Astrophysicists from the Dark Cosmology Center at the Niels Bohr Institute at the University of Copenhagen, conducted an experiment in Einstein's theory of gravity on scales that are larger than the solar system - galaxy clusters
All observations in astronomy are based on light emitted from stars and galaxies. According to the theory of general relativity, light is affected by gravity. Einstein had an astronomer friend from Berlin named Erwin Freundlich, who claimed to have performed an experiment on the stars and found evidence of gravitational redshift. Everyone remembers Arthur Eddington's great experiment from 1919 that confirmed Einstein's prediction regarding the bending of light rays near the sun's disc. Following this experiment, Einstein became famous throughout the world and became the great genius who came up with a theory of curved space-time.
All interpretations in astronomy are based on the correctness of Einstein's theory of general relativity. And what about experiments that would verify the effect of gravity on light, the gravitational redshift, on a scale that is beyond the solar system? Observations of great distances in the universe are based on redshift measurements. The wavelengths of light from distant galaxies are increasingly redshifted with distance. Redshift is used to know how much the universe has expanded since the light exited until it was measured on Earth. In addition, the theory of general relativity predicts that light and redshift are affected by gravity from large masses such as galaxy clusters and they cause gravitational redshift of light, cosmological gravitational redshift (redshift on cosmological scales). But this gravitational effect on light has never before been measured on cosmological scales.
Astrophysicists from the Dark Cosmology Center at the Niels Bohr Institute at the University of Copenhagen, led by the astrophysicist Radek Vojtek, approached this task and they managed to perform such an experiment in Einstein's theory of gravity on scales that are larger than the solar system. They were able to measure how light is affected by gravity on its way to galaxy clusters. The observations verify Einstein's theoretical predictions. The results were published in the prestigious journal Nature.
Einstein: elevators and clocks
The first prediction that Einstein proposed in his theory of general relativity was that gravity can bend light: "It follows that these light rays that do not propagate along (the parallel axis) are bent by the gravitational field". Einstein's second prediction was the effect of the gravitational redshift of light. If we take the light wave as energy, then the amount of energy carried by the light wave is proportional to the frequency of its vibration. When a wave escapes from a gravitational field it gives up some of its energy and as a result its frequency of vibration decreases. This is not the speed of light, but the frequency of light waves. On this basis, Einstein predicted that the Sun's strong gravitational field should cause a decrease in the frequency of the Sun's light reaching the Earth. Such an effect is called redshift because the frequency of light decreases (longer wavelengths) and the color shifts to the red end of the spectrum.
Gravitational redshift led Einstein to gravitational time dilation. He realized that the connection between the propagation of light in a gravitational field and time was immediately apparent. Einstein concluded that clocks in different gravitational fields behave differently. Gravity twists and distorts time. This can be explained by the experiment of the elevator, the clocks and the rays of light.
Let's imagine watchers and clocks inside an accelerating elevator. The viewers cannot decide in any way whether their elevator is at rest in a gravitational field or whether it is accelerating in space without gravitational fields and there are forces acting on the elevator. We will attach a clock to the ceiling of the elevator while we attach another clock to its floor. One observer sits next to the clock on the ceiling and a second observer sits next to the clock on the floor. Let's say these clocks don't tick, but they emit flashes of light. At rest, the clocks remain synchronized by using a flash of light that the same clock above emits every second. Now the elevator begins to accelerate uniformly upwards.
We first asked the viewer on the elevator floor for his opinion. Between each flash of light from the clock on the ceiling of the elevator, the elevator is already moving upwards, as it accelerates more and more to higher speeds. Each flash thus has to move a shorter and shorter distance towards the clock on the floor, which meanwhile has risen to meet the signal along with the movement of the entire elevator. "Each signal takes less time to reach the second clock than it did when the elevator was at rest in place. The same will be valid for the second flash and for the flash after it, and after that and so on. Anyone who checks the flashes will see that each flash from the first clock comes in a little less than a second, as the second clock ticks. Given this, there can only be one condition, the ceiling viewer's clock is faster. But my watch moves exactly as before at the same rate and I don't think the batteries need to be replaced."
