Human insights in exploring the universe
 

by Karl-Herbert Darmer

physik@darmer.de

Introdution:

The James Web Telescope shows us ever deeper insights into the universe. However, more and more images are being discovered that fit in no longer unproblematic in the standard model of cosmology. There are more and more voices loud saying: The model needs to be adjusted. But at what point would one have to start, with the changes?

In modern science, many statements are made and presented as facts or proven. What I am missing is a clear outline in assumptions, observational matters and with the help of what assumptions we interpret these observational matters. Only when these assumptions are exactly clear, do we know what our conclusions are hanging out. Because none of these assumptions has to be true.

Can a theory be “proven”? Each theory contains assumptions. Provided that these assumptions are correct, one can only mathematically show that the theory is in itself free of contradiction. If measured values can be mathematically summarize without contradiction, does this really mean that we have fully grasped the process? And what does it mean if we cannot summarize these measured values without contradiction.

Newton's gravitational laws provide us with good tools to describe the motion of celestial bodies. We cannot explain the discrepancy in Mercury's perihelion precession with this. In this case, the solution was to change the formulas used to calculate the expected measurements. Based on Einstein's theoretical considerations of the equivalence principle and based on the postulates of special relativity, he developed the general theory of relativity. With these formulas, it was then also possible to calculate the discrepancy in Mercury's perihelion precession.

Then it was discovered that stars on the edge of galaxies move too fast for the visible mass of the galaxies. To solve the problem without changing the formulas, Fritz Zwicky postulated dark matter in 1933. But was that the right way?

Later, Albert Einstein doubted that the basic assumptions were so correct, which earned him a great deal of contradiction. What he did express in a letter in late 1949 to Solovine. I would like to quote this here (probably with translation mistakes):

“I am very touched by your cordial letter, which so much differs from the other countless letters that come upon me on this unfortunate occasion. You imagine it in such a way, that I look back on a life’s work with quiet satisfaction. But it's quite different from the proximity. There's not a single term, of which I would be convinced that it will stand, and I feel insecure whether I am on the right path at all. But the contemporaries see in me at the same time a heretic and reactionary, who survived himself, so to speak. However, this has to do with fashion and short-sightedness, but the feeling of inadequacy comes from within. Well -- it can't be any different if you are critical and honest, and humor and modesty keep you in balance, despite the external influences.”

Einstein was not only a brilliant thinker, he also dealt critically with his own ideas throughout his life. If I have correctly understood, the few what I read about his late thoughts, he wanted to introduce a field to which you can move.

Almost a hundred years later, we still have no experimental evidence of the dark matter postulated by Zwicky. I want to take all this as an occasion to think again very fundamentally about human knowledge.

From these considerations, I developed an idea that, based on different assumptions about the properties of the gravitational field, could explain the motion phenomena observed in the universe, even without dark matter. It also predicts the outcome of an observation that could verify it and thus put dark matter in jeopardy. Alternatively, if the observation confirms dark matter, it would clearly refute my idea. Unfortunately, I had to learn from Prof. Pawlowski that the current measurement accuracy is not sufficient to decide this.

During the Gaia mission, stars were discovered that move in the opposite direction to the general motion of the spiral arms. According to my idea, based solely on visible matter, they should move along their exact orbit precisely at the rate by which the others move too fast. Based on visible matter, along with dark matter, they would of course also move too fast. Such an observation would clearly refute my idea.

Perception world :

I start with the saying of Descartes “I think, so I am”.

Anyone who has seen the movie “Matrix” by Lana and Lilly Wachowski will understand better what I am writing about. In this world, people live in only a nutritional cocoon, which they do not perceive as such. Everything you experience is done through a data cable and only takes place in a digital world. How do I “know” that it doesn’t go for me exactly like this? No matter how I think of to prove, there exists something else, differing from my experienced world of thought, it is inevitably part of the “reality of these thoughts.” So the “evidence” is only as “real” as this “reality of thoughts.” There are no limits in this world of thought, except the limits of my imagination.

This could be carried out further. But I want to take the next step. What does it mean to assume something, or to believe. I assume my world of thought is not the only one, but there are billions of other beings who have their own world of thought. With this assumption, the possibility is excluded that my world of thought is the only one. But I keep in mind that I may have been wrong with this first assumption. If I was not mistaken with this assumption, further assumptions will follow from it. Because I cannot perceive the thought world of others, there must be something that divides us. On the other hand, I can communicate with these worlds of thought. That's why there must be something, what connects these thought worlds.

I would like to make a comment on this. If someone in his own world of thought reads this text, he might think: what does he actually write about? I think and he thinks, so there are several worlds of thought. But how can he prove that I am not only the thorn that springs from his world of thought and wants to pretend to him that there is more than his thought world. Maybe with telepathy? But I also believe that this is only the product of an imaginative world of thought. The reasoning should become clear from the following.

From where does my world of thought get its information? About my sensory cells, which send electrical impulses into the brain via nerve pathways. Here is created a “world of perception.” This has not more to do with the reality of the universe surrounding us, than these electrical impulses do. From these impulses I shape my world of thought. That's why it just depends on only from these impulses. This world of thought does not have to correspond in any way to the reality of the universe surrounding me.

