One Universe, Two Universe

  

          

                   Foreword   

 

      These are reflections on cosmology—on how far we can see into space, on Hubble’s law and receding galaxies, on black holes and the relativity of the passage of time, on the expanding universe and its future. My thoughts are almost certainly not original ideas. For the most part, they are a compilation of other people’s ideas and popular science articles, imprinted in the mind of an amateur. An incredible amount has been written on this subject, and I do not have enough energy or time to master the serious contemporary literature on space and astrophysics, with all the accompanying mathematics. Some thoughts came to me on my own, but even those are most likely not new. If there is anything of my own in these notes, it is the path I took from one thought to another.  I would be very happy if they inspire you to embark on your own exploration.

     I think the best place to start is with my long-standing acquaintance with the Special Theory of Relativity. When, after much deliberation, the first glimmers of understanding of SRT cleared the fog in my mind, I was extraordinarily inspired by the idea that all distances are relative, and that a change in speed can turn any great distance into any small one. And so, even a space as unimaginably vast as the universe, provided it is finite, will, when an observer reaches nearly the speed of light, collapse into a flat “pancake” of (almost) zero thickness, with time frozen.

     Continuing their motion, the observer will quickly fly out of the “pancake” of our Universe and find themselves, in effect, in another Universe moving at the speed of light relative to ours. Although this would still be the same unified Minkowski space, and it would likely have to be completely empty—otherwise, the passage of our “flattened” universe through that universe would be a catastrophe of cosmic proportions.

     My imagination did not stop at flattening the universe into a plane; I wanted more. I naively assumed that if an imaginary observer could now, by turning his imaginary rocket, accelerate again to the speed of light in a direction perpendicular to the original direction, the original Universe would transform from a plane into a thin line. Moreover, if the observer were to accelerate once more, using a third, final spatial direction, then our entire present-day vast universe would shrink for him from a straight line into a tiny point. Just think about it: the entire universe—into a point!

I was thrilled by this idea; it seemed to me that I had glimpsed some kind of brilliant divine design, contained in such striking flexibility, in the boundlessness of space—it turned out that our gigantic world could become tiny, pocket-sized, so to speak, with a single “light flick of the wrist”—a change in velocity.

     Very soon, however, I realized I was mistaken. First, the relativistic rule for adding velocities would not allow a plane to be turned into a line, or a line into a point. The most one could achieve is to flatten space into a flat pancake, perpendicular to the direction of motion... no matter how much you rotate it. Second, I failed to take into account that the space of the Universe is expanding, and at great distances from the point of observation, it expands at a speed several times faster than the speed of light. Therefore, one can accelerate to the speed of light only relative to a relatively small local region of the Universe, and not relative to the entire Universe as a whole. Third, the finiteness of the universe remains in question, as does its curvature.

 

    Nevertheless, the very idea of the possibility of fitting the    entire universe    into a small volume, or even a single point, apparently took root in a corner of my mind. And when I later began to look more closely at black hole models, I became increasingly convinced that God (or nature—whichever you prefer) had not overlooked this possibility either…

 

 

                        The expansion of space and redshift.

 

     Our universe is expanding in all directions. All distant objects in space are moving away from us at speeds directly proportional to their distance from us. This is Hubble’s law, theoretically predicted by Georges Lemaître in 1927 and confirmed by Edwin Hubble’s observations in 1929. By extrapolating the motion trajectories of many galaxies backward in time, scientists arrived at the obvious conclusion: several billion years ago (the exact figure remained controversial for a long time), all the cosmic objects we see scattered out from practically a single point, from a very small region of space where the density of matter at that initial moment—the “Big Bang”—was monstrously high. This is, in simplified terms, the picture of the world that everyone or almost everyone knows.

     I would like to add that even if today the expanding Universe has a density of matter insufficient to appear to an imaginary external observer as a black hole (BH), in the past it undoubtedly was such a black hole. However, not an ordinary one, but a completely paradoxical one: it harbored a source of energy exceeding the energy of gravity—otherwise it would not have expanded. If the universe could not have had external space, just as it could not have had an “external observer,” then this colossal energy is exclusively internal, which is quite mysterious. But if there was an external space, then this colossal energy could have come from external space! This is an interesting thought that I suggest keeping in mind for the future.

     Incidentally, at the time of the publication of general relativity, Einstein did not assume that the space of the universe was expanding. He believed that the universe was infinite and stationary, and later called this his greatest scientific mistake. The model of a non-stationary closed universe with a non-zero and varying curvature coefficient—that is a universe capable of expanding and contracting— proposed by Mikhail Friedmann in 1922. Thus, the equation describing the universe, based on the General Theory of Relativity, was formulated as early as the 1920s (we will omit the equation itself so as not to get bogged down in overly complex matters; those interested can find it in articles on the “Standard cosmological model”). However, the equation contained several unknown parameters determining the dynamics of the Universe’s scale changes, its age, and future evolution—parameters that were unknown at that time and remain undefined today.

     As for the age of the universe, based on observations from the early 20th century, it was initially estimated to be 1.8–2 billion years old, which caused complete confusion, since the Earth itself estimated to be 3 billion years old. In 1952, an error was discovered in the previous estimation of Cepheid brightness, and the age increased to 4 billion years. Then, as data became more precise, the age was repeatedly revised upward, but it remained for a long time within an incredibly wide range of 7 to 20 billion years. Later, in the 1990s, following the launch of the Hubble Space Telescope into orbit, the range was narrowed to 9–14 billion years. And, finally, the most accurate (so it is claimed), canonical (as of today), value for the age of the universe was obtained by the European Space Agency’s Planck radio telescope in 2013, by mapping the cosmic microwave background (CMB) - CMB) and was found to be 13.8 billion years. The logic behind these calculations and the calculations themselves are beyond the comprehension of mere mortals like me. There is still a discrepancy between this age and the age determined by Hubble’s law in the latest observations, one that falls outside the acceptable margin of error—Hubble’s law indicates an age one billion years younger, and we will discuss this difference later. But moving on, in the diagrams, for simplicity’s sake, we will approximate the age of the universe as 14 billion years. For us, this is not so important.

     When reading about receding galaxies, you will inevitably run into a puzzle that requires a detailed explanation (and if you do not, either you are a genius in cosmology or cosmology does not interest you at all). Here is the thing: for three different questions—“how do you determine velocity?”, “how do you determine distance?”, and “how do you determine age?”—regarding very distant objects in space, you most often get the same answer: “by redshift”.

     Wait... How is that possible? Let us start with the fact that there are two types of “redshifts”: one is the classic Doppler effect for light, where the light wave stretched relative to the observer at the very moment of emission; the other is the gradual stretching of an electromagnetic wave during motion, due to the expansion of the reference coordinate space. If we intend to determine velocity based on redshift, we need to know which formula to use: there is one formula for the Doppler effect and another for uniformly expanding space. However, even that formula is significantly nonlinear at near-light and superluminal speeds (we still have to figure that out).

