass is concentrated in its center of gravity, in the Sun”.[30]  This is like saying that the universe is mainly made of the warped spaces surrounding the masses of the stellar bodies.

The heliosphere is so defined by the Oxford Dictionary of Astronomy:  “ The region of space around the Sun which the solar wind flows.  The heliosphere is thought to be about 100 AU in radius, and is bounded by the heliopause, beyond which interstellar gas exerts an equal pressure from outside.  The shape of the heliosphere is  unknown, but if there is a flow of interstellar material around it from a particular direction (an interstellar wind), the heliosphere may be like the Earth’s magnetosphere:  spherical on one side, but drawn out into a long tail on the other.”[31]

Following Einstein’s postulate quoted above, shouldn’t the gaseous pressure from outerspace be caused too by a “plasma” created in its own turn by the mass of a star?  Now, the nearest mass to our solar system belongs to the star Proxima Centauri or Alpha Centauri C, situated at about 4.2465 light years from us, a distance deemed to be the average distance among the stars inhabiting the disc of our galaxy.[32]  If the heliosphere radius is about 100 AU, this means that it flows until about 15 billion km from the Sun.  Therefore its border, ignoring the heliopause, is situated at approximately 37,837 billion km from Proxima Centauri :  4 light years = 37,852 billion km minus 15 billion km = 37,837 billion km.

But we know that Proxima Centaury is a red dwarf which has a mass 12.5% of the Sun’s mass while its actual diameter is about one-seventh (14%) of the diameter of the Sun.[33] To reach us, its light has to cover a distance 300,000 times longer that the actual distance between our Earth and the Sun.  The trip requires four years.[34]  Given its smaller size,  the radius of its plasmosphere (if I may so say) should be considerably less extended than the radius of the Sun’s plasmosphere (heliosphere).  Indeed, Proxima Centauri “has two confirmed exoplanets:  Proxima Centauri b & c.  Proxima Centauri b orbits the star at a distance of roughly 0.05 AU (7.5 million km)” while Proxima Centauri c “orbits roughly 1.5 AU (220 million km) away”.[35]  

5.1.  A massive, empty interstellar space between any two stars. 

Therefore, can we admit, at this point, that between the plasmosphere of the masses of these two stars (Proxima Centauri and the Sun)  there is a massive interstellar gap of about 38,000 billion km, a space that appears totally deprived of any stellar mass?   

Proxima Centauri is the nearest star to the Sun, but in the vast space between the two there appears to be no mass whatsoever to “warp” this same space with its own gravitational fields.  Clouds of gases, stellar dust, waves and rays of energy in its various forms, all sorts of cosmic débris seemingly flow and float in it, in a continuous “intergalactic tide”, but this “tide” seems to be a physical status quite different from the masses requested by Einstein’s postulate.  Can a ”tide” of diluted, scattered and eterogeneous cosmic débris circulating on a space of about 38,000 billion km be able to counterbalance the compact “pressure” exerted by the mass of our Sun?     One could therefore ask: can we still apply here the notion of the universe as a continuum of stellar plasmata?  And if there is no mass to generate gravitational fields for billions and billions of km, how can all this empty space be considered “bent”?[36]

6.  A reply to Eddington: stellar gravitational fields “warp” physical objects in space not space as such.

At this point of our analysis, we might dare to draw a conclusion:  space is not a continuum of stellar plasmata or “masses”:  it is an Euclidean vacuum interspersed with the ebullient plasmata surrounding stellar masses, run across by all sorts of débris and energies.  Does this conclusion maintain the ambivalent vision of space lamented by prof. Rovelli?  Let’s see. The dualism was originated by Einstein’s Postulate, that space had to be considered warped on the small scale represented by the masses created by every star and therefore bent on the cosmic scale, taken as a whole or as The Whole, being The Whole a continuum of spheroidal masses (image of the football ball).  Since the most recent calculations reject the existence of the curvature of cosmos, it follows that the stellar bodies and systems, being always in a quasi-circular and elliptical motion, must be moving in a space that cannot be different from the Euclidean space in which the subatomic particles fly.

