I had that this too till I read up on it. I’m sure we’ve covered this before here somewhere…
@PdotdQ Point well taken. That equation does not work at solar distances. SO in order to salvage my theory I had to find some function, dependent upon angle, that behaves proportional to 1/x^2 at solar distances, but behaves more like proportional to 1/r at galactic distances. I have high hopes for this one:
[rad((r/(2L))^2 + 1) GM cos[2arctan[r/(2L)]]] / (r/(2L))^2
I’ve not worked out the constant G yet, but this form looks better, doesn’t it?
What is your “rad” function?
Regardless, now this equation loses its simplicity - it becomes much more of a datafit than a theory, even more so than your original equation. You cannot keep introducing new complications to your theory to fit uncooperative datapoints. It is not difficult to fit anything well if one is allowed to put arbitrary complexity on the equation being fitted.
One good thing about your theory is that it has only one extra parameter, L, which makes it a bit more palatable. However, at this point you have to ask yourself: do you start with data, and try to find a theory that can fit the data, or do you start with a theory that you really like, and try to preserve (or in your own words “salvage”) it as much as possible in the face of uncooperative data? One of these approaches is scientific, the other is not.
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I can see what you’re saying, but whatever the process or motivations – let us suppose that I can get an equation that fits both solar rotation and then also fits galactic rotation rates — wouldn’t that then be worth looking into? Not saying that anything is proven yet.
rad just means square root to me
I can do it trivially by a piecewise function that is much less complicated than your equation, if you don’t like piecewise functions, then I can smooth it out by using some interpolation function. The thing is, I can come up with many functions that can do this, an easy example is something that looks Newtonian closeby and something that looks like MOND faraway. It is simply data fitting.
Would you mind using Latex scripts to render your equations in this forum? It’s difficult to read a bunch of nested parentheses. You can do this by putting in dollar signs $ between your equations.
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@PdotdQ granted about piecewise functions; but this isn’t piecewise and there is real data to try to deal with; I started with a hypothesis that gravity is dependent upon angle and was a sort of torque-like force – without knowing at all what the final function might look like. So I’ve tried various trig functions to satisfy the following conditions:
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Solar rotation
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Galactic rotation
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reverses at intergalactic distances
Now if I find a function that accomplishes all of that, and it is not piece-wise, would it not be significant?
As I said, I can turn my piecewise function into a smooth function by slotting in some interpolating function in between. This is not difficult to do and used very often in physics. For an example of such interpolation being done, look at the Schechter function, which is an interpolation to smooth out a piecewise power law and exponential function. The problem is that I can come up with many such functions that can fit the three things you listed.
Here is my advise: I don’t think you have fully explored your original theory. I think that before you continue adding more parts into it, you should delve deeper into your original theory and make it more rigorous first, for example by coming up with an equation that is valid for non-point masses. Perhaps you think your original theory cannot fit galactic rotation, but by exploring it more fully, you will be able to come up with a better way to modify it to fit for the three things you listed. This is a much better way to improve your theory than by brute forcing your way to an equation that behaves differently in different regimes - your way is just the same as coming up with an interpolating function in a very inefficient manner.
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I am sorry if I come across as being stubborn; but I would consider smoothing out a piecewise function to be “brute-forcing” my way to an uncritical solution.
If what I have done is very easy to do, might I ask for another function that accomplishes everything I listed but is not piece-wise with interpolating?
That’s my point exactly. I think what you are doing is very similar to smoothing out a piecewise function. After all, you want the following:
- You want that closeby, gravity goes as 1/r^2
- You want that faraway, gravity goes as 1/r
- You smooth out the transition so that there is not sharp break - this is what I meant by interpolation
Here is one that is trivial:
F = F_1 \exp{(-r/r_1)} + F_2
Where F1 is Newtonian and F2 is the Deep MOND force. The idea is that the exponential function kills off the Newtonian force beyond a lengthscale of ~r1, allowing the Deep MOND force to take over beyond r1.
