The problem with Mathematics in Physics

[anorlunda]

There is not really some way you can measure m, and then some independent way you can measure F and then do some observations and say you have empirically proved the formula.

Not true. Students do that as a lab exercise every day. Drag racers and thoroughbred horse racers deal with that day to day.

 

[Office_Shredder]

Anorlunda, how do you measure mass without using the fact that it's inversely proportional to acceleration when some force is applied?

Most normal people (by which I meant scales) measure mass basically by putting a weight on a spring and seeing how much it compresses, but that relies on the force being applied by a spring being equal to kx for some displacement x, and now you're only deeper into the theory because you're still relying on these forces offsetting to measure the mass in the first place, and also why do springs act like that?

 

[Vanadium 50]

You didn't come all that long ago and you are already parting?

He's been here for a while.

As for "The problem with Mathematics in Physics", I don't believe physics as it is in real life is much like he imagines it to be.

 

[gmax137]

how do you measure mass without using the fact that it's inversely proportional to acceleration when some force is applied

 

[anorlunda]

Anorlunda, how do you measure mass without using the fact that it's inversely proportional to acceleration when some force is applied?

I think you're assuming quantitative measurement where only qualitative or relative is needed. An ocean liner has more mass than a kayak, without quantitatively measuring either.

Here's a class f=ma experiment that shows a more massive object accelerates less with the same force as a low mass object. No spring scale measurement of mass is needed.
https://betterlesson.com/lesson/resource/3182211/78639/f-ma-experiment

But bright students will object, saying "But we did measure the mass. It is $\frac{f}{a}$."

Other students might be asked to look to the sky and to ponder the orbits of various bodies, some with much more mass than others. Why does Earth not orbit around the ISS? That leads to educational conversations about the center of mass of a system, and the acceleration versus radius for orbits. But still no spring scale measurements of mass.

This search points to yet another way approachable by students.
https://duckduckgo.com/?q=diy+mass+spectrograph
In a high school lab, we could have a blast of compressed air blowing normal to the paths of ping pong balls versus golf balls. That's a mass spectrograph. After seeing the balls sorted into collection bins, we ask, "What property of the balls determines which bin it lands in?"

 

[Office_Shredder]

gmax, that just tells you that one thing makes the scale tip one way vs another. What does that even have to do with mass in the first place? You need a theory of gravity to explain why things with more mass make it tip one way, and the mass is already being assumed as part of that theory instead. So you haven't really said what mass is outside of "the thing that's inversely proportional to force"

Anorlunda, how do you know the more massive objects in that first experiment even are more massive to begin with?

Orbiting bodies has the same problem that the theory of gravity just totally relies of F=ma to make assertions about the motion of things.

Spectrograph has the same issue. You say the things that are more massive move less. How do you know a golf ball has more mass than a ping pong ball? What IS the definition of mass you are using? It feels heavier in your hand? That's not super compelling as far as a scientific definition goes.

 

[gmax137]

So you haven't really said what mass is outside of "the thing that's inversely proportional to force"

But that is what we mean by "mass" -- it is the thing inversely proportional to force. Maybe I'm missing the point here.

 

[anorlunda]

Anorlunda, how do you know the more massive objects in that first experiment even are more massive to begin with?

Two discs of the same size and material mass more than one disc.

 

[PeterDonis]

that is what we mean by "mass" -- it is the thing inversely proportional to force.

That's one possible meaning of the term "mass", but not the only one.

For example, in relativity, "mass" can mean the invariant norm of an object's 4-momentum. It's not immediately obvious why that "mass" should end up being the same as the "mass" that shows up in the formula for the force necessary to produce a particular proper acceleration for that object.

 

[Office_Shredder]

But that is what we mean by "mass" -- it is the thing inversely proportional to force. Maybe I'm missing the point here.

No, that's exactly the point that was raised above. Someone saying F=ma, the next question isn't well why is that true, why is something that has twice as much mass accelerating half as much. By definition a thing has twice as much mass if it accelerates half as much. F=ma isn't describing how to take things you know and combine them into a new formula that needs explaining, it's creating a new thing (mass) that is only defined in the context of this equation to begin with.

 

[anorlunda]

How do you know a golf ball has more mass than a ping pong ball? What IS the definition of mass you are using? It feels heavier in your hand? That's not super compelling as far as a scientific definition goes.