     The second problem is that to determine the observed “age” of an object from its velocity, we need to know the distance at which we are observing it. And to determine the distance from the velocity, we need to know the object’s “age,” its lifespan since the Big Bang. Doesn’t all this lead to ambiguity and confusion? Aren’t we trying to calculate two unknowns from a single known?

      Fortunately, no. Because there is an additional method for determining distances to galaxies: based on the luminosity of stars of certain classes, called “standard candles”—Cepheids, red giants, and supernovae—whose luminosities are precisely known. The degree of scattering of the light coming from them, and, accordingly, the attenuation of their luminosity, gives an approximate idea of the distance, accurate to within hundreds of kilo parsecs (1-parsec ≈ 3.26 light-years).  It was this approximate knowledge of the distances to galaxies that made it possible to discover Hubble’s law and to abandon the calculation of their velocities using the Doppler effect formula borrowed from SRT.

      Let me explain. If galaxies were scattering across Minkowski’s static space like fragments from a colossal explosion, most of them would be moving away from us at nearly the speed of light... but no faster! They would all be located within a certain sphere—a sort of cosmic “horizon”—at a distance from us equal to how far light could have traveled. According to current, refined data, the age of the universe is approximately 14 billion light-years, which means we would see them at half that distance—7 billion light-years (light needs another 7 billion years for the return trip). And, being at nearly the same distance, they would differ sharply in age and redshift magnitude, due to the difference in time dilation, which increases rapidly as one approaches the speed of light. Furthermore, we would see literally all the stars and galaxies in the Universe, and the “Olbers’ paradox” would likely not exist—there would be no empty regions left in the sky. Such a kinematic model of the Universe, based on the explosive dispersion of matter from a single point and disregarding gravity, curvature, and the expansion of the spatial metric, was named the “Milne Universe” (by Edward Arthur Milne, 1935).

      However, such a picture not observed in reality. The distances to so many visible galaxies are significantly greater than 7 billion light-years; the most distant ones found at distances exceeding 13 billion light-years. And the Milne model later came to refer not to the recession of galaxies at a constant speed in Minkowski’s static space, but to the linear increase in the distances between them due to the uniform expansion of space itself. In this case, the speed of light is no longer a limit on the speed of receding objects.

      In the simplest model of a uniformly expanding universe, Hubble’s law holds true immediately from the moment of the Big Bang: objects that have receded from us over 14 billion years by a certain distance “x,” directly proportional to their observed velocity, were receding at the same velocity throughout the entire 14 billion years. That is, Hubble’s law has always been a linear relationship between distance and velocity, but the proportionality constant in it—Hubble’s “constant” H—is, of course, not a constant at all, but is true only at the present moment and varies inversely with the time elapsed since the Big Bang:

            H(T) = 1/T;

 —its current value, based on data from the Planck probe, H₀ = 67.5 [km/s/Mpc] roughly corresponds to the time T₀ = 13.8 billion years since the Big Bang. A coordinate system that expands along with space is usually called “co-moving”; in a co-moving coordinate system, galaxies are, as it were, fixed and immobile, and the increase in the distances between them occurs due to the stretching of the coordinate system itself.

     Expanding space has an important property: if it expands uniformly in all directions, then the luminosity of a receding object continues to decrease after it emits light, and by the time we observe it the luminosity will correspond to the current distance to the object! Therefore, if the luminosity of “standard candles” in a distant galaxy corresponds to a distance of 10 billion light-years, then this is the true distance to it right now (this is my own conclusion, but it seems obvious). And, knowing the current distance, we can correlate it with the magnitude of the redshift. Since a huge number of galaxies at various distances have been discovered in space, it was not difficult to construct a graph of the relationship between redshift and distance based on this data. Indeed, a linear relationship is visible in the graph.

     Now I want to show in a simple diagram what determines the magnitude of the redshift in the model of linearly expanding space, and what relationships it enters into. This diagram is valid only for galaxies relatively close to us, receding at a speed much less than the speed of light. But it was precisely using these relatively nearby galaxies as an example that Hubble’s law was discovered. The delay of the light signal on its way to an observer on Earth due to the expanding universe is not considered here; only the stretching of light waves (a decrease in frequency) corresponding to the expansion of space—the so-called “scale factor”—is considered.

The horizontal axis shows time (T), measured in years from the moment of the Big Bang (T=0) to the present (T₀~ 14,000,000,000 years); the vertical axis shows distance (X=CT) in light-years. The speed of light is C = 1[light-years/year], and we obtain the same numerical scale on both axes, which is standard practice in such diagrams. The paths of light are shown in orange—one (X=CT), starting from the origin, for receding light (or galaxies receding at the speed of light), and the other (X=CT₀– CT) for light arriving at us at the present moment from any distance less than CT₀. Let us make one thing clear from the outset: the assumption that light travels along this straight line is a gross simplification of the real picture, but we will address this refinement in the next chapter.

 

     The black line X=VT represents the trajectory of the observed galaxy, which is receding at a constant speed V from the initial time T=0 to the present time T₀, when it is a distance X₀away from us. Point A is marked on this trajectory, at which the galaxy emitted the light that has reached us today—the light from it traveled along the orange line from point A to point T₀. There is no need to plot a graph for the Hubble constant H(T) = 1/T, but it is clear that V = H(T) · X = H(T₀) · X₀.

      The redshift “z,” by definition, is the ratio Δλ/λ—the change in wavelength relative to the initial wavelength. The wavelength is not shown on the diagram, but for an expanding universe, it is clear to us that the light wave has stretched in the same proportion as the distance has increased—from X to X₀; and time has increased in the same proportion—from T to T₀. Therefore:

 

                           or    

     

     To these two ratios, which determine the redshift, we can add another one involving the distance CT. It is slightly more difficult to find the corresponding similar triangles in the diagram; nevertheless, they are also present (I suggest you find these triangles yourself, using point A’ as a reference). Did you find them? Let’s complete the chain:

 

                          ,                   (1)

— this is exactly what we needed to obtain — the redshift is proportional to the galaxies’ velocity and is expressed in terms of the ratio of the galaxy’s velocity to the speed of light; furthermore, if our linear model is correct and we have correctly determined T₀, then all other values—T, X, and X₀—can be uniquely determined via z.

 

     That would be fine, but for velocities V>C this formula is incorrect, and even for a velocity approximately equal to 0.4C, as in our graph, the error in calculating the velocity using the formula V=C·z will be too noticeable. And for galaxies receding faster than the speed of light, the redshift of their spectra turns out to be much greater than that calculated using the simplified linear formula. For example, Wikipedia provides data on the galaxy UDFj-39546284—a compact galaxy consisting of blue stars that have, at this moment, managed to recede from us to a distance of about 33 billion light-years, and whose age is only 380 million years after the Big Bang. Due to redshift, this galaxy appears dark red rather than blue in images. Its redshift, according to the latest estimates, is z=11.7. Such redshift, according to more rigorous formulas that account for the delay in the arrival of light in an expanding universe, corresponds to a recession velocity of about 2.3 times the speed of light, which is much less than the value of 11.7 obtained using the simplified formula (1).  

