I don’t think this is too difficult to calculate actually. You just need a few things:
For every point in the space-grid C, and mass M1 and M2, you need a formula on the force exerted by C on M1 and M2. This force will depend on the angle between C and M1, the angle C and M2, and the distances between C and M1 as well as C and M2.
The distribution of the space-grid. Are they in a rectangular grid, spherical grid etc? What are the distances between each grid points.
The information transfer protocol: how do each space-grid points know of the existence of the masses, and what is the information travel speed.
Of course the issue then is why the space-grid points behave the way they do, and depending on the answers to 1), 2) and 3), I already can come up with many issues with this theory that might make it even more unpalatable to me than your approximate one.
However, once you have these, you can just sum over the forces from each grid points. If the grid is fine, you can use integration which will make the problem much easier. If it is rough, you can write a program to sum the forces for you.
I am trying to communicate that, as a student of science, I am completely open to my idea being disproven; I am also open to the idea that it may be trivially silly to an expert, and very easy to disprove.
I was just trying to demonstrate to you why, once my idea was shown to be trivially wrong because of the Newton’s shell theorem, and because of the flat galactic curve, I was still proceeding with trying various functions to try to make it work.
So according to what you’re saying my complete idea might be even worse than my approximation. If that is so, I can accept that. If that is true, then no form of my theory could possibly be made to work.
In which case I would still conditionally believe in reverse gravity for now, but I would believe it functions in a way completely unrelated to my idea.
@PdotdQ : You can see why I was insisting that various types of space deformation were wrong; i.e. that Einstein’s relativity might be only correct about time dilation. According to Einstein, mass is affecting space, whereas what I am saying is the opposite: Space is affecting matter.
Now that you explained it, I can see where an expert with a program would be able to model it and pronounce judgment pretty quickly.
I imagine a model might be made that is relativistic – i.e. in this both GR and my idea would be partly correct, and matter and space mutually affect each other. Although I suppose GR already does this: “Matter tells space how to bend, and Space tells matter how to move.”
GR indeed already has the mechanism for pure space affecting matter. In fact, many of the most cherished spacetimes in GR, such as the empty FLRW metric in cosmology or the Kerr metric for black holes, already cause test particles to move sans any matter and energy, i.e. pure spacetime is causing these particles to move.
However, these days the internet facilitates one to learn physics much easier and much more quickly than even 10 years ago. @dga471 posted a website with resources you can check out. I found that there are also many excellent instructors on youtube.
Note that even before these resources, Ed Witten, one of the world’s most respected physicist was a political campaign organizer before moving to physics. Tadashi Tokeida, also one of the world’s most respected physicist, was in his 30s working on a completely different job before he even know what an integral is. It is certainly not impossible to learn physics while working on other jobs; physics is for everyone!
@PdotdQ I understand about learning Physics, and I am doing so. What I am disagreeing with is the idea that I not posit anything of my own or discuss any of my own ideas until I’m an expert.
I am saying that it contributes nothing to the discussion to remind me every few posts that I’m not an expert.
@PdotdQ@dga471 I know this post is wordy, so I’m not expecting a response until you have the time, but here are some other reasons why, in an informal speculative way, I find my idea attractive.
It potentially provides a mechanism for time dilation. It says that all motion has to do with angular velocity and angular acceleration. This means that for an object very distant from other objects, at non-relativistic speeds, angular acceleration, positive and negative, sum to very near zero. So constant non-relativistic velocity requires no energy.
As we approach the speed of light, increased velocity in the direction of travel becomes impossible, because the angular acceleration begins approaching infinity, and any forces directed along this line of travel are transferred to mutually opposing perpendicular forces. These forces are responsible for increased mass, caused by impulse to the object.
This means that any type of rotation out of the line of travel becomes impossible, even for something like a subatomic particle. This precludes any type of change, whether it be vibrational, rotational, or any vector at all that has even the slightest component in the direction of travel.
This stopping of change is what it means for time to slow down.
So the question is this: “Why has GR been successful in its predictions even though its conception of 4D spacetime is a mistake?”
Both phenomena, time dilation, and increased mass, whether you are talking about acceleration near the speed of light, or you are talking about descending into an intense gravity well, (note that in an intense gravity well, motion will be impeded for the same reason; i.e. any rotation out of the line of the gravity force is impeded) are caused by gravity. So there is some kind of mathematical correlation.