Now we will ask the viewer next to the clock on the ceiling. The flashes of light can only travel at the speed of light c. But the pulses that reach the ceiling come in larger and larger intervals. Each pulse has more distance to travel because the ceiling moves away. And so the pulse takes longer to reach the viewer at the ceiling. "The clock on the floor is slower. My watch is perfectly fine and I don't think it has run out of batteries."
Strange things happen in the elevator. Let's say the elevator was accelerating so close to the speed of light, really almost at the speed of light. What would have happened? The viewer hanging from the ceiling would claim that the clock on the floor had almost stopped. Now suppose the elevator could accelerate beyond the speed of light. Of course this is impossible from energy and mass considerations. But that's just an imaginary thought experiment. So let's say... what would have happened? The viewer hanging from the ceiling would see the clock on the floor of the elevator moving backwards in time.
The equivalence principle states that there is no detectable difference between acceleration and gravity, and therefore between the accelerating elevator in space and the elevator in a gravitational field. This means that the clocks in the gravitational field should behave in exactly the same way as the accelerating clocks on top of the accelerating elevator. A clock that is located where gravity pulls more strongly, closer to the center of the earth, must move slower than a clock that sits slightly further away from the center of the earth. What do you think about the first clock if the speed of light exceeds c? And what about the gravitational redshift?
Light search of galaxy clusters
We will return to the experiment. Radek and Vojtek together with colleagues Steen Hansen and Jens Hors examined measurements of light from galaxies of about 8000 galaxy clusters. Galaxy clusters are accumulations of thousands of galaxies, which are held together by their own gravity. This fact affects the light sent out into space from the galaxies.
The scientists studied the galaxies that lie in the center of the galaxy clusters and those that are on the periphery. They measured the wavelengths of light. Vojtek said, "We could measure small differences in the redshift of the galaxies and see that the light from the galaxies in the center of the cluster had to 'creep' out through the gravitational field, while it was easier for the light from galaxies that are farther from the center to emerge." Then they measured the total mass of the galaxy cluster and calculated the gravitational potential. Using the theory of general relativity they calculated the gravitational redshift for the different locations in the galaxies.
Vojtech summarized the findings. The result was that the theoretical calculations of the gravitational redshift, which are based on the theory of general relativity, are in full agreement with the astronomical observations. The analysis of the observations of the galaxy clusters shows that the redshift of the light proportionally balances the gravitational effect from the gravity of the galaxy cluster.
http://www.nbi.ku.dk/english/news/news11/light_from_galaxy_clusters_confirm_theory_of_relativity_/
Comments
Regarding the principle of equivalence: - "There is no detectable difference between acceleration and gravity". The wording is not accurate! The truth is that there is no "local experiment" that makes it possible to distinguish between a propulsion system in acceleration and a system that is under the influence of a gravitational field equal to the acceleration but opposite to it in direction. Gravitational field lines resulting from acceleration are parallel, while gravitational field lines resulting from mass in space are radial. Therefore, it is important to emphasize - "local experiment".
jubilee,
The understanding and lack of understanding of physics at the undergraduate level is lacking. Only after you study for a few more years will you realize how much you don't understand science today. The attempt to understand advanced science through its popular abstraction is essentially unfounded and leads to ideas that are mostly idiosyncratic.
Back to your example after studying for a few more years you will realize that there is actually no ball and no table and therefore the question of the disappearance and appearance of the ball is completely different from what you imagined.
sympathetic
Unfortunately, I can't answer you in depth about questions in philosophy, because I don't come from there.
After all, a parable for understanding: a billiard ball disappears into a hole at the edge of the table, and within a few seconds a ball appears on the way out of the table. The players believe that it is the same ball, and if someone doubts there are plenty of ways to prove it, for example marking the ball with a special mark. I do not doubt that it is the same bullet, nor do I ask for signs, but I do want to know how this miracle happened - in the simple case we are discussing what is the path the bullet took from the time it disappeared until it reappeared. I can ask the carpenter to make the table and I can also disassemble the table. I can also assume the existence of pipes and passages, and that would be a reasonable assumption.
