Why are Physicists so informal with mathematics?

[haushofer]

Well, there are some physicists who think you should go to the philosophy department if you ask about ontology. In my experience quite some physicists care more about calculation than interpretation and worse, they'll use faulty philosophy to justify that attitude.

 

[Sassan]

I agree completely. The applied/practical side of physics is engineering, and that is where calculations are justified. But that is the end of the journey. The beginning of the journey (which is germane to physics education) is starting with some reality, abstracting concepts from it, operationalizing those concepts, correlating those concepts, and then coming up with formulas that compress and summarize all that.

 

[pines-demon]

Yes, we know that EM waves propagate through the vacuum, but there is so much controversy amongst physicists as to exactly HOW this happens. I have read many accounts of it by folks with physics degrees, but they tend to accuse one another of committing misconceptions, and that only THEY have the correct explanation. This borders on religion: Accepting a statement on FAITH!

Is this a real example? I mean I guess most physicists agree on the "how", specially with EM waves. Maybe you mean on the "why?" or "why is it allowed?"

 

[Sassan]

Please provide me with that version of the "how" (EM waves propagate in the vacuum) that you say most physicists agree on?

 

[pines-demon]

Please provide me with that version of the "how" (EM waves propagate in the vacuum) that you say most physicists agree on?

It's called Maxwell's equations.

 

[Sassan]

Maxwell's equations do not explain the detailed mechanism by which EM waves travel self-propagatingly through vacuum. The equations essentially state that EM waves are the result of the mutual interactions of dynamic electric and magnetic fields, but the detailed "how" of it is another story.

 

[Frabjous]

Yes, we know that EM waves propagate through the vacuum, but there is so much controversy amongst physicists as to exactly HOW this happens. I have read many accounts of it by folks with physics degrees, but they tend to accuse one another of committing misconceptions, and that only THEY have the correct explanation.

Please provide some references. It is hard to tell exactly what you are critiquing.

 

[Orodruin]

Maxwell's equations do not explain the detailed mechanism by which EM waves travel self-propagatingly through vacuum. The equations essentially state that EM waves are the result of the mutual interactions of dynamic electric and magnetic fields, but the detailed "how" of it is another story.

That is not a physics question per se. Your question is about why the Maxwell equations appear like they do. That is not necessarily answerable through experiment and if so is not a part of physics.

 

[pines-demon]

Maxwell's equations do not explain the detailed mechanism by which EM waves travel self-propagatingly through vacuum. The equations essentially state that EM waves are the result of the mutual interactions of dynamic electric and magnetic fields, but the detailed "how" of it is another story.

I relate "how" questions to "how to describe their behaviour". The behaviour of EM waves is explained very precisely by Maxwell's equations. What you seem to ask is "why is this behaviour in particular". However "why" questions are usually thrown away and forwarded to the philosophy department.

 

[gmax137]

do not explain the detailed mechanism by which

Provide an example of physics which does explain the detailed mechanism by which the phenomenon occurs.

 

[Sassan]

Example of detailed mechanism in physics: When you talk and another person hears what you are saying, we understand the exact mechanism by which the spoken words generate waves that vibrate the eardrum(s) of the listener, leading to the effect we call "hearing".

 

[Sassan]

However "why" questions are usually thrown away and forwarded to the philosophy department.

Newton found the correct formula for gravitational force, but could not explain WHY action at a distance could occur and it actually bothered him. Had this WHY been thrown away, Einstein would not have tried to come up with a WHY-explanation in his General Theory of Relativity.
I am not saying all WHY questions are relevant in physics. But when some physics issues become perplexing, coincidental, or contradictory, then the WHY question becomes important.

 

[Sassan]

Provide an example of physics which does explain the detailed mechanism by which the phenomenon occurs.

Please provide some references. It is hard to tell exactly what you are critiquing.