To better understand what I mean, you have to imagine images with optical illusions. For example, you could search on the Internet for “Optical illusions simultaneously glasses and faces”. Then you get pictures where You can see glasses or two faces in the profile.

In the world independent of the world of thought, I would like to call that the universe, it is only color or lines on paper. No glasses or faces. In our mental world, the electrical impulses we receive from our eyes are mixed with earlier impulses and therefore we “see” glasses or faces. But that only exists in the mental world. In this mental world, the images are “real” but they do not exist in the “reality of the universe.” This reality is completely independent of the thoughts of the people. The universe works according to its own properties. It existed even before man developed on earth, observed this universe and thoughts about his observations were made. And it will also outlast man in its functioning, regardless of whether man even approximates the functioning of this reality in his world of thought retrofit.

Here, some assumptions have already crept in. The most important is my belief that there is a real existing universe. From this we receive about our senses electrical impulses, from which we create in our thought world a real world of perception for this world of thought. That this universe outside the human world of thought exists, man cannot prove. The electrical impulses that arrive in our brains could also come from a data cable from a computer program.

To make it more understandable. There are people who are color blind. This inevitably leads to the fact that their world of perception looks different than that of a not colorblind. This distinguishes the reality of their worlds of perception. But this has no influence on the reality that surrounds both. This is the same for both of them and it is from both independent.

I therefore assume that I can actually perceive something from the reality of the universe surrounding us through my sense organs. And I can process that in my world of perception. This reality of the world of perception coincides with the other only approximately as far as one interprets one’s senses correctly. But there are sensory illusions in very diverse way.

Measuring instruments :

What possibilities do we have to improve this. You can design measuring instruments that can determine many things more precisely. You can even use it to perceive physical phenomena that do not grasp our senses at all, such as Radioactivity or light of other wavelengths, from the infrared or gamma-ray range. Measuring instruments, like the James Webb Telescope, can show us images from very distant areas, that we could actually perceive with our senses.

Are we thereby freed from the problem of misinterpreting the electrical impulses that reach our brain? Do these measuring instruments allow our conception of the reality of the universe around us to be exactly as it is? Unfortunately, no. We have to equip our measuring instruments with some assumptions in order to obtain usable measurements. However, these assumptions do not necessarily have to be correct.

The most important is the assumption that our measuring instrument provides constant measured values. Therefore, measuring instruments must not change over time. As Example we take a plastic tape that slowly loses its plasticizers and shrinks as a result. This may be useful at the beginning, but in the long run it is unsuitable.

It must not deliver different values under different conditions. Let's take a balance scale and a spring scale. We weigh a sample mass of one gram. First with the spring scale and then with the balance scale. In both cases, we get the measurement result one gram. Then we repeat the measurement on the moon. On the moon with the balance scale, we again get the measurement result one gram. The measurement result of the spring balance is much lower. With both instruments we do not measure the mass directly, but only the force with which this mass is attracted by the underlying celestial body. It is different on earth and moon. In the spring scale, we measure this force by a spring tension. The force is lower on the moon, so is the measurement result. With every measuring instrument, we make assumptions about what it actually measures. This becomes particularly important when the measurement involves areas that we cannot monitor with our senses.

In the balance scale, we compare the force with which our sample is pulled down, with the force with which a calibrated sample is pulled down. Objects with the same mass are attracted with the same force. It is no different on the Moon than on Earth. That's why we get the same measurement result. From the constant measurement result of the balance scale, we cannot conclude that nothing has changed in the environmental conditions. In general, it means that we can never conclude from a constant measurement result that nothing has changed in the reality of the universe surrounding us. On the other hand, I cannot conclude from a changing measurement result that the thing to be measured has changed, here the mass of my sample. It could only be the changed conditions for my measuring instrument. The gram is still the same, even if the condition for the measurement result of the spring scale on the moon has changed. Mass is made up of matter. I can hold it in my hand and examine it in different ways with my senses. But what about 'time'? I cannot perceive it with my five senses. And what does my clock measure? I want to address that in the following topic of time.

Let's take an iron bar. Make two notches on it at the defined distance of one meter. We measure the length of other iron bars with that. Then we'll repeat that at different temperatures. We always get the same measured value for the length of the iron bars. From the constant measured values, we cannot conclude that the iron rods in the reality of the universe surrounding us actually have the same lengths at different temperatures. That is only in the world of perception of this instrument. Of course, you recognize very quickly that something can't be right. You can bring the measuring instrument iron bar and the iron bar to be measured to different temperatures and hold it next to each other. Then you can see how the different length also aligns with the temperature compensation of the iron rods. You can quickly see here that my measuring instrument changes under the changing environmental conditions just like the object being measured.

What about the speed of light? In the case of problems relating to the special theory of relativity, the time measurement is often carried out with light clocks. Also at Wikipedia is described in the explanation of the time dilation a light clock. The time cycle of a light clock is determined by the speed at which a light signal moves back and forth in the clock. If one measures the speed of light with such a clock, the logical consequence is, as with the iron bars, that even under different conditions the same measured value will be achieved. From this it can be concluded that even if in the human world of perception the speed of light is always measured with these measuring instruments at constant speed, it in the Reality of the universe surrounding us, can actually be different. All high-precision watches use light as the basis of the time cycle, if only on a lot smaller space. In principle, this makes no difference. What consequences this will get, I will explain later.
 