 

     We will have to look for a more accurate formula for fast galaxies. I believe it is appropriate, using the example of the galaxy UDFj-39546284, to provide a more detailed justification for the subsequent calculations. Any observer is equally entitled to consider themselves the “fixed center of the expanding Universe,” since we cannot see the edges of the Universe, and it appears to be expanding uniformly in all directions. No matter from which point in the Universe we observe, it expands equally in all directions; Hubble’s law holds true at any point in it. Therefore, we are justified in assuming that we are observing from a stationary origin point, and that the galaxy mentioned above, 380 million years after the Big Bang, has moved away from the origin by a certain distance X due to the expansion of space. The value of X was greater than 380 million light-years, since the speed limit imposed by the speed of light does not apply to expanding space. I am not performing precise calculations; I only wish to provide a qualitative picture: let’s say X was approximately one billion light-years. It was precisely at this moment (age: 380 million years; distance: 1 billion light-years) that the galaxy emitted light, which has now reached us—13.620 billion years after it was emitted. In other words, it took the light 13.620 billion years to cover the initial distance of 1 billion light-years!

 

     Why is that? It’s all due to the same expansion of space. The best illustration of what happens to light, in my opinion, is the example of a spider running along a web from the edge to the center at a constant speed C, while a person holding the edge of the web stretches it at a speed V greater than C (V>C). In the first few seconds of movement, the spider will not be getting closer but moving away from its goal; however, if the person stretching the web continues to move at a constant speed, and the spider is tireless and persistent, it will inevitably reach the center of the web. True, it will take him many, many times longer to do so than to run along a web that is not being stretched.

 

     On the "web" of our world, there is a certain spherical, rapidly expanding surface around us from which the spider-light has been traveling toward us for all 14 billion years of the universe’s existence—this light is the famous cosmic microwave background radiation. At the beginning of the universe, this sphere was tiny (almost a point), and now it is much farther than a distance of 14 billion light-years—somewhere at a distance of either 45 or 50 billion light-years; I have come across such estimates. This distance would be even greater if, from the very beginning, space had expanded linearly at the current rate, but at the very start there was indeed acceleration, held back by gravity. And now, in our time, with uniform expansion, new problems have emerged, which we will discuss later.

 

 

          Let’s complicate the model: the integral equation of motion of light.

 

     Earlier, we examined a simplified diagram showing the relationship between distance and age for relatively nearby galaxies, without considering the expansion of space. I did not want to discuss a possible violation of Hubble’s law without using formulas and graphs to show exactly how this law should manifest itself in the case of galaxies receding at near-light and superluminal speeds, —both in terms of the magnitude of the redshift and the distance from which the light reaching us was emitted, assuming this law were strictly observed throughout the entire evolution of the Universe. You’ve probably guessed it—we’re about to solve that very problem involving a spider, with the role of the spider played by a ray of light traveling toward Earth along a uniformly stretched web of space.

  

     It quickly becomes clear that points in uniformly expanding space must move away from the origin along an arbitrarily chosen coordinate x at a speed proportional to the coordinate x and inversely proportional to time T (elapsed since the beginning of expansion)—similar to the speeds of points on a uniformly stretched web:

 

                        u(x,T) = x/T

 

     Light from any receding object will travel along this web in the opposite direction—toward an observer on Earth located at the origin (x = 0). As we know, light always travels at a speed of C = 299,792,458 m/s.
Consequently, the formula for the speed of light relative to the origin is:

 

                        v(x,T) = -C + x/T,                                                                   (2)

     - the minus sign before C indicates an approach toward the observer, while the plus sign before x/T indicates that the expansion of space prevents light from traveling toward the observer.

 

     This equation (2) must be integrated over time to obtain the dependence x(T) for light, setting as boundary values a certain starting point on the motion graph of a uniformly receding object that emitted the light, and a finishing point [0, T₀ ] where the Earth-based observer is located today (x=0, T₀  = 14,000,000,000 years from the beginning of the Universe).

 

     But since I haven’t practiced integration in a long time and sometimes get confused with boundary conditions, I called on AI in the form of Gemini for help. I asked it, to start with, to solve the problem for light emitted by an object receding at the speed of light C, and then for an object receding at 2C. Below is my dialogue with Gemini (Gemini’s responses are highlighted in color).

 

Your query (problem 1, for velocity V=C):

Light begins to move along the X-axis from point x₁= C*T₁ to point x=0 at a speed varying according to the law v(x, T) = -C + x/T; T₁ - unknown time on the T-axis, and C is the speed of light. It is known that light reaches point x=0 at time T = 14 billion years.
What is T1 equal to?

Gemini's response:

This is a classic problem involving a differential equation describing the motion of light in an expanding medium (similar to a cosmological model with a linear expansion law).

 

1. Formulating the equation

The speed of light in this coordinate system is the sum of the intrinsic speed of light (opposite the X-axis, hence −C) and the expansion speed of space itself (x/T).

 

The equation of motion for a photon:

                                      

This is a linear, inhomogeneous, first-order differential equation. Let’s rewrite it in standard form:

                                            

 

2. Solving the differential equation

 

Let’s solve it using the integrating factor method or the method of variation of a constant.

 

    Let’s solve the homogeneous equation:

 

                   

 

    We will find a particular solution using the method of variation of a constant, assuming A = A(T):

 

                                  

     

                                   

 

      General solution:
                                   

3. Application of initial and boundary conditions

 

We have two points on the light path:

 

    Start: at T=T₁, the x-coordinate is x=C·T₁.

 

    Finish: at T = T_end= 14 × 10⁹ years, coordinate x = 0.

 

We use the finish condition (x(T_end )=0):

 

Since T_end  >0, then:  

Substitute K into the general solution:

                           

We use the start condition (x(T₁ )=CT₁ ):
                             

Divide both sides by CT₁ (assuming that T₁ >0):

 

                                  

We move to the exponential term:
                                        

                                                              

 

4. Answer

 

Let’s substitute the value T_end= 14 billion years:

 

 

 

 

Your query (Problem 2, for velocity V=2C):

The same problem starting at point x₂ =2*CT₂ and ending at point [x=0; T=14 billion years].

We need to find T₂.  And we need to draw two graphs—one where light begins to be emitted at the point x₁= CT₁ and one where it begins at the point x₂= 2CT₂

 

Gemini's answer:

General solution:

                           

We use the initial condition (x(T₂ ) = 2CT₂ ):

                                         

 

Divide both sides by CT₂ (assuming that T₂ >0):
                                           

We move to the exponential:

                                               ; 
                                                        

 

 

Answer:

Starting from the point x=2CT₂ , the light travel time T₂ ≈ 1.89 billion years.

Graph:

 

  

     - I want to clarify: the straight dotted lines are the trajectories of objects moving since the Big Bang at constant speeds C and 2C;
the curve is the trajectory of the light they emitted, which is arriving now; this is essentially the same function, which is why the blue graph overlaps the red one, which originates from the red point.

Your question:

What is the significance of the observed redshift for these two graphs?