Aren't you getting into philosophy there? What IS the definition of force? What IS the definition of acceleration? That's a bottomless path.

I think this question is pretty profound and gets to the point of defining mass for the students. When we sorted the balls into bins, we measured something. What IS the property we measured?

In a high school lab, we could have a blast of compressed air blowing normal to the paths of ping pong balls versus golf balls. That's a mass spectrograph. After seeing the balls sorted into collection bins, we ask, "What property of the balls determines which bin it lands in?"

 

[Office_Shredder]

Anorlunda, that's also exactly the point. Asking "why is F=ma true" is a little bit of a pointless question, since mass is defined to be the thing that makes it true. You could ask questions like why is mass constant across velocity and position in space and time (and it turns out it's actually not) but the most basic "why is this true, explain to me why mass has this property" is missing the point.

 

[gmax137]

This thread baffles me. I'm just going to listen, rather than say something foolish.

 

[anorlunda]

I too am exiting this thread.

 

[Dale]

Aren't you getting into philosophy there? What IS the definition of force? What IS the definition of acceleration? That's a bottomless path.

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

By definition a thing has twice as much mass if it accelerates half as much. F=ma isn't describing how to take things you know and combine them into a new formula that needs explaining, it's creating a new thing (mass) that is only defined in the context of this equation to begin with

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.

 

[Astronuc]

According to the Oxford dictionary, 'physics' originates from the late 15th century (denoting natural science in general, especially the Aristotelian system): plural of obsolete physics ‘physical (thing’), suggested by Latin physica, Greek phusika ‘natural things’ from phusis ‘nature’. See attached figure.

Natural philosophy or philosophy of nature (from Latin philosophia naturalis) was the philosophical study of nature and the physical universe that was dominant before the development of modern science. It is considered to be the precursor of natural science.
https://en.wikipedia.org/wiki/Natural_philosophy
https://plato.stanford.edu/entries/natphil-ren/

Mathematics is a necessary tool with which we quantify various elements of physics in a broad range of systems from the Universe we can see to the smallest part of the universe. The mathematics allows us to build models and make predictions, and perform experiments and measurements, from which we confirm a theory or prediction, or perhaps find we need to make adjustments/corrections due to other effects. We find that there are many cases where we make reasonable good predictions considering the complexity of what we are studying, or manipulating.

Besides the pure (theoretical) physics, there is applied physics, and the mathematics allows us to construct tools and systems that enable us to do many things were would not otherwise be able to do.

I'll leave the speculation of 'why' to the philosophers, because ultimately, outside of speculation, there is no definitive 'why', or reason. Sometimes the answer is, "that's simply the way the universe is", and we are not about to change it.

 

[anorlunda]

Newton’s 2nd law again becomes a definition.

But isn't it just a circular relationship between f, m and a? Nothing per se in the relationship that says one is the defining quantity and another is the defined one. That shouldn't cause a problem unless you see it as defining a quantity, and then expecting the quantity to prove the validity of the 2nd law. That would be circular logic .

We have other ways to prove the 2nd law. The Euler Lagrange equation for example. But so what? It doesn't influence our discussion in this thread.

We started this sub-thread talking about students. I still like the mass spectrograph as a way to make the students think. It measures something; not weight because the mass spectrograph works in 0 G. What is the thing that it measures? Students don't need the 2nd law to conceptualize mass. Next lesson would be to replay the practice session scenes from the movie Ender's Game. The students are smart, they'll see right away the significance of mass in 0G.

 

[Dale]

Nothing per se in the relationship that says one is the defining quantity and another is the defined one.

Of course not. You are free to define all three quantities as you like. You can define them each independently and test Newton’s 2nd law, or you can define any two of them independently and use Newton’s 2nd law to define the third. All of those can be done self consistently.

That shouldn't cause a problem unless you see it as defining a quantity, and then expecting the quantity to prove the validity of the 2nd law. That would be circular logic .

If Newton’s 2nd law is a definition then it is true by definition. That is not circular, but it is a tautology.

We started this sub-thread talking about students. I still like the mass spectrograph as a way to make the students think. It measures something; not weight because the mass spectrograph works in 0 G.

I have no objection to the mass spectrograph nor to your position. It is perfectly valid. I just think that it is reasonable to recognize that @Office_Shredder also has a perfectly valid position. They are different, but neither is wrong.

