The problem with Mathematics in Physics

[nuuskur]

Newtonian mechanics is a damn good approximation in case of small velocities. In light of this, I see no problem with mathematics nor physics. Different fields, different goals.

Also "the Problem.." sounds like the OP knows the ins and outs of both fields. I conjecture their knowledge in either is minimal

 

[Sophrosyne]

Sigh. This whole thread is about why physics does not answer "why?" questions... E.g. post #4 sums it up quite well:

So it’s not that you don’t think physics answers why questions. It’s just that you think there will always be a “why” after the “why”s now are answered. I can buy that.

But that’s a little different than saying physics in general does not answer why questions. It’s also different than thinking mathematics necessarily answers those questions.

 

[Sophrosyne]

How can a model both give correct predictions and yet tell you nothing at all? I don’t think that makes any sense.

Newton’s gravitational laws tell you the relationships between some variables such as mass and radius. But they do not give any insight as to why they should have that relationship necessarily, or how it works to give that relationship.

 

[weirdoguy]

Then what do you call the Higgs mechanism for an explanation for WHY objects have mass?

Why does Higgs mechanism look the way it looks? Why does it work? Why one Higgs field? For me it explains HOW some particles get their masses, not why.

 

[gmax137]

It's turtles, all the way down...

 

[Dale]

Newton’s gravitational laws tell you the relationships between some variables such as mass and radius.

That’s a lot more than nothing.

But they do not give any insight as to why they should have that relationship necessarily

That is just a wish for a bedtime story, or a modern take on traditional myths. It presumes that there is a reason why they should necessary have that relationship. The world doesn’t have to have such reasons.

 

[PeterDonis]

it’s not that you don’t think physics answers why questions. It’s just that you think there will always be a “why” after the “why”s now are answered.

Sort of. Pay careful attention to the answers that I gave examples of to "why" questions in the post of mine that was quoted. The whole point is that all of them were just "more physics". They were just explaining how the predictions of one model arise from the predictions of some lower-level model. None of them were explaining why the models are what they are--why they have the features they have, why those models and not others make correct predictions, etc. The latter kind of "why" is the "why" that people who ask "why" questions are actually looking for, and physics (or any science) never provides answers to those kinds of "why" questions at all.

 

[Sophrosyne]

That’s a lot more than nothing.

That is just a wish for a bedtime story, or a modern take on traditional myths. It presumes that there is a reason why they should necessary have that relationship. The world doesn’t have to have such reasons.

It doesn’t have to, but sometimes at least it does. We are working on many of those “why”s, and have even managed to answer some of them ovcasionally- from “why” objects have mass and inertia in Newton’s equations we have come up with the Higgs particle. From the “why”s of Newton’s gravitational equations we have general relativity, and are working on quantum loop gravity and string theory for even further answers to the “why”s. From the “why”s of magnets and electricity in Maxwells laws we have special relativity, quantum electrodynamics, and quantum field theory.

So while I agree nature is under no obligation to always answer the “why”s, it seems that with a lot of work and persistence, it is willing to give up at least a few once in a while.

I like PeterDonis’ answer above. It makes sense.

 

[Dale]

Hmm, now your position makes even less sense to me. You start with the claim that mathematical relationships don’t give insight into “WHY”.

Knowing the mathematical relationships ... doesn’t give you insight into WHY that relationship is necessarily the way it is- the physics behind it.

And now you explicitly identify several different mathematical models that do answer “why”.

from “why” objects have mass and inertia in Newton’s equations we have come up with the Higgs particle. From the “why”s of Newton’s gravitational equations we have general relativity,

Do “WHY” and “why” mean two different things to you? If so, can you explain your different meanings in the two posts? If not, then how can a mathematical model not give insight into “WHY” but can give insight into “why”?

Most importantly: if the mathematical models are acceptable to answer “why” then what made them unacceptable to answer “WHY” in the first place? This seems like a big inconsistency. If they can answer “why” then I personally don’t see how they could not answer “WHY”.

