And what about the mass
of the Universe?
Contents
Introduction
– why mass?
1. Let
us estimate the mass of the Universe
2. (Schwarzschild’s)
radius of the Universe
3. The
mass of the Universe is gradually increasing
4. The mechanism causing the increase in the mass
of the
Universe
5. Reflections
and thoughts in the context of estimations about
the mass of the Universe, or: let’s speculate. The problem of
saturation
Á propos
Introduction
– why mass?
One of the conclusions drawn already at the beginning
of our cosmological considerations was that the observable Universe, limited by
the Hubble horizon, constitutes an absolute Everythingness. To this thesis we shall
return repeatedly. It leads to the conclusion that the Universe is quantitatively
limited, and even to the conclusion that its substance remains invariant,
despite the multitude of changes occurring in it. Apart from it, the adoption
of the concept of the Big Bang, most acceptable according to current knowledge,
entails the possibility, if not the necessity (not always realized) of accepting
just such an approach. After all, if something exploded, it cannot be quantitatively
unlimited. This is somehow disregarded. Because it obvious? I'm not sure.
Already the
confirmation of (quantitative) predictions concerning the CMB radiation (see
the preceding, that is the seventh article) testifies to the fact that the
observable Universe is everythingness, and its current size is determined by
the value of H factor and, of course,
by the value of invariant c. Due to
the fact that the Universe is quantitatively limited, determining its mass makes
some sense since it is possible. It wouldn’t make much sense if the Universe
was infinite, or its dimensions were unknown and its material content undefinable.
Then the density parameter (W) would be the only sensible parameter informing about the material
content of the Universe. Today, its mass is not discussed. What does this tell
us? I think it tell us that, on the one hand, based on the existing (still in
force) views, conclusive determination of full dimensions of the Universe has
not been possible [alleged diameter of 92 billion light years is the result of a
concept, not of a measurement, the concept that may prove to be a dud – which
is about the so-called moving coordinates, in relation to the autonomy of expanding
space]; on the other hand, intuitively, perhaps subconsciously, the Universe is
still perceived as infinite being (or something like that), despite nearly a
century of development of science and today's assertions on the existence of
evolution of the Universe and on its changeability. Can something infinite be
variable?
So at present the mass of the Universe is not
discussed. Its determination on the basis of observations would be a Sisyphean
task. Simply “not everything can be seen.” Apart, the extensiveness* of mass in
the face of research necessarily based on observation (without the possibility
of conducting experiment), is not a basis for generalizations, for obtaining an
overall picture. For this reason, and at this stage rightly, contemporary cosmology
uses the intensive* parameter of density. For the record, it is equal to the
ratio of the average density of the Universe to its critical density.
And yet, if we abandon GTR and Friedmann’s equation
(worth checking out this possibility, if there is one), then according to the
conclusion to which we have come in the previous articles, the use of the concept
of critical density is kind of an anachronism, because, as it turns out, it is
the sole existing density. In this situation the density parameter Ω = 1, and its
usefulness in cosmology decreases to zero – since according to the observations
the geometry of the Universe is flat. So what remains? Of course, the mass (what
else?), provided that it is really possible to determine the global material content
of the Universe. Can it be done? Judging by the discussion conducted so far,
this possibility cannot be excluded. So let’s test it out.
We will therefore take
up the problem of mass. In this way we will create the basis for reflections
and conclusions that go beyond the standard, falsifiable conclusions, and even
anticipating the effects consistent with observation. After all, this is not
the Great New Theory, but only checking of specific concepts which would not
come about if everything in today's cosmology and astrophysics was ok. But it is not. In relation to "the mass of the
Universe", the validity of following this different path I signaled
earlier, at it is confirmed by the results of the investigations presented
hereunder - maybe quite encouraging... (or) to be rejected categorically and
without justification... (?). On this occasion, I strongly urge you to read the
articles on the duality of gravity.
And one more
thing. Below I will present the reasoning, logical sequence of sentences. This,
however, is not a guarantee that all the conclusions are certainties. It is not
easy, especially here, to avoid the traps of logic. For this reason, the emerging
speculations and hypotheses should be verified. At this stage not everything is
closed. Thanks a lot to those who will see the options that I have not taken
into account, options that would make the matter even more consistent. And by
the way, let’s separate the essential things from the details that further on
will prove not to be the most important. What is important are the starting
point and the final conclusions, hopefully consistent with the results of our
research.
1.
Let us estimate the mass of the Universe
This is
not difficult to do in relation to observable objects. The mass of the Earth is
equal to 6·10^24 kg, the mass of the Sun is 333,000 times greater than the mass
of the Earth, that is equal to about 2·10^30kg. The mass of an average galaxy
is estimated at one hundred billion solar masses, and the total number of
galaxies is estimated of the same order of magnitude. Finally, the mass of
luminous objects of the Universe can be estimated at 2·10^52kg. The estimation
can be also performed in another way. The observational count of galaxies gives
their average density. It turns out that on average one galaxy occurs per 1Mps
(megaparsec)**. If we assume that the farthest glowing objects are at the
distance of 15 billion light years, and assuming that the Universe is a sphere
of this radius, and is homogeneous, we get its total mass to be equal to 8.2·10^52kg.
This result agrees well with the previous estimate (the same order of
magnitude). It can be even “explained” that is greater because it takes into
account the mass of matter which doesn’t yet shine with stars, the matter
too young for that, located somewhere near the horizon. "Oh, the naivety!
It's just a coincidence".
In our first estimate we took into account
only the glowing objects, manifesting their presence by emission of radiation,
in particular light. We should also take into account the mass of matter
deposited near the horizon (as mentioned above in italics), the matter too
young to be able to shine with the light of stars. According to credible research
the shining matter of first proto-galaxies appeared about a billion years***
after the Big Bang. This time amounted to
10% of today's age of the Universe. So it can be assumed that the mass of its imperceptible
part is quite a significant component of the total mass (approximately 10%).
