The cosmological principle
and its underestimated importance
Contents
1. Wording of the cosmological principle. Is the Universe
oscillating?
The cosmological principle → cyclicality of nature
And what do
we see looking at distant galaxies? Global time and local
heterogeneities
of time
The
Universe is not infinite. And what about time in this context?
2. Models of the Universe
consistent with the cosmological
principle
3. Model with constant speeds (of the actual movement) and its
confrontation with models
adopted today.
4. The dimensions of the Universe. Space. The
speed of expansion, and
the invariant
speed of light.
Supplement: Constancy
or invariance?
1. Wording of the cosmological principle.
Is the Universe
oscillating?
Cosmological
principle is a postulate stating that the observed, general features of the Universe
are the same everywhere, that they are not dependent on the region of the
Universe where observer is located. This principle is based on the belief that
we do not occupy some special place. The first person in the days preceding
contemporary times, the one who changed the reference system in astronomical
research making the Sun the central object while deposing the Earth to the role
of a satellite, was Nicholas Copernicus (1473 – 1543). By his work he caused
the epochal upheaval in the way of thinking, created the basis for the
development of science released from theological imperatives and assertions not
supported by empirical data, and thanks to him nature came to be seen as an
objective being. Cosmological principle is the distinct expression of this
approach and for this reason it is often identified with Copernicus, although
in a more open and blunt way its meaning was expressed by Giordano Bruno, who,
as we all know, by the sentence of the Holy Inquisition was burned at stake in
1600. Well, true ideas are often dangerous to their proclaimers, not only those
who lived 400 years ago. And what about the false ones? They are dangerous to
all people. But they win elections. Long live democracy!
This
principle, issuing from the depth of human cognitive intuition, we accept a
priori, just as an axiom in mathematics (actually the only one in this work).
That intuition, unlike some hasty judgments, properly reflect the nature of
objective being, which as a matter of fact doesn’t always agree with
rationalism of cognitive activities.
On the basis of the cosmological principle
we will try in the subsequent articles to build the Universe, that is ascertain
its fundamental, immanent features. Is it or will it be all confirmed by
astronomical observation? Are all of these features consistent with today's
views? We will devote some attention to these questions as well.
So what characteristics of the Universe
should we expect based on the cosmological principle? First of all, we should
expect that in the whole Universe the structure of matter is the same with the
same chemical elements, the same features of radiation, the same physical
properties of matter, and the same basic characteristics of physical phenomena,
the same basic laws of nature. It's not just about objects very far away. The
Laws of Nature are identical in every inertial reference system. By the way,
what that reminds us of? Of course, it reminds us of the Einstein's principle
of relativity.
So we have
the spatial and temporal unity - if now, then always. Astronomical observation
confirms these expectations, and thus indirectly the consistency of empirical
facts with the cosmological principle. But that’s not everything.
In fact, hardly
anyone considers the content of this principle, for the majority its content is
dormant somewhere deep in the subconscious. Even the majority of academics, in
their daily struggles with the present, are not prone to reflection and
philosophical musings. Well, today we have mass science and mass culture.
That's good, because there is much more to be done, and this requires greater number
of personnel...
Today, not many people experience
reflection, spend time on philosophical reverie. The scientist simply observes,
examines, measures, counts (fighting like a lion for the position amongst
his/her peers...). A very well taught craftsmen is a dominant figure among the
people of science (craftsmanship is the focus of academic education), one for whom
the main thing is the method, not the idea. There is severe competition because
the practice of science ennobles. Naming here celebrity scientists is
unnecessary. Science is billeted in institutions funded by the state or by the
great scientific and industrial consortia. Formerly great artists and great
scholars were not supported, so they were free. Nowadays, to be intellectually
independent, one has to be retired (unless one invents something new, provided
that it is done under the mega-concept currently in force).
For most scientists the general homogeneity of the properties of matter,
it something beyond reflection, something ingrained as if determined (by the
very workshop, but at the same time the workshop itself suggests things which
are not necessarily consistent with what nature reveals or what one would like
to see in nature). For some of them the text stripped of mathematics, by the
very fact of this lack, is simply "unscientific." "Waffling is
for amateurs." Many of them (out of universal routine opinion, and not resulting
from the depth of reflection) recoil from speculative thinking and arguments.
This approach has become an all-encompassing trend. Who wants to read? The only
important is the last line.
However
the true science should avoid all trends and fashions. To avoid any
misunderstandings, I’ve been interested in astronomy since childhood, perhaps
that’s the reason I came to my own view of the Universe (obviously developed
through formal education). Today, "thanks" to the media, science has
become part of pop culture - for good and for bad, and those involved in it,
whether they want it or not, are its cogs. The world of finance decides
everything, even on grants, state subsidies for independent (...) research. Is
it wrong? After all, that’s the source of telescopes of the new generation and telescopes
on satellites, and LHC, and therefrom astrophysical trend - very photogenic for
the media; therefrom we also have research grants for big team projects... for
the development of new weapons. What the science of the Universe has to do with
it? Well, what about the Star Wars?
Ad rem...
The cosmological principle → cyclicality of nature
Spatial and temporal unity…
Hence the possible assumption of the genetic
affinity of everything the Universe is composed of, despite the remoteness of
most of these objects. Awareness of this supposition leads to the necessity
of considering two options. According to the first of them the
characteristics of bodies, substances, and radiations are determined and
eternal. However, would any phenomena take place in such a situation? Would
there be any interactions, any radiation? Would there be any differentiation of
matter in its substance and concentration? In this case the problem is rather
closed to further investigations, since even time, which manifest itself to us by
the existence of curiosity, would not have any
raison d'être (to say nothing of the subject). According to the second
one,
there is a global evolutionary process, variability, which actually indicates the
existence of time. This substantiates the empirical research, observation, and
confirms the genetic affinity of the physical characteristics of the matter the
Universe is made of.