Astrophysics teaches us that the Earth orbits the Sun at the speed of about 32 km/s, around 107,000 km/h.  At the same time, the Sun orbits the center of our Galaxy at the speed of approximately 200 km/s, circa 720,000 km/h.  The Earth “glides easily through empty space, as there is no friction that could keep it from coasting”.  Empty space is “a region of the universe that has been made as empty as it can be”.  This emptiness “is also called the vacuum”[37].

The Sun of course does not travel alone but together with all its planets and the fields of energies provoked by the Sun itself and by its own planets.  It is the whole solar system that travels nonstop at the speed of 251 km/s, advancing in a space “as empty as it can be”, i.d. in an Euclidean vacuum.  In the solar system we have the alledged “warping of space” on the small scale allowed by the new calculations; “warped”, that is, shaped by the mass of the Sun as an elongated spheroid that moves unhindered in an Euclidean vacuum.  Ahead the void, behind the void:  once the solar system has moved on second after second, covering 200 or more km per second, plunging in the empty space ahead, the space it leaves behind is as empty “as it could be”, as it was one second before the arrival of the same solar system. 

Therefore, if the spheroidal “warped” space  t r a v e l s  together with the “object” (the solar system) that is being warped by Sun’s gravitational fields, leaving the vacuum in which it glides completely unaltered, in my opinion the “warping” concerns only the “object” where it takes place, not the space it is traveling in.

     2^nd of June 2025

 

 

Endnote

This article on the notion of “warped space” is part of a research I have been developing over many years on the notions of space and time, in my opinion to be reestablished in a realistic way, i. e.  as realities in their own right, if we want to overcome the subjectivism and relativism still dominating our philosophical (and scientific) vision of the world.  More specifically, on the notion of space I have published, ten years ago:  Paolo  Pasqualucci, Metafisica del Soggetto  II -  “Il concetto dello spazio”, RIFD, quaderni della rivista internazionale di filosofia del diritto, n. 10,  Giuffrè editore, 2015, pp. 648.   

 

 

 

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[1] Sir Arthur Eddington, Space, Time & Gravitation.  An Outline of the General Relativity Theory, Cambridge UP, 1920, repr. 1995, p. 126.  Emphasis added.

[2] Isaac Newton, Opticks, Book Three, Part I, 1730 ed. , p. 339, Query 21, Dover Publications, New York - Internet Archives pdf, archive.org/details/Opticks.  Emphasis added..

[3] Russell Stannard, The End of Discovery, Oxford UP, 2010, pp. 48-49.  Emphasis by the Author.  See also:  Stephen Hawkins in his short Introduction to Einstein’s Geometry and Experience, in The Essential Einstein. His Greatest Works, edited with commentary by Stephen Hawking, Penguin, 2007, p. 248:  “The issues which Enstein raises in ‘Geometry and Experience’ are still with us.  Recent measurements from the Wilkinson Microwave Anisotropy Probe and other experiments suggest that on the larger scales, the universe is flat, while gravitational wave experiments like the Laser Interferometer Gravitational Wave Observatory (LIGO) […] aim to mesure the bumps and wiggles in space-time on the smallest scales”.  See also, for the popular science sources: Stuart Clark, The Universe, in: The Big Questions, series edited by Simon Blackburn, Quercus, 2010, p. 91;  Shape of the Universe, en. wikipedia.org/wiki/Shape_of_the_universe;  Leah Crane, Cosmological crisis: We don’t know if the universe is round or flat (www.newscientist.come/article/2222159-cosmological-crisis-we-dont-know-if-the-universe-is-round-or-flat/;  Cody Cottier, What shape is the universe?  As far as cosmologists can tell, space is almost perfectly flat.  But what does this mean? (astronomy.com/news/2021/02/what-shape-is-the-universe.).

[4] See:  Caleb Scharf, Ron Miller, The Zoomable Universe, ‘Scientific American’, November 2017, pp. 62-67.

[5] “I am using the word “flat” in a mathematical sense, but it is very closely related to ordinary usage.  When mathematicians say that a space is flat, they mean it is not curved” (James Owen Weatherall, Void.  The Strange Physics of Nothing, Yale UP, Templeton Press, 2016, p. 69).  