As mentioned, I don't know much about philosophy and I don't have the ability to judge whether or not it has the right to gain a foothold in any fields. I know that there is a field called "philosophy of science" from which we received a number of determinations and definitions that we follow. For example, through scientific practice it is impossible to prove but it is possible to disprove, or a claim that cannot be put to the test does not meet the definitions of a scientific claim.
I am a scientist by training. I graduated in biology in Jerusalem thirty years ago and now I am doing a third year in physics in Glasgow. In between, I also did math and computer science.
jubilee,
I understood from your words that you are not trying to contradict the accepted physical theories. I also understood that you come from the field of philosophy. In this context, let me ask you a few questions.
The main point of your claim was that we do not understand certain concepts taken from the field of science. What do you call understanding? In my opinion, understanding depends on language, and therefore in terms of scientific language, the concepts you are talking about are certainly understandable to us and are the building blocks of the theory.
Second, as a general rule, do you believe that philosophy can contribute to science? I believe that philosophy has an important role in defining what is justice, truth, beauty, etc. but many times it enters areas where it should not have a foothold. For example, Greek philosophers used their logic to make various claims about the world that all turned out to be unfounded. Science is a method to answer questions about nature. The answers to these questions are given in the field of science and in its language. An external discussion by people who have no connection to science in a language that is completely different seems to me to be absurd and therefore I recommended "not to make firm determinations on subjects where the commenter lacks a basic education on the subject". I do not look favorably on the attempts of philosophers to come into the field and try to teach those involved in it what they should do. For example, good philosophers of science are people who have a scientific education, for example the philosopher Hilary Putnam.
David,
Unfortunately, I am not a great expert in the field under discussion, so you must treat things accordingly.
As far as I know the big bang theory is a theory with considerable scientific basis.
The basis comes from:
1. Homogeneity of the universe in the large scales.
2. Abel's law which empirically shows that the farther an object is from us, the faster it moves away from us.
3. The amount of light elements observed in the universe. The big bang theory assumes that most of the matter was created when the universe was young and relatively concentrated, then the light elements were created and the heavy elements of which we are composed are from the production house of stars that ended their lives.
4. The existence and uniformity of the cosmic background radiation.
Regarding the announcement today in 2006 two Americans (Smoot and Matter) won the Nobel Prize for confirming the Big Bang theory.
As a general rule, for almost every physical theory there are "lunatics" who claim that it is not true. For the most part, those who claim this are ignored and ostracized from the scientific community (in almost all cases rightfully so), and therefore they also rightly claim that they are not listened to. Maniacs of this kind often write a book because this is the only way other than a website to promote their theory. Science, unlike religion, does not sanctify anything except solid facts and theories based on many facts (experiments and observations). In order to contradict a well-known theory, it is necessary to come up with very solid arguments, see for example the neutrino experiment cited today: this is a serious group that presents its results without claiming that the theory of relativity is wrong They just say what results we got try to explain them.
David, thank you for taking the trouble to bring us the things. I refrain from judging one way or the other, but the very fact that doubt exists strengthens the position I am trying to present.
Gali and Ehud, apologizing for last night's brevity. The rules of wakefulness and sleep apply to me too.
I know the physical models you mention and I do not disbelieve in them at all. I'm sorry if that's not the impression you got from my words.
The phenomena are known, quantified and confirmed and I do not doubt them (beyond the reasonable doubt that a scientist is obligated to). But in the current discussion I represent metaphysics, we are looking for more basic factors. The essence of things is known, but I seek to find not only the "what" but also the "how". That's why I said we're not talking about the same thing.
On this occasion I will add something from my knowledge of the history and philosophy of science. When a scientific theory is not perfect, it does not mean that it is wrong, but it is possible that it needs an extension - as the theory of relativity is an extension of Newtonian physics. Einsteinian physics also needs expansion because, for example, we still do not have a unified model for all the known forces.