References provided for Frabjous regarding controversies and disagreements in explaining how EM waves travel in vacuum.






https://www.youtube.com/watch?v=hk63uUhkZH4

The larger point here is the existence of controversies in physics theories that are supposed to be established and non-controversial. Two great examples of this are two videos produced by the Veritasium channel:

https://www.youtube.com/watch?v=oI_X2cMHNe0
This is about how electricity actually works. Tons of controversy.

https://www.youtube.com/watch?v=yCsgoLc_fzI
This is about a UCLA physics professor losing a bet about the outcome of a physics experiment.

 

[Frabjous]

Videos

 

[Sassan]

Videos

What is wrong with videos? A video is a medium through which information can be communicated. If I transcribed the contents of the same videos into words, printed them and bound them in the form of a book, suddenly that would have more credibility for you?!

Just because a UCLA physics professor expresses himself on VIDEO, it is unacceptable to you?!

 

[Orodruin]

Example of detailed mechanism in physics: When you talk and another person hears what you are saying, we understand the exact mechanism by which the spoken words generate waves that vibrate the eardrum(s) of the listener, leading to the effect we call "hearing".

That doesn’t explain anything. How do the waves propagate?

 

[Orodruin]

Had this WHY been thrown away, Einstein would not have tried to come up with a WHY-explanation in his General Theory of Relativity.

This is not necessarily true. GR was mainly developed because Newton’s theory was fundamentally incompatible with special relativity, which in turn was developed because Maxwell’s electromagnetism was incompatible with classical mechanics.

 

[Orodruin]

What is wrong with videos? A video is a medium through which information can be communicated. If I transcribed the contents of the same videos into words, printed them and bound them in the form of a book, suddenly that would have more credibility for you?!

Just because a UCLA physics professor expresses himself on VIDEO, it is unacceptable to you?!

It is not the mode of presentation. It is the purpose of the presentation. Most physics videos on YouTube are popular science, which is a really bad way of learning actual physics. Its purpose is different. This is true regardless of of where the presenter works.

If you want to be taken seriously, please refer to the actually published peer reviewed material.

 

[Frabjous]

What is wrong with videos? A video is a medium through which information can be communicated. If I transcribed the contents of the same videos into words, printed them and bound them in the form of a book, suddenly that would have more credibility for you?!

Just because a UCLA physics professor expresses himself on VIDEO, it is unacceptable to you?!

It is not worth the length of viewing time to try and figure out what YOU are thinking. I’m out.

 

[Sassan]

That doesn’t explain anything. How do the waves propagate?

That doesn’t explain ANYthing?! So if I gave that explanation of how we hear sound to people from 1,000 years ago (or to the children of today), you are saying they would not learn ANYthing?!

If you want to argue for the sake of arguing, then we are done. But if you want to be fair and engage in an honest dialog, I am going to continue.

Explanations exist at various LEVELS. You asked for an example of a physics explanation (the HOW), and I provided one at level 1. So now you can pick one word in it (“wave”) and ask for level 2 explanation, thereby going deeper. But at the point that the explanation corresponds to our common sense image of how the world works, we say we are convinced and we stop.

This is level 2 explanation of how a wave propagates in a medium. At level 2 we assume we understand energy transfer (like when a moving ball hits a stationary ball, it makes the second ball move). When I keep dipping my finger into and out of a calm pool, the energy of that movement gets transferred to water drops next to my finger making them likewise bob up and down. This energy thus gets transferred horizontally while manifesting itself at each location by the water at that location bobbing up and down. THAT explains how a (transverse) wave propagates. This is level 2.

Now if you pick one of the words above and ask for its explanation, then we go to level 3, but this process has stop at some point because we will never reach the level of certainty of 3=3.

 

[PeroK]

Example of detailed mechanism in physics: When you talk and another person hears what you are saying, we understand the exact mechanism by which the spoken words generate waves that vibrate the eardrum(s) of the listener, leading to the effect we call "hearing".

That's not really a detailed mechanism. That's a superficial description. How do air molecules vibrate your eardrum? It must ultimately be an electromagnetic interaction. And, how does the electromagnetic interaction work? Then you are back to EM and QM.