[6] Graham Nehrlich, The Shape of Space.  Secondo edition, Cambridge UP, 1994, p. 2 and 3. 

[7] Carlo Rovelli, Sette brevi lezioni di fisica [Seven short lectures on physics], Adelphi, Milano, 2014, pp. 47-48.  My translation from the Italian original.  This “unification” is pursued mainly through sophisticated lab experiments trying to detect a quantum behaviour on the part of the force of gravity. See, for instance:  Tim Folger, Quantum Gravity in the Lab, ‘Scientific American’, spec. ed., Winter 2021, pp. 53-59.

[8] Oxford Dictionary of Astronomy, OxfordUP, 2^nd revised edition, 2012, entry: Eddington, Arthur Stanley.

[9] For all these data, see:  Relativity and the 1919 eclipse, in the European’s Spacial Agency’s blog (www.esa.int).  See also:  Weatherall, Void:  there was a “long standing controversy concerning just what was shown by the eclipse data”  (note nr. 122 at p. 155, with the literature indicated).  

[10] The measurements of the Cosmic Microwave Background from the WMAP have demonstrated that space is effectively flat.  See:  Andrew Taylor, The dark Universe, in: On Space and Time,  Edited by Shahn Majid, Cambridge UP, 2008, pp. 1-55;  esp. pp. 26-32.  “From Figure 1.5  we can just read off the result at the first peak and we can see the CMB indicates the Universe is indeed flat” (ibid., p. 32).

[11] Eddington, Space, Time & Gravitation,  p. 112.  Words in square brackets always by me.

[12] The “normal position” of the stars resulted from “normal photographs for comparison taken with the same telescope in England in January 1917” (Eddington, ibidem, p. 115).  We must assume that the “normal position” of these stars appears to be the same whether investigated in London or in the Island of Prince, near the Equator, i.e. about 5,726.56 km south of London, though not too far from the Greenwich meridian.

[13] See:  Hyades (star cluster), en.wikipedia.org.

[14] Quotations from:  A Gallery of Einstein Rings, from the site: hubblesite.org/contents/media/images/2005/32/1788-Image.html;  Chelsea Gohd, Astronomers turn back time to solve Einstein ring mistery, in:  www.space.com/firts-einstein-ring-mystery-hubble-telescope.html, June 03, 2020;  Einstein Ring, in:  hyperphysics.phy-astr.gsu.edu/hbase/Astro’einring.htmil.

[15] A Gallery of Einstein Rings, p. 2 of 6.  Emphasis added.

[16] Article by Chelsea Gohd, quoted above, p. 2 of 12.  See also:  Scientific American, Dec  2024, p. 16:  “The Carousel Lens – named for its concenctric circular patterns, like the reflections in a fun-house mirror -  incorporates a cluster of galaxies about five billion light-years from Earth whose gravity is so intense that it magnifies the light of seven galaxies behind it, between 7.6 billion and 12 billion light-years away.  This phenomenon, called gravitational lensing, occurs only when galaxies line up precisely from our perspective”. 

[17] Steven Weinberg,  The First Three Minutes. A Modern View of the Origin of the Universe, updated edition, 1993, pp. 53-54.  Emphasis added.

[18] Weinberg, ibidem, p. 61.

[19] Dr.  Mike Evans, What is Light?, article in: ‘Sky at Night’, July 2013 # 98, pp. 66-69; p. 68.  Emphasis added.     

[20] For “smoothness” as a “property intrinsic to space”, basically to curved space, see: Nehrlich, The Shape of Space, pp. 98-99.

[21] Parmenide, Poema sulla natura, Greek-Italian, it. tr. and notes by Giovanni Reale,  philosophical commentary and introductory essay by Luigi Ruggiu, Rusconi, Milano, 1991, pp. 104-5.  English translation by me.     

[22] Weatherall, Void, p. 110.

[23] Weatherall, Void, p. 65.

[24] Weatherall, p. 128.

