The problem with Mathematics in Physics

[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

 

[Digcoal]

I don’t think that is a philosophical question. You have to define your quantities to do science.

This is reasonable. I generally think of Newton’s 2nd law as defining force rather than mass, but you could make a self-consistent approach defining mass that way.

However, you can also make it a true scientific statement. Often, the equations you use depend on the units you use. In SI units Newton’s 2nd law is ##\Sigma F= ma## and it is a definition since there is no independent SI unit of force.

But suppose that we have a system of units where force has its own unit, eg defined by a prototype spring. Then Newton’s 2nd law would be ##\Sigma F=kma ##. You could then measure ##k## and show that it was a universal constant independent of the type of force and the amount of mass. Eventually you would find that your uncertainty in ##k## was due primarily to your prototype spring and you might change your unit system so that ##k## was a fixed defined constant and Newton’s 2nd law again becomes a definition.

It is an equation. It defines a RELATIONSHIP between values. It does not define anyone of those values.

If you know the the MASS of an object and you measure how fast it ACCELERATES, you can determine the force applied to it. This is how you can determine the gravitational acceleration at various altitudes or on different planets and moons or around larger celestial objects like stars and black holes.

If you know the ACCELERATION due to gravity and the MASS of an object, you can determine the force that object will apply upon impact. You can determine how high it will go or how long it will remain in the air when a force opposite the force of gravity is applied to it.

If you measure the ACCELERATION an object undergoes, and you know how much FORCE is being applied to it, you can determine its mass.

If you want to be philosophical about it, think of it as the difference between Knowledge and Wisdom. Knowledge is the definition of an idea whereas Wisdom is the understanding of the relationship between two ideas. Knowing and Understanding are two different states of cognition, and it is why college "education" is so broken. Students learn things, but they do not understand how those things relate to other things much less understanding what to use that knowledge for.

 

[etotheipi]

If you know the ACCELERATION due to gravity and the MASS of an object, you can determine the force that object will apply upon impact.

Actually, you cannot. Even in the simplest model you also need the duration ##\delta t## of impact as well as the 6 initial conditions ##(\mathbf{x}(0), \mathbf{v}(0))## to find the average force required on impact to bring the body to rest. But it is really a much more complicated problem than that! The force will be dependent on time as well as position within the region of contact; see e.g. Landau/Lifshitz volume 7 for details on the elastic deformation of deformable bodies.

 

[Digcoal]

I returned because I am not sure many of you were getting my drift. I wasn't specifically asking why mass resists a force. It was only intended as an example of how having the mathematical equations fool us into thinking we understand the real Physics, or as it used to be called the Natural Philosophy of how the Universe actually works.

Another example - I sometimes use curve fitting in my work. However the resulting equations tell us nothing at all about the solid state Physics processes taking place inside the semiconductor. I agree they are useful for modelling and simulations, but that is all.

Moving on to an example in Cosmology, I have seen curves for inflation and dark energy expansion of the Universe. But I have not seen anyone attempt an explanation for what is driving them. However, I may have missed an explanation because I only spend a few hours a year on the subject.
My gut says that everything we need to explain inflation and dark energy is already within our Universe and not some place beyond. Perhaps there is a correlation with the rate of mass being converted into energy, during matter/anti-matter annihilation during the BB, and more recently in stars, BHs and other nuclear processes since then?

Anyway this is all I was trying to say, Mathematics is not necessarily the underlying Physics.

The brain is designed to accumulate information and remove superfluous data to achieve understanding. It does this in every region of the brain, and it is meant to provide a summary of the most pertinent information to the presented problem. However, the presented problem may not be adequately defined leaving the brain to exclude pertinent information in its calculations. This is why defining the problem is the most important step to solving any problem.

This means that "truth" is valid depending on perspective of the problem as well as the information used to solve it. Mathematics is merely a tool to abstractly describe all these things (problem, data, information, solution) which means it creates a universal language for multiple minds to work on the same problems. From one perspective, Mathematics may not be the underlying Physics, but another perspective may reveal that Mathematics is the underlying "Physics" making "Physics" the logical outcome of the Mathematics. This debate is at least as old as Plato's "Divided Line" allegory. It is also as new as the debate about the Simulation Universe.

If you are familiar with "collision detection" in computer game programming, you will see an eerie similarity to the "Physics" underlying electrons. If you are familiar with Procedurally Generated Programming and its associated seeds, you will see an eerie similarity to The Theory of Everything (Procedurally Generated Program) and the initial conditions of the Universe (seed). Perhaps the natural tendency to simulate our hypothesis is really just an innate drive toward building a new existence based upon the underlying "Physics" of our existence. Just like an AI that arises within an advanced Procedurally Generated Program will have no way of interacting outside of its programmed existence, we would have no way of doing the same. The singularity at the beginning of the Universe (seed) is the limit of what we can understand with 100% certainty. Anything before that occurred in a different reality (with, possibly, different Physical Laws/Universal Code) before the Physical Laws/Universal Code of our reality was written.

Even before we get to Physical Laws/Universal Code, our brains are computers designed to create simulations based off of data accumulated through interaction outside of our brains. Our "reality" is the result of psychoLOGICALly constructed representations of the patterns of data we accumulate. Whether it is technoLOGIC or psychoLOGIC, it all comes down to the state of one thing, the state of another thing, the relationship between those two things, and the evolution from one state to another: binary definitions and operations.

 

[Digcoal]

And what is "real physics" and how it differs from non-real physics?

No one says it is.

I said it was possible.

So, that's not 'no one.' lol

 

[Frabjous]

Actually, you cannot. Even in the simplest model you also need the duration ##\delta t## of impact as well as the 6 initial conditions ##(\mathbf{x}(0), \mathbf{v}(0))## to find the average force required on impact to bring the body to rest. But it is really a much more complicated problem than that! The force will be dependent on time as well as position within the region of contact; see e.g. Landau/Lifshitz volume 7 for details on the elastic deformation of deformable bodies.

I disagree. This is reductionism. I could just as easily refute the continuum approximation with the atomistic approximation. Which someone would refute with a nucleus/electron approximation. Which someone would refute with …

 

[Digcoal]

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

Any language is "gibberish" to those who do not understand that language. Even dialects WITHIN a language can be construed as "gibberish."

There is "gibberish" everywhere an attempt to understand an unknown language is made. Ever plug video cables into an audio port or vice versa? Ever heard of synesthesia? Ever try to run a program written for one OS on a different OS? Ever try to convert an executable into an ASCII format and try to read it? Ever try to navigate the web using IP addresses instead of URLs? Ever take a gesture of affection as creepy or have your gesture of affection taken as creepy? Ever try to have a conversation with a female or a toddler? Ever make a joke near people with no humor?

 

[etotheipi]

I disagree. This is reductionism. I could just as easily refute the continuum approximation with the atomistic approximation. Which someone would refute with a nucleus/electron approximation.

What?

 

[Mayhem]

Any sufficiently advanced mathematics is indistinguishable from magic rubbish?

Think about it.

 

[etotheipi]

Not going to lie: I think this thread is a one-way ticket to crazy town and I'd suggest it be closed.

 

[fresh_42]

Not going to lie: I think this thread is a one-way ticket to crazy town and I'd suggest it be closed.

I agree with this. It appears that we have lost focus and the discussion is turning towards philosophy, partly due to the subject itself.

Math is to physics as notes are to music. One can like it or not, but as long as anybody doesn't come up with a really, really, really good idea, that is capable to overturn many centuries of successful practice, as long will this fact remain the case.