On this occasion it is worth
noting that the affinity of the physical characteristics of
matter, despite the remoteness of objects, suggests that once upon a time we
were all together, and that the time flows equally for all. The development
that preserves the identical characteristics of dispersed matter (despite the
dispersion) requires some original adjustment, maybe even self-adjustment. The
whole matter should have common history. Hence the conclusion that the pace of
development is everywhere the same (which does not mean that it cannot
change while remaining the same everywhere). Once, long ago, we were all
together and as such we were something very small in comparison with what we
see today.
[Someone could say that it's not about self-arrangement,
but about creation of Everything by a transcendental object, period. And how this
It-She-He was created? And for what purpose? Did, at that instant, It-She-He
brought time to existance? At what point of no-time time came into being? ... And
did all that happened only so that some excrescence could keep on multiplying,
some excrescence which animal qualities are in perpetual struggle (and usually
win) against the essence of intellectual reflection, selfless curiosity of the
world perceived with benevolence, empathy and tolerance? And here we got ourselves
completely off the subject.]
Thus a long time ago, we were (as material existence) something
relatively small. And nowadays? Distances are huge. So there is expansion. Of
course, this is not the conclusion. This is one of the options. General shrinking
also requires time, variability, and if it takes place, then it must have been preceded
by expansion (due to the common characteristics and the necessity of
arrangement). In this situation the idea of cyclical nature simply imposes
itself. So thought the ancients.
But that's just first fitting. By the way, so little we needed to come
to these "findings". It was enough to adopt the cosmological principle
and undertake the most elementary observations (eg spectra). Also, assuming our
existence as a fact...
And what we see looking at
the distant galaxy? Global time and local
heterogeneities of time.
... Contrary to appearances, this is not
so obvious (That we exist?). Looking toward the distant objects we see the Universe
from other times. Is what we see out there in that remote space identical with
what we know from our surroundings? Rather not. Prominent examples of this are
quasars, existing only very far away (in a very distant past). This proves the
existence of the evolution, of changeability. Therefore the so-called strong
cosmological principle, according to which the Universe, not only everywhere,
but also always was and will be the same, does’t hold true. The Universe is not
static. This Everything is evidently changing. In fact, the discovery of
quasars and of galaxies’ evolutionary hierarchy, together with the
corresponding hierarchy of distances (quasars, active galaxies, galaxies around
us), made the observational basis for the overthrowing of the
"strong" ("generalized", "second") cosmological
principle. This (the overthrow) has been ultimately confirmed by the discovery
of CMB.
Does
this changeability contradict the Copernican principle? The fact is that far
away objects look different than the ones located at a closer distance. The
answer is no, since we find the same regardless of the viewing direction (and
the position of the observer). The Universe should be characterized by isotropy
and even homogeneity in an appropriately large scale. I think (of course not
only me) that variability, evolutionary character, does not violate the Copernican
principle. One can draw the conclusion that there is a global self-adjustment
concerning the whole Universe. As if it was a living organism. The fact that
further objects represent the past is a matter of observation from a particular
position. Right now the observers from an object that we see as a quasar, see
us as a quasar. However, all objects at a given moment of the global cosmic
time are timewise at the same distance from the Beginning. It is a pity that we
cannot observe the Universe from outside, so as to confirm this with our own
eyes.
Does the existence of time means that there was the beginning? We won’t
answer this question immediately. All observers, regardless of where they are
located, state exactly the same, among other things, that their neighbours are
lagging behind. So what is this global time? It’s the time of the observer
- the one at the head of the timeframe. Thus the adoption of the
cosmological principle leads to the conclusion that there exist the
cosmological global time. Not to be confused with the Newtonian absolute
time.
In this context the disturbing, and
maybe for this reason marginalized question (...) is the still unresolved problem
of heterogeneity of time. This is rather not thought about so there are no
chances for any solutions. Local inhomogeneities of the spatial distribution of
matter don’t pose a problem in an appropriately large scale. Even great
homogeneity disorders do not undermine the cosmological principle, because they
don’t contravine the essence of the uniformity of laws and properties of matter
in any scale. The serious problem is posed by (deemed to exist) inheterogeneities
in the pace of the passage of time, even though they have only local impact.
[Or maybe that's why?]. This problem is unthinkingly downplayed. Yet because of
this inheterogeneity, the global evolution is disturbed. The various local segments
are delayed with respect to the whole. If the evolution of the Universe is
cyclical – there are plenty of indications pointing this way - not only the
argument above, then at the time of inversion from expansion to contraction (if
we already accept the possibility of oscillation of the Universe), some segments
already begin to shrink, while some continue to expand. I may add, in fact I
can already reveal that the characteristics of matter in the phase of contraction
should be different (antimatter). At the time of inversion (stretched over time
as a result of local inheterogeneities of time) the cosmological principle
would be violated. And a mix of progressive antimatter with backward matter – well,
better to run away.
The
issue of inheterogeneity of time has been swept under the carpet. Validly? I
think so. Well, the reason for this inheterogeneity - in accordance with the doctrine
applicable today – is the gravitational time dilation, the bigger, the stronger
is the local gravitational field. If the cosmological principle is correct, then
this doctrine is incorrect. Personally, I am for reconsidering its validity.
The atomic clocks will not resolve the issue, because gravitational field affects
their pace of motion, but doesn’t affect the passage of time, just as it
increases the length of waves of electromagnetic radiation and, possibly, deviation
of its flow. I have also raised this question in another place. In the end,
according to my belief, the problem (under the carpet) will live to see its
non-existence. For now, in fear of it, it is sitting as quiet as a mouse.
[Kinematic time dilation in the cosmological dimension is an effect linking all
objects without exception, and as we shall see later, closely related to
distance. There is therefore no question (in this case) of infringement of the cosmological
principle.]