Most likely, there is also matter that is
not shining - in galaxies and galaxy clusters, and perhaps also in the vast
intergalactic regions. Its mass exceeds even the mass of visible matter, up to
five times according to today's estimates. The existence of this dark matter can
be apparently demonstrated by observational data. Already in the thirties of
the last Century there were noted “excessively” fast movements (radial -
red-shift) of galaxies in clusters which they form (in Coma Berenices - Fritz
Zwicky, in Virgo cluster - Sinclair Smith), and yet there haven’t been noted
any disintegration of these clusters. Apparently the total mass of the clusters
is much greater. It has been also noted that the rotation of many galaxies is
too fast for a large number of stars forming them to be able to exist as stable
systems. Conclusion: the actual mass of galaxies is much larger, and this is
attributed to the mass of dark matter.
Here
it is worth (and appropriate) to mention the attempt to create an alternative
to dark matter. In the eighties of last Century, Moti Milgrom, professor at the
Weizmann Institute in Israel, developed a theory constituting a modification of
the second law of Newton, called MOND (Modified Newtonian Dynamics). Thorough
research in the following years did not confirm the validity of this theory. At
this point, I suggest a quick return to the content of the first and third articles.
The existence of dark matter, this time in the intergalactic
space, is to be also testified by the intensive motions of galaxies themselves
which can’t be explained by anything else, and also by the result of
quantitative analysis of the effect of gravitational lensing, observed during
the study of distant clusters of galaxies. [The existence of dark matter is
indicates by the research carried out in recent years with the help of the
Hubble telescope. It turns out that galaxies are arranged in such a way that they
form a kind of foam structure. Using the method of gravitational lensing there
were explored the areas occupied by galaxies. It is exactly in these areas were
the dark matter was found.] To the possibility of the existence of dark matter
I pointed out earlier. It can be expected that the dark matter in the
intergalactic space, and in the galaxies themselves, is a relic of the early
stage of the Explosion, still before the appearance of today’s matter with its
weak and strong electric interactions that formed it before the expansion has
gained the current characteristics.
There, in that matter, atoms did not form,
there might have remained systems and particles unknown to us, which cannot
shine even if concentrated in dense formations, filling and surrounding the visible
objects. Perhaps fractals of dark matter had accumulated around themselves
other matter that gave rise to the first stars (made of hydrogen, helium and
lithium), and then, on a larger scale, galaxies. Perhaps that dark matter
contributed to the fragmentation of matter (in the first billion years after
the Big Bang), which resulted in the formation of clusters of galaxies, as well
as those separating them areas of intergalactic “emptiness”. An example of
such an “emptiness” is the Great Attractor, to which, surprisingly, tend
numerous galaxies in our area. Our galaxy moves in that direction with a speed
of about 600 km/s). Currently, although the existence of dark matter is acknowledged
as an unquestionable fact of nature, its structural features, even its material
essence, remains a puzzle... An indication as to the nature of this relic
matter is presented in the third article. I described this also in an essay dealing
with the genesis of galaxies (as for now published in the Polish language):
Here, however,
I proceed in a slightly different direction, while considering the Universe in
a more complete manner.
The contribution
of neutrinos to the total mass of the Universe is also often pointed out. That’s
quite possible. In this context it may be worth looking into the articles on
neutrinos (for now only in Polish):
Judging by their content, neutrino warp of space could
possibly explain the existence of so-called dark energy, which source remains a
mystery to everyone, but to, perhaps, neutrinos (we’ll discuss it further on, although,
for other reasons, we won’t pursue this line of reasoning.
Taking into account the presence of dark
matter with its mass five times greater than the mass of luminous matter and
based on our initial estimate, we can assume that the mass of the Universe
amounts to 10^53kg. This magnitude is generally accepted by many astronomers
(even if dealing with the mass of the Universe is in their opinion beside the
point). It is of course about an order of magnitude, and not an exact value. Is
it the mass of the entire Universe, or only of its visible part? Rather the former.
For those familiar with the subject that
estimate smacks of naivety. Professional approach starts with estimating the value
of density parameter Ω which is the ratio of the actual density of the
Universe to the critical density...
This approach enables to skip, in general
considerations, the problem of the mass of the Universe, which is a specific value,
something that could be philosophically quite awkward. In contrast, the density
parameter as the intensive value does not require an answer to the question
whether Universe is finite or infinite, it does not involve its “external”
parameters. [Exactly. There appear ambiguity,
I would say “indeterminancy”, which does not bring us closer to, rather pulls
away from the unambiguity of objective natural being, which is the Universe.]
It's
a good idea, but because of it something (the phenomenological approach) is
lost. So we will deal with mass not necessarily as being naive and not only for
pedagogical considerations. This approach is justified by the resulting
conclusions. Even stronger justification of this approach I gave already in the
Introduction, as well as in earlier articles, when discussing the CMB
radiation, and in particular when noting congruity of the results of measurements
with predictions. Let’s
continue.
... The determination
of density parameter is based on observational data, especially on the
evaluation of the content of deuterium in the cosmic space. Based on these data
it is estimated that the contribution of visible matter is approx. 5%. It is
surprisingly little, as observational data indicate that the density parameter
has a value close to (“maybe” equal to) unity (100%). What about the rest? The rest
is, in the (current) opinion of scholars: the dark matter (25%) and the
equivalent of the above-mentioned so-called dark energy, which, in Einstein's
field equations was expressed by the cosmological constant, which was introduced
(and rejected) by Einstein and today revived (up to 70%). To tell the truth,
these figures do not quite match our conclusion on the mass of the Universe. It
should be therefore rejected. But before we do that, let’s calculate...
It
may be worth to stop here for a moment of reflection. Is gravitational energy
everything (even if we reject the dark energy)? For there is also the
thermodynamic internal energy. The temperature of the Universe is not zero (and
it won’t be). It came into being, as we know, during the phase transition at
the beginning of BB, as a result of dissipation of part of kinetic energy of
the Urela expansion. The magnitude of this energy does not change in spite of
its growing dilution during the process of expansion. This factor must be considered
when balancing the total energy, which is obviously equivalent to mass. It can
be a significant part of the mass of the Universe. This thermal energy makes
itself felt at least by luminosity of all matter (in all ranges of the
spectrum), and by relict radiation. Maybe that's why in our initial estimate of
the mass of luminous objects was so accurate, maybe that's why our estimated
mass of the Universe, as we shall see, is the key to something quite new and
very promising. Here it is worth recalling the Appendix to the article fifth on
the energy contained in the gravitational field.
