Yehuda Sabdarmish wants to find a computational way that will avoid the need for huge amounts of dark matter to explain the movement of galaxies
Site Note: This article is a speculative article and should not be cited in school papers
A huge lack of mass in the universe is a consequence of the use of Newton's gravitation formula in cosmological spaces. Isn't it possible that there is another gravitation formula, also correct, that would eliminate the massive lack of mass in the universe?
In order to answer this question, we will examine how Newton's gravitation formula was obtained?
Newton's gravitation formula was developed by Newton as an intuitive mental inference for the movement of the planets known at the time, beginning with the planet Mercury, which is 0.39 astronomical units from the Sun, and ending with the last known planet at the time - Saturn, which is 9.54 astronomical units from the Sun. Based on these data, the cycle time of the planets, and Kepler's laws were known
During his time, Newton arrived at his well-known formula:
Where Fn is equal to the force of gravity according to Newton acting between M the mass of the sun, m the mass of the planet, where r is the distance between them, G is the gravitational constant.
But we must not forget several important facts:
A. This formula is proven in Newton's days only for these distances. At that stage it was impossible to say anything absolute about the formula at larger or smaller distances, and it may not be true beyond the distances at which it was measured!.
B. Even later, with the discovery of the new planets, it could be said that the formula was measured and proven only up to the planet Pluto, about forty astronomical units, which is a distance of less than a thousand light years!.
third. Using Newton's formula at distances of about one hundred thousand light years, and more (in galaxies), shows a mass loss of 90%.
d. Using Newton's formula at distances of about one hundred million light years (distances between galaxies and clusters) will show a mass deficiency of at least 99%.
In light of the huge lack of mass, wouldn't it be worthwhile to check the possibility of other gravitation formulas? Is Newton's gravitation formula (together with the conclusions from the theory of relativity attached to it) irreplaceable? Gravitation?, what are the conditions for that?,
Well, first of all, let's define what it means for a physical formula to be correct:-
God. A physical formula will only be correct if its calculated results are within the measured error.
and. Hence, there could be an infinite number of correct formulas that differ only slightly, within the uncertainty of measurements.
G. The uncertainty in the measurements in Newton's gravitation formula is at least the uncertainty in the measurement of G, which is about a thousand, because they never managed to measure the gravitational constant with greater precision.
H. Gravitational formulas that give deviations up to a thousandth from what is obtained by Newton's formula will also be correct within the range of measurements, but may give different values than Newton's gravitation formula, outside the range where measurements were made, that is, completely different results in galactic and intergalactic distances.
That is, if we succeed in finding a new gravitation formula, which will give us the following deviations from Newton's gravitation formula, we will not have a problem of missing mass in the universe:-
A. In values up to at least a thousandth of a light year, a deviation of no more than a thousandth is the result of Newton's formula.
B. In values of up to a light year, a deviation of up to ten percent from that obtained by Newton.
third. In values of one hundred thousand light years, a tenfold deviation from the value obtained by Newton.
d. In values of a hundred million light years, or more, a deviation of a hundred times more than the value obtained by Newton.
Since there is no precise and unequivocal definition to be required from the formula we are looking for, and the starting data are with great uncertainty, therefore there are many of them. Everyone will be able to try and find their own formula, and its reasons with him. The way this will be done is, for example, by plotting the starting data in a system of axes, preferably logarithmic, and looking for a formula that will connect all the points.
The formula I chose was obtained as follows:
On the X axis I marked points from minus 10 to plus 10. These points will form the logarithms of the distance R in the gravitation formula, which is expressed in units of light years.
On the Y axis I marked points from minus 8 to plus 4. These points will constitute the additional logarithm to be added to the gravitation formula calculated according to Newton.
For example, if for X=8 we get Y=2.48, this means that for R equal to one hundred million light years, we must add 10 to the power of 2.48 to the gravitational force obtained according to Newton, which is 302 times the result obtained by Newton's formula.
As I already mentioned, there are endless such formulas. The formula I found is the formula:-
Y=0.56*X-2
And the conclusion from this formula is:- if Fn shows the gravity according to Newton, Fg shows the gravity according to the new formula then:-
We will do a small calculation that will show us the result.
Let's take a galaxy whose radius, including the surrounding gas clouds, is about 150.000 light years. Let's see what its gravitational force will be according to the new gravity formula:-
Well, X= logR= log 150000=5.18
Hence Y=0.56*5.18-2=0.9
and hence (soon) Fg= 9*Fn
That is, we accepted that in the space of galaxies, the force of gravity obtained from a certain amount of mass is 9 times that obtained by Newton's formula.
For example, additional results:-
The gravitation obtained by the proposed formula is as follows at the following distances:-
At a distance of a billion light years, a thousand times that obtained according to Newton's formula,
at a distance of about 4000 light years, twice as far as Newton's
At a distance of up to a light year, a deviation of one percent,
And at a distance of one thousand light years (63.2 astronomical units), a deviation of 0.0002 from that obtained by Newton.