The Universe is
not infinite!
And what about
the time in this context?
It is extremely
important for the flow of our thoughts that we are able to see what happened even
billions of years ago (when we observe very distant objects). This does not
affect our insight into what we today affirm as the general and unchanging features
of the Universe. In addition, the same fundamentals (the same physics and the
same chemistry) despite such mutual remoteness of objects under observation,
and despite the inheterogeneity that we have already stated, could indicate
that the Universe (the one open to observations) is an integrated WHOLE, and that
is a sign that by its size the Universe is limited. It is not infinitely large. Even earlier we
were able to note that once upon a time, long ago, we were all together and we
were a very small something (in relation to the full selfadjustmrent of features).
In addition, spatial infinity would actually exclude any evolution (certainly
on a global scale, and probably also in local scales). In the case of the
possible existence of local changes, there would be no adjustment of features
of the whole, because how, when it comes to infinity. So there would be no time
relationship between (observable) objects. Yet the observations show that it
exists even in relation to the outermost objects. After all, looking in all
directions, we see the same gradation of evolutionary change. In addition, we
even see the pre-quasar Universe - a unified, faint glow, most likely created
by the primary stars which began to be formed after two hundred million years
since the beginning. One may say that we could see the Universe from the very
beginning, and we don’t only because of technical reasons. Today, it is
believed otherwise. But let’s not get ahead of ourselves.
And what about time? That there is, we have no doubt. And
when did it come into being? Contrary to appearances, there is no consensus on
this issue. And if evolution takes place, it is possible that it will never
end, that it was always taking place in unlimited past? Or maybe it had its begining
(with the comencement of evolution)? So what was its primary state? According
to the quite general opinion, at some point time came into existance (together
with space). Is this logical? What was before the beginning? ... Is this a
completely naive question? Also this: Now, after its triumphant beginning will
the time flow forever? Surely, these questions cause confusion. Sure of everything
are only those who do not think. So as to get free of these (and many others) questions,
it’s worth considering the option of cyclicality of nature, of the cyclical
evolution of the Universe. So we return to the idea, which has already
appeared. Does the Universe really pulsate, oscillate? That would somehow
reconcile evolution with the infinite. As you can see, a lot of questions
before us. Many cosmologists search for rationale of this, after all,
intuitive priority of cyclicality. But we need to get a foothold. Here we have it
all neatly set out. This theme will be often returning. Interestingly, the
ancient philosophies of the East accepted the cyclicality as the basic feature
of Nature. [Today, the priority of cyclicality seems to have lost its
importance. Thanks to dark energy and cosmological constant, which is a relic
of the early twentieth century (then the Universe was seen as infinite and
static), the Universe as it is perceived nowadays by most astronomers, expands
from zero to infinity.] But the priority of cyclicality comes back, and by the
same token we won’t do without the (horizontal) disaster.
As you can see, a lot of conclusions we have
(aleady) drawn from just one premise. And if in spite of all the cosmological principle
is not correct? In that case the conclusions based on it will lead us to contradict
the results of observation. So let us recognize, at least tentatively, the (Copernican)
cosmological principle as a base for further reflections (besides, we do not
have any other base), the more so that for the time being we have not came to
such contradictions. I would add that in our deliberations we have actually started
from zero (so as not to be governed by anything other than the facts of
observation). No theories and no private views of coryphaeuses. Will I live up
to it?
2.
Models of the Universe consistent with the cosmological principle
I
ignore the current models based on the concepts I reject utterly, in particular
the LCDM (Lambda Cold Dark Matter) model, perhaps the most accepted today,
though tempting quite a few Ockham’s razors. Nor is it about models defined as sets
of mathematical equations. I am skipping also any models based on GTR. I prefer
in the spirit of naivety to start from scratch; as I already mentioned, base my
thoughts on the cosmological principle, and not on today's "findings"
of science, about which, concerning this issue, I (and not just me) have
quite well-founded doubts.
First of all, as I noted above, we must
consider the possibility and even the necessity of the existence of the
universal cosmological time, formerly named sometimes the global time, which
measurement is possible only from our position and as our time. For us all the distant
objects are younger, their clocks indicate to US an earlier hour. The cosmological
principle says that any observer states the same thing as we do. He states,
according to what I mentioned above, also that far removed (from him) objects
are fundamentally different from those of his environment. Therefore, the residents
of quasars do not think that their galaxy is a quasar, or protogalaxy. They
think about us, what we think about them. The cosmological principle
categorically exclude any possibility of a violation of this symmetry.
Coincidently
this may (or rather should) mean that all
objects throughout the Universe share a common origin, a common history, and if
they were once formed, their formation was initiated at the same moment (and
of course in a common site), and the
pace of development is identical. A similar idea I have already expressed
above (also in bold) when I stated the existence of genetic affinity of Everything).
It is
interesting that such a far reaching conclusion can be reached on the basis of
adopting (a priori) the cosmological principle. Suffice to be a bit consistent.
In fact, its adoption necessitates acceptance of the thesis that the history of
the Universe is common to everything it is made of, that there is a link
between all of its elements. Makes one wonder, doesn’t it?
Let's try
now, on the basis of the cosmological principle, to draw conclusions concerning
the dynamics of objects of cosmological importance. What is their movement? In
the discussion below, by way of elimination, we will choose options (or
alternatives) which are the most internally consistent, the most consistent
with what we already know (or even have known for a long time). What’s essential
is that all of the options presented here, comply with the cosmological
principle. Of decisive importance for any conjectures will be, of course, the
results of observations. Here are the consecutive steps in the deliberation
process, including tentative proposals for specific models. Through consideration
and by the process of elimination we’ll come to conclusion that will provide
the basis for further investigations on the construction of the Universe.