Time :

Another example of the problems with measuring instruments is the definition of the second. It can be defined as the 86,400mth part of a day. For a person's wristwatch it may be enough. But with increasing measurement precision and consideration of astronomical times, that is not enough. The rotation speed of the Earth varies greatly short-term. This is important in astronomical considerations and must be taken into account. And in the long term, the earth revolution is slowing down due to tidal friction. What leads to this, that the days are getting longer. The day is not a suitable basis for defining timekeeping.

Today’s definition: “The second (sign s) is defined as the 9,192,631,770 time the period duration of the radiation that the transition between the two Hyperfine structure levels of the ground state of atoms of the nuclide cesium-133 (133 Cs) correspond to.”

Have we eliminated all fundamental problems of timekeeping? No! Since 1971, we have known through the Hafele and Keating Experiment that atomic clocks moved eastward are measured as slower-going and moved westward as going faster. Why are they doing this? It can be assumed that each system has its “own time.” Since the „own time” at westward moving clocks go faster, the clocks also have to go faster. Is the causality of the change in the time cycling actually given in this form?

Let's set an atomic clock next to a pendulum clock and synchronize it with each other. After that, we'll take them up a mountain. The distance to the the axis of rotation of the earth should not be changed, so that the speed has no influence on the clock cycle. If only the Earth's gravity is lower, then the atomic clock goes faster. On the other hand the pendulum clock is going slower. If the “own time” in the different places were the cause, then both clocks would have to behave in the same way. - Or does the pendulum clock have nothing to do with time, only the atomic clock does? I suppose both are clocks and the “own time” of a system is not the cause of the changed clock cycle, but the changed environmental conditions.

I suppose that the atomic clock and the pendulum clock are both measuring instruments that regularly mark repetitive events and thus in principle as time measuring instruments suitable. Since they are based on different physical functions, changes in the environmental conditions also have a different influence on their measured value, as in the case of balance scale and the spring scale. This difference in time readings consists only in the world of perception of these instruments, but does not necessarily have to make a difference in the time of reality of the universe surrounding us. Of course, these measuring instruments work in the reality of the universe surrounding us exactly as the properties of this universe determine it. How, from this world of perception of the instruments, our idea of time arises, depends on the assumptions with which we provide the functioning of these instruments. I assume that all “clocks”, better all repetitive events need a certain “time”. This “measured time” in our world of perception has no fixed or absolute connection with “time itself”, or better the time of the reality of the universe surrounding us This time itself would be only part of the reality of the universe surrounding us and with that it could always be the same for everyone. Depending on the environmental conditions, the time cycle of a clock changes relative to the time itself. Unfortunately, we humans cannot measure this “time itself”, but only compare two repetitive events with each other. The result of this comparison could be a constant value. We might also find that the values are changing. But we still don't know whether one process becomes faster relative to the “time itself” or the other one slower. The whole world of perception of the mankind is as relative as these comparisons.
 

Space-time :

But the relativity of the measured values in our world of perception is not the only problem in the perception of space and time. We can't isolate the measurement of time. Let's take the pendulum clock. It is quite obvious that the clock’s time cycle is determined by a motion in the room. Also in the atomic clock, a motion is measured, here the motion of a photon in a smaller spatial area, but ultimately it is also a motion in space. So far, we have not found a way to measure time without changes in space. Man will probably never can.

The time doesn't stop, only because I press for break on my video player. If I live with my mind only in a computer program, then the programmer could press for break. I wouldn't know anything about it, because until the program continues I am able to observe again. And only then does my clock continue to cycle. Only if there is a slow change in the reality of the universe surrounding us and there is an information that does not participate this change, then people could notice. More on this in the summary.

What about the space. In order to determine the distance between two spatial points, we need to compare this with a measuring instrument. Since basically everything moves in the universe, my measuring instrument would also move past the space points. If I want to get reasonable readings, I have to measure at both points at the same time. Thus, the measured values of distances in three-dimensional space depend on the time. All we can perceive about space or time are four-dimensional measured values. That’s why it’s no wonder that our models contain a four-dimensional space-time. Whether space and time are also linked in the reality of the universe surrounding us is a completely different question. In any case, man cannot perceive space or time separately from each other.
 

Speed of light :

Back to the Hafele and Keating Experiment. We don't have to circumnavigate the entire globe right away. Let's just look at a section of maybe 10 kilometers in east-west direction. Here we install two magnetic levitation railway lines next to each other, so that 2 systems can move past each other without wobble. I don’t care if these systems are train-railway experiments or represent rockets or simply on bars fixed atomic clocks. One in the middle and one on each end. In today's measurement precision, already 100 m long bars are enough to achieve measurable effects even at the speed of sound. The clocks should output the defined second as time and on the beam in each case be synchronized with each other after Einstein's simultaneity definition. These are not inertial systems, as they rotate with the Earth. Do you only take the times of these atomic clocks as measured values and use only light signals to compare these atomic clocks, we can still measure 1 to 1 exactly what would have to be measured when comparing inertial systems. No matter if the beams rest to the earth, or move in the east or west direction. Whenever the beams move past each other, the observers measure the other bar as length-contracted and the others Clocks as correspondingly slower to the Lorentz transformations. Although we know that of the clocks moving past the other bar in the west direction the clock cycle are faster. At least as long as they do not move faster than the other bar in the east direction around the Earth's axis of rotation.