Gemini’s Answer

For the linear expansion model (Milne model), calculating the redshift z is surprisingly simple. Unlike standard cosmology, where complex integrals must be solved, here there is a direct dependence on the scale factor a(T).

 

In the linear model, the scale factor is a(T) = k·T. The redshift determined by the ratio of the scale of the Universe at the time the signal is received (T_end) to the scale at the time of emission (T_start):

 

 

Let’s apply this to your two starting points at T_end= 14 billion years:

 

1. Case x = CT₁ (Red graph)

 

We calculated that in this case, the start time T₁ =14/e.

Substituting into the formula:

 

What this means is that the light from this object is redshifted such that all wavelengths have increased by a factor of 2.718. In modern astronomy, objects with z ≈ 1.7 are actively forming "midday" galaxies.

 

2. Case x=2CT₂ (Blue graph)

 

Here, the start time is T₂= 14/e².

Substituting into the formula:

 

                                                          

What this means: this is an extremely high redshift. Objects with z>6 belong to the reionization era (when the very first stars were born). The wavelength of light from such a galaxy has stretched by a factor of nearly 7.4.

 

Summary table for your model

Parameter	Case 1 (x=CT)	Case 2 (x=2CT)
Start time (Tstart )	≈5.15 billion years	≈1.89 billion years
Redshift (z)	1.72	6.39
By how many times has the light	2.72 times (e)	by a factor of 7.39 (e2)

 

This is a direct consequence of the logarithmic nature of light’s trajectory in a linear universe.

If light starts from the line x=n·CT, then the observed redshift will always be equal to:

            z=eⁿ−1

Your query:

And where in our example is Hubble’s law regarding the proportionality of distance and the speed of objects observed?

Gemini’s Answer

This is an excellent question that gets to the very heart of how the geometry of an expanding universe works. In a model with linear expansion, Hubble’s law holds perfectly, but there is an important nuance: we need to choose correctly which “distance” we substitute into the formula.

In cosmology, there are several types of distances. Let’s examine them for our case.

 

1. Instantaneous distance (Co-variant)

Hubble’s law in its classical form (v=H·D) describes the relationship between velocity and distance at a single point in time (as if we had frozen the universe and applied a ruler).

In your model, the expansion velocity at any point x at time T is defined as:

v = x/T

Let’s compare this with Hubble’s law v = H·x:

From this, we see that the Hubble parameter in your model is: H(T) = 1/T

At the “present” moment (T = 14 billion years), H₀= 1/14 ≈ 0.07 (in units of 1/billion years).

Hubble’s law holds: the larger the x-coordinate at a given time T, the higher the expansion velocity at that point. This is direct proportionality.

2. Distance at the moment of emission

Let’s check the proportionality for our two cases at the moment of launch:

1.                  Case 1: T₁= 4/e. The distance was x₁= CT₁
The expansion velocity at this point was:
 v₁ =x₁ /T₁ =1C.

2.                  Case 2: T₂ =14/e². The distance was x₂ =2·C·T₂.
The expansion velocity at this point was
 v₂ =x₂ /T₂ =2C.

The connection is clear: An object that was twice as far away (in CT units) was receding exactly twice as fast. This is Hubble’s law in its purest form.

     Let me pause to emphasize: AI speaks of the proportionality of velocities and distances “in CT units”—meaning it is not the distances x₁ and x2 are proportional to the galaxies’ velocities, but the distances divided by their corresponding time (sometimes referred to as “time-scaled”).

     And one more important point: we observe objects and their angular sizes (if they are distinguishable) as they were long ago; but the luminosity of the objects is attenuated and corresponds to the current distance. That is, for distant cosmic objects, there are two observable distances: on the one hand, the current distance to the object, as observed by its luminosity (brightness); on the other hand, a much smaller distance at which the object was located at the moment the light was emitted. The first distance is proportional to the speed with a coefficient H₀—today’s Hubble constant—for all cosmic objects. The second distance turns out to be proportional to the speed with a coefficient inversely proportional to the time of emission and calculated from the redshift; that is, the second distance is proportional to their speeds with coefficients H = 1/T that vary for different speeds. It is precisely the second distance that fits the graph constructed by Gemini, while the first (today’s, located on the vertical line T = 14 billion years) — unfortunately — does not fit.

 

            Let us complicate the model even further: the non-uniform expansion of the Universe.   

 

      We are now more familiar with the laws and graphs for a linearly expanding universe in the Milne model. We now know that the formulas are not so simple, and the graphs are not entirely linear. But if, based on some newly obtained data,      we find evidence of non-uniform expansion in the distant or recent past, then the graphs of the distance from time of receding objects cease to be simple straight lines, and the graph of the motion of light in an expanding space—already non-linear—must become even more complex. We have to rely on the professionalism and mathematical rigor of the calculations made by astrophysicists, who determine, based on certain deviations of observations from the graphs, whether the expansion of the universe is accelerating or decelerating over a given time range. Tricky questions arise: do the new observations contradict the Big Bang theory itself, and are we not simply fitting the new results to the 14-billion-year timeline since the universe’s inception? These are complex logical problems. And as we have seen time and again, scientists need to be watched closely (a joke with a grain of truth).

 

     In this regard, I won’t deny myself the pleasure of sharing an excerpt from my next conversation with Gemini. It began with my question: How will the blue graph change if the expansion of the universe has been accelerating over the last billion years? How should this affect the redshift?  

 

      Gemini replied that the redshift would decrease, and then, in an attempt to mathematically justify this conclusion, “proved” that the redshift would increase. Of course, I could not forgive him for that… continuing with the chat:

 

Your query:

You’re contradicting yourself. So will the redshift decrease or increase?

Gemini's Response

You’re absolutely right; I made an unfortunate mistake in my logical reasoning in my previous post. Let’s correct that right now and figure out how the physics of expansion actually works.

The short and correct answer: The redshift will decrease.

Let’s walk through the logic step by step to see where the contradiction arose.

1. The redshift formula

In any cosmological model:

Where T_now is the scale of the universe today, and T_then is the scale at the moment the light was emitted.

2. Comparison of two scenarios (Linear vs. Accelerated)

Let’s imagine two Universes that had the same size (a=1) at the moment the light was emitted (T_then).

Scenario A (Linear): The universe expands uniformly. By the time T = 14 billion years, it has grown, say, to a = 14.

Scenario B (Accelerated at the End): The universe expanded just like the first one, but in the last billion years it “sped up.” So today (T=14x10⁹) it is larger than the first one. For example, a=16.

Would it seem that z has increased? NO. And this is where the main trap lies, the one I fell into in my previous answer.

3. Where is the truth buried? (The photon’s trajectory)

We forgot about the condition: the photon must arrive at point x=0 exactly at time T=14.

If the universe began expanding faster in the last billion years, it started “pushing” the photon back harder (that very “headwind”). For the photon to reach us now despite this additional resistance, it must have been closer to us at the moment of launch (or launched later).