That is, at small distances it is still within the uncertainty set by G the gravitational constant,
So that no experiment or measurement can prove that the new formula is incorrect (a mental challenge for the readers of the article!).
Also, at large distances, the new formula prevents the need for a missing, dark mass with special properties and the like.
The author of the article found a linear formula for demonstration purposes. But of course others will be able to find other formulas, linear, parabolic, sinusoidal, and the like, and perhaps even a formula that at distances above a certain size will give a repulsive force, all according to the reader's mathematical knowledge!
Disadvantages
Apparently, everything is fine and dandy, but this formula has the same fundamental shortcomings that Newton's gravitation formula also has and they are:-
A. The short range of measurements, i.e. based on a formula that has been measured as correct for a distance of a thousand light years (the limited solar system) we are trying to project to distances of billions of light years and this is something that will not be done.
A solution in the form of a "cosmological principle" is not effective because it throws off both Newton's formula and the new formula, and is unable to decide which of the two is correct at large cosmological distances.
The new formula even has an advantage over Newton's formula because it gives correct results even at great distances, galactic and even intergalactic, without the need for dark mass.
B. Another disadvantage, we proceed from the point of view that what is known to rotate the solar system is the one that is supposed to rotate the galaxy as well? There is no proof of this, and something else can also rotate the galaxy and move large cosmological systems, for example:- What do the readers think about force arising from pressure differences? This idea must not be dismissed outright. Scientists who knew how to introduce a huge amount of dark mass into the galaxies, would also be able to introduce a little gas to create the pressure difference required for the rotation of the galaxy, less than a billionth of the atmosphere between the center of the galaxy and its edges! But, about that in another article.
third. The possibility of a force of attraction acting between two bodies without any contact between them is problematic, and even Newton in his book "Principles" insisted on it, but again, on this in another article.
d. The new formula does not explain the "strange" distribution of gravitation which is supposed to rotate different regions of the galaxy at different speeds (just as Newton's gravitation formula does not explain either).
In conclusion
I showed the possibility of the existence of a new and correct gravitation formula, which does not require the reality of dark, missing mass, etc. in the universe, as in Newton's!
It will be difficult, if at all, to contradict the correctness of this new formula!
6 תגובות
To Noam
You said: "A well-known rule in physics is that even a thousand confirmations are not enough to prove the correctness of a theory, on the other hand, one refutation is enough to disprove the whole theory." End quote.
I completely agree with you, but tell me, isn't Newton's formula disproved in all galaxies (except M94)?, for every galaxy the formula does not give correct results unless we add "a little" mass to it! What does it mean to add dark mass at will and as required? What does it mean that the formula is correct only if we change the measurements to fit it like a glove? If this is not a refutation, then I don't know what a refutation of a formula is. Think about that before you claim that my ideas are "delusional and without any mathematical sense".
Good Day
Yehuda
To Noam
I had no intention of replacing Newton in this formula. This formula is just a mental exercise that shows a formula that is usually more accurate than leaving the Newton formula with the addition of dark matter, although in the case of M94 it is wrong. In any case, I am not a follower of it just as I am not a follower of the MOND theory. What I do support is the idea of the pressure difference of the masses of particles that exist in the vastness of the cosmos. They are able to take care of the tiny pressure differences that will cause the galaxy to rotate.
Details on my blog.
Good night
Yehuda
The thing with Sabdarmish theories that are delusional, far-fetched and lacking any mathematical sense.
Another note:
The explanation for the so-called distant action of gravitation is given by the theory of general relativity. According to this theory, the presence of masses causes the curvature of space-time and therefore their trajectory appears as if a gravitational force is acting on them from a distance, but in fact they move in the shortest path across the curved space-time.
The diameter of galaxy M94 is 33,000 light years
http://www.astrofx.com/H9/M94/m94.htm
If we apply the Sabdarmisch formula to this diameter, we will get that the gravitational force according to the formula is 3.39 times greater than the gravitational force according to Newton's formula.
The problem is that the observations prove that this galaxy behaves exactly according to Newton's formula, and not according to a 3.39 times greater gravity.
A well-known rule in physics is that even a thousand confirmations are not enough to prove the correctness of a theory, on the other hand, one refutation is enough to disprove the whole theory.
What does this say about Sabdarmish theory?
They've already done it before you. It's called MOND and it was first proposed by Mordechai Milgrom of the Weizmann Institute and today there are a handful of scientists working on it. But it is not as simple as saying: "What a beauty, I have a linear fit on a logarithmic axis", a physical theory on such a fundamental subject cannot be satisfied with that. Today there are quite good theories on all kinds of subjects, and the theory of gravity, which at least according to what is accepted today shapes the space, should match the theories around it, or at least explain why it is not suitable.
And in other words, as you might have guessed beforehand, you have to work a little harder to say something smart about a subject that the best human minds have been thinking about for three hundred years.