Mathematical equations to ask questions about physics- Who teaches this skill?

[Lou Arnold]

I'm a retired Engineer. I want to learn methods to formulate equations to ask questions of physics phenomenon. What school teaches this and by whom? Can anyone point me there?

 

[symbolipoint]

I'm a retired Engineer. I want to learn methods to formulate equations to ask questions of physics phenomenon. What school teaches this and by whom? Can anyone point me there?

Looking for an emoticon to mark a reaction, I find none that I really want. When someone responds to your question, that and maybe other posts could be interesting.

 

[malawi_glenn]

Can you provide an example? I have no idea what you are after

 

[symbolipoint]

Can you provide an example? I have no idea what you are after

I want to ask the same thing. What does @Lou Arnold really want to know or understand. Retired Engineer means he is experienced and educated, so has used Mathematics to explore and make decisions with the use of Physics and whatever Mathematics which describes concepts and past-used applications. One would believe he has already learned to do much of what he may be trying to ask. @Lou Arnold, maybe the connection between Physics and Engineering has not been very clear for you? But if this, then readers very possibly do not understand how these are disconnected for you.

 

[Lou Arnold]

First, I would like a recommendation for a course that teaches and explains what I want help with, please.

I understand the typical equations that are taught in undergrad and graduate physics. These equations describe the static and dynamic behaviour of physical phenomenon. However, when one wants to ask a question of this phenomenon, how does one use these equations - i.e. the goal is to formulate an equation which when solved, gives a answer. Example: Given the equation of a pendulum, how to find the length that gives a specific frequency of oscillation? i have never seen a course that teaches how to formulate this in an equation. This may be simple for this problem, but is more complex when you want to use General Relativity equations to find the degree light is bent coming from a star around the sun.

And no this information does not exist in Schutz's book.

 

[PeroK]

Given the equation of a pendulum, how to find the length that gives a specific frequency of oscillation? i have never seen a course that teaches how to formulate this in an equation.

I doubt you need a course to learn that. It's one line of algebra, surely?

This may be simple for this problem, but is more complex when you want to use General Relativity equations to find the degree light is bent coming from a star around the sun.

And no this information does not exist in Schutz's book.

It is in Hartle's book:

https://web.physics.ucsb.edu/~hartle/gravity.html

 

[gmax137]

Do you mean, given:
$$ T=2 \pi \sqrt{\frac L g} $$

Here T is the period, the inverse of the frequency. Use Algebra, solve for L

$$L=g \left(\frac {T} {2 \pi} \right)^2$$

I'm sure you know this, makes it hard to understand your question.

 

[berkeman]

I understand the typical equations that are taught in undergrad and graduate physics. These equations describe the static and dynamic behaviour of physical phenomenon. However, when one wants to ask a question of this phenomenon, how does one use these equations - i.e. the goal is to formulate an equation which when solved, gives a answer.

Are you already comfortable with Lagrangian mechanics?

https://en.wikipedia.org/wiki/Lagrangian_mechanics

 

[Lou Arnold]

Are you already comfortable with Lagrangian mechanics?

https://en.wikipedia.org/wiki/Lagrangian_mechanics

Look. The pendulum problem is a simple example. I don't need the solution. I need a plan of attack that works in general. Try the light bending problem that I meantioned. Try Langrangians for that.

Do you mean, given:
$$ T=2 \pi \sqrt{\frac L g} $$

Here T is the period, the inverse of the frequency. Use Algebra, solve for L

$$L=g \left(\frac {T} {2 \pi} \right)^2$$

I'm sure you know this, makes it hard to understand your question.

Did you not think that I already knew that method?? Can you not take the question further?

 

[topsquark]

Look. The pendulum problem is a simple example. I don't need the solution. I need a plan of attack that works in general. Try the light bending problem that I meantioned. Try Langrangians for that.

Just to clarify: You are looking for a general method to solve any problem? I doubt that one exists. If it did theoreticians would be out of a job!

-Dan

 

[fresh_42]

Did you not think that I already knew that method?? Can you not take the question further?

How should anybody of us know? You left us guessing due to your imprecise descriptions. It really sounds as if you wanted to study

I doubt you need a course to learn that. It's one line of algebra, surely?

Try the light bending problem that I meantioned.

Do you read the answers you receive?

It is in Hartle's book:

https://web.physics.ucsb.edu/~hartle/gravity.html

I, too, read your contributions like the question: "How can I learn to rearrange problems such that B instead of A is asked?"

Did you not think that I already knew that method?

Yes, I know it looks different when you read our threads on PF. The fact is, however, that we do not have crystal balls.

If you really study a certain theory, then it won't play a role from which perspective you look at it. But generally, it cannot be ruled out that some problems become unsolvable if seen from the other side. I doubt that there is a book about such a general approach.