4. Final calculation for the blue graph

If we force the photon to arrive at x=0 within a fixed time frame (14 billion years) assuming acceleration at the end:

-          Distance: A photon from point n=2 (superluminal zone) simply won’t have time to reach us if space begins to expand faster at the end of its path. It will be “blown” back.

-          Time: for us to see light from the “blue” object today, that object would have had to be closer (for example, n=1.8 instead of n=2).

-          Result: Since the object started from a closer point (or later), the scale ratio of the universe (a_now/ a_then) for it will be smaller than in the linear model.

Consequently, the observed redshift z will be SMALLER.

Summary:

Linear model: z≈6.39.

Accelerated-at-the-end model: z will be smaller (e.g., 5.8), because acceleration “cuts off” the ability to see objects that are too far away. The ones we still see must be closer to us, which means their light has been stretched less.

I apologize for the confusion in the previous step—acceleration “works against” the photon, forcing us to see only “closer” (with smaller z) events from the same era.

     This is downright ridiculous (or perhaps sad). You should not trust AI’s explanations when it tries to “eyeball” something, mimicking human-like heuristic reasoning; it would be better if it performed calculations using rigorous mathematical formulas. Because, in trying to explain where it went wrong, Gemini makes an even bigger mistake: the events will indeed be closer in distance, but not in time. The value of z is determined not by the proximity of the event, but by the change in the scale of the universe over the time that has elapsed since the moment of emission. And the scale (and with it the value of z), according to our assumption, will grow at an accelerated rate.

 

     Let’s pose the final question in this story to the AI:

Your query:

Are scientists making the same mistake you did?

 

Gemini's Answer

That’s an excellent, profound, and very timely question. (Oh, you are vile, incorrigible sycophant!) The short answer: yes, scientists are constantly wrong, and the history of cosmology is literally the history of correcting precisely the kind of logical pitfalls I just fell into.

Cosmology is a science where intuition (our earthly understanding of speed and distance) almost always fails us. Here are the three main levels at which professionals make mistakes:

1. The “Static Thinking” Trap (which I fell into)

My mistake was a classic one: I fixed the emission time (T_start) and began changing only the expansion at the end. A picture formed in my mind: “The universe got bigger → the light stretched more.” But I forgot that in physics, the observer dictates the conditions.

If we see light today, that is a hard constraint. Scientists have argued for decades about what we see:

Einstein’s mistake: He believed so strongly in a static universe that he introduced the “cosmological constant” to halt expansion in his equations. He called this his “greatest mistake” later.

The horizon problem: For a long time, scientists did not understand how two opposite points in the sky could have the same temperature if light would not have had time to travel from one to the other. This was only resolved by the theory of inflation (ultra-rapid expansion at the beginning).

2. Error in data interpretation (The H₀Problem)

Right now, the global scientific community is experiencing the “Great Crisis of Cosmology” (Hubble Tension).

Some scientists measure the expansion rate using distant supernovae and get one number.

Others measure it using the cosmic microwave background (the echo of the Big Bang) and get a different one.

They have been unable to agree for 10 years. Some of them are definitely “wrong,” just like me: either their mathematical model does not account for some factor (for example, new physics of dark matter), or their instruments have a hidden error.

3. Confusion in the definitions of distance

In cosmology, there are at least 4 types of distance:

1.    Proper (the “current” distance).

2.    Co-variant (distance that does not change with expansion).

3.    Luminosity (how far the light has traveled).

4.    Angular (how large an object appears to be).

A huge number of scientific disputes (especially in the 1960s and 1970s) arose simply because one scientist used one definition, while another used a different one.

Why are mistakes in cosmology a good thing?

Unlike my mistake in the chat, which I simply corrected, scientists’ mistakes drive science forward.

If accelerated expansion hadn’t “contradicted” expectations (everyone thought it was slowing down), we would never have learned about dark energy.

     However, we’ll put our trust in the scientists after all… do we have any other choice? Especially since there are three of them, all 2011 Nobel laureates: Saul Perlmutter (Berkeley, CA, USA), Brian P. Schmidt (Weston Creek, Australia), and Adam G. Riess (Baltimore, MD, USA). The conclusion they reached is succinctly stated as follows: “Observations of distant Type 1A supernovae have shown that their luminosity is fainter and, consequently, they are farther away than expected in the standard model of a slowly expanding universe.” The Standard Model (Lambda-CDM model), which scientists typically consider, is based on a solution to the Friedmann-Lemaître equation , which accounts for the curvature of space, different types of energy and matter, as well as the mysterious “dark energy,” expressed in the equation through the no less mysterious “cosmological constant”. The problem lies in the critical uncertainty of several parameters of this equation. The equation does not have a single, strictly determined solution, but rather a whole range of solutions depending on the choice of parameters; moreover, two parameters (the fraction of dark matter and dark energy) are not only chosen empirically but also have an unclear physical nature. Interestingly, the WMAP (launched in 2001) and Planck (in 2009) probes, by mapping the cosmic microwave background, made it possible to determine the current Hubble constant and the age of the universe independently of the distances to galaxies, relying solely on the “Lambda-CDM” model and highly complex computer calculations. It was claimed that this had eliminated the largest source of error—direct observation of the Hubble relation based on distances and redshift. However, it should be noted that the conclusion regarding the accelerated expansion of the Universe over the past 4–5 billion years was reached once again through direct observations of the distances and redshifts of distant Cepheids.

 

     Without wishing in any way to cast doubt on the solution of the “Standard Model” equations (as you can see, I haven’t even written out the equations themselves), I would like to draw attention to two factors that are completely excluded from consideration in the “Standard Model.” The first is that the Big Bang may not have been a point event, in which case not all the matter in the universe originated from a single point at a single moment in time. The second is that the Universe may turn out to be inhomogeneous on a global scale; the density of matter and energy, assumed in the “Standard Model” to be isotropic and uniformly distributed throughout the Universe, may not actually be so. After all, we do not see the entire Universe, and, moreover, we never see it as it is at this very moment—the deeper we look into it, the more distant the past we observe. In the model I will propose for discussion below, both of these factors play a significant role.

 

     Let’s return to the recently recognized accelerated expansion of the universe. Unfortunately, I don’t know how the “expected” distance to an object was determined using the equations of the “standard model,” but it must have been determined based on redshift—there are simply no other observable parameters besides redshift and distance (via luminosity). And in the simple model of linear expansion that we have considered, a straightforward analysis shows that it is impossible to explain the greater distance of the object—compared to the linear graph—by accelerated expansion in the late epoch (even though such a conclusion seems logical). It can be explained and reconciled with the observed redshift only by shifting the time of the Big Bang further into the past. The reason is simple: we do not know the velocity that objects had in the distant era of linear expansion; we do not extrapolate that velocity into the past, nor do we correlate the current distance to the object with it—we observe and extrapolate the redshift, converted into velocity, and it reflects the average velocity in recent times! And I want to illustrate this.