There are also excerpts in the text of the points against the big bang theory
http://bigbangneverhappened.org/
Many thanks in advance
Ehud with your permission, if you are already here 🙂
I hear how much you understand a matter, I would be interested in hearing your opinion (if you have time of course)
I watched a very interesting movie where scientists talk that the big bang theory contradicts the observations
And the plasma cosmology theory does fit.
Also, the scientists there talk about how they are really oppressed in the scientific establishment.
http://www.youtube.com/watch?v=L6EGpg_BVBg
what do you know about it
Thanks Gali. A restful night and good sleep 🙂
jubilee,
Ehud is much more than an excellent physics student. He accurately described to you what is accepted today among physicists.
Prof. Max Ymer died a year ago and he was a friend of Einstein. He wrote the book Einstein and Religion and when he passed away I wrote a review of the book and his views here in science. Yamar was a great physicist as well as a historian and philosopher of science.
I will explain to you a very important principle in science. Something general and then I'll go to sleep...
Physicists work under one dominant theory at a given time. That is, now the theory of general relativity "dominates", so we do not work, for example, with the equations of the ether theory or the Newtonian theory of the universe. This ruling Torah, the theory of general relativity, is well studied: the principles, the equations, the various solutions to the equations, problems, experiments carried out, etc. After you have thoroughly studied the theory, its implications and you know the equations and know how to build models, find solutions, solve problems, sit in the laboratory and perform an experiment, etc., then you can start thinking about modern research: quantum gravity, dark matter, string theory and fields that I don't either So knowledgeable about them beyond what I read here and there in articles. But first of all, you need to learn the basics well: that is, take a course in both special and general relativity and really go through everything. And only then can we talk about the dark matter. And from my general acquaintance with Ehud, I am sure that Ehud did it.
lion!
It's nice that you mention Prof. Moshe Yamer.
I remember him. Many years ago I was offered a meeting with him. It didn't work out, which is a shame.
sympathetic! You are absolutely right in everything you say. You correctly and accurately cite the existing models and I assume that you are an excellent student in physics and sciences in general.
The thing is, we don't talk about the same things at all.
And your advice is good and wise, here and everywhere.
And thank you for that.
jubilee,
I didn't mean to hurt or offend. I hope that's how you took my words and if not please accept my apologies!
Many years ago I heard Prof. Moshe Yamer raise the possibility that mass is nothing but a curvature of space.
Nice recommendations. Thanks.
jubilee,
In my opinion, you again take your basic misunderstandings and see them as something general. Einstein showed the close connection
Between gravitation and geometry. Mass curves time into space and within time the curved space moves bodies. It is precisely for this reason that the path of light curves near a mass, light simply travels the shortest distance between two geodesic points. The basis of the theory of relativity is the understanding that the gravitational mass and the inertial mass are the same.
As for the rest of your claims, they are not related to science at all. The electron is not a reservoir of photons. An electron is a fermion while photons are bosons. An electron causes a change in the electromagnetic field, while this field can be developed using photons. The photons do not sit, stand or lie inside the electron!
You write "we still don't know what is going on there at the micro level" where exactly is that and again who exactly are we? Physicists developed the theory of quantum electromagnetism some fifty years ago or more
What does it mean "In recent years, not even a decade, we have begun to become familiar with the essence we call "dark matter". "? The existence of dark matter was postulated by a scientist named Tsvuki about seventy years ago. What exactly happened in the last decade? As a general rule, I recommend not making firm determinations on subjects where the respondent lacks basic education on the subject.
Thanks Glee.
Apologies for the inaccurate wording. Not a mechanism. But the gravitational field contains something that causes at least two apparently unrelated phenomena, and we are looking for this something. After all, photons are massless and therefore should not be affected by gravity, yet they behave as if they are. For this reason I believe that the same thing whose existence creates the gravitation also creates the paths of the photons.
And by the way, an electron, I don't see it as a mechanism but just a reservoir, a "bank" of photons. And from indirect measurements (mass differences between a proton and the hydrogen atom) we know that its presence affects the gravitational field around it or is affected by it (or, to put it simply, "the electron has mass").