(Note: Unfortunately, the geometry is not so easy. Only for a complete circumnavigation they actually go faster. Relative to Universal Time Coordinated UTC but also on every section. See also the notes in the axis of evil section.)

On the beam itself, the speed of light for the back and forth path is always measured together with c. (I now want to disregard disturbing effects, for example caused by the air).

And the fact that they measure the speed of the light signals in both directions equally quickly is already the result of the spatial synchronization of the clocks after Einstein's Simultaneity Definition.

Since it is a rotational movement around the Earth's axis, we still have other ways to compare the clocks with each other. Does the clock go on the middle of the beam with the Universal Time Coordinated UTC synchronous, then the eastward clock is late compared with the UTC and the western clock is bevore compared with the UTC. If we turn the beam around its middle, then nothing changes. The clock, initially located to the east, goes faster while turning on the way to the west. The clock, initially located to the west, goes slower than the other clocks. They do it exactly in such a way so when they arrive the oposite position, their time differs to the UTC, as the clock previously located there. This corresponds to the Sagnac effect and this is what Hafele and Keating already have in their experiment described. This is independent of the speed at which the beam is rotated around its center. The faster you turn the more, an additional time dilation effect comes to bear. The slower you turn, the more can be avoided of this time dilation. The value of the Sagnac effect contained in this motion is always the same.If the beams are at rest relative to the Earth, then the value of the Sagnac effect depends only on the tangential velocity relative to the Earth's axis of rotation and the distance between the clocks. If the beams move relative to the surface of the earth, then of course the other tangential velocity is to consider.

Michelson-Morley Experiment MME :

One can reduce the Michelson-Morley experiment to a one-arm measurement, which is equivalent to the Kennedy-Thorndike experiment. It can be further reduced by replacing the mirrors in the middle and at the end of the arm with clocks. These clocks emit light signals as time signals. With today's precision of clocks, this is easily feasible. Then it becomes a one-way measurement. So far, no observation has been made in which the measurements are not consistent with the Lorentz transformations. According to the Lorentz transformations, even when turned slowly within the clock beam systems, no measurable effect arises. The time signals from the middle clock always arrive with a constant time difference relative to the displayed time of the end clocks. In the opposite direction, it is the same. A time signal reflected at the end clocks would always arrive at the middle clock with a constant time difference. If a one-way measurement already has no effect, then the Michelson-Morley experiment, in which only the round-trip is measured, also cannot show any effect.

The clocks on Earth are spatially synchronized in the UTC. A locally limited spatial synchronization according to Einstein's definition of simultaneity would not lead to contradictions within this system. However, it would not be compatible with the measurements otherwise possible on Earth and is therefore also incorrect relative to the entire universe. Within a system, like the one represented by the clocks fixed to the beams, synchronization according to Einstein's definition of simultaneity can be carried out. In the perceptual world of these systems, the speed of light is then measured to be the same in both directions. However, we know from UTC and satellite navigation that for the propagation of light relative to the Earth's surface, a lower speed is measured in the eastward direction than in the westward direction. Only on a non-rotating planet, on which such a bar system rests, does their spatial synchronization according to Einstein's definition of simultaneity also correspond to the UTC of this planet. Accordingly, it is only in this case that the one-way measurement of the speed of light is the same for both systems in both directions.

For me, there is no reason to assume that the straightforward and thus inertial motion is fundamentally different. There is no doubt that, under the valid definition of time and spatial sizes, the speed of light in each inertial system must be measured with the same value. And under Einstein's simultaneity definition, the Speed of light is also measured equally quickly in both directions. Just like in the example in the 10-kilometer section that co-rotates with the earth's surface. In the perceptual world of each individual inertial system, the speed of light has always a constant measured value. But, just like in the systems on the magnetic levitation track, these measured values do not have to agree with the reality of the universe surrounding us.

MME on Earth's orbit around the sun :

Let us transfer the effects on the Earth's surface measurable to the Earth's orbit around the sun. Again, there must be the same effects. Let's think of a ring along the Earth's orbit, which orbits the sun with the Earth. Let’s put on these ring watches and synchronize these according to the UTC. Then clocks moving faster relative to this ring, also cycle slower. And watches that move slower relative to the ring, also cycle faster. The measured light speed has also to be slower in the direction of earthmoving, and faster spread out in the opposite direction. One might think that must cause disruption in the area of satellite navigation.

I assume that the actual conditions of the universe around us correspond to the geometry of the Lorentz transformations. The Lorentz transformations have their peculiarities. Within systems that correspond to Michelson-Morley experiments, or within which measurements are made only with atomic clocks and light signals, one cannot detect any effects of differing clock rates or the propagation of light. The satellite navigation basically corresponds to a huge Michelson-Morley experiment. That is why no effects can be detected within this satellite navigation either. If one synchronizes the clocks along Earth's orbit spatially in a way corresponding to UTC, then compared to these clocks an effect would be noticeable.