2. ...(Schwarzschild’s) radius of
the Universe
For the record (and to put it simply), it is about the
radius of the black hole, in other words, the radius of the gravitational
horizon corresponding to a particular mass fully contained within it. It is
expressed by the equation:
This formula we
derive easily on the basis of a secondary school mechanics (Newton's law of
universal gravitation) and here we don’t need the general theory of relativity
(based on it Schwarzschild derived this formula while approaching the matter
with much deeper premises). We simply start with the equation for escape
velocity (such as the second cosmic speed 11.2 km/s) and assume that the escape
velocity is equal to c.
If we substitute into this formula our estimated
value of the mass of the Universe, we obtain the following value of the radius
of its gravitational horizon: R = 15.6 billion light years. We can see that
this value is similar to the value of the radius of the Universe which we calculated
on the basis of Hubble’s law (fifteen billion light years, assuming H factor = 20). Almost exactly the
same. Let’s note, however, that the possible equality of radiuses: R(grav.) = R(H)
is not at all so obvious. H factor (and
on its basis the Hubble radius of the Universe) is determined from direct
measurement of the distance and relative velocity of specific objects, while
the mass of the Universe (and hence the radius of the gravitational horizon)
were evaluated on the basis of extrapolation of counts of visible objects,
taking into account additional (estimated) correction for the mass of the non-radiating
matter.
But maybe it's just a coincidence? No!
It's very unlikely, given the magnitude of the number (coincidence of such
large numbers is almost inconceivable). The claim that this coincidence has
always existed and is a peculiar feature of the Universe, is not devoid of
rational sense. After all, we most probably do not live in some special time.
It would be difficult to accept such a thing, unless we would refer to the
unique malice of the Creator. He made a prank, did He? No, I personally (and I
think all of us) do not suspect Him of it. Anthropomorphization of the Absolute?
No! That would be the pinnacle of conceit, peak of self-deception.
More reasonable is to accept (more modest)
thesis that from Nature’s point of view this part of space-time in which we
find ourselves is not unique. Already Giordano Bruno voiced that opinion (until
1600). No, I do not intend to be his incarnation. After all, we have
accepted the cosmological principle. So let’s assume that this is not a
coincidence, that there is something more in it; perhaps even an indication of
some deep, fundamental truths of nature.
Let us assume that these radiuses are
(even) identical, as the difference between the results of our calculations, which
is in fact very small (the lengths of radiuses), may be caused by the method we
used: the mass of the Universe was our rough estimate, while the H factor we
adopted in an arbitrary manner without knowing its exact value, although on the
basis of currently accepted estimates. So
let us rephrase our conclusion in a more ceremonial manner: The
gravitational horizon of the Universe coincides with the Hubble horizon.
This equality and even identity is of a universal
character. In other words, the gravitational horizon of a being
with the mass of the Universe coincides with the “sphere”, which distance from
the observer (no matter where he is located) corresponds to the invariant speed
of expansion (c), which, as we know, is the upper bound of the relative speeds
of objects (galaxies), as it is indicated by Hubble’s Law. We shall call this
distance call the radius of the Universe. We'll see where this will take us.
And what about the interconnecting horizon? It will probably leave the
stage although today that’s the one that plays the main role. It can be defined
as follows: It is the greatest distance from which photons can reach us today,
kindly informing us about the presence of something somewhere there. This
definition is absolutely correct if the Universe is infinite (in addition
static) and, of course, if it never exploded.
Let’s note on further
reflection that the above postulated equality should not present any particular
novelty, it shouldn’t even surprise. It is simply a natural thing. After all,
the escape velocity from the black hole is equal to c, the same as the upper
limit of the relative velocity of objects of cosmological significance (Hubble's
law). And it does not matter where the observer is
located... As one can see this
equality is even consistent with the cosmological principle. Therefore,
with the above postulate, in spite of the initial hesitations, I have not taken
too great a risk. It's just a little percussion cup in comparison to a powder
keg on which I sit. By the way, how comes that this has not been noticed
before? [Maybe it was noted, but the thing did not fit into the system. What
was needed was a boy in the crowd admiring magnificent robes of the king.]
The culprits are the curvature of space and the related conclusion that
considering the mass of the Universe as such, “does not make sense.” Humans are
half-blind beings that see primarily what they want to see. I (as a human being)
did not immediately notice this thing either. And anyway, I had it easier, because
somehow I look at things a little differently. Just something got left in me
from the times I was a schoolmaster. And at those times dealing with me wasn’t
a piece of cake.
And here comes
the doubt concerning our estimate of the mass of the Universe. The fact is that
the number of luminous stars and galaxies has been and will be different at
different ages. So our estimation smacks of naivety, since we want to learn
about the invariant, omnipresent features of the Universe, independent of the
time when we study them (apart from special circumstances, such as the very
beginnings of expansion). We can be pretty sure that our time is not unique.
How to reconcile this with a fantastic convergence of Hubble and gravity
radiuses arrived at on the basis of counting the stars and galaxies,
convergence which, one may think, is universal (?) Here it may be worth returning
to reflection at the end of the previous section of this article, relating to
the thermodynamic component of the total energy. I think, at least at this moment,
that the primary as invariant, is the equality of radiuses, which constitutes
the basis for (exact) determination of the mass of the Universe.
An accident? If so,
then not isolated. Nature helps the brave. It helped Hubble for example, who
announced his law based on the insignificant number of data - more than a dozen
galaxies. That was certainly not sufficient for this observation to be announced
as a law. Of course, such an example is not any proof. What is sure in any case
is that the “revealing observation” is verified by life. As it will soon turn
out, equality of radiuses leads to the result consistent with the known ascertainments
(not mine).
As we will
see in a moment, the just postulated equality of gravitational and Hubble radiuses
of the Universe implies a different approach to the issue of the mass of the Universe.
The mass of luminous matter, due to inability of its full evaluation, is
actually the supportive concept. It should be noted, however, that its initial
estimate led to an insight that gained the rank of a postulate. In what follows
we express the mass of the Universe as a quantity directly resulting from
the postulated equality, not messing up in uncertain measurements based on observation,
among other things, mindful of the aforementioned thoughts. It's good
when the data obtained from the study of local systems, allow for inferences on
global features and enable verifiable generalizations.