This means that there is some mathematical connection that, when treating with these problems as 4D spacetime, enables finding the correct answer to a lot of problems, even though the model is not correctly depicting reality.
This is why I believe it may be possible to come up with a model that keeps flat 3d Euclidean space while accommodating time dilation and increased mass such that the successful tests of GR are duplicated.
Lastly, two other phenomena might be explained: spooky action at a distance might be dependent upon angle rather than distance. Also, this might mean that objects that are sufficiently far apart, and therefore most angles in space with most other objects are near 180 degrees, these objects may recede from each other at faster than the speed of light, as is posited about the most distant galaxies observable.
Sorry, one more thing. It might explain the structure of light, i.e. why light generates two perpendicular, alternating force vectors as it travels.
@PdotdQ@dga471 so modelling this idea and trying it out along the lines of what @PdotdQ explained, (again, I thank you for that!) , would mean doing a triple integral of a volume. This integral would have to incorporate the distance each point in space is from the two objects, modifying the torque force based on the lengths of the two arms, noting that sometimes it’s positive and sometimes it’s negative. If the objects are in motion at non-relativistic speeds, I’m assuming this would modify the integral. If they’re in motion at relativistic speeds, I’m sure that would affect the calculation …
I would hope that doing this volume integral would end up reducing to proportional to 1/r^2 at solar distances, and match up with the behavior of gravity regarding galactic rotation rates at larger distances, and then reverse at still larger distances. This reversal would also then further help with galactic rotation rates, because of the matter existing between galaxies and also the influence of the galaxies upon each other.
You’re reading me completely wrong. Have you noticed the number of posts I’ve contributed to this thread, commenting and even attempting to mathematically translate on your theory in various ways? If this is all what I wanted to say, then I would have stopped talking with you a long time ago.
So, I’m not saying “come back to me in 10 years after you’ve gotten a PhD in physics.” I was very happy by the fact that you were going to try different ways to simulate or calculate your initial theory and match them up to galaxy rotation curves. I was expecting that in a few days or weeks you would post some plots or simulation results based on that. In the process, you would have learned something about math, physics, astronomy, and computational simulation. I have mentored undergraduate and even high school students with similar starting level of expertise as you, and within a summer got them to become somewhat competent in a very narrow field of physics relevant to their project.
What I’m saying is that I honestly think we would have a more productive and enjoyable discussion if we focused on a specific, narrow part of your theory, and worked out the implications of that rigorously, so that you gain some competence in Newtonian mechanics, manipulating equations, and understanding the observational evidence relevant to your theory. I do not think it would be very productive if you keep throwing out what you view as grand consequences of your theory and asking trained physicists to translate that into actual math. Of course, if you want to keep doing this, I might still reply back to you, if I feel some of your points are interesting
Anyway, I have some questions to ask about your latest speculations:
And also, can you elaborate further to me how “spooky action at a distance” can be explained by your theory?
I will be blunt. You are not at all honestly portraying my statements or my actions. In a speculative discussion like this, some things get thrown out that are just that: speculation. Now I will answer your questions, but I would like you to note something:
I spent a great deal of time precisely explaining something that could be rigorously confirmed or refuted in the mathematical way you’re describing. Thus far you ignored that completely, and so far have shown no interest in discussing it. You ignored the central important idea that fits your desire for specificity.
Instead, in contradiction to your own statements, you seek out and demand rigorous explanations for the most general and most speculative of my statements – while deliberately mis-characterizing all of my statements to be like this. In doing this, you seem less interested in discussion, but more interested in searching for weak points to attack.
But I will answer your questions. My ideas suggest that at sub-atomic distances, nearly all of the vectors I described in surrounding space would have very small angles between nuclear particles. Under my theory, the smaller the angle, the more summative the gravitational force – so it might be very strong indeed. Of course, under my idea the gravitational force is stronger when the point in space is nearer – so there may be very strong negative forces by certain points in space in the nucleus as well; which might contribute to the instability of a large nucleus. My problem, as you know, is that I am ignorant of particle physics, so I have no idea if this mechanism makes sense in that context; it is the mere speculation of a novice.
About spooky action at a distance: That is even more speculative. I am merely saying that since my idea places a great deal of emphasis upon the idea of angle, and since an angle does not change with distance, this might suggest some connection to the idea of spooky action.
