I had a question about math applied physics

[chosenone]

I know that math is used to interprete physical events like the motion of a object,so you can find where it is by how much distance it traveled in a certain time.thats easy,but I never understood how math relates to hypothetical models of different types of black holes,or universes,or particles like superstrings.so can anyone give me a example keeping in mind I'm in intermediate algebra,and try to explain it to me,because i like math,and i think if i understand how it works it will open up a new world to me.!

 

[chosenone]

Gee no billiant geniuses out their can take on such a task as to answer this.
I thought I was talking to the best!

 

[chroot]

Math is used to predict the results of experiments. In many cases, we try to model the math around a prior physical understanding of the phenomenon -- for example, we may speak of the momentum of a particle, because we deduce from physical understanding that such a quantity is meaningful. So we try to isolate the various characteristics that a phenomenon can have (like charge, spin, momentum, etc.), and represent them quantitatively. We also assume some basic axioms, such as physics is the same everywhere in the universe and physics is the same now as it was in the past, and as it will be in the future. From such basic axioms and mathematical suppositions, we can derive many other things.

In the end, if a model correctly predicts the outcome of an experiment, the model is good -- even if we have no idea what its internal workings mean in a physical sense.

- Warren

 

[arcnets]

Originally posted by chosenone
so can anyone give me a example

Well I'm afraid this is not much help, but I think this is sort of how it started:
- It's easy to notice that the moon & planets keep moving in complicated patterns with respect to the background of stars.
- The most primitive idea is, this is all caused by a god or something who moves them at his own will. Problem: What divides God from Man?
- To find out His plan, you make some measurements, draw some maps, and see there is some regularity in all this. Mathematical aspect: numbers, equations. Problem: What's behind this?
- PTOLEMY explained it by the planets being fixed on large crystal spheres which rotate. New mathematical aspect: spheres, symmetry. Problem: How can Earth be so imperfect in a perfect sky?
- KEPLER found that the observations can more simply be explained by the planets moving in ellipses. New mathematical aspect: coordinates, curves, transcendent equations, transformations. Problem: Is Earth just another planet?
- NEWTON found that the Keplerian motion can be explained by the Law of Gravity. New mathematical aspect: calculus. Consequences: Do mechanical laws determine everything?
- EINSTEIN found that the abnormity of Mercury's orbit can be explained by General Relativity. New mathematical aspect: differential geometry, higher dimensions. Problem: How about Black holes? Gravity waves?

See, I tried to illustrate how math gives solutions but also new problems. You may say this doesn't make much sense, and maybe that's true...
Please note that I don't intend to hurt any religous feelings.

 

[chosenone]

o.k. I see in the motion of planets you use formulas to predict its motion to find its position at any given time,and where it will be in the future.but what about relativity e=mc^2.I always hear that relativity makes preditions about things that their trying to test to see what happens.thats what I'm talking about.I thought they used math to make these preditions so they can tested.or am I wrong and its something else.

 

[arcnets]

I think you're talking about tests of General Relativity. That was only Einstein's second big theory. I agree it's not so well-tested, but the majority of physicists seem to accept it. Einstein first big theory was Special Relativity. This includes E=mc^2 and many other formulae, which have been confirmed very well in many experiments.

I think this is what the 2 theories are meant to explain:
Special Relativity: Explains why e.m. waves move at the same speed for any observer, even when he's moving.
General Relativity: Explains why inertia is always proportional to mass.

 

[chosenone]

O.K. I guess I have'nt had my question answered yet!what I mean is when relativity predicts something how does it translate into real events for experimentation?how do you create a model of a black hole and use math to predict its internal workings,or superstrings for that matter?I'm just asking for a example of how this is done,because I'm taking algebra right now,going into trig next semister.so if I see a example,I can try to interprete it,because I've never see it.

 

[Integral]

Chosenone, you are attempting to fly before you can walk. The math of GR and SuperString Theory are the most complex mathmatical models in modern Physics. The full depth of the math is understood by very few (relativly speaking) and is simply out of reach of most people. All you can hope to do is read some of the lay oriented articals and learn of the predictions made. Well, not for SST because it has made NO meaningfull predictions.

If you wish to understand how mathematical models are created you must study math. This means start with Algebra, continue through Calculus and finally when you get through Differential Equations you will be at the STARTING point of mathematical modeling. This is, by the way 2 years worth of university level mathematics.

Differential equations is the key here, all we can observe is how things change, and differential equations is the math of how things change. Thus is the basic language of math models.