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Thanks for clarifying. Now I have to learn to live with the fact that I’m a brute. 
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Don’t say this. As I said in the very beginning, I am very glad that you as a layperson is so interested in physics that you come up with your own theory. This is a good thing.
I would say that you have the dedication to contribute to the field of modified gravity. Perhaps you just lack training. But training is much easier to obtain than dedication.
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So true. This is the most important thing on my mind when I’m interviewing graduate students.
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At the present, if I had the choice between getting 10x more willpower or 10x more intelligence, I would probably choose the former. It is said in our lab that we prefer people who are smart, but not too smart, since that tends to lessen experimental productivity!
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@PdotdQ @dga471 I ask for your patience. When I use the words “salvage my theory”, it comes across wrong to you. It seems to you that what I am saying is that I value my theory more than I value the truth. This is a misconception. And it is a poor choice of words on my part.
I have not until now shared with anyone all of my thinking about my theory, because the math for it would be very challenging, even for an expert. And I knew I would never get an expert to attempt it. So I pushed on hoping that my ideas would summate to some kind of elegant, simple formula based upon angle, r, and L. That is why I haven’t given up, and keep trying various functions involving trig functions and so forth. Also my theory has very good reason why gravity would behave differently at short distances, and become constant for a while, and then become negative.
This is why I was not put off by the velocity curve, Newton’s shell theorem, or with the different way things look at solar distances … So I would like to give you now the full explanation of my theory that I have not shared with anyone else; my reddit article just tries to give a simplified version sort of as a teaser.
Imagine if you will something similar to a vector slope field. Imagine space is quantized and discrete, and each point in space can be drawn with an infinite number of slope vectors on it. I say this because each point in space “points” (as in pointing your finger) at any mass “near it”. I say “near” because angle is quantized too.
To speak anthropomorphically, space does not like differing perspectives; i.e. , it is a lower energy state to be pointing at one thing rather than two things. So when two masses are separate, each point in space works to push them back together. This is what I mean when I say that gravitational force is a property of space acting upon matter.
So in this case, each point in space operates like a torsion spring, obeying an angular form of hooke’s law, trying to force masses back together.
If this is the case, then why does gravity decrease with distance? If each point in space is operating like a torsion spring, then gravity should INCREASE with distance.
This is where things become more complicated and the math becomes insanely difficult. There are several factors to consider. Let us consider just a single point “looking” at two masses. I used a torsion spring as an analogy, but I think that once the angle between the two masses is greater than 90 degrees, the spring suddenly begins pushing the other way, moving the two masses further apart. I believe this is so because objects at 180 degrees can have no angular effect upon each other, so this also is a lower energy state.
So the gravitational force can reverse. That is one factor. The second factor is how far away the point in space is from the two objects being considered. A point nearer in space will exert a greater influence than points further away. Because I believe that force is quantized, points very far away will exert no force at all. When I use the words “very far away” I am saying larger than galactic distances.
So my point is that points in space very near to the objects will have a very great influence upon them, and points in space very far from the objects will have less influence, and I am assuming there is some kind of super-galactic distance limit beyond which influence is zero since force is quantized.
Now to answer the question of why force decreases rapidly with distance at solar distances. It is because many of the points in space nearby, looking at the two objects, are past 90 degrees already and are already exerting a negative gravitational force. This action is so powerful that gravity decreases with distance. This same mechanism explains why at galactic distances the acceleration curve flattens out, as the angles causing gravity to increase and the angles causing gravity to decrease sort of fight to a draw.
This also explains why, once the galaxies are a certain distance apart, L, they start moving away from each other, and gravity is working in reverse.
So this is a fuller explanation of my theory. You can see how difficult it would be to try to come up with an accurate mathematical formula. You can also see why I was so willing to acknowledge that my formula was mistaken and naive. I hope you can also see why, even though my formulas do not work, I have not been willing to give up on the general idea.