I have spent time examining your basic modification of gravity, which does have a mathematical expression. I believe if that does not manage to fit galaxy rotation curves, then the main application of the idea will be disproven and it doesn’t make sense to keep dwelling on the theory. So I’m waiting for you to test the theory.
Regarding your longer explanation of the nature of space, I might take a closer look at it in the future if I have time, to see if there is anything I can easily translate into mathematics. Perhaps PdotdQ will have also translated your speculations in a more understandable, palatable way by then.
What I’m trying to impart to you is the proper attitude of a physicist, which is to hold off on further speculation before the main application of the theory (explaining dark matter) has been proven to work. Doing otherwise damages your credibility.
By the way, this is an attitude that I learned myself when observing other physicists. I’m not just saying this because you’re untrained in physics. I apply this attitude everyday in my reports to my professor and fellow graduate students. I even apply this attitude when interacting with you. Notice how I often prefer to ask further what you mean rather than just saying that it is surely bunk?
How does this fit with your original modification of gravitational force, where we had F = F_{Newton} \cos \Theta?
At small angles \Theta \approx 0, then we recover the original form of Newton’s law, where gravity is very weak at short distances compared to other forces like strong and EM.
Spooky action at a distance refers to the phenomenon that the effects of quantum entanglement seem to be capable of traveling faster than the speed of light. Is this what you are referring to? Does your theory suggest that information can travel faster than c?
@dga471 Any mathematical or scientific analysis you give is very much appreciated. Where we are at conflict is your attitude. I am a 55 year old man who has taught science and math for decades. I have not the slightest interest in your condescension to teach me the “proper attitude” of a Physicist. I have tried to communicate this to you politely. I have tried being blunt. I have tried any way I know how. I do not want to discuss my attitude with you, and I am not at all interested in your opinions on my attitude. So I will repeat this again: Can you please self-edit your comments so they are about the topic at hand? Can you please skip the preaching?
About my simple version: It was exactly that: A much simplified version of what I was thinking in the vain hopes that it would work out to be that simple at large distances. This hope was shown to be naive. I have put forward the fuller explanation just in order to try to convince you that I was not simply being stubborn when I tried to find other functions that might work.
I have not ever considered the implications of information travelling at c. As I tried to make clear, I have not proposed or thought of a mechanism for how spooky action at a distance works. I have already shared why I speculate that further work on my theory might clarify this down the road.
How does teaching math and science in a high school tell you anything about the proper attitude of a physicist? Each of us has different skills and knowledge. If I wanted to learn about how to teach high school math and science I might ask you what the proper attitude is to do that.
You initially posted your theory in response to a paper about dark matter. You go all over the internet trying to get critique on your theory, including from actual physicists. You even characterize yourself as a “student of science”. How are you a good student if you refuse to listen to your teachers? You’ve switched hats from high school physics teacher to an amateur, learning theoretical physicist. Some of us are willing to help you (and they have), but I think people have a right to talk about the “rules of the game” as well. After all, we’re doing this for free and for fun.
In addition:
I am merely responding to your speculation with further speculation based on what I know about mainstream physics. Otherwise what is the point of writing out a list of speculative statements based on your theory? Do you expect people to simply accept them to likely be correct without further explanation?
You’re also free to ignore my preaching, Joe. I’m speaking up out of a sense of obligation to respect the profession of science and scientists. To respect expertise and accumulated knowledge. Even if you don’t care, someone who reads this might. You cannot basically claim that scientific expertise is wrong in a forum called Peaceful Science and expect me to sit down and ignore that.
What I don’t understand is, on what basis do you make your speculations if you have not even vaguely thought of any proposed mechanism for them to be connected? I could also claim that your theory could explain the Problem of Evil, evolutionary biology, world peace, or Intelligent Design How is that any different?
I actually like this. That you’re still trying to model your basic idea according to what was discussed earlier. I urge you to finish this project before going on work out the implications of your more general theory of the nature of space.
I believe you can start out with just doing this in 2 dimensions, at least to get the basic mathematical machinery set up. Going to 3 dimensions after that will be easier.
I think what you want to do is to find an expression for the density of mass for a spherical/circular womb. Then think of a point far from the center of the galaxy but inside the womb. Come up with an expression for the force exerted by each infinitesimal of mass on the womb and the large mass in the center. Then integrate the entire expression for your modified force law, i.e. F = \frac{F_{Newton}(r,\theta)}{\mu(r/L)}
over all r and \theta. You do not need to integrate this by hand; you can use WolframAlpha. That’s the easy part. Then you now have the the force or acceleration of a point mass at a single point far from the galaxy but within the womb based on your modified gravity law. You can then figure out the velocity.