1. All objects are moving at the same speed
(Which is? Good question.) regardless of the distance between objects. It is
not, of course, about the "internal" speeds of objects in the local
systems, but speeds at cosmological scale, say 100 million light-years at least.
This ensures that our place is not unique. According to this model, the Universe
is static and infinite. But concerning the
existence of those other, local speeds – which are proved by observation – don’t
they contradict a little the one and general? What about the relativity of
motion? And an additional question - "What is this common speed?" - is
not meaningless, yet the answer to it does not seem possible.
2. Speeds are varied, with the proviso that they are
not defined by a particular spatial arrangement, which means that in every
viewing direction the average speed in the set of objects is the same. However, we immediately ask: What is the average
speed? The answer can be either zero or the speed of light, as any other speed
("which is? Why this and not another of the infinite set of speeds?")
is undoubtedly very questionable. Let’s note that the second possibility of the
two just mentioned must be eliminated because the speed of light is reserved
only for photons, the more so it cannot be the average speed of speeds lower
than c.
So maybe the average
speed is equal to zero? Is it feasible? What comes from observations?
Astronomical observations confirm the existence of relative movements of
galaxies (in any case the movements of galaxies relative to us). But the distances
between galaxies change on the basis of movements in the local group of
galaxies, which doesn’t mean that one can unequivocally ascertain the existence
of certain trend of the cosmological importance. For example, the famous
Andromeda galaxy (M 31) approaches us at a speed of about 300 km/s. It turns
out, however, that judging from the observations most of the galaxies drift
away. So it is hard to expect zeroing of the average speed of a large number of
galaxies. And if, regardless, we would opt for a model with an average speed equal
to zero, the matter would have been closed. Further exploration would not make
sense. Yet “the basic stability "of the model of the Universe is a little
at odds with our, indeed, very variable existence, with the existence of
evolution in nature, with aging and (more scientifically) with gradual increase
of entropy. It is also at odds with the finding (above), that the Universe is
changing. On the one hand, nature exhibits, everywhere and in all
scales, the same general features, while on the other hand, these features are
characterized by changeability. Nature develops, evolves. Changeability is its
peculiar feature. This comes from observations, also of ourselves. So the option
of zero speed sholud be therefore rejected.
Let’s clarify the thing further. If we don’t
concern ourselves with the own motions of galaxies (in any directions), with
speeds relatively small (which apply to local systems), and will focus on the
movements of cosmological significance, then our attention will be directed
exclusively to the study of radial movements. Put it simply, in case of huge
distances, the particular (tangential) movements are impossible to detect, and it is hard to expect
the discovery of some regularity in terms of distance. Besides, its existence would
rather violate the cosmological principle, like for example, most of the
galaxies would be moving to the right. In this context, it is possible that in
isolated cases such (individual) movements can be detected, but they cannot be
of cosmological significance, so they can’t serve as a basis for conclusions
pertaining to the general characteristics of the Universe. Besides, with
respect to radial speeds, we have the tool for objective measurement: examination
of spectra, in conjunction with the Doppler effect.
3A. It can
be assumed that the cosmological principle is not violated by a specific
distribution (determined by the distance) of various radial speeds of observed
objects, in relation to a particular observer (located anywhere), provided that
the dependance of these speeds on distance
can be mathematically defined. If in the eyes of each observer such a distribution
is defined in the same way, it is consistent with the cosmological principle. For example, it
can be that in a certain viewing direction half the galaxies are coming closer
a half drift away (which corresponds to the second model). If so, then the
average radial speed is equal to zero, because each approaching galaxy corresponds
to a galaxy receding at the same speed. And what would be the relationship, the
dependency of the (drifting away - approaching) speed on distance? Let think
further. Is such a model acceptable? I think so. What we have left is to check
radial speeds of galaxies. But before we check let us continue our
"theorizing". It's nice when a prediction, even if based on
speculation (and the knowledge of the fundamental laws of nature), is confirmed
by empirical studies. But I already managed to blurt out something. I said above
that, as it turns out, the vast majority of galaxies move away. If so, then the
model just described (underlined portion) is rather unrealistic.
3B. Let's go back
to the first sentence of the previous paragraph – passage written in bold: “..the dependance
of these speeds on distance can be mathematically defined.” In the
simplest case [These simplest cases in the description of nature should be
preferred. As an example we can mention the Fermat's principle.] speeds are
constant for a given pair of objects and proportional to their mutual distance.
[Further on we will accept that the v/c ratio
– the speed of an object to the speed of light – is constant.] The further away
from us is a given galaxy, the greater is its speed in relation to ourselves.
Reverse tendency is not realistic because it would create a situation where the
closest neighbors should be moving at a speed close to the speed of light (if
not the speed of light) which is absurd. There are, however, two speed modes:
towards us or away from us. The answer can be provided by astronomical
observation. Already this possibility (recourse to observation) is an advantage
of this variant. Thus, the relative (radial) speeds in relation to a specific
pair are constant and proportional to the mutual distance. For an observer on
Earth a galaxy twice as distant moves twice as fast. Below I present the proof
that this model is consistent with the cosmological principle. According to
this model, the Universe is either expanding or contracting. This model is no
longer a static model. The Universe developes in a certain direction, evolves,
not only on a local scale but as a whole.
The mere existence of a universal movement, including
the relationship between the speed of objects and their mutual distances, would
suggest, either: 1. The existence of absolute beginning (once in the past) or:
2. Continuous drive from an infinitely distant past to the final end, when
everything shrinks to a point, or else: 3. The ciclicity of changes. This
periodicity arose in earlier thoughts (described in the first chapter), based
on other premisses. Also the quantitative limitations, which I pointed out
earlier, suggest just that. What’s the best of the three options above? Please choose,
in any case, cyclicality seems to be a noteworthy trail.