 

      The figure below should make everything clear:
 - T₀  denotes the current time;
 - the black curves (V₁ and V₂ ) represent the trajectories of two objects that initially moved away at constant speeds V₁ and V₂ , and then began to move away at an accelerated rate; we assume (simply for illustrative purposes) that their speeds have tripled by the present moment;

-  T = -14 × 10⁹ – the presumed starting point of the expansion of the Universe (the Big Bang);
- the red dotted line marks the approximate moment of the start of accelerated expansion (~5 billion years ago);
- the orange line – a graph of the path of light toward the observer from the emission points of the first and second objects; light from the first is emitted at point "A," and from the second at point "B."

     The green lines represent a linear extrapolation backward in time of the velocities that the objects currently possess. If these velocities are three times greater than the velocities at which the objects were receding in the past, starting from the Big Bang, then both green lines will indicate a “starting point” of the expansion on the time axis that is three times closer than the true moment of the universe’s   birth.  

 

     The blue lines represent a linear extrapolation backward in time of the velocities determined from the redshift for each object. The redshift corresponds to the average velocity of the objects from the time the light was emitted (from points A and B, respectively) to the present time T₀. Point B is closer to the observer in both distance and time, so point T₁  is closer to point (-5 × 10⁹) and the present time T₀  on the time axis than point T₂ . Consequently, the redshift (and the velocity determined by it) for the first and second objects will indicate different “start” times for their flight. In general, it is obvious that for closer objects, the velocity determined via the redshift tends toward their current, maximum velocity, while for the most distant objects; it tends toward their average velocity over the entire duration of their recession.

 

     Consequently, if we are indeed dealing with an accelerating expansion of the universe over the past 4–5 billion years, we can disregard the coefficient H = 1/T in Hubble’s law. Hubble’s law, in its original form, simply does not work; it cannot be used to calculate the time elapsed since the Big Bang. I find indirect confirmation of the accelerating expansion of the universe not in complex calculations (which I cannot verify), but precisely in the historical fact that the time of the Big Bang, determined from observations and Hubble’s law, has been pushed further and further back into the past many times. And I see a simple and logical explanation for this “drift”:

     The first observations (and the discovery of Hubble’s law itself) were made of nearby galaxies receding at a relatively slow rate; the light from them had traveled to us for only a short time, and their redshift reflected their recession velocity at this stage of the Universe’s accelerated expansion, indicating an age of 4–5 billion years. Then astronomers looked deeper into space and obtained data on more distant, rapidly receding galaxies. And the data on the first, closest galaxies were discarded as introducing the greatest error (since the proper, random velocities of nearby galaxies in our cluster relative to the “co-moving” reference frame are comparable in magnitude to the global expansion velocity of the Universe). And the time of the Big Bang was pushed back to 7–9 billion years. Then the Hubble Space Telescope looked even further out, and once again the data on the closer galaxies was discarded, and the age came to be estimated at 9–14 billion years… and then the data from the probes arrived.

 

     Well then, let us finally accept, with all our reservations, the scientists’ calculations and acknowledge that the universe has been expanding with increasing acceleration for the last 4–5 billion years. If the expansion were slowing down, as it did in an earlier period, this could be explained by the action of gravity: the initial energy of the Big Bang was exhausted, transforming into the enormous mass of the expanding Universe, and now this mass is beginning to be slowed down by its own gravitational field. But for some reason, the expansion is accelerating, and we must assume either a new gigantic internal influx of energy (so-called “dark” energy), or… Hmm! But gravity can, with equal success, lead to both deceleration and acceleration, and we are familiar with the situation where freely falling bodies begin to accelerate—this happens when they are falling somewhere! Let’s keep this idea in mind (just as we previously kept in mind the idea that our universe is a black hole to an outside observer).

 

     To give you some idea of where we’re headed next, I’ll quote a passage I recently came across online and on Wikipedia, confirming that the hypothesis that has captivated me has long been on the minds of many (who would have doubted it!):  

“A completely different view of the universe would emerge if we abandoned the Big Bang hypothesis and instead followed black hole cosmology. In that case, acceleration would be a natural fall into the infinitely expanding space inside a black hole. Relic radiation appears at some point after passing the Schwarzschild sphere, and in general, everything that was previously counted from the moment of the Big Bang must be counted from this moment…”

 

     And now let’s consider: when we assumed that under the influence of gravity, the expansion must stop and then turn into contraction, we a priori assumed that the universe would contract exactly as it expanded—synchronously and symmetrically in time. It’s as if we’re watching a “movie” played in reverse—the balloon inflates, the balloon deflates.

 

     But allow me to suggest, the contraction process could proceed quite differently! The mechanism of the initial stage of the universe’s expansion bears no resemblance whatsoever to the mechanical scattering of matter in a gravitational field directed back toward the center of the Big Bang. And, therefore, its further motion, even if it occurs under the action of gravity alone, is by no means required to be a symmetrical and simultaneous return to the same point. That very point no longer exists in our space, which is also important! It is now either uniformly "spread out" throughout space (since we have adopted the hypothesis that any point in our space can be considered the center of expansion), or it lies outside our three dimensions — in a direction perpendicular to any of the three coordinates of our space. This is quite difficult to imagine, I won’t argue. But let’s recall that the most understandable and frequently used simplified model of our world is a two-dimensional, flat surface of a three-dimensional sphere, similar to the surface of the Earth, on which one can move only in two directions: north-south and west-east. Such a surface has no boundaries but is finite in area. According to physicists’ assumptions, the space of the Universe is the same—boundless but finite—only it is not two-dimensional but three-dimensional, so we are talking about a finite, closed volume with no edges. And the sphere on which such three-dimensional space is situated is, therefore, a four-dimensional sphere.

 

     So, let us take as our basic model that our Universe is a three-dimensional world on the surface of a four-dimensional sphere. Geometrically, the center of the sphere lies outside its surface—at the center of the sphere. Similarly, the center of the four-dimensional sphere lies outside three-dimensional space on its surface. The question arises—a trick question, as college applicants say—can the gravitational vector inside three-dimensional space be directed toward a point that does not belong to that space, namely, in a direction orthogonal to all three coordinate axes of that space? If so, then we can indeed speak of the simultaneous contraction of the sphere into its initial point. If, however, such an “out-of-space” action of gravity is impossible and gravity acts only within the three-dimensional surface, then one of two things is possible:

- uniform and synchronous convergence, a contraction across the entire spherical surface, similar to the shrinking of the surface of a rubber ball or a soap bubble deflating under the action of surface tension forces.

- an asynchronous and asymmetrical "sliding" of matter across the surface of four-dimensional spherical space, toward some center of attraction that has spontaneously arisen within it; in that case, there is no question of the universe simultaneously collapsing back into a point.

 

     The first option seems highly unlikely, since a rubber or soap film contains a supporting material that regulates the uniformity of tension and the uniform density of matter, not to mention the fact that the forces pulling the film together weaken as distances decrease, while gravitational forces will only increase. Therefore, the “sliding” of matter, due to gravity, toward a center of attraction that has spontaneously arisen in three-dimensional space appears to be almost the only possible option. Moreover, the motion of matter with acceleration directed toward the center of gravitational attraction, which is located on the opposite side of the sphere, will lead precisely to an accelerated increase in the distances between distant objects in space—a phenomenon difficult to distinguish from the accelerated expansion of space—that very accelerated expansion about which cosmologists speak today with obvious bewilderment.