We still do not know everything about what is going on there at the micro level, and how the phenomena at the macro level are created from this. Until we know, I do not rule out the possibility that both phenomena arise simultaneously from something we do not yet know. Only in the last few years, not even a decade, have we begun to become familiar with the essence we call "dark matter". It is possible that the same something that produces the two phenomena above also produces the dark matter, but it is possible that the dark matter is this something that produces the two phenomena, and for that reason I see it as a possible candidate.
jubilee,
Here is another article in Science regarding a possible Israeli breakthrough regarding gravity waves. I hope it will lead to some discovery on the subject of gravitational waves.
There is no such thing as a mechanism that produces gravity. Even if you think about the electron for example. It is not a mechanism that produces electricity, because it is not a generator. Regarding gravity and the bending of light: the rays of light passing close to the sun are deflected by the gravitational field. This is Einstein's original formulation and it is still true today.
General relativity talks about a structure called the inertial-gravitational field which is represented by the metric tensor field. Einstein built field equations. The metric tensor (Einstein) is the geometry. And the momentum-energy tensor is the material. And the equations are non-linear.
It is true that due to general relativity it is implied that there is dark matter, but this has nothing to do with the bending of light by the gravitational field. Gravitational waves is a prediction of Einstein from his theory that has not yet been confirmed.
You give an interpretation of "hidden variables" to the theory of general relativity and look for dark matter at the basis of the phenomenon of gravity and the bending of light. Whereas Einstein did exactly the opposite in his field unification theory. He strove to build a unified theory based on gravity. After all, he was looking for such hidden variables elsewhere, in quantum theory.
Regarding the Higgs, ask Prof. Elam Gross who is looking for the Higgs everywhere... 🙂
Leave Ehud. Really cool. The interaction between us is like that of checkers players who each play in squares with their suit.
Leave Ehud. Really cool. The interaction between us is like that of checkers players who each play in the squares with their suit.
jubilee,
On the question "How does she do it?" They already made a movie. If we talk about scientific issues, the Groyton is an ecstasy of the Groitian field, so it has not been discovered yet, so what? As I wrote to you and you ignored it, the Higgs particle needed to give the particles mass according to the standard model has not yet been discovered, so why is the theory incorrect? It is very difficult experimentally to discover Groyton and that is why it was not discovered. What does all this have to do with the far-fetched claim "a good candidate for the common factor is the dark matter that was recently discovered and the research on which is still in its infancy". It's just complete nonsense, no dark matter particle has been discovered beyond any doubt yet and let's assume that it will be discovered what it has to do with mass.
Your concept that a particle "carries" the interaction is a field theory concept. Einstein's theory of gravitation is a classical theory and its explanation does not require an interacting particle. Thus the mass causes the curvature of space without the need for an interacting particle.
And frankly I also think your worms are more wormholes than worms.
sympathetic. Your question is excellent.
If it's convenient for you, then "we" is me and the worms I inhabit in my stomach (attributed to Yeshayahu Leibovich).
It is clear that the mass distorts the space. But me and my worms also want to know how she does it. does she have muscles Does she send arms? Does she threaten sanctions?
We assume the existence of a particle that acts as an intermediary between masses and call it a "graviton". We expect a wavy behavior from it that we call "gravitational waves" but until the afternoon of last Thursday (when I last visited the gravity laboratory at the university where I study) we were not able to find these. If and when they are willing to reveal themselves to us, I and my worms will also demand that they give an account of their actions with the light.
jubilee,
You write "we still don't know the mechanism that produces gravity" or "but for the time being the knowledge we have is not enough to establish this claim in rivets", who exactly is it to us in these claims?
The theory of general relativity, as Michael wrote to you, claims exactly that, it is the mass of bodies that distorts time and space. What exactly is considered for you to establish a claim in rivets? Are the observational confirmations of general relativity not enough for you? What exactly are the questions that you think prevent us from stating that mass warps time and space and how is all of this related to the discovery of the Groyton? After all, we haven't discovered the Higgs particle yet, and despite that, almost all scientists swear by the standard model. Our understanding of what gravitation is is excellent and the addition of dark matter does or does not affect this understanding.