[25] See:  Paul Sutter, What if Space-Time Were ‘Chunky’?  It Would Forever Change the Nature of Reality, article on November 20, 2019, www.livescience.com/is-space-time-smooth-chunky.html, pp. 11;  Whitney Clavin, Is Space Pixelated? Article on November 29, 2021, www.//magazine.caltech.edu/post/quantum-gravity, pp. 10.  “Though the electromagnetic field appears continuous at the large scales” we should consider if “does  spacetime also become a frothy sea of particles at the smallest scales, or does it remain smooth like the surface of an unbroken lake?   Scientists generally believe that gravity should be bumpy at the smallest scales; the bumps are hypothetical particles called gravitons. But when physicists use mathematical tools to describe how gravity might arise from gravitons at every tiny scales, things break down” (Clavin, pp. 4-5/10).     

[26]  All the information on the cosmic voids comes from:  Michael D. Lemonick, Cosmic Nothing, ‘Scientific American’, spec. ed., Spring/Summer 2024, pp. 20-27.  See also: Istvàn Szapudi, The Emptiest Place in Space, ‘Scientific American’,  Aug 2016, pp. 22-29.  Now it seems that the fabric of universe is full of holes,” like a Swiss cheese”:  see Lemonick, ibidem and map of the universe at pp. 24-25.

[27] “The force between two bodies, according to Newton’s law, depends only on distance; time does not enter the picture.  The force has  to pass from one body to another in no time!  But, as motion with infinite speed [i.e. instantaneous] cannot mean much to any reasonable person, an attempt to make our drawing [of Newton’s model of gravity] something more than a model leads nowhere”(Einstein, Infeld, pp. 127-128).   Newton too considered the “action at distance” as something absurd but accepted it, while Einstein tried to eliminate it from his cosmological model. On Newton’s opinion on this matter see:  Alexandre Koyré, From the Closed World to the Infinite Universe, The Johns Hopkins UP, Baltimore, 1957, chap. IX. 

[28] David Z. Albert and Rivka Galchen, A Quantum threat to Special Relativity, ‘Scientific American’, spec. ed., Summer 2013, pp. 94-101.  On the “quantum entanglement” experiments:  Ronald Hanson & Krister Shalm, Spooky Action, ‘Scientific American’,  spec. ed., Spring 2019, pp. 92-99;  Philip Ball, Quantum Physics may be even spookier than you think, ibidem, spec. ed., Winter 2021, pp. 48-51; Daniel Garisto, The Universe is not locally real, ‘Scientific American’, spec. ed., Spring/Summer 2024,  pp. 60-65.   See also:  Lee Smolin, Einstein’s Unfinished Revolution.  The Search for What Lies beyond the Quantum, Allen Lane, 2019, chap. 4.

[29] Albert Einstein, Leopold Infeld, The Evolution of Physics.  From early concepts to relativity and quanta, 1938, with a new introduction by Walter Isaacson, Touchstone, New York, London, Toronto, Sidney, 2007, p. 235.  Emphasis added.

[30] Ester Antonucci, Dentro il Sole [Inside the Sun], il Mulino, Bologna, 2014, p. 44. Emphasis added.  My translation from the Italian original.  Most of my information on the Sun comes from this excellent book for the  non-specialist.  

[31] Oxford Dictionary of Astronomy, entry:  heliosphere.

[32] Clark, The Universe, p. 14.

[33] Https;//en.wikipedia.org/wiki/Proxima_Centauri, p. 1 of 20.

[34] Antonucci, ibidem., p. 16.

[35] En. wikipedia. org./wiki/Proxima_Centauri, p. 2 of 20.

[36] On the ongoing research on “interstellar space”, see:  Meghan Bartels, Beyond the Solar System.  The Voyager spacecraft are overturning everything we thought we knew about the boundary of interstellar space, ‘Scientific American’, 4, 2025, pp. 63-69. According to the article, an exhaustive description of the “boundary” between the heliosphere and “interstellar space” or “medium” is still far from being accomplished, notwithstanding the large amount of data already produced by the spacial probes.  

[37] Matt Strassler, Waves in an Impossible Sea.  How everyday life emerges from the cosmic ocean, Basic Books, New York, 2024, pp. 38-39.  It would take the Sun 250 million years to complete one orbit (ibidem, p. 339).