I readily acknowledge that the whole idea is probably false. But I think that accurately modelling it in order to comprehensively disprove it would be a monumental task. I don’t know if any expert would be willing to waste their time testing it out in a comprehensive way.
So you can see that in my reddit article, when I use the arbitrary point “C” and the arbitrary distance “L” , I was doing a gross over-simplification.
@dga471 I know that you find my speculations about particle physics amusing, so here is another one: If by some slim chance what I’m saying is anywhere near the truth, it would mean that in the zone of sub-atomic particle distances, gravity might be so strong as to be a contributor or related to the strong force … but again, this is a leap in the dark.
Can you explain how gravity can become a strong force at short distances based on your theory? I’m not sure which version we’re talking about.
Joe, I think the problem with this is that you do not yet have sufficient math and physics vocabulary to refine your ideas and make them more precise. You have what you believe is some spark of intuition, but because you cannot translate that into mathematical language, it is hard to prove or disprove your intuitions, because they are at this point either vague or hard to communicate. Without mathematics, it would be similar to trying to disprove an argument in philosophy, theology, or literature. This is why Newton was a genius: more than just being right, he was able to turn his observations into rigorous mathematical expressions that are easily communicable and testable.
Sure, I can try to read this long text of explanation very carefully and try to guess what you are trying to say, in order to compare it with what I know is true from mainstream physics. But it’s hard to do this, because it is also possible that even you yourself do not yet have a clear enough idea of what your theory is saying.
This is why again, I am stressing that the best chance for your theory to develop into something real is for you to learn the basics of the field yourself - and not just at the popular, intuitive level, but the full blown picture with mathematical rigor.
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It also seems to be a very phenomenological approach. He calls it reverse gravity, but it isn’t derived from some lower level reality in a mechanist way. This would contrast with, for example, some of the emergent gravity formulations. So, even if a formula is found that fits the data, all we really have is a new pattern in the data we have observed, without any good explanation of why said formula arises. In a way, it might be something like a cosmological constant. We know thee data doesn’t fit current law, so we just find the formula that does fit it, but it doesn’t have the coherence we need yet to be certain it is anything more than “data fitting” in a pejorative sense.
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@dga471 I would appreciate if you read it; it’s only a few paragraphs.
Everything you said is very right and very wrong.
Very right in that you are completely correct about the formal development, publication, testing, and application of a rigorous scientific theory.
You are completely wrong about discussion: Every formally developed theory started with observations about the world, then it went into an informal intuition, then it progressed to development into a testable theory, and then proceeded with formal adjustments from there.
We are in a discussion between an expert and a novice, and we are discussing something at the very beginning of this long process. We are discussing something (i.e. dark matter and dark energy) about which even the experts are stumped and do not have satisfying answers for.
I know you are not trying to be rude because I’ve seen that you will at least take the time to respond to my statements and questions, and I know that you’re not intending anything negative, but your comments amount to this:
“Unless you’ve had the proper training, your only role in any discussion with an expert is to ask questions and accept the answers the expert gives you.”
Daniel, from the perspective of a novice, that sort of discussion is very boring. I am a teacher. I understand about putting in the time to learn how to solve problems; I know the value of doing the homework. But I am fully busy with my current job and with my family. I do not have the capacity to earn a phd in each of the relevant fields in any reasonable amount of time.
So I’m just here to informally discuss. I would ask that if I make a statement that you think is not worth the effort of responding to, then don’t respond. If you feel this entire thread is not worth your time, then don’t participate in it. It serves no purpose at all to keep telling me that I’m not educated enough to understand any of this.
The only exception I make to this is if you want to offer me a job and training. If I can have an income capable of supporting my family while I learn all the relevant information, I will gladly shut up until I have all the prerequisites to satisfy you.
So I’m giving you a warning: The next time you tell me I can’t speak until I learn more, I’m going to assume you’re offering me a job that pays about 80k per year.