Strange

You haven't done the math, which is why I see no reason to believe you. What does that even mean? What is invariant? You have two changing (and apparently related) values. In what sense are they "invariant"? If you want people to (a) understand what you are talking about and (b) believe it then you need to post the mathematics of this relationship. (Or pay someone else to do it for you.) You "know how to produce the model" and you "have done the math" so why don't you create these graphs? Until you show us that math, I see no reason to believe that. And stop blaming other people for your laziness and inability to do the necessary maths.

Why don't you read what I said, instead of making stuff up. 1. You said that it is implicit in Mathematica. Therefore it is not explicitly described by the code you have posted (which, BTW, I haven't looked at because I am not familiar with Mathematica). 2. The fact is is implicit in Mathematica does not necessarily mean it is complex. The implementation of the sine function is built into Mathematica. That is not particularly complicated. 3. I never said it was simple. But I can't imagine it is particularly complicated. 4. I never said no one should waste time on it because it is so simple. I said that you are the only one interested in the function so either you need to learn enough basic trigonometry to work out the equation for yourself or you need to give others a reason to look into it (cash has been suggested). So if you have quite finished with the lies and straw man arguments, we can move on. If you know how to create the model then you can work out the equation. Or does "knowing how to create the model" have the same level of truthiness as "I have done the math"? That sounds about right. You have made a series of incoherent and largely meaningless posts about direction, vectors and scalars . It wasn't until 110 (one hundred and ten!) posts that you said you were looking for the equation that related the angle between two planes. Splines are usually used to fit a curve to a series of points. I don't see how that is relevant here.

Good. Then you can answer the following questions: Come on then, if you have done the math, let us know. Stop all the vague handwaving about how complex it is and just tell us.

Why would anyone try and solve this problem for you? Then show us. I just took the numbers from your animation and put them into a spreadsheet. That has always been my argument. Which is why no one is going to do this for you. The graph I posted goes over the full range of your animation. So you can work out the values at 30 and 60 from that. But 30 degrees is one of the numbers in the animation. 30 -> 35.3 60 -> 15.5

The one for Texas sounds wrong... http://www.etymonline.com/index.php?term=Texas

No. YOU have to do the math. You claim it will show something new and insightful. It is up to you to support your claims. No one else is going to waste time on it. What makes you think that this animation has the significance that you claim? It just shows some planes being rotated around the surface of a cone. One thing that isn't clear is what it means by the angle between two planes. I decided that the easiest way to define that is in terms of the surface normals, which are vectors. You are looking for a trigonometric relationship between two planes. This will give a result in standard mathematical terms (lengths, angles, vectors, etc.) There is no magic here. Funny. But also untrue: So it ISN'T in the cdf file. It is implicit in Mathematica. So now you want people to reverse engineer the code (*) for Mtahematica to solve your non-existent problem. (*) Illegal in some jurisdictions.

Then can you use that model to generate some useful results? Or are you just making a wild guess based on some pretty animations? Then you need to put it down on paper so it can be properly reviewed. I suspect what is really going on is that have some vague mental images of "something" that you think is significant. But because it is vague and not mathematical, I doubt it has any substance or validity.

This really doesn't make much sense. (As I am sure has been explained before.) If it has direction then BY DEFINITION it is a vector. 1. Why do you think that? 2. How do you intend to do it? (You keep making vague claims that this is possible/meaningful. It is time for you to get specific.) Please show, in detail, how you do that.

It seems to imply that dark matter has some connection to "anti-gravity". Apart from the fact that anti-gravity is science fiction, the whole point of dark matter is that it behaves, gravitationally, just like matter. There is no known connection between dark energy and dark matter (beyond the name). There also doesn't seem to be a spectrum here (in the usual sense of a range of frequencies). The expansion of the universe is well explained by one of the best theories we have (General Relativity) and, again, this doesn't have much to do with dark energy or dark matter. So what is your model supposed to add to this?

It is not a property of the object (whether photon or pool [billiard] ball) though. It is observer-dependent. In other words, it can be changed arbitrarily by choosing different coordinates.

Surely the whole point of this experiment is that you don't know the direction of travel (or, at least, of you do then you don't get interference).

"Stick to the atmosphere"

Apart from the fact that velocity is a vector. So this is wrong. Please show that this, and your other incorrect equations, produce the same results as the standard equations. If they don't then your "theory" doesn't match reality and is therefore wrong.

I really can't think of a better explanation than the circle animation you posted earlier. Take another look at that and think about what it shows in relation to that statement.

https://xkcd.com/327/

I see nothing new here. It makes no difference who measures first (or if the measure at the same time). They both know that they will measure opposite spins.

If the problem really is with image editing, then I always recommend IfranView as a really simple and fast image viewer and editor.

There is no reason to think that a singularity, or a black hole, can explode. Although it does remind me of Asimov's Last Question: http://multivax.com/last_question.html

Radio waves. (Although it is autonomous to a large extent because of the long delays.) For various reasons, they don't fly in a straight line. The direction is controlled by rocket engines. http://www.spaceflight101.net/mars-orbiter-mission.html

Yes. But not really an approximation. It is a sinusoidal wave. I don't mind if you post pictures to illustrate problems with trigonometry. We don't need the jokes and pictures of your girlfriend (or you, or whoever it is).

I think the cheapest way to get your won satellite up is the CubeSat initiative: https://en.wikipedia.org/wiki/CubeSat#Costs

You could have done it yourself in a few minutes. But, as usual, you expect everything to be done for you. Maybe you need to offer a prize as an incentive (as there is no reason for anyone to reverse-engineer this animation for you). $1,000 for the first person to come up with the equation?

He will measure the value (of whatever property it is). He will not be able to tell if Alice has previously made her measurement or not. The only difference that entanglement makes is that when they compare their measurements later, they will find there is a correlation between them.

If I had meant most I would have said most. I haven't seen any statistics but I doubt a majority of scientists are religious (in a formal sense). Although it is quite possible a majority have beliefs of some generally "spiritual" sort. But I really don't know. But there are enough scientists who write about their religious beliefs to make it clear that there are a lot who are religious. Not really they point. Wherever they come from they are arbitrary and, in some ways, irrational. So there is nothing special about religion, in this sense.

But, presumably, you have certain moral beliefs and ethical standards. These are a result of beliefs and opinions that you have picked up over your life. They are not a result of science. Some people get their moral beliefs from religion (or claim to) and others don't (or claim not to). Shrug.