The Tree of Physics: Exploring Mechanics and Beyond

[Omega0]

The "Tree of Physics"

Hi,

I know this is pretty complicated in the end but I would be interested in something like "the Tree of Physics", more exactly speaking it would be a graph (and please don't take it literally how I describe the complexity).

Say for example I have one particle without interaction I simply have nothing. If I have n particles without interaction (not moving relative to each other) I have a reason to define a coordinate system. If they are moving I need to think about what coordinate system we have (SRT) and I have to think about boundary conditions. If for example relative speed is << c you don't need SRT. But you have BC so now it is important that the particles are allowed to have mass. If they have mass it is interesting which speed they have (momentum).
If there is a BC you need to define the interaction of a particle with the bounds. You need to take in account if particles are allowed to collide (if so what it means for the momentum, the "energy" is interesting) - but it's more: QM teaches that one single particle is enough to behave different "if the scale is small enough".
If the number of particles is bigger then say 1M it makes no sense to track them all. Now we think about statistics and as we already have added the feature "energy" we try to describe the system statistically (pressure etc.)
Now let's make it more complicated, let's allow interaction by forces. Let's focus on the "well known" interactions, electricity and gravitation.
For more than 3 particles we have an analytic problem but nature has much more. So we use numerics - but a planet is not a particle. Say Phobos as the satellite of Mars. In a planet or moon or simply a bar we have lots of particles and summing it up we get tensor effects.
So here we see that "simple" mechanics is not simple at all.
I didn't write about the complex mechanics of a rotating bar falling into the Earth atmosphere, thermodynamics, electrodynamics, the coupled equations and so on.

Hopefully you didn't fell asleep while reading, my question is: Does there exist a graph ("tree") to explain when which methods need to be applied or in other words: When which model is sufficient?


Jens

 

[Simon Bridge]

Short answer: no.
The basic approach is to use the model that makes the math easiest without losing the ability to match up with experiment. Sometimes you need a statistical approach even with very few particles for eg.

There are no simple mechanics, just simple situations.
The catchphase is "real life is messy".

 

[Omega0]

Short answer: no.
The basic approach is to use the model that makes the math easiest without losing the ability to match up with experiment. Sometimes you need a statistical approach even with very few particles for eg.

There are no simple mechanics, just simple situations.
The catchphase is "real life is messy".

Thanks for your answer but I am not convinced that this is true. If you are right it makes no sense to search for a unified field theory.
In my eyes the major point is that many students (at least) mix the definition of physics. Physics allways mean to describe the nature, the theory has to fit to the experiment. Physics does not explain the nature at all.
I totally agree with "there a no simple mechanics, just simple situations" if you mean that this is what you tell a student to not confuse the student.

What about an engineer or scientist?

As an example, how long does it take that a rotating bar falls down?
This question is senseless until you describe the exact conditions but if you describe the conditions it does not mean that the question makes sense.
In classical mechanics, say you have the Earth and a small bar and vacuum... suddenly you have to ask yourself "when is the moment of touching the Earth is reached", now it depends from the definition of contact. If we didn't speak about normal gravitational fields the question gets more senseless: If it would be a black hole it is way more complicated, beginning with the definition of time and so on.

"Real life is messy", that's it - but if the question is correct and the conditions are well defined you will find an answer (if the theory is complete).



Statement: The number of conditions is countable.

Statement:With respect to a full set of conditions you will get a unique answer to a well defined question.

Statement: The number of questions is countable beeing parametrized under the number of conditions.

This means that there is an algorithm to break down from basic laws to the solution of a problem.
So there is a graph.

This is a monster but it exists. There is no "this or that" decision, the result of the measurement just verifies the correct questions and conditions.

If I am wrong there should be a counterexample.


Jens

 

[Bobbywhy]

Omega0,
Will you please explain what do these abbreviations stand for?

1. (SRT)
2. BC
3. "If the number of particles is bigger then say 1M"

Thank you.

Is the purpose of your post here to advance a "personal theory"?

 

[Simon Bridge]

Thanks for your answer but I am not convinced that this is true. If you are right it makes no sense to search for a unified field theory.

No, it is perfect sense - the unified field theory will be a very simple set of relations that will not be useful at large scales.

In my eyes the major point is that many students (at least) mix the definition of physics.

It's called "confusing the models" ... I agree it is a common mistake.

Physics allways mean to describe the nature, the theory has to fit to the experiment. Physics does not explain the nature at all.

Except in the narrow sense that a description of how Narure comes to have the properties we see is an explanation. It's a "how" explanation rather than a why one - which would be metaphysical yes. That's why I like to say that science does not do "why" questions.

I totally agree with "there a no simple mechanics, just simple situations" if you mean that this is what you tell a student to not confuse the student.

What about an engineer or scientist?

Same thing.

As an example, how long does it take that a rotating bar falls down?
This question is senseless until you describe the exact conditions but if you describe the conditions it does not mean that the question makes sense.

In classical mechanics, say you have the Earth and a small bar and vacuum... suddenly you have to ask yourself "when is the moment of touching the Earth is reached", now it depends from the definition of contact. If we didn't speak about normal gravitational fields the question gets more senseless: If it would be a black hole it is way more complicated, beginning with the definition of time and so on.

The parameters you choose depend on what you care about.

"Real life is messy", that's it - but if the question is correct and the conditions are well defined you will find an answer (if the theory is complete).