These effects can also be transferred further to the orbit of the sun around the centre of the Milky Way. Here, too, they must perform. Now we're almost at the straight motion. Why should it be fundamentally different with this? Just because we have no way of checking spatial simultaneity in linear motion other than with direct light signals, I see no reason why it should be fundamentally different here.

(Note: If we could actually send Morse code using the effect of entangled photons and generate a response quickly enough, we could limit spatial simultaneity causally more strongly than with light signals. Spatial synchronization according to Einstein's definition of simultaneity would be possible, but causally incorrect.)
 

Axis of Evil :

Such effects could probably also be detected when comparing the clocks with processes outside the solar system or the Milky Way. Astronomical Measurements must be provided with endless corrections. And the effects should be only small, so that they could be quite below the measurement accuracy. But it could also the cause of the „axis of evil” in the measurement of the microwave background radiation CMB. It would be nice if there would be astronomers or mathematician who would be willing to check this with me.

In my idea, the important factor for the effect is the speed at which the clocks move relative to the gravitational field. Unfortunately, we cannot directly measure this movement so far. If we compare the satellite clocks with a synchronization of clocks along the Earth's orbit corresponding to the UTC, then we have a clearly limited reference system. This represents a non-rotating ring. No matter how the ring moves relative to the gravitational field, every watch that has completely circumnavigated the ring has relative to the Gravitational field a longer way back. So she moved faster and must have gone slower in sum.

When comparing the clock cycle with the CMB, we can precisely determine the speed of motion relative to the CMB, i.e. the dipole. A state of motion in which no dipole is measured, could be considered as a calm to the CMB. However, it could still mean a motion to the ruling gravitational field. Then a clock resting in the gravitational field observes a measurable dipole. It would still go faster than the clock resting to the CMB.The speed of movement relative to the CMB would therefore not be a measure from which to calculate the expected slowing of clocks.

In a ring that does not rotate to the gravitational field, the clocks can be synchronized accordingly to the UTC. When this ring moves sideways to the gravitational field, then in this system there is nevertheless a synchronization gradient compared to a ring resting in the gravitational field, in which the clocks are synchronized accordingly to the UTC.

The clocks on a non-rotating ring, which moves sideways relative to the gravitational field, are spatially synchronized with each other according to UTC. If one now moves a clock along this ring, it will run slower in each section by exactly the amount corresponding to the time dilation for that orbital speed and distance. The clocks on the ring move straight through the gravitational field, but this watch in a sinusoidal curve. It has made a longer way through the gravitational field with each re-encounter with a different clock of the ring (each after a complete circumnavigation). It was therefore faster and must accordingly have gone slower. On one side of the ring, the watch actually moves faster to the gravitational field than the other clocks. On the other side of the ring, it is necessarily slower. That is why the clock also runs, in the reality of the universe surrounding us, on one side much more slowly than it would correspond to according to the Lorentz transformations relative to the ring. On the opposite side, it actually runs faster than the other clocks. Nevertheless, the moving clock is measured from the ring, in each segment, as running more slowly in accordance with the Lorentz transformations.

Coincidence :

Here I would like to make clear another of my assumptions and I have to go out of it. I believe that everything in the reality of the universe surrounding us causal expires and that this is also logically comprehensible. This also applies, for example, to radioactivity. I can imagine a model of how the events in the atom are going. According to this model it is a very causal process. Of course, this model does not correspond to the actual conditions in the reality of the universe surrounding us. But I think that it is also in the independent reality a completely causal process that provokes radioactivity. Only we humans are not yet in a position to understand this process and to transfer it into our world of perception and thought. Maybe we will never be able to do that either.

A more vivid example of this, that supposedly “random” sequences are actually causal, is the roulette. You might think that roulette delivers purely random results. Why do you have to replace the croupier after some time? It is to be done, because you have found that croupiers, depending on the previous number, where they the pick up the ball and then get the wheel going, throw the ball into a particular sector of the wheel. Logical, this can only be if the process contains a causality and is not pure “coincident”. Even if we can’t calculate this causality, the result in roulette is not a random result. The result depends on the initial conditions.
 

Entangled light particles :

What about the strange remote effect of entangled particles of light? If the measurement of our own particle determines the result of the measurement of the other particle, then there is a causal connection. No matter how this connection may be transferred. I would like to call it information. If no such exchange of information has taken place, then we did not determine the measurement result of the other particle with the own measurement. Then the measurement result could be in the reality of the universe surrounding us have already been determined at the entanglement. And only with our measurement, this measurement result is determined in our world of perception. Then there is in our world of perception a mysterious remote effect. In reality, in the universe that surrounds us, this would not have happened at all.

Or there is this remote effect. Anton Zeilinger once described this measurement in such a way that it is logical to derive from this a possibility for Morse marks to send. With the help of these Morse marks, you could also send time signals. Within the time it would take for the other observer to send back the answer, one could the spatial simultaneity causally narrow. This should only take seconds with instantaneous remote effect even with an observer 50 light-years away. Let's position more Observers in between. Then a causal universal simultaneity plane would result here with measurement inaccuracy amounting to only seconds.