One may add
to it that despite the postulated here proportionality of the the
distance-speed relation, this speed doesn’t even come close to the speed c),
which is the unachievable upper bound of relative speed of material objects. So
here is yet another sign that the
Universe is limited in size, and that gives the chance for cyclicality,
perhaps even oscillation (it’s hard to talk about oscillations of a creation
infinitely large). Yes, but how to reconcile this periodicity with the
proportionality of speed to distance? Enriched by new findings we will come
back to this issue in other articles.
Thus it can be expected that all
models built on the principle of proportionality comply with the cosmological
principle. But are they all physically viable? Take the simplest model, the one
with variable speed, in which acceleration is proportional to distance. Is it
physically possible? This question buffles and arouses doubt, because the
source of the acceleration is the force, which is a vector. This is in conflict
with the assumed isotropy of the Universe. Besides, according to the
cosmological principle, in accordance with the assumption of homogeneity, forces
coming from objects located on opposite sides (anywhere) should compensate each other. The resultant force
acting on each object should be therefore equal to zero. This would lead to the
conclusion that the intensity of
cosmological gravitational field is everywhere equal to zero. It's quite a
weighty argument in favour of the proposition that the cosmological relative speed
(of two specified objects) is constant. Even a pupil of an elementary school would
say that this is consistent with the first law of motion.
In such a case we would have an inertial
motion. Are we going that far??So in these circumstances would we be also
dealing with „the naive cosmology”? So as to make it less naive let
say that it would be actually about the constant ratio of the speed of an
object to the speed of light, bearing in mind that the radial speed is
determined by observation based on the Doppler effect (as it concerns the speed
of an radiating object relative to the speed of light). Whichever way you look
at it, it's something new. And it doesn’t really agree with the view prevailing
today, based on altogether different assumptions.. Moreover, the invariant
speed (c) does not have to be constant... We will come back to this question.
However, you can approach the matter
differently. Cosmological principle is invariant with respect to time. This
means that the acceleration (or deceleration) can take place, since at a given
moment the Universe seen from wherever remains the same. This can serve as a
guidepost in accepting the possibility of global acceleration (or delay) as viable.
And what about forces? Now, if we assume that space expands (or contracts),
there is no possibility of motion in the Newtonian sense. Therefore,
"everything’s all right." And if in spite of everything it is about
the actual movement of diverging (or converging) galaxies, rather than swelling
balloon of curved space? Then it is rather difficult to talk about acceleration
(or deceleration), if only in relation to the reasoning presented above. In
this situation, the science of the Universe would have to build from scratch. And
that’s how it will probably turn out... [I
am not reffering here to today's efforts - on the one hand GTR with the
Friedmann equation (attraction), and on the other some dark energy driven by
the cosmological constant, which is to draw in the opposite direction. And so
that there would be no forces, the matter is resolved by expanding space-time.
Four-dimensional balloon, and we on its riemannesque curved surface. Riemannesque?
Not necessarily. Maybe that’s better.]
3. Model with constant speeds (of the actual movement)
and its
confrontation
with models adopted today
Let us
therefore hold to the model with constant relative speeds (with respect to c). We
will illustrate it below. This is actually the simplest model. We expect that Nature
prefers just these kinds of models. Yet so far it hasn’t been seriously taken
into consideration (which makes you wonder). Although constant speed as such
was considered, but in a model that was regarded as simplified, more for amateurs
than professionals, used here there to illustrate the cosmological principle,
which in itself no longer constituted the essential element, and all the more
the basis for research (as it does in my explorations). The reason for this
approach is of a historic character rather than based on substance. Even before
Hubble discovered his law (1929), the general theory of relativity came into
being (1915). At once, practically everyone with an interest in this field of
research, heedlessly rushed to this new theory, as if it was a hen that lays golden
eggs, which was fully justified in view of its tremendous heuristic potential. Within
the next several years models of the Universe based on the new theory which
was, after all, elaborated by a genius, multiplied dime a dozen. The road to
other (potential) concepts was therefore closed. Einstein himself, captivated
by the influx of enthusiasts, seized by this flow of research, rather quickly
lost sight of what originally propelled his explorations: the quest for
unification of gravity with electromagnetism. Good motivation for this research
was provided by the Kaluza-Klein theory. But he never freed himself from the cosmological
stigma of his inquiries.
Coming back to the point we can say that
cosmology was embraced by the general theory of relativity, making space an autonomous
being. Here I’d like to emphasize that it happened before the discovery of
regularity called Hubble's law (which greatly surprised the scientific world),
before (due to Hubble’s discovery) the obvious model of the Universe infinite
and static was laid at rest. Was it really burried? After all, contrary to
Einstein’s decision, the cosmological constant returned as an important element
in the modeling of the Universe. I modestly suppose that Einstein was right, if
only because the Universe is not static and infinite. In addition, there came the
dark energy which in another essay I will send to oblivion. Sorry the esteemed Noble
Committee. You can visit the aforementioned essay in which I introduced the
concept of horizontal disaster. It is significant that even today, the general
theory of relativity is a source of remarkable ideas. This shows in her favor. And
yet.... Today’s cosmology based on the general theory of relativity, in spite
of appearances and its quite developed dogmatics, is facing a lot of trouble.
Not to everyone’s awareness. The confidence of epigones and numerous feisty
forum users on the Web will not be of much help, neither the exuberant math. In
addition, the attempts to connect GTR with quantum mechanics, remain so far in
the realm of wishful thinking (with strings also something doesn’t fit – those endless
tuning troubles...). The dark energy won’t help either, nor the
"theory" of inflation. Well, the inflation of theory. And razor? It
simply becomes blunt. Even Ockham starts to worry.
A reasonable thing is, therefore, to do what
- due to the enthusiasm for the new idea - was not done then, a hundred years
ago. Do what may today represent an alternative
to today's modeling. This may include the "naive" model, which I am
trying to present in my works, the model with constant speeds (of actual
movement). From it virtually everything begins. But first of all we must prove
that this model is consistent with the cosmological principle. Below I present the
reasoning which is not my invention. You can find it in many textbook of astronomy.