So we can combine the formula: v = Hr ... → c = HR, expressing the Hubble’s law
with formula (1) for the gravitational radius. We get:
Specific calculations which we will conduct based on
this, will enable us to decide whether indeed there is something in it, or whether
it’s just a coincidence. Here's what we get:
This definition of the mass of the Universe has
nothing to do with the counts of galaxies or the content of deuterium, and at
this point we do not consider the question of what this mass is composed of. So
let's call it the Assumed Mass of Universe
(AMU). From this moment on, speaking of the mass of the Universe, I mean just
this CMU. In addition, let us note that we are talking about the gravitational
mass, which with the passage of time, judging by the formula (2)... But let’s
not get ahead of ourselves.
We will now conduct calculation which will
answer the question: “To what mass correspond the dimensions of the Universe,
calculated from the assumed value of H factor (20)?” Applying the formula (2) we get: M = 0.957·10^53kg.
Calculate it yourself (not forgetting the units). I remind you that the value
of H is estimated on the basis of observational data. Our findings fit very
well with the mass of the Universe which we estimated at the beginning. If we
accepted the value of H factor to be equal to 17.5 (middle of the range of
values H, considered as possible), we would obtain: 1,085·10^53kg. As you can
see the exact value of the H factor, as of now, is not of a critical importance,
is non-essential to the crux of the matter. What’s the conclusion from all
this? Well, the one that we are inside a black hole! We live, and we
even discover such things! (And nothing rips us apart as in a nasty black hole
with singularity. Actually, we could have anticipated it a long time ago. So to
sum up, we can say the following. The Universe is expanding (it is already
known from observation), and its size is determined by Schwarzschild’s radius
(depending on the mass); and it is understood that if today, then at any time,
because our time is not unique. What follows from here? it follows that...
3.
...The mass of the Universe is gradually increasing¹.
After all, the magnitude of the mass directly
determines the value of the gravitational horizon which increases along with the
increase of Hubble radius.
The mass of the Universe is
increasing, is it? Is that possible? Can this be explained based on the current
knowledge? Is it acceptable? So what is the mechanism of mass increase? That is
the question. Let's try to find an answer. What immediately comes to mind is
the Steady State theory, which creators were: H. Bondi, T. Gold and F. Hoyle
(1948), quite popular in the fifties and early sixties of the last century. It
assumed, among other things, continuous creation of matter out of nothing, which
was to ensure stationarity of the characteristics of the Universe despite its
expansion. This “out of nothing” finally
buried this theory, even though it was not all that absurd, considering that it
was a preliminary attempt to preserve the stability of the characteristics of
the Universe, because “after all, it’s the Universe”; and considering today's
multitude of ideas, no less interesting and accepted with deep, if not pious
“understanding” as if the Philosopher’s Stone was just around the corner. Oh, to
be Harry Potter, even for a moment... And by the way, not everything that
exists must be visible.
So
what is the mechanism of mass increase? The answer should be definitely sought somewhere
else. Let’s consider the following possibility. The Universe is expanding,
which means broadening of the horizon. As if we watched from the rocket taking
off or even from an ascending plane, seeing more and more extensive landscape,
noticing new details, more and more distant from the starting point. This
analogy suggests that we are talking here about the interconnecting horizon ****.
If
we look at the globe from an increasing distance, we would actually see the
growing area. However, we would never see the whole globe. From an infinitely
great distance we would see at most the area of a hemisphere. And what is further?
Anti-world?... For the record, we find ourselves within the Universe. So do we
therefore see everythingness?
Horizon defined by invariant c is
something else, since it creates an absolute boundary between being and
non-being. [By the way, this does not preclude the existence of particles with
superluminal speed - about this elsewhere] However, if this is an interconnecting horizon,
something behind it certainly exists. By expanding, it encompasses spaces which
were beyond our perception. We are joined by objects that so far, from our
point of view, "did not exist". Are these new objects gradually
increasing the mass of the Universe? What would result from the joining process?
We should discover suddenly emerging objects, like novae and supernovae stars, although
on the very horizon. Would we recognize this from very large read shift?
Infinitely large? Not necessarily since it's not Hubble horizon but interconnecting
horizon. So there emerge those whose light has just reached us. Where they
emerge? For we know very distant objects that we have seen for a very long time.
A little further than quasars? But no further than the horizon. Wait a moment.
Objects that we are finally to see were there before, although we have not seen
them because photons of these objects “were still on their way”. These objects
existed at least since the dispatch of these photons. So their mass was already
then a component of the mass of the Universe, since long before they were observed.
So it's not about whether we perceive some extra matter or not, but rather
whether it exists as an integral part of the Universe. Objects possibly just
noticed (through photons), have nothing to do with what we are looking for. So
would it be about the mass as if brought into existence? Again, we are
reminded of yet utterly rejected steady state theory. The reason for doubting
such an approach comes also from our determination that the gravitational
horizon coincides with Hubble horizon, which implies that the mass of the Universe
is increasing. And let us remember that the “visible” horizon is the Hubble horizon,
which is the locus of points with invariant speed c. All concrete
objects, galaxies, even the most distant are, of course, closer, drifting away
at lower speeds and are visible today, if only potentially: we should just wait
for better telescopes and remember that stars were formed not immediately after
the Big Bang***** . All the (very distant) objects we detect due to the
relatively high value of redshift. However, they already exist. Contrary to one
of the paradigms accepted today by many physicists we cannot condition the
existence by observability (!). In this context, clinging to the concept of
interconnection is rather pointless, in any case, it does not explain the
increase in the mass of the Universe.
So what is the mechanism of this mass
increase? We assume that all of this makes sense, because as yet we haven’t
come to some logical contradiction despite the persistence of the habits of
thought.
4. The mechanism causing the
increase in the mass of the Universe
“There is an
increase in the mass of the Universe” - is the essential conclusion of the preceding
chapter. Previously, we found that the material content of the Universe is
limited (not infinite), even substantially invariant. The premise for this
assertion is the accepted as fact occurrence of the Big Bang. So there should
come the time when this “fun” will end because due to the limited amount of
matter the Universe will run short of it. We'll come to the limit of the mass
increase. What then? In this context the hypothesis
that the Universe will start to contract seems logical. It is difficult to
count on the fact that the expansion will suddenly stop. “All of a sudden? And what will come next?” Thus we have
an oscillating Universe. Let’s note that we again reached this conclusion, and by
starting from different premises than those in the first article on the
cosmological principle, where I prioritised this very option of the development
of the Universe. This confirms our (say mine) opinion concerning this matter.