 

[MidgetDwarf]

Judging from your unclear post. Are you talking about mathematical modeling with ODE? Optimization?

 

[Lou Arnold]

I don't know what the form of the solution is. Using Schwartzfeld's mathematical solutions are, in a sense closed form mathematical solution that makes the equations work, but they don't ask a question about the phenomenon.
ODE maybe, but optimization may be part of the solution, but its the making of the question that I am after.

How should anybody of us know? You left us guessing due to your imprecise descriptions. It really sounds as if you wanted to study
Do you read the answers you receive?
I, too, read your contributions like the question: "How can I learn to rearrange problems such that B instead of A is asked?"Yes, I know it looks different when you read our threads on PF. The fact is, however, that we do not have crystal balls.

If you really study a certain theory, then it won't play a role from which perspective you look at it. But generally, it cannot be ruled out that some problems become unsolvable if seen from the other side. I doubt that there is a book about such a general approach.

 

[CrysPhys]

OP: What is your background in engineering? Didn't you face a similar situation in engineering? That is, you learned various equations applicable to particular model systems. Then when you were faced with a particular problem to solve, you had to decide which particular model systems were applicable and which particular equations were applicable.

 

[fresh_42]

I once thought it would be great to have a lexicon with differential equation systems (and solutions, approaches to solutions, and graphics whenever possible) according to problem statements. However, if you think a bit about it, then it's probably rather an encyclopedia with many volumes.

 

[Lou Arnold]

Just to clarify: You are looking for a general method to solve any problem? I doubt that one exists. If it did theoreticians would be out of a job!

-Dan

Well, a "method" is perhaps a misnomer. I would call it an "approach". I'm surprised that no one seems to have asked this same question - how to ask a mathematical question -somtimes when the equations seem not to have a formulation that doesn't even mention the information wanted. It seems such an essential method of testing physics. But how do "I" get better at this if I don't ask how to ask?

OP: What is your background in engineering? Didn't you face a similar situation in engineering? That is, you learned various equations applicable to particular model systems. Then when you were faced with a particular problem to solve, you had to decide which particular model systems were applicable and which particular equations were applicable.

Question well to the point. I have a software engineering background. Its my problem to program those mathematical questions, but all through my physics courses no one even thought about asking mathematical questions. From all the material I see taught, it teaches the HISTORY of physics and not the physics itself simply because you can't experiment with the defining equations. The Schrödinger wave equation is a perfect example. It was simply presented and that's all.

OP: What is your background in engineering? Didn't you face a similar situation in engineering? That is, you learned various equations applicable to particular model systems. Then when you were faced with a particular problem to solve, you had to decide which particular model systems were applicable and which particular equations were applicable.

Yes, but the equations didn't necessarily contain variables that gave the information. It was not simply a matter of solving for variables.

How should anybody of us know? You left us guessing due to your imprecise descriptions. It really sounds as if you wanted to study
Do you read the answers you receive?
I, too, read your contributions like the question: "How can I learn to rearrange problems such that B instead of A is asked?"Yes, I know it looks different when you read our threads on PF. The fact is, however, that we do not have crystal balls.

If you really study a certain theory, then it won't play a role from which perspective you look at it. But generally, it cannot be ruled out that some problems become unsolvable if seen from the other side. I doubt that there is a book about such a general approach.

But there may be a course. Someone must have considered this matter before me. How do experimental physicists test problems if they can't ask questions using the defining equations? After all. the GR equations can't directly be solved for the angle that light is bent through. Nor can Schwartzchild's solutions be used to ask that question.

I read the answers, but I can't get Hartle at this time and so I can't determine of the book shows how to ask questions

 

[PeroK]

I read the answers, but I can't get Hartle at this time and so I can't determine of the book shows how to ask questions

Is the question how do physicists devise experiments to test a theory? Sometimes it must be obvious - like the pendulum, where you simply time pendulums of different masses and lengths. Sometimes it's not so obvious - the Schrödinger equation and its solutions for energy levels are tested indirectly by measuring the emission and absorption spectrum of hydrogen. Sometimes it takes an insight amounting to genius - such as Bell's theorem to test quantum entanglement against local hidden variable theories.

The deflection of light is a somewhat complicated calculation, although the concept is clear enough. And a lot of modern physics is tested through calculating the cross sections of particle interactions, which involves yet more complicated calculations.

The books I've studied from tend to have a mixture of theory and calculations explicitly for experimental purposes. It's all part and parcel of learning physics.

 

[Lou Arnold]

Is the question how do physicists devise experiments to test a theory? Sometimes it must be obvious - like the pendulum, where you simply time pendulums of different masses and lengths. Sometimes it's not so obvious - the Schrödinger equation and its solutions for energy levels are tested indirectly by measuring the emission and absorption spectrum of hydrogen. Sometimes it takes an insight amounting to genius - such as Bell's theorem to test quantum entanglement against local hidden variable theories.