Imagine
four galaxies: A, B, C, D, equidistant from
each other, making one straight line. We inhabit galaxy B. If the
movement of these
galaxies is of a cosmological character (they follow a defined,
common to all, general trend), then all are either
moving away or approaching. Let’s assume that they are drifting away, and
moreover, that they are all moving at a constant speed. Galaxy C moves away
from us at a speed v. [We are not
considering here the v/c ratio because c
is treated as a constant. Any change of this value would be global and would be
time-dependent. We, however, examine the thing at a given moment.] With
the same speed galaxy D moves away
from galaxy C (on the basis of the
assumed proportionality of speed and distance). It follows that galaxy D moves away from us at a speed 2v. Galaxy A is moving away from us in the opposite direction, also at the
speed v. That’s how we see it. And
what would say an inhabitant of the galaxy C?
That we move away from it at a speed v,
just as Galaxy D in the opposite
direction, and galaxy A at a speed 2v. According to the inhabitants of
galaxy A, galaxy D drifts away at the speed 3v. The same state residents of galaxy D with respect to the galaxy A. Thus, regardless of the galaxy where
the observer is located, the distribution of speeds of adjacent galaxies is
identical. So it all complies with the cosmological principle.
This model the based on constancy of speed,
but there is also the possibility of constructing other models also meeting the
cosmological principle. Here, however, we prefer the simplest. Nature also
prefers the simplest models. And besides, the compatibility of other possible
models with the cosmological principle does not in itself ensure their physical
reality. We have already arrived at this conclusion when we were considering
the accelerated movement (assuming that it is a real movement, not the swelling
space). So we can conclude that relative speeds of (distant) galaxies are
constant over time (v/c = const) – in relation to specified pairs of objects,
and proportionate to their mutual distance. Based on this finding, we will
(arrogantly) attempt to describe the Universe. Let’s treat this statement as an
anticipation awaiting observational confirmation.
Today it
is widely believed that the solution to the problem is to assume that any
expansion (or contraction) is not related to the actual motion, but is the
result of changes in the metric of space. Is that right? We’ll come back to
this question more than once. But let's say that this makes the acceleration option
feasible (this is possible according to the doctrine of expanding space, which
is a departure from the Newtonian model). According the cosmological principle the
acceleration itself would be proportional to the distance. In this situation
the following questions immediately come to mind: What is the cause of
acceleration? Is it about the "outward" acceleration? Despite the
fact that gravity acts in the opposite direction, and although general theory
of relativity describes only the attractive force of gravity (if you do not
count the so-called cosmological constant, introduced and then rejected by
Einstein as "the greatest mistake of my life")?
Is the
acceleration at the given moment of observation increasing with distance? If
outward, then the acceleration of quasars should be very high despite the fact
that their speed in relation to ourselves is huge, close to the unattainable
speed of light... Yet there (when the Universe was small) gravity was the
strongest and most powerfully slowed down expansion. "Acceleration rather
decreases"... And if the opposite takes place - decreases with distance,
then the galaxies closest to us are moving away (or approach us) with the
greatest acceleration. What? This, as a matter of fact, is not observed. Acceleration
decreasing with distance is therefore also hard to accept, just as its increase.
Looking at it with Friedmann’s eyes we may think
that it is not so much about acceleration, but rather about delay, delay
diminishing with distance (due to gravity becoming weaker with continuing expansion).
This would determine the
dynamics of the Universe. The horyzont and flatness problems, appearing on this ocasion, are
resolved by inflation”*. But really?
In this situation,
more or less, the astronomers made an observational discovery: light of distant
supernovae was weaker than expected. Again, the facts surprised the
world of science (it's very telling in view of the belief that here it is, and
we will be able to understand everything...). And when there is a surprise,
every idea, especially "one from our crowd" weakens the incentive to
search on the basis of what is already known. And so the dark energy came into
being, and right away got associated with the cosmological constant. The whole
world already knows (...) about the existence of dark energy, the more so that
its main spokesmen and researchers have been already honored with the Nobel
Prize (Adam Riess, Brian Schmidt, Saul Perlmutter - 2011). In cosmology in
recent times, due to this fact, there was a lot of excitement. The most popular
today is the already mentioned LCDM cosmological model (LCDM - Lambda Cold Dark
Matter). Lambda Λ is the cosmological constant, which
Einstein renounced, and today it is a star of the first magnitude. Everything
is based on a single standard pattern (GTR + Λ),
as if somewhere there was the Holy Grail (or Santa Claus). This model immediately
gained in importance. In the context of our current considerations acceptance
of the existence of dark energy, however, seams groundless. After all, we are
building everything from scratch. And the "dark energy"? No one has
seen it. And what about observational evidence? There is, as you will see,
better interpretation. So what to do with the cosmological constant? It is not
my problem. Ask Einstein.
Supposedly in the past this dark energy,
due to a stronger universal gravitation (the Universe was smaller), was
accelerating the expansion at a lower pace, and even until approx. seven
billion years after the Big Bang, gravity still continued to slow down of
expansion. So looking at very distant galaxies, which means very young, we
should even expect the delay of expansion THERE, that is brightening of
supernovae. And in our world? We should find that that acceleration caused by
dark energy should be the greatest, because now, as a result of the expansion
of space, gravity is weaker than before (and for this reason to a lesser extent
it compensates the dark energy). Therefore the light of supernovae in the
nearest galaxies should be much more subdued (it is this observation that
lead to the invention of dark energy) than it actually is, making them
the model of brightness... This is simply absurd. It is worth considering. In
the essay entitled „Horizontal Catastrophy” I will bring dark energy to
non-existence, indicating the possibility of completely different explanation
of observational evidence, allegedly testifying to accelerating expansion.