We could now move inertial systems along this line. These should, as required in special relativity, synchronize their clocks according to Einstein's definition of simultaneity. Then all effects can also be measured exactly as predicted by special relativity. Just as described earlier for the movement of clock systems along the magnetic levitation railway tracks. But only in one of the inertial frames can the spatial synchronization of the clocks coincide with the spatial synchronization along the path that has been causally synchronized with the effect of entangled light particles. In all other inertial frames, it deviates and is therefore causally incorrect. This could show that spatial synchronizations according to Einstein's definition of simultaneity are also possible in linear motion. However, just like in rotation, they are causally incorrect. Then the conditions in rotation and inertial motion would have to be evaluated equally.

We can spatially synchronize the clocks in inertial systems according to Einstein's definition of simultaneity. However, the perceptual world of these inertial systems would then be a measurement-induced false interpretation. One could say: the illusion arises because we calibrate our measuring instruments incorrectly.

I do not want to go into this long-distance effect any further, as it doesn't really agree with me either. The claim that the transfer of information does not happen via the 'normal' channels is, in any case, insufficient. It would only confirm spatial synchronization according to Einstein's definition of simultaneity in one inertial system. In all systems moving relative to it, it would causally refute it. But it would be easily compatible with a gravitational field that one can move through and relative to which the speed of light is constant. In my view, this solution would also be much simpler for explaining all observed phenomena, including rotation.
 

Gravitational field :

Sometimes gravitational effects are explained with a stretched rubber mat on which balls roll around. The rubber mat is a wonderful medium to which one can move. Needles can be inserted for marking and the motion of the balls to the preferred preferred frame of reference can be described exactly. You can't stick a needle into the gravitational field that surrounds us, but if you're willing to accept the existence of such a field, you can also think about what effects it might have. In particular, one might consider how to measure a motion in a gravitational field. I presented one of the possibilities at the DPG conference in 2021. An you could look it up under www.darmer.de/smuk2021.

I assume that the gravitational field is formed by all the mass particles of this universe. I don't want to worry about how exactly that happens or what this field might be made of. However, I can observe that mass particles influence each other and there must be something between them. I want to call it a medium. You can imagine a rubber mat or a tough liquid, but these have got concrete properties, just like it was thought about the ether. I want to think about this medium as it is used to think about dark matter. The only known property of dark matter to date is that it complements the mathematical formulas, so that these describe also the motion of the too fast moving celestial bodies.

Of course, this also applies to gravitational lenses. My analogies may confuse people who think in terms of language more than they help them understand what I want to express. People who think in terms of content are likely to find it easier to grasp the fundamental meaning of these comparisons. Let's imagine we want to weigh rice against gold. On one side of a balance scale, we put the rice, and on the other, the gold we have at our disposal. Then we notice that the scale tips toward the rice. Since we have no more gold, we add some iron pieces to the gold until the scale shows equilibrium. The rice is meant to represent the phenomenon observed in the universe. The gold represents the visible matter present there. And the scale is the formula used to try to calculate both. One finds that the calculation doesn't work out. And that is why, in the universe, we add dark matter to the visible matter, or, using the analogy, iron alongside gold. I can take the iron, hammer it or examine it in other ways, and determine that it is not gold (visible matter). As far as I know, dark matter has never been investigated in any other way than by postulating that it exists there in exactly the amount needed for the formula to describe the observed phenomenon.

The gravitational medium should also have only exactly the properties that can also be observed. Maybe it is simply a mathematical reference field, but it has plastic properties and is altered by the masses moving within it. Let's start from a dormant medium, such as a rubber mat, but without its further properties. When the medium is formed by the mass particles of the universe, then it would also have to be influenced by mass particles that move to the medium.The relationship should be like that of the prevailing medium in relation to the fields of the moving mass particles. The resulting medium should then also move somewhat in the direction of the moving particles, relative to the surrounding stationary medium. This effect then also decreases with increasing distance from the mass particles. What consequences would that have?

The sun would lead with its rotation to a gravitational field rotating in its immediate vicinity. That would then also lead to the anomaly in the rotation of the perihelion of the Mercury. Einstein meant that would only be a superposition of the gravitational field to which one cannot move (there would be no preferred reference field) and that is why it can not move itself. But what would be the difference in the view? Observing the discrepancy in Mercury's perihelion would be the same and the formulas for calculation would be the same. Only the idea of what the underlying reality of the universe surrounding us might actually look like would be different. The earth rotation must then have a similar effect, as the general theory of relativity predicts and has now also been experimentally proven. This is called ship effect, frame dragging or Lense-Thirring-Effekt.

But if this is not only a purely rotational mathematical superposition of the gravitational field, but an actually plastic one motion of the field, then an approximately straight-line motion of masses must also have an effect. Like the motion of the earth on its orbit around the sun.