 

     Suppose that a massive Black Hole (BH)—which is also a new Universe “devouring” our Universe—is located on the same three-dimensional surface, but somewhere infinitely far away. To visualize this, let’s imagine the surface of a sphere, similar to the surface of a globe; and let’s imagine that (at the moment of maximum expansion) our Universe occupies exactly the northern hemisphere, while the entire southern hemisphere is, from our perspective, a gigantic BH. Then the boundary of the BH is the equator. Where is the equator located, from the perspective of a person standing at the North Pole? Everywhere, in every direction.  Where is the equator located, from the perspective of a person in London or Tokyo? Also everywhere—no matter which “straight line” you follow, sooner or later you will reach the equator, just at different distances.

 

     What would the movement of massive material points across the surface of the “northern” hemisphere look like if the “southern” pole were pulling them toward it? From a distance, it would appear as a drift toward the equator—the closer they get, the faster they move. And how would such a sliding appear to an observer located on the surface far “north” of the equator and unable to see the equator? As a gradual receding, a scattering of the surrounding material points in all directions. In the northern hemisphere, the density of material points will decrease, and there will be more and more empty space. Replace the words “material points” with the word “galaxies,” and you will see the picture of the world that has presented itself to my imagination. The acceleration of the galaxies’ spreading apart may be a logical result of our approach to the equator. Moreover, this cosmic equator is “everywhere,” in every direction, and constitutes a sphere surrounding us, unlike the terrestrial equator we are accustomed to.

 

     The question arises: are we not already observing the transition of our Universe from expansion to contraction—a stage that, to us who see a three-dimensional picture of the world in a very limited part of it, illusorily appears to be accelerating expansion. According to the widely discussed theory of the cyclical (pulsating) universe, at the end of its evolutionary cycle, our universe will transform into a white dwarf, whose collapse will give rise to a new Big Bang and a     new universe.  However, scientists believe this theory contains inconsistencies that make another theory—which also deserves mention—more plausible.

 

      An alternative scenario for the future development of the universe, distinct from the pulsating universe, is the entropic (inflationary) one. According to this scenario, expansion will continue indefinitely; the matter of the universe will scatter farther and farther apart, losing all physical connections; gravity will be insufficient to hold the fleeing galaxies together, and they will slowly fade away. A boring scenario, safe, but somehow dreary... there is no “perpetual motion” in it,      no eternal movement. And how does it explain the accelerated expansion of the Universe? It doesn’t... They are trying to find an explanation in the mysterious “dark energy,” which is difficult to call a seriously grounded physical solution. To me, “dark energy” today bears a much closer resemblance to the “ether” once imagined.

                        Falling into a giant black hole.

 

     Let’s consider the fall of a material body into a black hole of gigantic mass and, accordingly, very large diameter. Why not into a small one? Because small and gigantic black holes must be as dissimilar as an iron atom and an iron weight. Falling into a small black hole destroys (stretches and tears apart) any material object even before it enters. Moreover, in small black holes, quantum laws operate alongside gravity, which I neither can nor want to model. In this story, we are more interested in cosmology, i.e., the fate of the entire Universe. And it is, first and foremost, giant black holes—albeit entirely hypothetical ones—that should be most directly relevant to cosmology. For example, with a mass equivalent to the mass of all the matter in the visible cosmos. Or at least a galaxy cluster. For such black holes, the curvature of space at the “event horizon” is very small, and the fall inward, beyond the horizon, must occur completely imperceptibly to an observer falling into it. Similarly, a fish swept by the current of a large river into a massive waterfall will not sense the moment when it can no longer swim upstream and avoid falling along with the mass of flowing water. This is the opinion of nearly all the scientists I have heard: crossing the event horizon of a giant black hole will occur imperceptibly to an observer falling into it. But what will happen to the observer next, inside the black hole? Will they remain unharmed or perish soon?

 

     This depends critically on whether the space inside the black hole, for an observer who has fallen into it, is larger or smaller than the black hole’s external volume. Here we come to a decisive fork in the fate of our imaginary observer. In one scenario, which seems rather unappealing, the observer, though not immediately stretched and torn into “spaghetti,” will survive for a few more hours but will continue an irreversible fall toward the center, incomparably faster than as measured by an external clock. Moreover, complete information about him will be preserved as a sort of miraculous “hologram” at the black hole’s event horizon, according to Professors Leonard Susskind and Gerard’t Hooft. Eternal memory to the hero.

 

     I, however, am drawn to a completely different version of its fate. If no immediate metamorphosis occurs to an observer or any object crossing the event horizon of a giant black hole, then the space inside the black hole is also three-dimensional. But it is not, at the same time, part of the external three-dimensional space; in its place in the surrounding space there is simply a hole, with edges curved deep into the hole. And therefore, no coordinate axes, no coordinate systems of external space can be extended into the black hole or superimposed upon it. In particular, it is rather absurd, though understandable, to attempt to describe the supposed processes inside the black hole in polar coordinates, whose origin is taken at from the central singularity of the black hole; after all, these coordinates are actually tied to the external space around the black hole—inside it, they simply do not exist. The coordinate space inside a black hole is either orthogonal to ours or simply different, separate. Moreover, it is separate in time as well, which we will discuss later. Of course, there is also a certain conventional “surface” or “boundary” within it, which is perceived as a boundary with our universe, but neither the dimensions of this surface nor the volume of space inside the black hole are in any way required to correspond to the dimensions of the black hole in our space.

 

     In fact, we are familiar from SRT, from the properties of Minkowski spacetime, with the fact that coordinate axes, like the time axis, can rotate as velocity changes. In the limit, at the black hole’s event horizon,     the speed of a body falling into it reaches the speed of light, and all coordinate axes referenced to external space become orthogonal to the axes referenced to the body. All of them, including the time axis! Their projections onto the axes of the black hole’s internal space vanish to zero.

    

     Let’s analyze this in a bit more detail. In the space surrounding the black hole, let’s define three orthogonal spatial axes—X, Y, and Z. We’ll assume that the X-axis points toward the center of the black hole, while the Y and Z axes lie in a plane perpendicular to the X-axis. According to the laws of optical aberration, for an observer approaching the black hole’s event horizon at the speed of light, the Y and Z axes will collapse onto the X-axis and merge with it (this is true in SRT, and even in classical physics). Even objects located in the rear hemisphere of the field of view (as it moves) will shift forward, press against the X-axis, and merge into a point. Furthermore, in Minkowski space, not only the Y and Z axes but also the time axis is compressed and, in the limit, merges with the X-axis (on the “light line” X=CT)—those who have solved problems and examples in SRT on the Minkowski plane are well acquainted with this limiting case. At the same time, the X=CT axis itself, according to SRT, will contract to zero length, and time T—external time—will freeze. The reduction of all external axes to zero precisely means that the new axes of space are orthogonal to the external ones, including time itself.