 

[Sophrosyne]

One of my favorites, Leonard Susskind, likes to say that physicists are not interested in truths, they are interested in things that are useful.

Useful to make predictions that can later be verified or refuted by experiment.

Edit: Then engineers use the useful physics to build things useful to ordinary folks.

Yes. Even in philosophy, the only way out of the dead end of postmodern nihilistic despair is the philosophy of pragmatism. As the Neopragmatist philosopher Richard Rorty points out, the concept of “truth” does no useful work. How would we know we have ever finally achieved the ultimate truth? There is no way we can know for sure, because that would mean then then there would be no further observations, no new ideas which could come along and change our minds. Being convinced that whatever we have is ultimate truth leads to close mindedness, and stagnation. The ultimate truth could all be that, as children like to sing, all life is “but a dream”. So we may be better off just not wasting our time arguing about what is truth, and focusing instead on what is the most useful (the most clever models, based on the best current observations we have, jibes with everything else we know, allows us to do and build useful things, make more accurate predictions, etc...), and what kind of world do we want to leave for our children and grandchildren.

https://www.amazon.com/dp/0231140142/?tag=pfamazon01-20

 

[Tanelorn]

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.

 

[weirdoguy]

the real Physics

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

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

No one says it is.

 

[PeterDonis]

I have seen curves for inflation and dark energy expansion of the Universe.

Where? Please give specific references.

I have not seen anyone attempt an explanation for what is driving them.

That may just be because you have not been looking in the right places. Or it may be because you have already seen such an explanation but have not recognized it for what it is.

The only way to figure these things out is to know where you have been looking, i.e., to have specific references.

 

[Sophrosyne]

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.

Yes, this was stated very eloquently here, thank you.

It’s reminiscent of how Newton’s gravitational equations were a useful first step in trying to get a handle on understanding gravitational force and allow us to manipulate and exploit it. It gave us the relationship between the variables involved, but did not really explain the mechanism behind that relationship and why it was happening. Newton himself also seemed to have recognized this limitation. Even today we still don’t know the physics of what is really happening there to make these equations work the way they do- whether it’s gravitons or loop quantum gravity or something else. Or more recently we have all these elegant quantum mechanical equations, but have no idea why they work the way they do. Even Einstein called it “spooky action at a distance”. Maybe hopefully someday we will. I know there is a lot of work going on in that front. But the point is just knowing the equations and the relationships between the variables is not helpful in that regard, or at best only a good first step.

Knowing the mathematical relationships between variables empowers you because it gives you the power to manipulate them accurately. But that is only one aspect of knowing about your subject. It doesn’t give you insight into WHY that relationship is necessarily the way it is- the physics behind it. It’s like a trained seal who knows every time he jumps through the hoop he gets a fish. But he has no idea why- it’s just a relationship he knows holds between two variables, and so he uses it (this analogy is not meant to be derisive towards physicists- figuring out the relationships between variables is an important aspect of knowing something. It’s certainly better than nothing. , But I’m just trying to stress the point that it is by no means everything, even though it may give that illusion).

 

[weirdoguy]

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

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

No, "why" questions are not part of physics, or indeed of any science. At least not if you expect a final answer to any of them.

For example, I could answer the question "why does mass resist force" by saying something like "because the local spacetime geometry tells the object to move along a geodesic, and the object resists any force trying to push the mass off of that geodesic trajectory". And then you would ask the obvious next question: "why does the local spacetime geometry tell the object to move along a geodesic?" (That's assuming you even accepted the answer I just gave, which is the best answer "science", in this case General Relativity, can give.) And physics has no answer to that question, other than "just because".

Even if, someday, we have a theory of quantum gravity, which can answer a question like "why does the local spacetime geometry tell the object to move along a geodesic?" with something like "because the underlying quantum gravity degrees of freedom produce effects that, in the low energy limit, look like a spacetime geometry that tells matter how to move", that still won't be a final answer, because the answer to the obvious next question, "why do the quantum gravity degrees of freedom produce those effects" will again be "just because".

And that will be true of any "why" question in any science: ultimately it will come to a point where the only answer is "just because".

 

[Dale]

the resulting equations tell us nothing at all about the solid state Physics processes taking place inside the semiconductor

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

 

[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?"