 

[Vanadium 50]

I'm starting to ask myself "why?"

 

[Sophrosyne]

Why does Higgs mechanism look the way it looks? Why does it work? Why one Higgs field? For me it explains HOW some particles get their masses, not why.

Higgs was the answer as to why particles have masses. As to why it works, that’s the next why. There are always further whys. That doesn’t mean they cannot be answered.

 

[Sophrosyne]

Hmm, now your position makes even less sense to me. You start with the claim that mathematical relationships don’t give insight into “WHY”.And now you explicitly identify several different mathematical models that do answer “why”. Do “WHY” and “why” mean two different things to you? If so, can you explain your different meanings in the two posts? If not, then how can a mathematical model not give insight into “WHY” but can give insight into “why”?

Most importantly: if the mathematical models are acceptable to answer “why” then what made them unacceptable to answer “WHY” in the first place? This seems like a big inconsistency. If they can answer “why” then I personally don’t see how they could not answer “WHY”.

Yeah I know it must look confusing. That’s because I changed my mind after reading PeterDonis’ post. It happens, you know. :)

Now I think it’s OK to answer the whys of certain mathematical models with further mathematical models. I am starting to think of mathematics as just a sixth sense we can use. Of course like the other senses, it is not infallible. It is not the secret glimpse into the world of ideal forms and ultimate truths Plato had hoped for. But it does a pretty good job for many things.

 

[Dale]

Yeah I know it must look confusing. That’s because I changed my mind after reading PeterDonis’ post. It happens, you know. :)

Now I think it’s OK to answer the whys of certain mathematical models with further mathematical models. I am starting to think of mathematics as just a sixth sense we can use. Of course like the other senses, it is not infallible. It is not the secret glimpse into the world of ideal forms and ultimate truths Plato had hoped for. But it does a pretty good job for many things.

Haha, yes @PeterDonis can be quite persuasive! It has happened to me too.

I agree with you now.

 

[Dale]

Of course like the other senses, it is not infallible. It is not the secret glimpse into the world of ideal forms and ultimate truths Plato had hoped for.

I completely agree here. The main reason that we need experiments is precisely because of this. Experiments and the scientific method is what tells us when we have the math wrong.

 

[fresh_42]

The mystery behind such debates is in my opinion, why never ever anybody asks why
$$
\text{Vol}=l \cdot d \cdot h
$$
or
$$
U=R\cdot I
$$
but nobody seems to be satisfied with
$$
\mathcal{L}_{QED}=\bar{\psi}\left(i \gamma^\mu\partial_\mu -m_e \right)\psi - e\bar{\psi}\gamma^\mu\psi A_\mu-\dfrac{1}{4}F_{\mu\nu}F^{\mu\nu}+\dfrac{1}{2}m_\gamma A_\mu A^\mu
$$

 

[pinball1970]

The mystery behind such debates is in my opinion, why never ever anybody asks why
$$
\text{Vol}=l \cdot d \cdot h
$$
or
$$
U=R\cdot I
$$
but nobody seems to be satisfied with
$$
\mathcal{L}_{QED}=\bar{\psi}\left(i \gamma^\mu\partial_\mu -m_e \right)\psi - e\bar{\psi}\gamma^\mu\psi A_\mu-\dfrac{1}{4}F_{\mu\nu}F^{\mu\nu}+\dfrac{1}{2}m_\gamma A_\mu A^\mu
$$

The last one looks complicated so I googled it. (I thought the middle one was V?)
Is this a matter of the deeper something goes the more questions are raised?
Or a macro system is more intuitive?

 

[fresh_42]

Is this a matter of the deeper something goes the more questions are raised?

Yes. The question here is: Why does our mathematics describe the phenomena? But nobody ever doubted the formulas for volume or voltage. As soon as 'quantum' comes up anywhere, the entire trust seemed to be gone. Now it's me asking: Why is that the case?

