@Joe_Bakhos… it looks like your new theory has the gravitational acceleration due to the sun oscillating wildly in the space between planetary orbits? I hate to be the bearer of bad news, but I can assure you this is false. Humanity has sent a lot of interplanetary probes out into those spaces. We would have noticed. I’m pretty sure the differences between your theory and Newtonian gravity are orders of magnitude more than something like the Pioneer anomaly (and haven’t they figured that one out? I thought they’ve pinned it on thermal recoil).
Also, your expression \sin(0.00004\sqrt r) is meaningless without some units of inverse square root length attached to the .00004.
Also, calling your equation for a a wave function would probably not be considered correct usage, especially not without a wave equation (like, the Schrodinger equation, or the Klein-Gordon equation) that a satisfies.
@structureoftruth: “oscillating wildly” : There might be large oscillation near to the sun, but by the time you get to planetary distances we’re talking about an oscillation in acceleration of between .04ms^-2 to -.02ms^-2. This slight oscillation would be spread over tens of millions of miles. I guess “wild” is in the eye of the beholder.
Likewise with your comments about “orders of magnitude” differences in acceleration. I don’t think you are realizing the probes travel at speeds like 15,000 meters per second, while at these distances the differences in acceleration I am talking about are very, very slight – as I noted above.
About units: When you take the sin function of something, that something is considered an angle, and it is not necessary for it to have units since angles are dimensionless. All that is necessary is that you use the same units for r that you use in the outer equation.
@Joe_Bakhos, I’m too busy right now to look at your work in detail. Here’s some comments:
First, you need to clean up your equation and provide details on what each of the symbols meant. What is G here, what is its units and numerical value? What is x here? Also, as @structureoftruth already said, your \sin(0.00004 \sqrt{r}) makes no sense unless you attach a unit to the 0.00004.
Second, you need to fix your model so that it gets 9.8 m/s^2 on Earth. 11.8 m/s^2 is too far off; as it stands, even high-school experiments can falsify your model.
Third, in general you need to demonstrate your claims mathematically and quantitatively. Here are some examples in which you need to do this:
You need to mathematically demonstrate that this reproduces Bertrand’s theorem when the “where acceleration according to equation (1) intersects with the blue line representing acceleration according to current theory”.
For Solar system stuff: you need to mathematically show that your theory actually reproduces the orbits of solar system bodies, both ~circular ones like the Earth and eccentric ones like Pluto, and even extremely eccentric ones like comets. Just claiming that it does is not enough.
For Galactic stuff: again, you need to mathematically show that your theory actually reproduces the flat rotation curve, etc. It is not enough to claim that it does.
And so on for cosmological expansion, CMB, etc. You need to show things mathematically instead of just claiming it with words. If you cannot do it yet for a particular example, take it out and put it in a future paper.
On testing and falsification: you need to go to the literature to see what sorts of bounds have been set by previous experiments, and show quantitatively that your theory is still within the bounds.
Excuse me @Joe_Bakhos, he did respond. @PdotdQ laid out precisely what is necessary to convince him your idea has merit. He did respond to the general idea, telling you that you have much more work to do.
@PdotdQ: We are talking past each other. In my opinion, you’ve listed the obvious work that needs to be done to turn a speculative hypothesis into a theory. I am not disagreeing at all with your list.
I am disagreeing with the idea that it’s not worth discussing until it is proven.
Science obviously goes in stages. In the early stages, a researcher needs to discern what is worth investigating and what is not worth investigating.
If at a very early stage I say, “Hey, what about this? Might this be worth investigating?” You are basically saying: “Well Joe, complete your investigation, and prove that it’s true, and then I’ll tell you whether it’s worth investigating.”
So to try to be clear, you outlined a sensible course of action – but I already knew most of that list. That really wasn’t what I was asking. What I was asking was this:
Being an expert in the field, given your first impression of the general idea, would it be worth my time to go through that entire course of action to validate this? Or, in your opinion as an expert, can you see obvious flaws in the idea that tell you there is no possible way it can be true and is therefore not worth pursuing?
Now as I said before, if you’re not interested in answering this type of question, or if you do not have the time to look into it that deeply, I understand.
It is difficult to figure out whether your theory is worth further investigation given the details are so sparse - which is why this is a chicken or egg problem. If you can answer some of the comments (perhaps not all) that I outlined previously, then the theory will have more meat that I can evaluate to see whether it is worth it to continue or not.
I don’t know what you mean by “obvious flaws”. Perhaps the first two points I mentioned qualifies:
Here are a couple more that perhaps what you mean by “obvious flaws”:
If you plug in your acceleration to F=ma, then your equation is not symmetric with respect to the two masses, m and M. This means that the force disobeys Newton’s third law.