The deflection of light is a somewhat complicated calculation, although the concept is clear enough. And a lot of modern physics is tested through calculating the cross sections of particle interactions, which involves yet more complicated calculations.

The books I've studied from tend to have a mixture of theory and calculations explicitly for experimental purposes. It's all part and parcel of learning physics.

1. My question is: how do physicists calculate expected results for a future experiments.
2. What are those books?

 

[fresh_42]

1. My question is: how do physicists calculate expected results for a future experiments.
2. What are those books?

It is not as if there was nothing out there:

https://www.enago.com/academy/how-to-develop-a-good-research-hypothesis/
https://www.scribbr.com/methodology/hypothesis/
https://www.wikihow.com/Develop-a-Theory

You can, of course, always argue that such contributions are barely on a textbook level. Read my null hypothesis:

It is impossible to write a high stake textbook on how to create a working hypothesis under the condition that it fits all applications, without knowing them.

 

[fresh_42]

Could it be that you have to some extent a theory and you are now looking for a prediction to test it?

Am I right that you are a string theorist?

 

[berkeman]

After all. the GR equations can't directly be solved for the angle that light is bent through.

Is that true?

But there may be a course. Someone must have considered this matter before me. How do experimental physicists test problems if they can't ask questions using the defining equations?

Are you basically asking for resources/classes/books about how to invent new things? I can offer some insights on that question, if that is what you are asking in general...

 

[Lou Arnold]

Could it be that you have to some extent a theory and you are now looking for a prediction to test it?

Am I right that you are a string theorist?

No. Neither.

 

[Lou Arnold]

Is that true?Are you basically asking for resources/classes/books about how to invent new things? I can offer some insights on that question, if that is what you are asking in general...

Nothing to do with invention. The best example of problem that might interest me is the calculation of the degree of bending of a light bean from a star as the beam passes the sun. All one has for that are the Einstein equations. Einstein and Eddington calculated some 3 to 6 possible answers but don't say what approximations they used and why.

 

[Mark44]

I want to learn methods to formulate equations to ask questions of physics phenomenon.

As already noted by several people responding in this thread, the above is very confusing. Physicists don't formulate equations in order to ask questions; they formulate equations in order to explain, or model, physics phenomena (plural of phenomenon).

The hard part is coming up with an equation that reasonably approximates the phenomenon you're interested in. Once you have an equation, it's relatively easy much of the time, to solve for the variable of interest. The example earlier in this thread about the length of the pendulum and the period of its motion is a simple example.

In your later example of the bending of a beam of light, you mentioned that Einstein and Eddington calculated 3 to 6 possible answers. This in itself is somewhat disturbing to me, that so little of their work is known that an exact number of answers isn't known. In any case, I would think that there must be some record of the models (i.e., equations) they used to arrive at these results.

 

[Vanadium 50]

I just reread the Eddington paper (which has a co-author F. Dyson - and not the one you are likely thinking of) and it was a delight. What I did not see any reference to multiple GR predictions.

 

[Kenwstr]

I'm a retired Engineer. I want to learn methods to formulate equations to ask questions of physics phenomenon. What school teaches this and by whom? Can anyone point me there?

While I don't know what schools, I did some regression analysis in my training. Back when I was working as an analyst programmer in GIS, I had to do a run time optimisation of a data analysis between map layers. This was taking a prohibitively long run time on large data sets. So, I gathered run time data in Excel & used the regression analysis tools there. There are several basic regression curve types available, linear, exponential etc, based on curve power. If you run the same data set through the available options, the one with the highest correlation coefficient is the mathematical expression that best describes your data.

Maybe that isn't necessarily a purely correct description, but in practicality, it revealed the cause of my runtime problem to be geographic data clustering. I was able to break up processing according to data density to achieve in excess of a 100 fold efficiency improvement.

So regression analysis is a practical way to find an expression that describes empirical data. You can then use that expression to make predictions within that data sample range. Note that making predictions outside of the defining sample range is likely to be wildly inaccurate & is therefore highly unprofessional.

Is this the kind of thing your looking for, to find unknown mathematical relationships from which you can make future in engineering predictions?

 

[gmax137]

I just reread the Eddington paper (which has a co-author F. Dyson - and not the one you are likely thinking of) and it was a delight. What I did not see any reference to multiple GR predictions.

Is this the one you refer to? Thanks!

 

[symbolipoint]

1. My question is: how do physicists calculate expected results for a future experiments.
2. What are those books?

One would be curious of what your education was. A person who earned a degree, especially an advanced degree, in a Natural Science or a Physical Science would have had those questions satisfactorily answered a long time ago. As for graduates of Engineering or Computer Science, I (myself) would not guess about it.

 

[Vanadium 50]

That's the paper, yes.