But we don't have a "complete" theory of nature - and not all questions are "well defined" (i.e. in the sense of "well posed") ... instead we have to make do with a bunch of approximate models and incomplete data.
Fortunately, we don't usually need complete or exact answers.

With the Bar we may just need to know when it is safe to enter the room (bar has stopped moving and sits on the floor) or we may want to know when the spinning bar is going to chop branches off a tree (because it has blades and trimming trees is out job). The model we choose depends on the answers we want ... which is why you'll also see a response here where someone asks for the context.

Context is everything.

You can construct approximate decision trees for when one model or another applies ... i.e. if the forces are balanced then use statics else: if the acceleration is constant then use kinematics, else use general dynamics. Something like that. They can be as complicated as you like ... but you will tend to miss something out. Before the tree is "complete" you'll have made it more complicated than the problems you are trying to solve - it's self-defeating. That is why the answer to your question is "no" ... there is no general overall decision tree to tell you when to use one model or another.

It's more useful to get students into the habit of thinking about each problem they are faced with instead of finding some algorithmic/tree-lined approach that they can apply blindly.

 

[Omega0]

Omega0,
Will you please explain what do these abbreviations stand for?

1. (SRT)
2. BC
3. "If the number of particles is bigger then say 1M"

Thank you.

Is the purpose of your post here to advance a "personal theory"?

1. SRT = sorry, better known as STR "The Special Theory of Relativity"
2. BC = Boundary conditions, given if you have to do with physical problems
3. M just stands for 1000000

 

[Omega0]

No, it is perfect sense - the unified field theory will be a very simple set of relations that will not be useful at large scales.

I agree in the meaning of "useful". Unification means that you will have a full set of equations which is always valid. The same for QM: It holds if you break down to classical mechanics, called the Correspondence principle.
You wrote "a simple set of relations", I agree. The set of describing equations, see GTR, looks friendly, too - but if you work with them they are the hell on earth.
I (not a teacher) say something like "you can write always something like A = B but the hard work begins if you want to solve it"

It's called "confusing the models" ... I agree it is a common mistake.

That's it.

That's why I like to say that science does not do "why" questions.

Very good. Hats off!

But we don't have a "complete" theory of nature - and not all questions are "well defined" (i.e. in the sense of "well posed") ... instead we have to make do with a bunch of approximate models and incomplete data.
Fortunately, we don't usually need complete or exact answers.

Every approximation is just an approximation. What I am speaking about is that if there is a complete theory than there is an algorithm to break down to more simple statements. If there is no complete theory you will have a serious problem to describe nature in the extreme cases.
Nevertheless you will have a "charged graph".

If you are a teacher you will do that daily, breaking down. From the teachers point of view it seems to be correct, why should I tell the student the full set of conditions (which are not given without a complete theory, if this exists at all).
The more I want to say that without a complete theory you have also decision trees in your daily science or engineering or teaching.

Context is everything.

This is what I said.

You can construct approximate decision trees for when one model or another applies ... i.e. if the forces are balanced then use statics else: if the acceleration is constant then use kinematics, else use general dynamics. Something like that. They can be as complicated as you like ... but you will tend to miss something out. Before the tree is "complete" you'll have made it more complicated than the problems you are trying to solve - it's self-defeating.

I completely disagree. In engineering you have constantly the situation: "The precision should be worth its price". Is a problem static? Is it dynamic? Does it depend from which conditions?
Is it linear? Nonlinear (your answer to another topic was great ;) )?

You already have this decision "tree" (I don't like tree, it is incorrect because you have interaction between the branches).

That is why the answer to your question is "no" ... there is no general overall decision tree to tell you when to use one model or another.

See above, it is a graph with charged branches. I disagree. The correct decision exists.

It's more useful to get students into the habit of thinking about each problem they are faced with instead of finding some algorithmic/tree-lined approach that they can apply blindly.

This is the problem or the approach. I would say that there is a need to be able to understand the basic physics to solve a problem - but if you have this understanding?
In the engineering field there is a hope to describe a problem and the solution say "clickable". Automized optimization is nowadays standard for an example - but the way you search for nonlinear optima is still in the hand of the engineer and you will get several answers.

My question is beyond "if we have a complete theory", it is a practical one which is in the end very theoretic. If my statements above hold then their will be a machine which can "exactly" do this decisions (in a statistical way). My question is not "do you have a gut feeling that I am right" but am I right. I say that I am right, the graph exists - without any application for a student, this is not the point.

 

[Simon Bridge]

My question is beyond "if we have a complete theory", it is a practical one which is in the end very theoretic. If my statements above hold then their will be a machine which can "exactly" do this decisions (in a statistical way). My question is not "do you have a gut feeling that I am right" but am I right. I say that I am right, the graph exists - without any application for a student, this is not the point.

It's a compelling idea isn't? Look up "Godel's Incompleteness Theorem".

 

[Omega0]

It's a compelling idea isn't? Look up "Godel's Incompleteness Theorem".

Good point, but is physics based on axioms?
Are we speaking about a "proof" at all? Is there a physical theory which has to be proven?
In the end we are speaking about measurement.
A theory holds if the measurement confirms it in a statistcal way.
Physics is sort of starting in the branches.
The branches do exist and you can find next branches. Sure, this is exponentional. Thats no fun - but we still speak about descriptions. Simply set a counting point 0 for say a paper of Newton or Einstein or so, simply count the "proven" papers.
The number is countable. You try to climb up the tree, or you try to climb down. There is no mystic thing about that, it is physics.
It is not axiomatic.

 

[ZapperZ]

Closed, pending moderation.

Zz.