Regarding Bertrand’s theorem: a cursory look at wikipedia’s entry for the derivation of Bertrand’s theorem already disagrees with your acceleration law. c.f. “β must be a rational number. What’s more, it must be the same rational number for all radii, since β cannot change continuously”.
An additional observation: your equation for acceleration is
a = \frac{GMr^2}{x^4+GM}(1 + 2 \sin (0.0004 \sqrt{r}))
Am I getting this correctly? What is x? If I assume that x^4 has the same units as GM, your formula will result in a having units of r^2 or length squared, which doesn’t make sense. (In addition to the units anomaly inside the sine function which others have mentioned.) Can you explain what is going on?
So you have discrepancies on the order of 10^(-2) ms^(-2). The Pioneer anomaly was a discrepancy on the order of 10^(-10) ms^(-2). It took maybe a decade, around 10^9 s, to become noticeable. Your anomalous acceleration would become noticeable somewhere on the order of seconds to days, at most.
@PdotdQ: G is numerically, the gravitational constant with appropriate units. What “appropriate” means, I don’t know yet. Same goes with your other concerns about units; put in whatever units make it work for you.
When you say the model needs to get 9.8 m/s^2 on Earth … please. This is obvious. I’m putting forward a general, rough idea in its rudimentary stages. Hey, how would MOND theorists feel if they got their predicted accelerations to within 20% of the observed value? As I keep explaining, I would appreciate a comment on the general idea rather concentrating on details. About Newton: Yes, it contradicts Newton. It also contradicts Einstein.
About Bertrand’s theorem: The entire point of my citing Bertrand was to point out that I think the gravity law does NOT follow his theorem. Newton followed his theorem based on observations. What I am saying is that over the course of billions of years, the dust, gas, and other matter around the sun eventually settle in a way consistent with Bertrand’s theorem, because the matter has sometimes been pushed further out, and sometimes pulled nearer in. You are very correct in that I certainly have not proven this mathematically – this must certainly be done before I can claim to have an actual theory.
@dga471: I would like to thank you for your ringing endorsement of my idea. The concept of triage is applicable here. It is natural to gravitate to the most glaring defects that an idea has, before moving on to the details. I’ve put forward an idea whose fundamental concept contradicts both Newton’s and Einstein’s theories. For you to look at it and conclude that the most glaring defect that needs most immediate attention … is appropriate units … seems like a huge endorsement to me.
@structureoftruth: The boundaries for acceleration I gave were maximums and minimums around Mercury. By the time you get to Pluto, the differences would be on the order of what you’re talking about.
As far as researchers “noticing” other deviations: In fact, they have:
I think you misunderstand. The problem with your units is not an insignificant detail. It is different from complaining that you are writing your lengths in inches instead of centimeters. Instead, this is a problem with the dimensionality of your basic formula. The crux of your theory right now is the formula for acceleration that you have offered and the resulting plot it gives. But I would say that it is meaningless, because you’re doing the physics equivalent of adding apples to oranges.
@PdotdQ In quantum field theory people are often more liberal with their units, because they assume they can throw the right combination of factors of h and c in until the units make sense. Is there an equivalent thing for gravity?
I think our different backgrounds are making us communicate past each other. Your border between “general ideas” and “details” is different than what I am used to. To me, everything that I posted is still in the “general ideas” category. “Details” to me is something like running a numerical simulation, or a full formalism of cosmological perturbation theory with your gravity model - and I didn’t say that you need to do any of that. I honestly don’t know what you want me to evaluate that is within your “general ideas” category.
You ask me whether I see any “obvious flaws”, and in my posts I have given the ones that jump out most immediately.
It explains the effects attributed to dark matter and dark energy. This hypothesis also explains the odd acceleration of Oumuamua, the interstellar asteroid that recently passed through our solar system. It also explains the Pioneer anomaly and the flyby anomaly. You can download a pdf of this hypothesis here:
@PdotdQ , @dga471, @swamidass, I made a new video wherein I ran a simulation using GaaWF just to show that functions like this can evolve stable circular orbits:
@PdotdQ , @dga471, @swamidass, This past week, for the very first time, I saw an article wherein professional astrophysicists were proposing something like my idea. i.e. doing away with dark matter entirely, and replacing it with +/- gravity.
What is very encouraging is that their modeling shows that the acoustic variations in the CMB can be explained by this. Here is the article:
@swamidass, @PdotdQ, @dga471, I played around in Desmos trying to find one that looked like the one in the article that was valid at all scales, used only whole numbers or universal constants, had proper units, gave approximately correct values for orbital acceleration of the planets, and gave the correct sign on the surface of each planet, and is also fairly close in magnitude at the surface.
I succeeded and then submitted it to the MNRAS. Here it is:
a = (GM/x^2)[1 + sin((2pi^2)ln(x)) + cos((2pi^2)(e^2)ln(x+2(pi)r))]
Where x is the distance from the gravitational source, and r is the radius of the gravitational source.