Certainly we'll follow a different (than the publicized) track. But let’s go back
to our current investigation.
For the sake of completeness: …unless the
Universe collapses... Theoretically, this option is also possible. Anticipating
the rush of opinions that could arize in connection with this possibility I’d
like to repeat something well known to
the general public. The observations indicate that the Universe (currently)
expands. So in this contex the collapse option must be rejected.
[As we shall see later, it's not
all that obvious (and still one more criterion is needed), since also during
contraction spectra will shift toward the red (?). Some patience, please, the
restless are put to the test, but it can’t be helped. Let them know that quite
a lot of no less painful (psychosomatically) experiences await them. For those
more prescient this will be the last article they’ll read on ths subject.]
So how is
the Universe expanding? Does it according to the model described above
(galaxies A, B, C, D), that is at speeds proportional to the distance? But maybe
the whole process keeps on acceletating? For now, however, this possibility as
well as the possibility of an accelerated contraction, we’ll put aside, the
more so since it is less attractive because of the arguments presented above.
Perhaps this simpler model, in which the relative speed of the two specified
objects is constant, will agree with observational data. If not, there will be
still other things to discuss, we will also have the base for doing it, among
other things, by being aware of the discarded concept.
4. The dimenssions of the Universe
And
now, dear readers, please pay attention. For very high speed, relativistic with
respect to the most remote objects, the distance separating them from us keeps
on increasing (from object to object) otherwise, slower, in a manner
synchronized with increasing speed, proportionally, as it is postulated by the
cosmological principle. The point is that due to the upper limit of possible
speed which can’t exceed the speed of light c, also the distance has its upper limit.
This means that the dimensions of the Universe are also limited. Earlier we
have come to this conclusion based more on philosophical premises. This reinforces
our thesis. The Universe cannot be infinite
in its dimensions! Note the existence of convergence between development,
evolution, clearly targeted movement and the finitude, the spatial limits of
the Universe. Surely this is not an accident.
Can we, on the basis of these considerations,
determine the size of the Universe? Yes, we can, while bearing in mind the
assumed proportionality of (relative to us) radial speed of galaxies to their distance,
and the existence of the utmost limit of speed (c). This is, of course, possible
provided that the proportionality can be detected observationally. This proportionality can
be expressed in the following way: v/r = const. The dimension of the Universe
(R) would correspond to the speed of light (c). To calculate it, we would
need only... to determine the value of the proportionality coefficient (that const.)
We would have to refer to observations. It is a very important finding. You could say that
this concept is falsifiable.
But this is not the end. We should also
draw attention to the seemingly obvious consequence of this finding. On the
basis of mutual dispersion of objects of cosmological significance, we conclude
that the Universe as a whole is expanding; while the utmost speed of mutual distancing
of objects tends to c (since it cannot be greater). So we can (for now
tentatively) assume, that c is the speed of
expansion of the Universe. [Today, the pace of expansion is
defined quite differently, but that's not important. After all, we start from
zero with an another different concept.] These objects, which have been moving
at the highest speed (basically constant from the very beginning), are now at
the greatest distance and their speed (theoretically) tends to c. Thus, the
space of the Universe is flat (Euclidean) since it is determined by the actual
inertial, relative motion of objects, while its size is limited by the radius
of the Universe, increasing, of course, with the speed c; radius defined as the
greatest possible mutual distance of
physical objects (at a given moment).
So what defines
the space of the Universe? Is it the shape of its curvature, or simply
relative, inertial motion of objects? I tend to just such a view of things. And
what it is further on, beyond the material everythingness? Probably some undefinibility,
or (being consistent) we should simply conclude that other space outside the Universe
does not exist. The space expands with increasing distance. Let me even say
that the observable Universe is Everything, is the complete and only
Existance/Being. Am I overdoing (judging by the current conceptions)? I don’t
think so.
And where is
the centre of the Universe, that is the place of the Big Bang? There is no
problem with that, if the observable Universe is and has always been everything
in terms of both matter and space. All the points, all the current positions of
the bodies together constitute the point of explosion, because "once upon
a time we were all together."
Here we are
approaching the problem of the typology of the Universe. This subject will be
also explored. As a reward for patience.
Let us note on this occasion, just in
passing, that the speed c, is not only the speed of light. It is also, and
actually above all, the speed at which increases (if it increases rather than
decreases) the radius of the Universe, that is the maximum, outermost (for the
given moment) distance between physical objects. No matter which direction we
look - everywhere is the same. Here also the cosmological principle manifest
itself. Let’s note that if for any observer, regardless of his location and
movement relative to other local and non-local objects, theoretically the
farthest objects, regardless of the viewing direction, according to the cosmological
principle move at the same speed, then this speed does not depend on a
reference system, in other words, it is invariant. Right here lies the secret
of the invariance of the speed of light !!! The speed c is invariant
exactly because it is the speed at which the Universe expands, equal for all
observers.
One hundred years ago, without this cosmological premiss, but only on
the basis of electromagnetism, the postulates of the invariance of the speed of
light constituted a revolutionary heuristics making the essence of the special
theory of relativity. [Einstein might not even known about the the
Michelson-Morley experiment.] Today, after hundred years, the invariance of c
is the conclusion drawn from the cosmological principle (subject to application
of the concept proposed in this work). The very existence of the upper limit of
(relative) speed follows from the essence of electromagnetism. I pointed this
out in my booklet dedicated to teaching Special Theory of Relativity**. And
what has this cosmology to do with electromagnetism (in the context of the
speed of light)? Apparently this effect appeared (as a separate phenomenon)
exactly when the speed of expansion of the Universe got settled. It is
therefore a secondary thing. "The speed of light" is a relic of this
unique moment in the history of the Universe. In this context, it may be
justified to assume that the speed of electromagnetic wave can be locally
varied (even in vacuum), due to inhomogeneous distribution of matter on a grand
scale. Is that a reasonable assumption? The future will tell.