That could explain the fly-by anomaly of space probes.If they move past the earth, they would also have to pass through the gravitational field dragged from the Earth and would experience a small thrust in the direction of the earth motion.If they move after the passage in the direction of the earth around the sun, then we would measure a slightly higher speed, as they should actually have without this effect. As far as I know, no spacecraft have left the Earth's environment in the opposite direction. In this direction, they would have to move away from the earth a little slower than you would expect. It will be more difficult to measure this effect when they move away perpendicular to Earth's orbit, for example because they are sent to more distant planets. Here, too, this effect would have to accelerate them towards the Earth's orbit. Which does not lead to faster moving away from the earth, but their further path should differ in the direction of the earth's motion. If we can determine the speed of a probe relative to Earth very precisely by the Doppler effect, the calculation of the expected direction with which the probes should continue to fly after the Earth passage is much more difficult to determine. Therefore, this effect could be concealed, caused by the measurement inaccuracy.

There is another celestial body where we can observe this effect. The motion of the sun must also produce such an effect. A celestial body called Oumuamua has raced through the solar system. After its trajectory was deflected by the sun, it is leaving the solar system in the direction in which the sun moves around the center of the Milky Way. It was found that its deceleration is slightly lower than expected. For this effect, the direction of the sun's movement relative to the center of the Milky Way should be decisive, rather than its speed within the local group. According to my concept of the gravitational field, the celestial body should receive a small acceleration in the direction of the sun's movement, which leads to the observed effect.

If the motion of masses has an effect on the resulting gravitational field,then the aligned motion of the masses, determining the local gravitational field, should have an even greater effect. This could cause the gravitational field of spiral galaxies to rotate as well. Since this gravitational field is decisive for the centripetal force, the stars move relative to the locally prevailing gravitational field exactly at the speed they would have to have because of the visible matter. Only considered from the outside, they seem to be moving too fast.

Limits of mathematical formulas:

The interpretation of mathematical formulas has its limits, especially when we approach singularities. In these cases, we can be almost reliable making statements only if we have actually investigated this area experimentally. We also need to study this area with measurement methods other than those on which the mathematical Formulas are based. Otherwise, we measure the lengths of iron bars with iron bars, or the speed of light with light signals.

I would like to use the formula for the illuminance of a light source to present the problem of singularities in these mathematical formulas.

The illuminance is measured in the SI unit lux (lx). 1 lx = 1 lm/m²

It states that the illuminance of a light source is the luminous intensity divided by the square of the distance. If you double the distance, the illuminance is only a quarter. However, you can also reverse it and keep reducing the distance. If you approach a candle flame from 10 meters to 5 meters, its illuminance is quadrupled. But how do you approach a candle flame from one millimeter to half a millimeter when the candle flame itself is 5 millimeters thick? As you get very close to a point light source, with the distance approaching zero, the illuminance value approaches infinity. This relationship can be called a singularity. However, you cannot tell from the formula alone that it loses its validity at very short distances. We can already recognize the problem just with our senses if we try to bring our measuring device very close to the candle flame.

What about the formulas for the Schwarzschild horizon or the limit for the speed of light? Can we be completely sure that they still hold when approaching their extremes? In the reality of the thought world of man, this mathematical gimmick has its justification. But I assume it has nothing to do with the reality of the universe surrounding us.

Everyone will know the saying: It’s not always what it says on the tin. In other words, just because we label something with the same letters doesn’t mean it contains the same underlying principle. Just because we call one thing a car and another thing a car as well, it doesn’t mean that they function in the same way. A gasoline car differs significantly from an electric car, simply because of the different energy usage.

1 car + 1 car = 2 cars - Everyone will accept that. But the translation could be:

1 gasoline car + 1 gasoline car = 2 electric cars.

What is stated by the numbers is not determined by mathematics, but by our measuring instruments. And what the measuring instruments measure is determined by our assumptions. Mathematics is, for me, a language with which you can actually describe everything. You just have to search long enough for the appropriate formula. That is why you cannot deduce how the universe works from mathematics alone.

With the language of mathematics, the wave functions, we can describe the electromagnetic processes. With the same formulas, we can also describe the interference phenomenon of light photons. In my opinion, however, one cannot conclude from this that both actually rest on the same physical basis in the reality of the universe around us. This requires further discussion. Here, it is only meant to show that there could be additional limitations to the interpretation of formulas.

In formulas, numbers are used to determine quantities, for example, an angle or a speed. If we now want to specify the angle and the speed at which one atom moves relative to another, the exact values could have infinitely many decimal places. Even God would need infinitely long to write down these numbers. Humans can only approximate them, even with the most powerful computers. If this one motion does not appear exactly in the calculation, the calculation of the result cannot be exact either. Thus, the relative movements can only be indicated with a certain probability, but cannot be calculated or predicted exactly. Just like in the example mentioned above with roulette.

In the reality of the universe surrounding us, it is much simpler. In it, things simply happen at the exact speed and at the exact angle. The inaccuracy exists only in the human thinking and in the inability to describe it precisely.

I'm not a mathematician or a theoretical physicist. I can only put together actual observations and the associated assumptions, such as puzzle pieces and check if they fit together logically and causally. I have not yet come to any conclusion whether mathematics belongs only to the reality of the thought world of man or, whether it also belongs to the reality of the universe surrounding us. Ultimately, that doesn't matter. Do we approach the reality of the universe that surrounds us with our ideas or not, depends only on how exactly our idea of the functioning of our measuring instruments and the assumptions necessary for the interpretation of these measuring instruments, with that of Human thought independent reality of the universe surrounding us agree.