The hypothesis of such a Universe simply imposes itself. So we have yet another
argument in support of the thesis of periodicity of spatial (maybe also physical)
features of the Universe. So the arguments in favour of this thesis deepen. Thus
we could draw the conclusion that, in half-time of the collapse, the mass of
the Universe should decrease. Well, yes, but...
So far we have estimated the mass of the Universe
treating it as the value specifying the material (say: substantial) content. [Here
we do not take into account the invariant thermodynamic component, which I
mentioned at the end of the first chapter.] And here we’ve got a surprise. The
mass increases, though I don’t think that there is an increase in the number of
nucleons, electrons and other particles. So wherefrom this additional mass? [“In
fact, it is about the Assumed Mass of the Universe” – but this is not too
reassuring.] According to the earlier determination the Universe is everything,
is the closed creation, so nothing comes from outside. We also reject the
possibility of matter being created from nothing. Or maybe this extra mass is
simply equivalent to energy? What energy? What energy increases with the growth
in size, what energy is a function of mutual distance? We know that, it’s the
potential energy. Does it mean that this
additional mass comes from the increasing potential energy of gravitational
interaction of all objects without exception - from smallest to largest?
Because from where else? This energy should therefore gradually increase due to
the increase of mutual distance between bodies.
And was it always like that? Even when there weren’t any known to us
nucleons and electrons? So what there was? In this context it is worth
reminding ourselves of dual gravity, of Urela, the ending it phase transformation.
I think that this is the direction we should follow to resolve the issue of
mechanism causing the increase in the mass of the Universe.
The mass of the Universe, as in fact the mass of each object, is the
gravitational mass (according to the definition given in the fifth article).
This mass increases with increasing distance between the components of the system,
with the increase in the potential energy of the gravitational interaction
between them. The mass defect decreases.
Similarly the Universe. After all, its material content does not change. In
this context the steady state theory can be calmly rejected. Thus, the increase
in mass of the Universe is linked directly, we can say synchronized, with the
increase in its gravitational potential energy... Easy to say...
It
sounds a little strange for those dealing on a daily basis with the general
theory of relativity. The potential energy is not considered by the GTR.
According to the concept preferred in this work, the space in the scale of
material beings is rather not an autonomous, “primordial” being, a background
for geometry changing stillness into “movement”. On the contrary. It is formed
by relative motion of matter. Therefrom, most likely, its immanent (yes, yes
...) flatness. Here the “balloon” model is not adequate, and the flatness
problem simply does not exist. As a result, the potential energy has here a
specific meaning in spite of today's views. [By the way, this is not at all inconsistent with the
possibility of a fourth spatial dimension, “responsible” for the specific
topology of the Universe, the dimension (actually an additional parameter),
which is about the periodicity of its features, both spatial and physical.] As it is known, these current views lead to two,
classic by now, cosmological problems: the aforementioned flatness and the horizon
(and these problems will be also soon de-problemised). This demonstrates the
inadequacy of today's general approach to the immanent features of the Universe.
Beggars can’t be choosers. The salvation for the Einstein-Friedmann concept, sweeping
under the carpet these cosmological problems, was to come from Alan Guth’s hypothesis
of inflation, which simply offends by its artificiality and typically human wheeling
and dealing. On the one hand we have the quantum field theory, eschewing
gravity which cannot be renormalized, and on the other hand the theory of
gravity (GTR). It's only a modus vivendi, the Creator is not a bungler. As for the
people... it’s a great adventure in search of Truth.
We should add to this one more thing. According
to the Friedmann equation a possible option is infinite expansion, in case of
the development of the Universe according to the critical and open models. In
this situation, consideration of the potential energy would cause additional
trouble of the philosophical nature. While reaching towards the objective truth,
infinity (and singularities) should be avoided.
In this
work, as you can see, I deliberately avoid using the general theory of
relativity as a base (I understand perfectly the inexcusableness of this approach).
So as to be OK I would have to do nothing, proud (without any prodding) of the
achievements of science. I'm proud of these achievements, but it is not enough.
So (in my arrogance) I undertook an attempt to test the problems by means of
conventional methods, though, what is important, taking into account the
relativistic effects. Contrary to appearances, I do not reject GTR. However, I
believe that this theory is so far incomplete: in case of astronomically
macroscopic systems it works fine, but it is irrelevant for describing the Universe
as a whole, which is more than it can take. [By the way, once again I warn
against ontologisation of calculation procedures, which includes concepts of mathematical
character.]
I think that is should, for instance, take
into account of the existence of mass defect. This can be the reason for a
mismatch between Friedmann equations and cosmological reality, the explanation
why, in relation to the Universe, GTR doesn’t meet expectations. It doesn’t,
although as yet none of those who use it in cosmology have the courage to
declare it openly. Declare? Realize. In general they dabble in mathematical modeling,
proud of the excellence of their workshop. Here is one of the reasons that I
decided to say my thing and approach the matter in an unconventional way.
And how
is it in the microworld? Gravity is simply not taken into account, allegedly
because of its weakness. In this scale they ceded everything to quantum field
theory, which does not consider gravity. Why it cannot be renormalized in
calculations?... Certainly not because it is too weak in the scale of
particles. Weakness, contrary to some, does not mean non-existence. That it cannot
be renormalized in calculation provides quite a strong incentive for treating
gravity not so much as an interaction but as a state (such or another) of the
curvature of space-time. But that’s easy.
And still deeper, in the scale of particle
structure, gravity is extremely strong, and even forms the basis for all
interactions (judging from my transgressions. See articles on dual gravity.). This
alone constitutes a sufficient excuse to consider the option of its duality and
in fact the reason for taking it into account.
So I have
restored to favour the potential energy. The concept of potential energy of the
two bodies is widely known, and its definition is strict and unambiguous.