I suggest not thinking of it in terms of torques or lengths of two arms. I think the above way is simpler, to me at least.
After you do this, you can then play around with different functions for the mass distribution of the womb, and seeing what happens when you integrate to different limits. You should also try to repeat the above exercise for the MOND case, to ensure that you get understandable results that make sense for a theory that is known to work.
I urge you not to worry about this at the moment. As we’ve covered above, your notion of a length scale for gravity is not yet defined in a way that makes sense in a relativistic limit. Based on the fact that MOND took two decades to get an relativistic version, I don’t think we’ll get there anytime soon.
@dga471 Thank you very much for your suggestions. As far as the math and physics I agree with you, and as I said, I am grateful for your help.
As for your analysis of discussing science, I could not disagree more. Well, I do agree with one thing you said: I am free to ignore your preachy comments in the future; so to show you that I am sometimes willing to follow your preaching, that is what I will do.
I promise however that I will never ignore any of the math or science that you present.
@dga471@PdotdQ I’ve been thinking about your statements regarding piecewise functions cobbled together with interpolating functions. If I proceeded in this manner, would you find it more intellectually honest? I am going to try it, but let us suppose that my triple integral does not work out.
State at the outset that I am data-fitting and am not trying to present my idea as a gravity equation, but simply as a mathematical challenge:
Assume that the gas and dust in the interstitial space between galaxies is dispersed in a relatively even, uniform manner, but there is much more than expected out there. @PdotdQ : the reason why I dropped my initial equation is that I am criticizing existing dark matter theory for positing convenient masses that we cannot observe and are composed of something we’ve never encountered. My idea would be no improvement if I start doing the same thing: I.e. just positing convenient accumulations of matter wherever I need them. In contrast to this, I think positing evenly dispersed dust and gas is reasonable.
Use the ~ 1/r^2 function at solar distances.
Use the ~ 1/r function at galactic distances.
The ~ 1/r function would also reverse at L, so that galactic rotation rates would receive help from the negative gravity from the dust and gas, and also from other nearby galaxies. This function in combination with the first function would also need to be able to explain why matter was able to form its large structures since the CMB.
Use the acceleration of galaxies away from each other to make a last function that works at super-galactic distances, and is based upon reverse gravity.
THEN cobble all these 3 functions together using interpolation.
THEN rather than claim that I’ve found a new equation for gravity, instead I throw this artificial, cobbled together function out there, and ask mathematicians if they can find a relatively simple and elegant function that duplicates this artificial frankenstein’s monster?
I am okay with this. The biggest challenge might be the fact that this equation has to be valid for big galaxies as well as small galaxies - this is why MOND uses acceleration as their scales instead of lengths.
However, note that the answer will not be unique, i.e. there are many ways to stitch up the different functions together so that they have the behaviors you want at different length scales. For example, here is an entire family of functions that can do what you want:
F = F_1W_1 + F_2W_2 + F_3W_3 + ...
where F_1, F_2, etc are the forces (1/r^2, 1/r, reverse gravity, MOND-like, or whatever have you), and W_1, W_2, etc are window functions that only open up in the length scales where you want them to take over. For example, F_2 might be a deep MOND like force, and W_2 is only nonzero around the galactic scale.
Of course, there are many window functions that can be used. There might also be different ways I can write the forces that still give the behavior you want. The resulting function is very “Frankenstein’s monster” and artificial. Given this, I don’t know if there is much value in:
At this point, we might as well give them the piece-wise function.
@PdotdQ@dga471 I wasn’t able to contain myself until I manage to do the integral some day. So I played around with trig functions just to see if I could do it that way. This form seems to work for gravity in our solar system and also comes very close for galactic rotation rates at the same time. Here is the equation for acceleration due to gravity:
G(ln(M))(sin(2arctan(L-r)))^2(cot(2arctan(r/L)))
Here G is a gravitational constant that is 3.458*10^28
r is the distance
and L is the distance that gravity reverses. It is 5.44*10^21
@PdotdQ , might you try it and see if it seems reasonable to you? I am hoping that when the integral is finally done it might look like something roughly in this form.
This form doesn’t have the right units. Note that the entire thing should be in units of Force, and things inside logarithms and arctans should be unitless.
How is that any different?