If we can sort our measured values mathematically without contradiction, then the corresponding concept could also come very close to the reality of the universe around us. If we cannot mathematically sort these measured values without contradiction, our idea of the reality of the universe surrounding us could be false. But we could even have not yet found the appropriate formula. From mathematics alone, we cannot discern, as with the formula for luminous intensity, what the reality of the universe surrounding us actually is.

For the discrepancy in the peri-helion of Mercury (not alone, of course) we decided in the situation to change the mathematical formulas. On the other hand, we have decided to change the assumptions about the reality of the universe surrounding us in the case of the stars in the galaxies that are moving too fast.

For the reasons mentioned above, I am of the opinion that it was the wrong way in the second case. I'm not able to come up with a formula by which my imaginations could match with the actual measurements of the stars. I am even less able to do this with the possibly freely accessible observational data from astronomy. That would have to be done by mathematicians or astronomers who are truly willing to question their own ideas and examine other lines of thought impartially.

The formulas of the general theory of relativity, in my opinion, already offer a good approach, because they describe the discrepancy in the perihelion of Mercury and the Lense-Thirring-Effekt. However, such effects should not only be allowed in the rotation of masses, but also in their straight-line motion. That, of course, is incompatible with the notion of an absolute constancy of the speed of light. In my opinion, this assumption or the corresponding postulate in the special theory of relativity prevents us from the realistic Assessment of the universe surrounding us.

Summary :

What I find lacking in modern science is a clearer distinction between observational facts, which are supported by experiments, and the assumptions one makes to interpret the experimental measurements. These assumptions remain assumptions and never become proven facts, as it is gladly presented. These assumptions could only be refuted as “Probably not valid”.

Also, it is too rarely made clear what is experimentally proven and what is only the conclusion of a theoretical assumption. For the use of ideas (or expected measurements) derived purely from theory, a formulation should become common that makes this clearly recognizable. In general, I lack a list of all the assumptions that are for the logical correctness of a statement are needed.

First example: To conclude that from the observational fact that the general redshift of the spectral lines increases with increasing distance, that the universe expands, more assumptions have to be made than probably most physicists can imagine.

Second example: In terms of measurement, the moon should slowly move away from the Earth. But no matter where we look around the universe, everywhere the mass has a tendency increasingly clumping. Neutron stars or black holes are said to circle around each other and then plunge into each other. Why should the moon move away from the Earth?

The most important assumption for both examples is that our atomic clocks provide a constant measure of time. What if the period of the radiation corresponding to the transition between the two hyperfine structure levels of the ground state of atoms of the caesium-133 (133Cs) nucleus gradually decreases. This would also shift the corresponding spectral line toward the blue. Naturally, this would apply to all spectral lines. Relative to the current position of the spectral lines, those contained in the starlight, would be shifted more to the red as longer as they were moving. This redshift of the spectral lines would then have nothing to do with a Doppler effect.

As I described at the beginning, we cannot measure changes over time that affect the entire universe. Only if something is conserved, which does not go through this change. Something that concerns our clocks but does not change with time, like the spectral lines in starlight.

If our clocks run increasingly faster, then the measured value for the time it takes a laser signal to go to the Moon and back will keep increasing. However, this would have nothing to do with an increasing distance, but with the atomic clocks running faster. The Hubble constant roughly corresponds to the rate at which the Moon is moving away from the Earth. If you multiply the Hubble constant of 74 km/s/Mpc by the Moon's distance of 384,400 km, you get a speed of 2.91 cm/year. The actually measured speed is 3.28 cm/year. So they are almost identical.

The Big Bang theory already has a flaw in itself. We have a formula that describes the expansion of space. We can reverse it and calculate back to the singularity, to the size of zero. I read a description in which the Big Bang starts with the size of a football. If you pack all the visible mass of the universe together densely, how large would the Schwarzschild horizon be? In any case, larger than a football. Whatever happens within the Schwarzschild horizon is said to be beyond our ability to judge. So let's start with the size of the Schwarzschild horizon. Then space can expand, but it would only contain a single black hole. So you have to start with a size where the mass is distributed finely enough that it doesn't immediately settle into black holes. Of course, in the reality of thought, one can reverse the formula for spatial expansion. But one must not forget that it loses its validity long before reaching the singularity, just like the formula for luminosity.

With this article, I want to make it clear that reality has no limits in the thought world of man. The of us independent reality of the surrounding universe is something completely independent of it. In order to get closer to this reality, there are considerable obstacles for humans. Probably humans are not capable to ever recognize this reality correctly.

He will only ever be able to create relative models of it in his mind. These are as relative as the relativity of his measuring instruments. Even if his models, hypotheses, or theories can only be tested with imprecise measurements, I believe that the processes in the reality of the universe around us are both causal and precise. So far, I see no reason to doubt this.

At this point, I would like to ask all those interested in theoretical physics and mathematics: If one considers the postulate of the absolute constancy of the speed of light to be incorrect and, for example, supplements the formulas of general relativity with a term that includes the velocity relative to the gravitational field, could one perhaps calculate all the measured values of the observed motion phenomena in the universe even without dark matter? Regarding gravitational lenses, I just want to ask: Have we really fully understood the properties of light?