However, when considering the potential energy of the Universe, talking about some
bodies does not make sense. Besides, searching for a specific value of the
total mass of all objects of the Universe also seems pointless. For this
reason, in the third chapter I introduced the concept of Assumed Mass of the
Universe (AMU). The same applies to the potential energy. So as to express it
we will need to use that AMU. In addition, in the system (for example) of two
bodies, this energy depends on the distance, is a function of their mutual positions.
As for the Universe, the only universal spatial parameter is the value of the gravitational-Hubble
radius. So in the context of our discussion we should present (not yet defined
quantitatively) the Potential Energy of
the Universe, treating it as a global parameter which value is a function
of the global time of the Universe.
The ideological basis for just such an
understanding of matters is the firm belief (including mine), that the Universe
had a beginning (at least in the sense of the start of a new cycle), that it was
the beginning common to all the elements of its structure, that all
objects share a common history. With the latter all seem to agree. And the Universe
is an integral whole. Due to its expansion and continuous increase of the global
potential energy, the global mass also increases (its deficit decreases). This
can be written as follows:
according to
Einstein's famous formula (E = mc^2). This time the increase of mass is
directly related to the increase in size, because the increase in potential
energy is generally conditioned by the change of position (a classic school example
is tossing bodies up). Maybe we found the right track. In this context it is worth noting that this gradual
increase in the mass of the Universe retains its condition, that is ensures
(known observationally) “criticality” of development as it were in the nature
of things, making the density parameter Ω = 1 kind of a universal
constant, (or something that
has become unnecessary). Worth remembering this sentence, even as a base for
thought during further reading. This opens to us new horizons for further
considerations, but of course does not release us from the “increase problems”,
on the contrary. This idea of an increasing mass of the Universe, increasing,
moreover, as shown here, I have never come across in written sources, constituting
the standard basis for general cognitive awareness.
“Naive cosmology”? Potential energy of the
gravitational mass defect? What else? Modern
cosmology simply does not focus its efforts on mass (and even less on energy),
for reasons that we already know. Am I to be so terribly wrong? But the
conclusions resulting from the adoption of this concept leads quite far, to
unconventional, yet consistent, model of the Universe and its beginning (!),
the model generating anticipations coinciding with the results of observations.
And that’s the most important. We’ll see it further on. In this context, the
models built on the Einstein-Friedmann equations may gain another practical
sense (for example, educational). Is it really possible that this idea (of the
increase in mass synchronized with the growth of the global potential energy) is
the right one? Would this possibility be excluded due to its rejection based on
the habits of thought currently in force? In any case (and for the time being) this
idea is consistent with the presented here (that is in my works) fairly particular
treatment of gravity.
To sum up, we can say that
the gravitational mass of the Universe (in accordance with the concept outlined
here) gradually increases through the increase of its potential energy. This
causes the decrease of mass defect of the Universe. According to today's views,
its expansion in a natural way gradually slows down, and according to recent
discoveries, something accelerates it. [It's not so much about changes of
relative speeds, but about the change of curvature of space in conjunction with
an increase in scale factor.] In this sense, the rate of expansion decreases
(or increases). Without taking into account the dark energy this is compared
with the deceleration of a body thrown upwards, although in this example there
is a movement as such. Space in case of the Universe, and the actual
movement in case of bodies... Not the best visualisation. Movement, or change in
the curvature of space-time? As it can be
seen, in the traditional approach (and in the example of a body thrown upwards)
we have at the same time two fundamentally different approaches (actual
movement + the curved space-time with changing scale factor, in relation to the
Universe as a whole). Inconsistency? Well, uh, yeah, but this is only for the
sake of visualisation.
5. Reflections and
thoughts in the context of estimations ofthe mass of the Universe, or: let’s
speculate
Admittedly, the discussion of the mass
of the Universe has any sense only if we assume that the Big Bang actually occurred.
This is because if something explodes it cannot have an infinite mass, and the
Universe simply oscillates. [From philosophical point of view, the explosion
itself, all of a sudden, followed by the endless expansion is a serious
problem, which cannot be downplayed. For avoiding philosophy cosmologists -
there is no problem.] I have already drawn attention to it before. The mass of
the Universe (no matter how it is defined) is therefore limited, is of a
specific magnitude, no matter how great. So it makes sense to deal with the
mass, despite its extensiveness. In particular, we have here a very interesting
question: "What will be the maximum mass of the Universe at the moment of
inversion between expansion and contraction?" My preliminary estimate (as
of today) is of the order of 10^63kg (in relation to today's unit values).
And here comes the problem. Each specific
real number, except zero, is an element of an infinite set of equivalent numbers
in the context of the fact that they have to express specific characteristics
of a definite natural being. All of them equivalent to each other. “So why the maximum
mass of the Universe is such, and not another?” [That is not infinite, results
from the postulated cyclicality, existence of oscillations (and of course from
the fact of the occurrence of Big Bang).] Totally natural question, given that
we expect the Universe to be vested with features of a unique, fathomless ideal,
and that is built according to the unequivocal and objective laws of nature. This
global amount should indeed exert its influence on the measurable general
characteristics of the Universe, and at the same time it should be validated by
the values of universal constants. In particular, there should be some
relationship between dimensions and variation of global mass and the value of constant
G. Although this is speculation, it is worth to think about it.
And now, giving (still more) rein to
imagination, one can think that either there is a number other than zero, a
very large number, and, just as zero, the only one, or there are infinitely
many universes forming a continuous mass spectrum. If we include the necessity of
existence of a specific structure and the complexity of such a creation, and
therefore the existence of restrictions as to its minimum size, the matter gets
complicated even more. So it is probably better to find that single number,
perhaps representing an end of counting justified by need. Or, simply, the
maximum mass at the time of inversion is precisely this unique number. But there
are more of such exceptional numbers – such, for instance, as universal
constants. The maximum mass would be one of them. We’ll have to wait a little
before it’s determined. To whoever determines it I promise the right to call it
by his/her name.
First,
however, we should probably find the period of oscillation. And we’ll deal with
it in later articles, which does not mean that we will find it, but we’ll get
some clues.