Any mechanism in nature/physics must eventually boil down to some fundamental theory, which does not rest upon a more fundamental mechanism. Your criticism that the fundamentals of physics do not have any more fundamental underlying explanations is fairly pointless.

Mathematics has essentially the same issue, where eventually it can be boiled down to the axioms of set theory, which cannot themselves be based on even more fundamental postulates.

 

[AndreasC]

Yes, that is exactly my point about semantic consistency. If from the very beginning a wave is defined without reference to a "medium", then later on when it is learned that a wave can travel through vacuum, no inconsistency arises.

Mathematics is literally full of cases where you may start with a definition that is in terms of something specific, then generalize it to a larger domain. There is no difference between that and what you are saying.

 

[Orodruin]

That doesn’t explain ANYthing?! So if I gave that explanation of how we hear sound to people from 1,000 years ago (or to the children of today), you are saying they would not learn ANYthing?!

I am echoing your sentiment from earlier because it is the exact same argument. Please explain to the people of 1000 years ago how the wave works. Please follow through on your line of argument. You will see where it leads …

Explanations exist at various LEVELS. You asked for an example of a physics explanation (the HOW), and I provided one at level 1. So now you can pick one word in it (“wave”) and ask for level 2 explanation, thereby going deeper. But at the point that the explanation corresponds to our common sense image of how the world works, we say we are convinced and we stop.

”Common sense” is an utterly useless argument in physics. It works decently on scales we have natural intuition on because intuition is built on familiarity. The world at very small and bery large scales simply does not work in the same way. The aim of physics is not to ”make sense” to you. It is to give an accurate description of how the world works.

If you are the only one allowed to require a deeper explanation, you are being utterly disingenuous.

Now if you pick one of the words above and ask for its explanation, then we go to level 3, but this process has stop at some point because we will never reach the level of certainty of 3=3.

Exactly, but this is not what you are arguing above. In fact, you are arguing the exact opposite: that Maxwell’s equations necessarily require further explanation. So please go on. I want to know what the water consists of and why the molecules in the water collide because this is integral to understanding your wave phenomenon.

 

[Orodruin]

It must ultimately be an electromagnetic interaction.

Spoiler alert! Spoiler alert!

 

[AndreasC]

Yes, we know that EM waves propagate through the vacuum, but there is so much controversy amongst physicists as to exactly HOW this happens.

Maybe 150 years ago.

I have read many accounts of it by folks with physics degrees, but they tend to accuse one another of committing misconceptions, and that only THEY have the correct explanation. This borders on religion: Accepting a statement on FAITH!

People on the internet are often wrong. Actually people in general are often wrong. And often people do have misconceptions. I don't understand what that has to do with religion. Some people being confused about something doesn't make it controversial, and even if there is controversy I don't understand what that has to do with religion.

 

[symbolipoint]

What is wrong with videos? A video is a medium through which information can be communicated. If I transcribed the contents of the same videos into words, printed them and bound them in the form of a book, suddenly that would have more credibility for you?!

Just because a UCLA physics professor expresses himself on VIDEO, it is unacceptable to you?!

Depends on the video. Depends on the quality; depends on the precision; depends on the faithfulness to concept.

 

[Sassan]

”Common sense” is an utterly useless argument in physics.

Correct. I should have said, "common logical sense" by which I mean LUCIDITY in explanation vs. shoving an equation down someone's throat.

I am sorry it has not been clear that I am approaching this topic from the viewpoint of not physics but physics education. I have an undergraduate degree in physics, another in math, and have been a professor at the university level for the past 45 years in a different field: Computer Information Systems. I am approaching this topic only pedagogically. Physicists can discover their truths, celebrate, and move on. But how do we teach those truths to truth-seekers?

Case in point: There is a video entitled "Why is the speed of light what it is? Maxwell equations visualized". The interesting thing is NOT the video itself but the comments written below it. This is only a small sample . . . . . .