Albert Einstein's
first paper on Relativitiy is an execelent example of how real world changes are translated into differential equations. It is not that hard of a read and contains only simple math. Remember, this is not a novel and cannot be read casually, you will find it necessary to reread sentences and paragraphs to extract their meaning. Good luck.

 

[arcnets]

Originally posted by chosenone
how do you create a model of a black hole

OK, here's my 3rd attempt.
One of the basic ideas of General Relativity is space(time) getting curved by any mass (or energy) present.
Imagine space as a large, horizontal sheet of rubber, fixed at the edges under some tension. Now you place a metal ball in the center. The sheet will sink in, forming some sort of funnel or crater. This is a model of space being curved by the mass of a star.
Now take a small ball (say, a marble) and place it near the edge of the sheet. It will move towards the star as if it was attracted by the star. You may even be lucky and get it to orbit the star.
This is a model of how space curvature is the cause of what we call gravitation.

I think you agree that the curvature of the sheet can be calculated quite precisely, and so can the motion of the marble. Even in the full 4-dimensional theory, this can be done.
However, it turns out that there are some solutions which correspond to a hole in the sheet, at the bottom of the funnel, where the walls get vertical. This happens for very heavy and dense central objects (say, neutron stars).

It all gets difficult when we try to predict the behavior of matter or radiation close to a black hole. I think there are many theories with different results. IIRC, Hawking suggested a black hole would radiate quite brightly because of some pair production processes going in the neighborhood. I'm really no expert at this. This is as far as I can help you...

 

[chosenone]

O.K.I'm in intermediate algebra,going into trig in the summer.so I'll probable be doing precalculus in the fall,with a physics course when I get there,so can you tell me a good book to read on relativity,that i can find Integral?

 

[Integral]

Did you look at my link to Einsteins first paper on relativity. Have you attempted to read it? There are many books about Relativity out there, go to your local liberary and see what they have. An interesting one is Mr. Tompkins in Wonderland

It should be available in your liberary or local used book store.

 

[Perspectives]

Question about math applied physics

Dear Chosenone,

I have listened to your thread and have some observations that may be helpful. I have three books for you to find. Read and ask for help, make notes when epiphanies occur and they will. Take it slow as you develop your method of discovery. You are considering stuff that most find dry and for a small few very exciting. If occasionally you feel inadequate to the task, remember all of the great ones have felt the same.

1.”The Art of critical Thinking” by Organ Houghton Mifflin Company Boston
Copyright 1965
2. “The Riddle of Gravitation” by Peter G. Bergmann Dover Publications
Copyright 1968, 1987, 1992
3. “Relativity, the special and general theory” by Albert Einstein Crown Publishers
Copyright 1961 Einstein estate

Einstein was Bergmanns teacher and friend. Both texts will illuminate Cosmology from Einstein’s perspectives. Gravity may be the tip of Realities iceberg so book 2 is important. The art of critical thinking is very important as it assists in training the individual to organize and structure ones critical efforts.

Your original request,

Observation leads to investigation, given enough found clues a hypothesis is created. Not all of the clues need to support the hypothesis just enough to provide a reasonable standalone. The remaining clues, which at this point do not support your hypothesis, may later support it.

From this point a method of exploration needs to be developed to verify the adequacy of your hypothesis. Mathematics is an accepted tool as it is an objective method to reveal the strengths and weaknesses of the hypothesis. In many cases not all aspects of a hypothesis may be modeled by mathematics. But if it stands the test of being reasonable the important parts can be.

The best way to see this is to use an established principle to demonstrate. Have you any suggestions that suit you?

Perspectives

 

[chosenone]

thanks!I printed a copy of special and general relativity off the internet,from a site I found.so I'm reading it.thanks for the suggestions.Plus I passed my algebra class,I think,finals on wendsday.

 

[Perspectives]

I have always had questions about math and applied physics

Chosenone,

Congrats on the test. If Mathematics is to become a tool in your chosen fields, then don't become discouraged when there are set backs in the learning process. I have been at it a long time and I discover new things each time I start a process.

Remember, Math has two parts, one, mechanics and two, why. Most schools teach mechanics and few teach why. The why is most interesting and requires the most time to learn. The changing environment of abstract thought as applied to physics is a delightful supprise. There have been rumblings about the speed of light being exceeded, variable and not necessarily a limit on it's speed. Apparently constants are not. It's a lot like being given a wood plane to remove wood and then discovering a saw exists and is more applicable to the task.

Good luck

Perspectives