For now, let us note once more that the speed of expansion
is equal to c. And remember that this is also the speed of light, the speed of
photons. Physically, it’s about completely different kinds of thing. But these
speeds are equal. According to cosmological principle,
the speed of expansion is equal for any observer, which means that it
doesn’t depend on the reference system. It is also the upper bound of the relative speeds of
massive bodies. And what about the speed of light (electromagnetic waves)? It
was assumed (as a postulate) as invariant. The special theory of relativity was
created on the basis of this invariance. It anticipates, among other things,
the existence of the upper limit of speed of material objects, including
distant galaxies. And here we meet. But this is not the end. What does the
speed of electromagnetic wave have to do with the speed of expansion? This is
definitely not an accident. It is quite possible that the electromagnetic
interactions appeared just at the moment when the speed of the expansion settled
at the value c. [If that’s right, then we have one more argument for the thesis
that the Big Bang actually took place (ignoring other weighty reasons).]
Earlier, as we already know, there was Urela ending the phase transition. Thus
c speed is the relic from the beginning of Hubble expansion, and from the
moment when the electromagnetic interaction came into being. So we have the
explanation of the meaning of such an astounding fact as invariance of the speed
of light. A hundred years ago it was a postulate, and today, thanks to my
fantasies, is the obvious conclusion, directly resulting from the cosmological
principle. As you can see, this thread from time to time comes back in my
essays. Am I repeating myself? No harm, because it's quite important. Apart,
each of these essays are basically separate entities.²
The problem of saturation
We found that the dimensions of the Universe gradually
increase, although they are limited. Beyond the horizon there is not even
space, because the Universe is everything. The existence of anything beyond the
limit of the horizon would be even contrary to the cosmological principle, if
only because the area beyond the horizon would have to have completely different
characteristics than our Universe as we know it. This would be also demonstrated
by the parameters of the relic radiation. This should mean that despite the
non-zero global gravitational mass there is no external field. The Universe is,
in a sense, gravitationally saturated. How to digest it? First of all, it is
worth to confront this reflection with the content of the sixth article, which
deals with planckons. But this is not a calming bath, on the contrary. The Universe
is not a photon.
Or is
saturated - invisible to the objects possibly existing outside of it, other
universes, or nothing beyond it actually exists, and the saturation as such
does not apply to the case. Does this cover all the possibilities? We cannot
see the other universes, because no signal from there can penetrate the horizon
of our Universe. [It is difficult to treat the Universe like an ordinary black
hole.] Also, no signal can be sent beyond the horizon. We do not disclose our
existence just as they don’t disclose their. So around us (the Universe) there cannot
exist a gravitational field. Thus, the Universe is the gravitationally
saturated object, and this implies an assumption, maybe even the conclusion that it is also saturated with
the amount of matter - it can contain neither more nor less.
And yet it
has mass. It has positive mass as well as negative potential energy, so we have
zero – we’ll talk about it further on. Maybe that's why it is saturated (?).
The question of zero gravitational mass of a system of material points was
already discussed in the first part of the fifth article devoted to the duality
of gravity. Yes, but what makes the Universe an object saturated in the
likeness of a photon (the mass of a photon is equal to zero), although
according to our estimate, its mass is not at all zero? The Universe is not the
photon (“total mass-energy equal zero” - see above). With these statements I blurted
it out. Because there is much to go on, but let's go back to the original line
of thinking.
Once upon a time, long ago, the Universe was (still)
so compressed that its gravitational mass was equal to zero. Not now, of
course. Despite the comments above, I persistently ask: So how can it be
saturated? Is it because there is no existence beyond the Universe? Can we make
this assertion a priori? There is still a long way before we close this matter.
Or maybe “saturation” does not necessarily mean zero gravitational mass, and
the magnitude of the mass of the Universe does not affect it? In addition, if it
(this saturation) exists, then it takes place all the time, from the very beginning,
always, in every phase of the oscillation of the Universe. Here, let us
remember the cosmological principle. It implies that the intensity of
cosmological gravitational field at any point in space is equal to zero,
because due to the uniformity of the Universe, forces acting on any given body
from opposite directions balance each other out. And for that to take place,
the Universe does not have to be infinitely large – which could result from full
compensation forces (cosmological principle). The case of absolute balance of forces
is resolved by the specific (still unknown) topology. [I am writing this with
the full knowledge that invoking something unexplored is not an argument (and can
be associated with a razor), it only indicates the possible direction for
further investigation.] Soon we shall
see, for a change, that the potential of the global field is constant, not
necessarily zero, and it is everywhere the same. [It reminds very much an
electrically charged conductor (under electrostatic equilibrium)]. Saturation
despite the existence of gravity... Is it possible? Soon we’ll give some
thought to gravity of the Universe.
This, however, raises the question whether the gravitational potential
of the Universe has some value outside of it. That’s how it is with a charged
conductor. In the context of our considerations the answer can be only one: the
Universe is everythingness, so the question does not apply to the case. The
problem of saturation would deepen the thesis that there is no existence whatsoever
outside the (observable) Universe.
Or maybe the reason for this saturation is
some determined, yet unknown to us topology of the Universe as a whole? Where
is the cause of this topology? Is it somewhere deep in the “sub-dimensions”? It
is interesting that the space in the “middle” is flat, Euclidean (more about
this in consecutive articles), and outside... It is possible that this
“outside” does not exist. But let’s not get ahead of ourselves. So if outside no
field informs of our existence, then the Universe cannot be visible to “colleagues”,
it does not exist for any outside observer. For its inhabitants is therefore
the only existing, even if it is an element of infinite multiplicity. This
plethora is known only to scientific fantasists. If This One, then also other
Universes from an infinite set (either one only or infinitely many) are not
visible. So for an “objective” observer who is “outside” there is only the
infinite emptiness. Then what he is doing there for heaven’s sake? Is there a
sense for the existence of an infinite emptiness? For the existence of an
infinite Nonexistence? That this nonexistence may be apparent, false: full of
energy “False vacuum”? Or that the Explosion, and therefore the Universe, is a bubble
locally created from infinite energy, and that there is infinity of such bubbles
– universes? An attractive fantasy - is not it? But ... What's that got to do
with our problem? Will it help us understand our Universe? In addition, our
existence bears absolutely no influence on the existence (or nonexistence) of
something outside of us.