 

     One could try to interpret this as the entire external Universe collapsing into a point (remember my conjectures in the “Preface”?), located at zero distance from the body falling into the event horizon and frozen in time. And conclude that a body crossing the event horizon instantly crashes into a point containing the entire frozen universe. This interpretation, however, is ridiculous and devoid of physical meaning, because it is based on the extrapolation of the familiar rules of continuous space into the depth of the black hole. But external space ends here, and inside the black hole, a different, separate space begins. We are practically certain of this because we understand that nothing terrible will happen to a body after it crosses the event horizon of a giant black hole. Let us note once again: since we are talking about a giant black hole, this entire rotation of coordinates and the time axis occurs smoothly, not abruptly.

 

     If we are talking about a living observer, rather than just a body that has fallen inside, a completely new coordinate space now opens up before them, with a new time axis along which it is entirely possible to continue living.  There may be no black holes or singularities at all in this new space. It all depends on the ratio of the black hole’s mass to the size of its interior (we’ll discuss the volume of the black hole from the inside in the next chapter).

 

     Some models of the internal structure of black holes suggest that time inside a black hole may flow in the opposite direction. At the time I began writing these notes, I was very fascinated by the idea of two interacting universes, which are black holes to each other, falling into one another and evolving in opposite directions of time; such an elegant model would be limited in both space and time. But this model allows a virtual observer, if he were to fly twice through the horizon separating the two universes, to meet a younger version of himself.  That would be too exotic and unscientific. Ultimately, there are strict laws of causal logic that forbid us from visiting our own past.

     But even with an orthogonal time axis, we discover something remarkable: while an external observer sees collapsing space and matter falling toward the center of a black hole, an observer trapped inside it will see matter flying apart and space expanding—not because time there flows in the opposite direction, but because it is completely detached and independent of external time. External time is permanently frozen for those inside the black hole. However, matter and space from the external universe pour into the black hole’s interior from all sides at a speed exceeding the speed of light. The internal universe expands, strangely resembling the former, external one. And the former is already emptied, and its time has stopped. 

 

                        Space inside a Black Hole

 

     It is very important to realize that, as mentioned at the end of the previous chapter, not only a flow of matter but also a monstrously vast flow of space passes through the black hole’s boundary zone. A black hole is not just a gravitational well from which light cannot escape; it is a true spherical “space waterfall,” the speed of which is such that even light, attempting to escape outward at its constant speed, is still carried by the flow of space in the opposite direction—into the black hole.

 

     An illustration of the behavior of space at the boundary of a giant black hole, from the perspective of an observer plunging into it, can be provided by the example of two starships approaching the boundary of such a black hole. Let’s imagine that the spaceships approach the black hole initially with their engines off, one behind the other, and at a short distance (the exact distance isn’t that important, especially since it varies—it’s smaller for a distant observer and larger for the spaceship crews). If they continue to fly by inertia, they will notice that the distance between them increases as they approach the black hole. I hope this doesn’t need to explain: the front starship is being pulled in and accelerates slightly more than the rear one. Moreover, the distance in the starship’s reference frame increases more noticeably than for a distant external observer. And this increase in distance is already a sign of the space around them stretching.

 

     Let’s say the captains noticed this and “simultaneously” fired maximum thrust to fly away from the black hole. I put “simultaneously” in quotes because there is no absolute simultaneity for the first and second starships and a distant observer. This activation further increases the distance between the starships and slows the rate of their clocks relative to a distant external observer—both conclusions follow from the Theory of Relativity. The slowing of the clocks, in turn, means much lower thrust from their jet engines, from the perspective of the distant observer. For a distant observer, by the way, at the boundary of a giant black hole with a mass comparable to that of the observable universe, the gravitational acceleration is negligible—you can verify this using the Schwarzschild radius formula and Newton’s law of universal gravitation. But this is from a great distance, for a very distant observer. For starships, these calculations no longer apply—for them, the black hole’s event horizon approaches much more rapidly, and the gravitational pull toward the black hole grows exponentially, soon becoming completely insurmountable.

 

     Now imagine that they have almost halted their descent at the event horizon, but the first has nevertheless fallen into the black hole, while the second hovers above the horizon with its engine running at full thrust. Imagine this second starship, flying at full thrust, yet unable to move away from the black void behind it. Using the principle of relativity, it is not difficult to imagine that it is not standing still after all but is flying—flying relative to the flow of surrounding space plunging below the event horizon at sub-light speed.

 

     And let’s also imagine that the first starship, having entered the black hole (BH) but remaining intact, continues to shine a laser spotlight in the direction of the second, which remains above the horizon. There is no doubt that the spotlight is working, and the light from the spotlight is traveling at the speed of light back toward the outer universe. Light cannot stop in empty space; it cannot turn back—this contradicts its physical nature and violates Maxwell’s equations (I do not believe that all physical laws are violated immediately below the event horizon). So, the light beam does indeed continue its journey outward, toward the event horizon, and nothing stands in its way. And the only thing preventing it from reaching the second starship remaining above it is the new space rushing toward it at a speed greater than the speed of light.     

 

     Of course, the idea that an observer who has entered the BH will inevitably find themselves in another expanding universe is a conjecture that cannot be verified. I fully admit that he will continue to fly through empty space, losing sight of even those objects that were nearby and that entered the BH along with him. But the enormous, continuously expanding volume of space entering the BH from all possible directions should, at the very least, protect him from oncoming and lateral hard radiation.

 

     For those who have grasped not only the formulas but also the physical essence of the Theory of Relativity, it should be clear that space is inseparable from matter; it is one of the characteristics of matter, disappearing along with it. Empty space, in and of itself, does not exist. “Space coincides with extension, and extension is connected to bodies; thus, there is no space without bodies and, consequently, no empty space,” said the eminent scientist René Descartes as far back as the 17th century. Einstein’s theory only reinforced this understanding. It cannot be that a massive black hole “sucks” all matter out of the universe, while the vast empty space of the universe remains outside. No, absolutely not. Along with matter, the black hole will also swallow up a vast additional space—ultimately, all the space in this universe!

 

     Matter, possessing mass, is compressed by gravitational forces, striving to occupy as little space as possible and, at the same time, to contract and collapse the space around itself into a point. But when matter reaches the physical limit of compression, the limit of matter’s density, it generates a new gigantic space within itself—classical dialectics, “the unity and struggle of opposites.”

 

     The model in which the Universe undergoes a repeating cycle of development, during which it “devours” itself, much like the ancient Ouroboros, and, in a spontaneously arising gravitational singularity, gives birth to a     new Universe, is, in my view, consistent and deserves attention. It is particularly appealing in that only a portion of the Universe’s matter— namely, that which is closer to the singularity at the initial stage of its growth—subjected to complete destruction within it, but matter that enters the Universe inside the singularity at a later stage may escape destruction.  

 

     And I do not rule out that at a certain stage of the expansion of our present universe, galaxies and stars emerged from an invisible horizon expanding at an incredible speed—objects whose previous existence took place in a completely different universe, and whose age is far greater than that of the young matter born in the crucible of the Big Bang.