 

[anorlunda]

As soon as 'quantum' comes up anywhere, the entire trust seemed to be gone. Now it's me asking: Why is that the case?

I would guess that many people are like Einstein, believing, "God does not play dice," and rejecting any contrary evidence.

 

[Vanadium 50]

but nobody seems to be satisfied with

Well, what you write isn't gauge-invariant for one, not with that last term there.

 

[fresh_42]

Well, what you write isn't gauge-invariant for one, not with that last term there.

I was satisfied understanding the left-hand side. And, yes, the first lecture note I found on Higgs-field ...

 

[pinball1970]

Yes. The question here is: Why does our mathematics describe the phenomena? But nobody ever doubted the formulas for volume or voltage. As soon as 'quantum' comes up anywhere, the entire trust seemed to be gone. Now it's me asking: Why is that the case?

We evolved to understand the large? not particles, fields?

QM measurement?
Not one agreed picture of what is going on? Interpretation?
Gravity an issue?

 

[gmax137]

There are always further whys. That doesn’t mean they cannot be answered.

No. "Why" not. Do… or do not. There is no why.

Maybe he was on to something there...

 

[Office_Shredder]

People don't ask why $V=RI$ because they are told why, it's electrons flowing through a wire that cause it to happen.

The formula for volume is a formula for counting, not physics. Though I would guess most people would not be able to describe it as such I think intuitively that's how they think about it.

 

[pinball1970]

Yes. The question here is: Why does our mathematics describe the phenomena? But nobody ever doubted the formulas for volume or voltage. As soon as 'quantum' comes up anywhere, the entire trust seemed to be gone. Now it's me asking: Why is that the case?

We live in an ordered universe with rules

Particles have a fixed mass have charge and interact in predictable ways (forgetting all the unknown weird QM stuff for now)

Why should we be surprised that an ordered system describes it?

If we lived in a universe where these relationships did not exist and we lived in a jumbled mass of chaotic masses/ fields varying from moment to moment then no system would describe it.

Surely mathematics would not only not describe physics in that universe, it would not describe anything all, or be a thing?

 

[russ_watters]

We live in an ordered universe with rules

Particles have a fixed mass have charge and interact in predictable ways (forgetting all the unknown weird QM stuff for now)

Why should we be surprised that an ordered system describes it?

If we lived in a universe where these relationships did not exist and we lived in a jumbled mass of chaotic masses/ fields varying from moment to moment then no system would describe it.

Surely mathematics would not only not describe physics in that universe, it would not describe anything all, or be a thing?

I'm not sure you were following @fresh_42 's point and he knows all that. He's observing that people don't ask "why" or "what's beyond" for mundane things like the formula for volume, but they do for QM (Relativity too). The answer to his question surely is; because it's weird and hard to understand, therefore hard to accept at face value.

[Edit]
Though this thread's premise seems to me to be a wholesale rejection of what physics is. ...which I find mind boggling.

 

[BWV]

Any sufficiently advanced mathematics is indistinguishable from magic?

 

[Rive]

Any sufficiently advanced mathematics is indistinguishable from magic?

If you take math as the language of physics, then that should be gibberish instead, right?

 

[BWV]

If you take math as the language of physics, then that should be gibberish instead, right?

either way, seems though that the threshold for physics woo seems to be that individual's level of mathematical understanding. Never heard F=MA invoked to support mysticism.

 

[fresh_42]

either way, seems though that the threshold for physics woo seems to be that individual's level of mathematical understanding. Never heard F=MA invoked to support mysticism.

But only because ghosts have no mass!

 

[Digcoal]

The Pythagorean theorem states that the area of the square whose side is the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides. But it doesn't state why. It is just an observation.

View attachment 280257​

If you go further down that wiki article you pulled that picture from, you'll see a better geometric proof.

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