Is there not a kind of internal loop in the calculations?
According to what I read here, the scientists made calculations based on the mass of galaxies or clusters of galaxies. I didn't understand just how to calculate this mass? Is it according to a formula related to the amount of light emanating from the cluster? If so, then do you calculate a redshift from an estimate of the mass of the cluster which itself depends on that shift?
Second question - isn't another explanation possible for the same red shift? For example, is it a higher frequency radiation beforehand?
correct. It's not a coincidence (nor did I say it was) but an exact coordination. It is very possible that it will also be proven that the mass is the direct cause of the curvature of space. But in the meantime, the knowledge we have is not enough to establish this claim in rivets.
jubilee:
It is not just phenomena that occur side by side.
It is about the theory of relativity providing accurate (non-trivial) formulas for predicting the degree of curvature of light.
The probability that this is a coincidence is zero.
The curvature of space is predicted and measured in places where there is mass - whether it is dark mass or normal mass.
There are places where there is no dark mass and the curvature of space is also measured there.
A few words about "gravity can bend light":
We still do not know the mechanism that produces gravity. For example, we have not yet discovered the graviton and we have not found confirmations and confirmations for the existence of gravitational waves. Because of this, we cannot say with certainty that gravity is the one that bends the light, even though we see that the two phenomena, gravity and the bending of light, occur together and in coordination; It is not impossible that both arise separately from a common factor that is currently unknown. A good candidate for the common factor is the recently discovered dark matter, of which research is still in its infancy.
Michael,
Thanks for the enlightening comments.
I didn't want to give in the article the more technical explanation that I gave in the comment above because then it drives away readers who are not well versed in physics. And so I gave the famous explanation of the elevator that is also found in Louis Jagerman's book.
In Einstein and Enfeld's book you can find the examples with the elevators. I don't think there is this specific example of the elevator that I brought here. But all the other famous examples of the elevators that are told in the theory of general relativity are there and Einstein and Infeld were the first to invent them. I mean, Einstein invented them... here is the source:
Einstein, Albert and Infeld Leopold, The Evolution of Physics,
The book has now been reissued with an introduction by Walter Isaacson who wrote the Einstein biography. Einstein and Enfeld's book was first published in 1938 and has since been translated into many languages.
And with another thought, even the phrase "accelerates so close to the speed of light" can be given a meaning under which the reasoning is correct.
The meaning that can be used is that if the speed of light is C meters per second, then we are talking about an acceleration close to C meters per second squared (ie - we are talking about an acceleration with a magnitude close to C and not an acceleration when the speed is close to C).
With such an interpretation - what would have remained of the problem I warned about is more a matter of wording than a matter of substance.
Unfortunately - although this was probably the intention of the author of the quoted text - this is not the interpretation given to the words in the article and that is why the article speaks of a situation in which the elevator exceeds the speed of light at a time when, according to the interpretation I proposed, it should have been said that the acceleration of the elevator increases beyond C meters per second squared and that is why it is spoken Also about the fact that "the pulses that reach the ceiling arrive at larger and larger intervals" when what actually happens is that the intervals are fixed.
I must admit that I was also hasty in stating that the article does not give the news itself what it deserves.
Upon re-reading, I see that the subject of measuring the differences between the light emanating from the center of the galaxy and that emanating from its circumference does appear in the article (in the first reading I did not notice this because I thought that once the description of the elevator began, the article did not return to the news itself when the situation is apparently different and after the description of the elevator there is a continuation of the translation of the news) .
This fact does appear there without explanation, but this is also the case in the original news.
I was indeed hasty in stating that the clocks in the ceiling of the elevator and on its floor would agree, but that is only because of the error in the explanation that appears in the article.
The error in the explanation is that although he mentions the acceleration - not the acceleration but the speed is what he is basing it on.
This is especially noticeable when it comes to an elevator whose speed is close to the speed of light, something that is not at all clear what it represents (the expression directly raises the question "close to the speed of light in relation to whom?")
The difference in clocks does exist, but it stems from the fact that when the signal is received on the floor/ceiling, the speed of the elevator is different from its speed when the signal was transmitted.