This alone leads to the conclusion that what
we perceive as the Universe, is the uniqueness and Everythingness at the same
time and at the same time is quantitatively limited. The observational
fact indicating the correctness of such a view is the known to all, without
exception, fact of the night sky blackness. Interested (and a little less informed)
can read about the so-called Olbers’ Photometric Paradox. The thesis of
saturation and quantitative limitations of the Universe will come up many times
in this work. And by the way, in connection with non-zero mass and
saturation, something will already emerge in the Annex to the first article on
the neutrino particle. As for now...
...turning back to the Universe, most
likely gravitationally saturated, we can assume that even if there was an
infinite multitude of other universes, their discovery is not be possible,
because, as we can suppose, they would be also saturated, not letting us know
about themselves. A material system pretending to be the universe (one of the infinite number of them) should be large enough to
comply with the cosmological principle, and thus should be saturated. The
larger the object, the closer to saturation. Why would we have to stand out? If someone still doubts, let’s look at
it from another angle. The detection is not possible not because everything
that we see is part of the Universe, according to the definition of the concept.
If there are objects that do not belong to our Universe, they should be breaching
known to us observational patterns: the cosmological principle, and, of course,
the Hubble’s law.
So far nothing points out towards the possibility of
making such a discovery, even towards any sense of such expectations. Although... it’s strange what is happening in connection
with the existence of the Great Attractor... The conclusion would be that either different universes cannot
penetrate each other (as for example, in a collision of galaxies) or their
parts cannot be mutually detectable, due to differences in their physical
characteristics; or else the whole absolute material and spatial everythingness
is the Universe open to our perception. Personally, I prefer this to an
infinite number of undetectable entities. Not only for practical reasons. And
what about the Great Attractor? Some explanation will be found.
Á propos
¹) Or maybe this independence of equal radii from time
(and the current appearance of the Universe), this universality, means that the
units of measurement themselves gradually increase with the expansion of the Universe?
So there are no more kilograms despite the gradual change in brightness,
despite the gradual increase in mass. This is possible if all the changes occur
in absolutely each scale – down to Planck’s. It's as if in terms of global measurement
the Universe was static. However, it would be a “dynamic staticity”. The units
of measurement would change in such a way, for example, that numerically the
mass of the Universe would be always the same. Is this a correct conclusion?
We'll see further.
Let’s suppose
that the values of units of measurable entities are constant. We can do that, since
the system of units cannot decide on basic matters. The fact of measurement and
type of units used, cannot affect the objective characteristics of physical
systems. [Yes, yes, quantum mechanics, observable, uncertainty...]
In this cosmological context, I agree with Einstein's famous statement: “If I
do not look at the sun, does it mean that it does not exist?”
Following this consideration, we can however say
that this “staticity” could be directly related to the invariance of the
general laws of nature - the independence of these laws of the place, time and
scale. Time, obviously, exists, and it is proved by the existence of variation,
evolution. Evolution, however, would be demonstrated only by the given to
observation local changes – up to inversion of the Universe and beyond.
Would that
imply a change in the values of the universal constants? There is no basis for
such a view (at least for now), if only in relation to what I stated a moment
ago (the underlined sentence). After all, any permanent changes would have to
be of a global character. This concerns in particular the gravitational
constant, which changes I exclude, since planckon constituting the quantum of
gravitational field, and at the same time the absolutely elementary being,
cannot be something variable. The question of any changes in the parameter c I
have already addressed a number of times, and I will still come back to it.
²) And
another connotation. As we know, in our environment the particles of the
microworld move (and as a matter of fact, it's not about accelerators) very fast,
even with relativistic speeds. With the same speed move very distant galaxies. This
alone says something. [Actually, why natural speed of particle is so high,
having nothing to do with the relative speed of objects that surround us? Or
maybe this is related to the history of the origins of the Big Bang? Perhaps. We
have to admit that the magnitude of this natural speed is significantly
influenced by (relatively strong compared to gravity) electromagnetic and
nuclear interactions, in which these particles are directly involved. However,
I get the impression that this is not all. Does anyone share my uncertainty?] And
now, if a particle originally belonging to the now distant galaxies, in its inert
motion headed toward us once upon a time and reached us, then it should have exceptionally
large amount of kinetic energy. Indeed, such particles were detected in cosmic
radiation. Already some years ago, in a KASCADE experiment (Germany), with the
participation of Poles, there were obtained (in the atmosphere) cascades of
multitudes, even millions of secondary particles resulting from collisions of
the particles of cosmic radiation, having an extremely high energy, with
particles from the atmosphere. Their kinetic energy is estimated to be 10^19
eV. By the way, these particles are so fast that their speed is almost
invariant. They are relatively rare. It is believed, I think rightly, that they
are extragalactic components of corpuscular cosmic radiation. In addition, in
accordance with the above stated supposition (and of course with the
cosmological principle), these particles should arrive from everywhere. They
should create a homogeneous and isotropic corpuscular radiation. This thing
should be examined. (For now) we do not know where they acquired that huge
energy. There are various hypotheses, more or less feasible. Now we have one
more - see the beginning of this reflection.
*) Extensive parameters – proportional
to the amount of matter in the system: mass,
volume.
Intensive
parameters – independent of the amount of matter in the system: temperature,
pressure, density.
**) Megaparsec is million parsekcs. 1
parsek equals to 3,26 light years.
***) According to presumptions
signaled in the literature of the subject, already after 200 million years. It
is about the stars forming from fluctuations in density in a very limited
scale, still before separation of systems which were to transform into galaxies
- objects that we can see. They should be star with an extremely low content of
metals (elements heavier than lithium). The vast majority of those of them that
have survived to this day are certainly advanced stars in evolutionary terms. Let’s
note that in those distant
times matter was very highly concentrated. So many stars came into being. The
mentioned in the text number of 1.5 billion years applies to pre-galactic
objects which can be observed by means which we already have. It is mainly
about quasars, seen thanks to very intense energy transformation occurring in
them.
****) Coordination of properties and processes cannot proceed
at a speed greater than the speed of light. Regarding the situation described
here, the given object, as I already pointed it out, can be seen only after the
time it takes for light to get from it to the observer.
*****) This is not fully compatible with today's interconnecting
understanding of the issue: “we see because of photons that have reached us”, which
does not take into account the fact that with this, “once upon a time, billions
of years ago, we were all together.” I will devote a lot of space to this issue
in the following articles.
Brak komentarzy:
Prześlij komentarz