I teach electrical theory at university and I’ve never seen such a brilliantly clear explanation of the Maxwell equations and their consequences - Many Thanks.

I've learned more about electromagnetism and the meaning behind Maxwell's equations in these 13 minutes than in 5 years of studying electrical engineering.

As a former undergrad in physics and grad in oceanography, I wish all educators were required to be at this level of understanding, enthusiasm and preparedness.

Thanks. I learned more in 13 minutes then in a semester of Fields and Waves when I was in college 25 years ago.
If only I was taught physics like Arvin does, oh my lost life! No matter then, I will savour the delightful insights of physics in my remaining late years.

If only I had these videos explaining these concepts 20 years back, maybe I would've been a physicist today.

These same reactions can be found to MANY other pedagogical physics videos in which LUCIDITY is the key. Or the teacher can walk into the classroom, write the Maxwell’s equations on the board, and say, “That’s it. If you don’t understand, you don’t belong. Get out”!

 

[Orodruin]

That sounds more like a teacher-specific problem than a problem of the subject. I have known professors in both physics and math who suffer from this. It is hardly something subject specific.

It should be noted that while Maxwell’s equations were important in the historical development of relativity, the modern view is rather the opposite. The speed of light is named so for historical reasons and the main insight of relativity is the geometry of spacetime and the existence of an invariant speed. That this is the speed appearing in Maxwell’s equations follows unambiguously from EM theory being one of the simplest relativistic field theories that can be written down. It is not so much that the speed of light results from Maxwell’s equations as Maxwell’s equations having to contain it in order to be a self consistent relativistic field theory.

Unfortunately, videos that present things seemingly lucidly can still be wrong or not in line with a modern theoretical viewpoint.

 

[Sassan]

That sounds more like a teacher-specific problem than a problem of the subject. I have known professors in both physics and math who suffer from this. It is hardly something subject specific.

It should be noted that while Maxwell’s equations were important in the historical development of relativity, the modern view is rather the opposite. The speed of light is named so for historical reasons and the main insight of relativity is the geometry of spacetime and the existence of an invariant speed. That this is the speed appearing in Maxwell’s equations follows unambiguously from EM theory being one of the simplest relativistic field theories that can be written down. It is not so much that the speed of light results from Maxwell’s equations as Maxwell’s equations having to contain it in order to be a self consistent relativistic field theory.

Unfortunately, videos that present things seemingly lucidly can still be wrong or not in line with a modern theoretical viewpoint.

Thank you for your explanation. You sound like there is perfect consensus amongst professional physicists who read only peer-reviewed journals, and also that this elite group feels no need to communicate their knowledge to those at a lower level in a lucid, clear, logical manner. There is almost a feeling of disdain for clarity and lucidity, never mind that Einstein's own book (The Evolution of Physics) is the very picture of lucidity and clarity.
I hope you agree that even among living professional physicist who read only peer-reviewed journals, there is a lot of deep disagreement on a number of topics.

 

[Orodruin]

You sound like there is perfect consensus amongst professional physicists who read only peer-reviewed journals, and also that this elite group feels no need to communicate their knowledge to those at a lower level in a lucid, clear, logical manner.

I believe you are misrepresenting some things here. Outreach is an integral part of doing science.

However, yes, for things such as special relativity and basic electromagnetism there is consensus among physicists on how it works. These theories are over a century old and have been studied in excruciating detail. The issue you are experiencing is more likely arising from the fact that popularising these theories for general consumption presents its own set of issues precisely because they are not as easy to intuit about as perhaps classical mechanics. Speaking in a more popularised setting invariably leads to making analogies and simplifications and many times - nay usually - things are distorted in translation and concessions on accuracy have to be made for the sake of presenting a digestible message.

I hope you agree that even among living professional physicist who read only peer-reviewed journals, there is a lot of deep disagreement on a number of topics.

A number of topics at the very fore front of research, yes. That is the nature of the scientific discourse. However, special relativity and electromagnetism certainly do not belong to these topics.