I did not read the researchers' article but only the link you provided and what I said in connection with it.
There is no need for another article because what I had to say already appears in the response.
Michael, I forgot to answer the second part.
Besides the elevator example, I translated the Niels Bohr Institute press release up to the dark matter part.
And that is what is presented here.
If you want to explain the experiment in more depth because you read the researchers' article, you can of course publish another article about it here.
The sentence above should be:
The gravitational potential at B is greater than at B. A emits some amount of energy towards A.
The example of the elevator is well known and is, for example, nicely explained in chapter 8, page 63 of the book:
Louis Jagerman, The Mathematics of Relativity For the Rest of Us. ,
The example of the elevator is accepted as a popular explanation for Einstein's own complicated explanation. Below is the complicated explanation of the connection between the slowing down of time and gravitational redshift, which is given as a service to high school students:
In the special theory of relativity, Einstein linked the Doppler effect to the lengthening of time. In general relations he examined two systems, for simplicity we will call them A and B. Each has poles and clocks. A and B are located on the Z-axis of system S in a homogeneous gravitational field. A is near the origin of the coordinates while B is at a height h above A. The gravitational potential at B is greater than at A. B emits some amount of energy towards A.
If we apply the principle of equivalence to this situation, then instead of S, which is in a homogeneous gravitational field, we can imagine S', a system free from gravitational fields, but it moves with a uniform acceleration in the Z direction. On its Z axis there are two systems: A and B . System B sends energy towards A and we look at the process from another inertial system. This is how we can apply the theory of special relativity. Looking at this, we come to the conclusion that the energy that reaches A is greater than the energy that is measured by the exact same means, but emitted by B.
Now in private relations the Doppler principle is related to the slowing down of time. We will once again examine the two systems A and B on the axis of the accelerating system. System B radiates towards system A. The radiation reaches A when its frequency relative to A's clock is different from the frequency at which it was sent from B. The frequency is higher.
Einstein again applied the principle of equivalence to the S' and S systems and the same should apply to the S system in a homogeneous gravitational field. Therefore, if at a certain gravitational potential at B a light beam is emitted towards A at a certain frequency - relative to the clock located at B - it will reach A at a different frequency, relative to the clock located at A.
Einstein calculated the gravitational potential of B from the frequency data and the height difference between A and B, when the gravitational potential at A is zero. And he assumed that what he got for the homogeneous gravitational field was also valid for other field forms. From this he got the ratio between the frequency sent at B and the frequency received at A: the frequency received at A is equal to the frequency that B sent plus the frequency that B sent times the gravitational potential difference divided by the speed of light squared.
From this equation Einstein deduced the gravitational redshift effect. Suppose B is located in the sun and it emits light there that reaches the earth at A. We measure the frequency of light. The negative gravitational potential difference between the surface of the Sun and the Earth is calculated. Therefore the spectral lines of sunlight towards the Earth should be shifted towards the red. Einstein calculated the exact amount of displacement: the gravitational potential difference divided by the speed of light squared.
The example with the elevator is incorrect.
The spectators on the ceiling and on the floor of the elevator are at exactly the same acceleration and their clocks will remain synchronized.
This is different from a gravitational field where when you move away from the mass that creates it you experience a weaker field.
This is a special case of the so-called tidal forces - forces that exist in a gravitational field and do not exist in an accelerated body (another difference lies in the directions of the force at different points in the elevator. If it accelerates - the forces experienced at the different points are parallel. If it is in a gravitational field, the forces are directed to the center of mass that creates the gravity and therefore are not parallels)
Most of the article is devoted to this thought experiment and not to the knowledge itself - which is a shame.
In relation to the experiment reported in the article, it is worth emphasizing the following point:
Light originating from behind the galaxy cluster cannot be used by us in the experiment conducted because this light experiences gravity in both directions and the effects cancel each other out.
Only the differences between light emerging from galaxies in the center of the cluster and that coming from galaxies that are far from the center can be used to confirm the theory of relativity and if you read the original article you see that this is indeed what was done.
Fascinating, thanks.