There will be still quite a
bit on these topics in other articles.
And one more thing. According to the Noether’s
theorem, invariance of the fundamental laws of motion is linked to the fulfillment
of certain rules of conservation. In particular, invariance concerning the
direction in space is associated with the principle of conservation of
angular momentum. The principle of conservation of angular momentum is
universal, as shown by experiments. Thus, there is the complete symmetry
with respect to the direction. What does this remind us of? Obviously, the
cosmological principle. As we can see, the cosmological principle is not only a
requirement of our cognitive intuition. It's simply the conclusion resulting
from the undoubtedly correct and universal findings concerning physical
phenomena, the findings based on experiments and confirmed in all phenomena
without exception. It says something.
Many
findings coinciding with the concept presented here could have been be reached
as early as in the sixteenth, seventeenth centuries. It is not an exaggeration.
It’s another thing that such a model certainly would not be preferred. Even in
the early twentieth century, science perceived actually only one possibility,
indicated here as the second (adopted without deeper reflection, particularly
in relation to the general dynamics of objects). The infinite, static Universe
was then a matter of course. Eintein used this as a basis when in his field
equations (GTR) he was introducing the cosmological constant (Λ), giving the possibility of repulsion, so as to neutralize the
general force of attraction constituting an immanent feature of gravity. [After
a short time, he pulled out of this thing, reffering to it as his biggest
mistake.] And yet, it was a glimpse of the brilliant intuition, considering
that he came to it (exactly) a century in advance.That’s how many years have
passed since his work on the general theory of relativity. Today, as I write
these words (consecutive reading), we have 2015. However, contrary to
appearances, his brilliant intuition has nothing to do with the alleged
existence of dark energy (the invention of epigons - with all due respect and
no offence). In my arrogance, I think that if in his studies he had gone in the
other direction, if he had not based his work on the relatively new (at the
time) mathematical ideas, on geometries, in particular Minkowski’s and Riem’s;
he might have come to the idea of the duality of gravity. A separate set
of articles deal with this subject. I suppose that somewhere in his
subconscious something was stirring, but then it was still too early). I guess
Einstein sensed this exactly possibility, though he had no basis for its
verbalization. At the time the knowledge of the Universe was not sufficient. It
wasn’t even known that beyond our galaxy there are billions of others. In
addition, the knowledge of the microworld was still in its infancy.
Although already in Galileo's time one
could go in this direction (cosmological principle), and Giordano Bruno fantasized
in the spirit of this principle (and badly finished), yet even in times of
Einstein it was definitely too early. It turns out that even today... In any
case, changing the habits of thought is a very slow process, simply
generational. Maybe that's why the discarded concept of the cosmological
constant "triumphantly" returned. Beggars can’t be choosers. When
there is no niche, then it has to be created.
By the way,
I might add from myself, that the recent return of the cosmological constant,
even before the "discovery" of dark energy, contrary to appearances, testifies
to the objective existence of a deep crisis of cosmology which in a totally
uncritical manner is based on the general theory of relativity that should be
today somewhat supplemented and maybe even modified. "Is it a slander of
holiness?" True science likes to slander.
I am convinced that Einstein would not go in the direction that he rejected
(and rightly so). And now, well, a drowning man will clutch at a straw? (in
this case Ockham's razor).
But let’s go back to the Universe. In
the final conclusion of this (as a matter of fact the first) article, on the
basis of the cosmological principle we can even commit the statement that the Universe
is a selfcoordinated over-object, and the pace of its development is determined
by the global time. The development of the Universe in its every element, even
in the smallest scale proceeds in the same was. On the basis of various
premises this assumption will be confirmed in the following articles.
We have come to far-reaching conclusions, and by and
large built the foundations of a coherent model of the universe. And yet we
needed so little. Everything now depends on the results of astronomical
observations. If they don’t confirm the validity of the model that we're going
to build (based on the proportionality of speed and distance, as deduced from
the cosmological principle), then either we should look for another solution,
in accordance with the cosmological principle or this principle is not correct.
This conclusion I would withold, however, till the very end.
*) These problems
will be discussed in anothe place. Their „solution” lies in the hypothesis of
inflation.
**)
„Elementary introduction to the special theory of relativity a bit (…) differently”
(Toruń 2010 – 2016); published in Pland in Polish language.
Supplement:
Constancy
or invariance?
In the just mentioned booklet I have written:
... Often, too often it is the “constancy” of the speed of light which is emphasized, and not its “invariance". The invariance is even replaced by constancy - not only in high school classes. Example: Wikipedia - "the speed of light is the same for all observers." I do not know whether according to Einstein, constancy meant also invariance. I am inclined to believe that the unfortunate use of the word "constant" at the very beginning (1905), resulted in the fact that now everyone, including scientists, wrongly equate these two concepts. For this reason, if one considers the possible variation in time of the speed of light, then such a person "infringes on (or even invalidates) the special theory of relativity." No, such a person does not refutes this theory if he/she recognizes the invariance of the speed of light. So it's not about carelessness. Constance and invariance are not the same. Looking at it cosmologically one can even consider the possibility of variation of c in time, though rather not in space, because the demand of compliance with the cosmological principle is no less important than the invariance of the speed of light – and that goes beyond STR. Today, constancy seems obvious. So it seems. (...)
There is no center of the universe
According to
today's views, the space that makes the Universe, is a "balloon" of Riemannian
space of positive curvature. The Universe of matter makes, kind of, the the
surface of the balloon. This concept precludes the existence of some special
point, there is no centre. But this is not the only possible way to get rid
of this unique point (to satisfy the cosmological principle). One can also reason otherwise. See above.
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