Philosophia Naturalis
- Questions on the notion of a
“warped space”
by
Paolo Pasqualucci
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”. I
know 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” (to use the
terminology of philosopher Graham Nerlich) seems to have its importance for an exact knowledge of the physical world.
2.
Death of the “closed universe” hypothesis? Briefly
resuming for the larger public the theory 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]
If the “closed universe hypothesis” is to be
considered “dead”, what would be the consequences for the prevailing Image
of the World? None, it seems: the
“closed universe hypothesis”, that shapes the universe as the continuous,
unlimited “curved space” of a spheroid, is
still taught in the Universities and seems to be still predominant with the
larger public . Yet, we know that the
tridimensional, infinite nature of the Euclidean “flat” space was never effectively
eliminated from physical theory: it is still alive as the only “shape of space”
suitable for quantum mechanics. In his
recent 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.[4]
Given this unsatisfactory situation, I dare say that
reasonable questions on the effective “shape of space” are legitimate, even on the part of the
non-specialist.
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.”[5] Eddington’s
accuracy should perhaps be questioned again but 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.”[6]
In this short paper, I will try to pose some questions on the “shape of space” problem, with
special regard to the revolutionary notion of a “warped space”, key-notion to
Einstein’s theory of gravitation.
A. What might be the consequences, as far as the
notion of space is concerned, of the fact that light coming from the Hyades
cluster to skim the Sun and reach our retinas here on the Earth, seems to
travel always on a straight line, as if it were always traveling in a vacuum?
B. The light beams deflected by the warping of
space around the Sun originate from stars situated in a cluster calculated to
be at 153 light years from the Earth, quite a remarkable distance. If this whole distance is covered by light
always traveling on a straight line (a straight line that is also maintained in
its course from the Sun to the Earth, after the slight deflection caused by the
Suns’s gravitational field), can we assume that space is in itself flat (“euclidean”)
and subject to a “warping” only in the
proximity of celestial bodies, under the action of their gravitational field? That is, that it is “warped” at the level of
the small scale only?
*
*
3.
Light always traveling on a straight line, as if it
were always rushing ahead in a smooth and transparent medium. 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.”[7] 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. 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 perifery of the Sun to us, otherwise we would
not be able to see it as a luminous point on that same tangent.
As said above,
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 of km. [8] 9,463 times 153 = 1, 447,839. This means :
one million 447,839 thousand billions of km, 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”.
Eddington’s last 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. Let’s consider some other examples.
i. Personal experience. During
Spring 2007, on the 29th 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 km, 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’s Rings. We could say, I think, that the same occurs
in the case of the so called Einstein’s 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
upfront] & observer [the Earth or the Hubble Space Telescope].[9]
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.”[10]
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).”[11] 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’s ring”!
iii. Light never scattering, space run across appearing
always transparent and smooth.
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 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 best understood from the standpoint
of quantum physics. Prof. Steven Weinberg explains 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 take 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.”[12]
There is, then, a precise
relationship between the energy of the single photon and the energy of the wave
in which it is traveling. Indeed,
Einstein, applying the quantum theory, has formulated the correct explanation,
according to which, “the energy of any photon is inversely proportional to the
wavelenght”.[13] 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 relatively recent 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.” [14]
So, no “wiggly path” 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. A path that does not
“wiggle”, is generally considered a straight one. The accepted postulate on light dictates that
light travels in a straight line in a vacuum.
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 a tridimensional vacuum, i.e. in
an Euclidean space?
The result of the experiment commented by dr. Evans makes it clear that space should be considered
“smooth”, an adjective which implies, in my opinion, the notion of a “flat”,
Euclidean space . On the other hand, as
underlined by professor Weinberg, if
space is full of matter, whatever its status, all this matter must be
sufficiently “transparent” as to let light pass through undisturbed in its (rectilinear)
motion. Therefore: whether full of matter or empty, space shouldn’t
be always considered “smooth”, i.e. Euclidean, as demonstrated by the continuous,
rectilinear proceeding of light from regions as far away as billions of years
and light years?
Space that to us appears
empty is in itself smooth and
the matter it contains must be transparent to light traveling in it, no matter how great the distances run across. This image of space seemingly applies to the
whole cosmic space. But how do we relate
it to the notion of a space warped by the masses of the stars, the space that deflects light?
4. Interstellar space not shaped by masses. 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.”[15]
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 “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”.[16] 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.”[17]
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.[18] 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.[19]
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.[20] 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”.[21]
5. A massive, empty interstellar space between any two
stars? Therefore, can we admit, at this point, that between the thin plasmosphere of the masses of these two stars there is a massive interstellar gap of about 38,000 billion km, a space totally
deprived of any stellar mass?
Proxima
Centauri is the nearest star to the
Sun, but in the vast space between the two there is no mass whatsoever to “warp” it 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. 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”?
At this point of our
analysis, we can perhaps provisionally conclude: 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. Indeed,
such a conclusion seems to maintain the ambivalent vision of space lamented by prof. Rovelli. But does it, really?
Paolo Pasqualucci
15 December
2021
[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:
Stuart Clark, The Universe, in: The Big Questions, series edited
by Simon Blackburn, Quercus, 2010, p. 91.
For more recent popular science sources:
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/;
Natalie Wolchover, What Shape Is the Universe? A New Study Suggests We’ve
Got It All Wrong, Nov 4, 2019 (www.quantamgazine.org/print); 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.); Ethan Siegel, Ask Ethan: Why Is The Universe Flat?, Mar 5 2021
(www.forbes.com/sites/startswithabang.)
[4]
Carlo Rovelli, Sette brevi lezioni di fisica [Seven short lectures on
physics], Adelphi, Milano, 2014, pp. 46-47.
My translation from the Italian original.
[5] Oxford
Dictionary of Astronomy, OxfordUP, 2nd revised edition, 2012,
entry: Eddington, Arthur Stanley.
[6]
For all these data, see: Relativity
and the 1919 eclipse, in the European’s Spacial Agency’s blog
(www.esa.int).
[7]
Eddington, Space, Time & Gravitation, p. 112.
[8]
See: Hyades (star cluster),
en.wikipedia.org.
[9]
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.
[10] A
Gallery of Einstein’s Rings, p. 2 of 6.
Emphasis added.
[11]
Article by Chelsea Gohd, quoted above, p. 2 of 12.
[12] Steven
Weinberg, The First Three Minutes. A
Modern View of the Origin of the Universe, updated edition, 1993, pp.
53-54. Emphasis added.
[13]
Weinberg, ibidem, p. 61.
[14]
Dr. Mike Evans, What is Light?,
article in: ‘Sky at Night’, July 2013 # 98, pp. 66-69; p. 68. Emphasis added.
[15]
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.
[16]
Ester Antonucci, Dentro il Sole [Inside the Sun], il Mulino,
Bologna, 2014, p. 44. Emphasis added. My translation from the original. Most of my information on the Sun comes from
this excellent book for the
non-specialist.
[17] Oxford
Dictionary of Astronomy, entry: heliosphere.
[18]
Clark, The Universe, p. 14.
[19]
Https;//en.wikipedia.org/wiki/Proxima_Centauri, p. 1 of 20.
[20]
Antonucci, ibidem., p. 16.
[21]
En. wikipedia. org., ibidem, p. 2 of 20.
