Nope, you're on your own.

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Don't try this at home - We're what you call "professionals" - MythBusters.

You don't get to keep college exams. The school keeps them.

Agreed, from this point of view

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IF I´m wrong you MAY be right

Die Lücke, die wir hinterlassen, ersetzt uns vollkommen (Carl Heinz Schroth)

I have to toss-in my two cents here. My passion since I was 9 years old was to be a chemist, but I hated math.

To understand chemistry like I wanted to, I had to take everything up to and including calculus and differential equations. Something blinked in my head in second semester calculus.

What I previously saw as an impediment to my goals suddenly became a priceless tool for what I wanted to learn.

I finally saw where these trigonometric, geometric, and physical equations came from. Calculus taught me to visualize 4th, 5th and 6th dimensional functions in ways that could be expressed precisely and systematically in a language called mathematics that other people could understand.

I ended up learning to love calculus and DE in the process. Nothing could have done so much to enhance my understanding of chemistry as being forced to learn the maths behind it.

So I ended up with a major in chem, and a minor in math.

Get the fundamentals down first.

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Wanted: Diabolical Plan for World Domination.

I understand what you want to do: You don't want to go to a university and pursue a formal curriculum of study. You simply want to follow the fastest possible path to an understanding of what gravity is and how it works. I suppose you could follow a plan something like the following:

Find a good book on general relativity, one that derives the Einstein field equations and explains what they mean. There are a number of such books around. You could start to read it. You would very quickly discover that you need to be conversant with tensor calculus, the form of mathematics on which the Einstein field equations are based. They relate the Riemann-Christofel curvature tensor to the stress-energy tensor. You'll find that you need to learn about tensors and calculus, so you'll need to look into each of those fields before you can begin to make any headway in learning how to understand the requisite tensor calculus operations. So you need to set the general relativity book aside and find books on tensor analysis. When you start to look into tensor analysis, you'll find that you need to learn calculus, specificially differential calculus. For that, you'll need to learn analytic geometry and algebra. You'll also need to learn elementary physics to deal with the physical concepts that you'll encounter in the book on general relativity. For analytic geometry, you'll need to learn algebra. I've probably left out several secondary subjects you'd need to learn such as determinants, matrices, and trigonometry that you might tun into along the way.

I can assure you that it will be a long, hard process consuming a number of years, but I see no reason why you'd not be able to do it if you have sufficient interest, aptitude, intelligence, determination, and time.

Yeah I have done those courses too. I just want to study gravity now.

I have a degree in chemical engineering I have taken Calc 1,2,3 + dif-eq physics 1,2,3 material balances thermo 1 and 2 and a bunch of other courses. I just want to learn about gravity for fun. If I need more math then I will learn it as needed. What I wanted to do is organize a study plan that would have the workload equivalent to a 4 year BS in gravity.

I completely underestimated your education level. I still think most of what I suggested would be applicable, the only difference being that you've already taken a number of the courses I suggested. And you've demonstrated that you do have the intellectual capacity to master the requisite courses leading to an understanding of the concepts involved in the general theory or relativity.

I note that you've taken a course in differential equations. I bet my instructor in that course made a bigger dent in the history of the world than your's did. Mine was Stanislaus Ulum. He found the mathematical solution to the problem that Edward Teller ran into in trying to produce a hydrogen bomb. Without Ulum's solution, Teller's bomb would have required a refrigeration component so massive that would have precluded its being carried in any sort of aircraft.

If you have some specific questions about the theory to which you'd like to get some answers now, perhaps I can give you some qualitative answers without belaboring the underlying mathematics.


Hey, I just noticed that I've just become a senior member!

OK here are my questions:

What is gravity?
Why does it exist?

Gravity is the curvature of space.

Gravity exists because matter-energy and space-time are linked. The curvature of space links these 2 beasts.

Can space-time exists without matter and energy?

tommac: Here are answers to your questions:

1- What is gravity? Gravity is a manifestation of curvature in the fabric of spacetime. A model frequently used to explain this in layman terms is a rubber sheet stretched tight with a bowling ball resting in its center and pressing its center downward. This is a misleading model, but one aspect of it is helpful. The victim of this model is likely to be derailed by the fact that it's gravity that's pulling the bowling ball downward, thereby distorting the surface of the sheet, gravity then causing the path of a tennis ball rolling across the sheet to the sheet to be curved around the bowling ball.

What really happens is that the presence of the sun in the multidimensional spacetime in which it is embedded causes that spacetime to become distorted in such a way that the shortest distance between where the planet, say the earth, is now and where it will be later is not a straight linie but what is called a "geodesic". The principle of least time dictates that the planet will follow that geodesic rather than a straighte linie between those points.

The theory of general relativity was derived by developing a mathematical expression describing a tensor expression for the shape of spacetime in the neighborhood of a body such as the sun and equating that to an expression for the mas-energy in that space to form the field equations of general relativity. The problem then becomes that of finding solutioins to those field equations. That's such a difficult task that I haven't the faintest idea how to do it for even the simplest case.

Note that there's not the slightest mention of forces. The force of gravity is a total fiction, Newton notwithstanding.

2- Why does it exist? I don't think anyone can answer that question. Science deals with what things are like, not why.

3- Can space-time exist witthout matter and energy? The answer would appear to be "yes" since there are regions of space that are essentially empty of both matter and energy, ignoring dark energy, and both space and time owuld seem to exist in those places. Spacetime would be totally flat in those spaces, hence, no gravitational effects. Note that I said "effects", not "force" since gravitational force is a mythological beast as far as general relativity is concerned.

Does gravity curve matter as well as space?

Why do you persist on asking the same questions over and over again?
You have asked this over on this thread and have generated discussion from it.
Why would the discussion be any different here?

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Numbers are not case sensitive. (me)

tommac: Does gravity curve matter as well as space?

dcl: The answer to that would seem to be "yes". Space is severely distored in the vicinity of a black hole. GThe matter that fell into the singularity in spacetime to form the black hole became compressed into a dimensionless singularity, a mere point.

tommac, I note that you're a chemical engineer. I hope you're not anything like a chemical engineering graduate student I once encountered at Ohio State University. Immediately after the MacArthur firing by President Truman, this graduate student wrote a letter on toilet paper, saying, "This is what I think of you", sealed it into an envelope, addressed it to President Truman, placed his own return address on it, and mailed it. He wrote a second letter at the same time in which he said, "If you ever come through Columbus, Ohio, you can depend on me to blow your head off with a high-powered rifle". Both letters were intercepted at the post office in Columbus, Ohio, and turned over to the FBI. I was told by the occupants of the apartment in which he was renting a room in the same apartment building my wife and I were living in, that seven cigar-smoking FBI agents showed up and arrested him. He spent a month in jail while the investigation went on. He was eventually released as a "harmless nut". He dropped out of the university.

Are all chemical engineers like that? I wouldn't know since I'm a physicist!

I went to school for ChemE but I do not work in that field ... but I think your assumptions about ChemEs could be correct.

I don't know how to say this without sounding rude, but I'm a bit skeptical.

ETA: After reading some more of your posts, I'm sad to announce that you're the first person on my ignore list.

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Wanted: Diabolical Plan for World Domination.

This post is soooooo last week. I think everyone is tollerating me now. Please get with the program.

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Everything I need to know I learned through Googling.