Why are Physicists so informal with mathematics?

[Sassan]

Thank you for your reply.

Imagine an equation describing the behavior of an automobile. Then when someone asks, "What is an automobile?", we simply respond "that which obeys the automobile equation". While this answer may be correct, it is neither complete nor enlightening.

Equations are the end-result of physics inquiry. The earlier phases begin with observing, conceptualizing, hypothesizing, quantifying, experimenting, and deducing conclusions from all that, which can be summarized compactly in the form of a formula -- the formula being the "telegraphic" summary of all that came before it.

My original question about semantics in physics was formulated at the conceptual level. This is an important level of inquiry, because if we don't get things right on this level, then the subsequent formulas may look pretty but will be wrong. It was at this level that Einstein re-conceptualized gravity as the curvature of spacetime due to matter, not at the formula level, which came later on.

 

[gmax137]

There is little respect in physics for semantics.

I think you are correct. Physics respects the ability of a model to predict.

 

[Frabjous]

I think of a wave as the process by which knowledge of a disturbance is transmitted to other points in space at a finite propagation speed.

 

[Sassan]

This is a very good definition, but the word "space" is used generically in order not to commit specifically to either "matter" or "vacuum". We know/see how that knowledge of the disturbance travels through matter, but it is not intuitively clear how it travels through vacuum. Perhaps one should give up intuition at this point, just as we are required to give up intuition in understanding phenomena at the quantum level.

 

[Frabjous]

This is a very good definition, but the word "space" is used generically in order not to commit specifically to either "matter" or "vacuum". We know/see how that knowledge of the disturbance travels through matter, but it is not intuitively clear how it travels through vacuum. Perhaps one should give up intuition at this point, just as we are required to give up intuition in understanding phenomena at the quantum level.

Lack of intuition about a mechanism does not invalidate the definition. There are multiple types of waves. There are waves that propagate through a medium and waves that are self-propagating.

 

[Sassan]

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.
In mathematics, we are very careful that one statement follows from the previous statements, or is at least logically consistent with them. This gives rise to a continuity in thinking. Physicists do not seem to be as sensitive to this conceptual continuity. Even definitions become controversial. There are so much discussion on what F=MA "really means".

 

[gmax137]

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.

Well for quite a while most (?) physicists believed that EM "waves" necessarily implied a medium, namely the electromagnetic aether. Progress is made when previous definitions (even those centuries or millenia old) are recognized to be artificially limiting thought.

This is admittedly quite different from mathematics. It seems there you start with definitions set in stone, as it were.

 

[Sassan]

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!
My concern is not so much about the body of knowledge we call physics as it is about teaching it to others. It is sometimes taught as a form of religion: "Trust me when I tell you that ....". The only things trustable in physics are the outcomes of experiments, not the interpretations of those outcomes that are unfortunately subject to so much controversy.
In mathematics definitions are not set in stone; they are conditional: "IF you accept definitions A/B/C (and axioms M/N/P), THEN conclusions XYZ follow from them". But if you don't accept those definitions and axioms, then those conclusions don't follow! The perfect model of this is Euclidean Geometry. It got invalidated when the assumptions were challenged in non-Euclidean Geometry. It is like a chess game with very clear rules, and if you follow those rules the game makes sense.
Not so in physics!

 

[gmax137]

My concern is not so much about the body of knowledge we call physics as it is about teaching it to others. It is sometimes taught as a form of religion: "Trust me when I tell you that ....".

I guess we went to different schools.

 

[Sassan]

I am not alone in this.

The following passage is from:
https://www.quantamagazine.org/what...ition to photons — the,that fill all of space
...............................

Mark Van Raamsdonk remembers the beginning of the first class he took on quantum field theory as a Princeton University graduate student. The professor came in, looked out at the students, and asked, “What is a particle?”

“An irreducible representation of the Poincaré group,” a precocious classmate answered.

Taking the apparently correct definition to be general knowledge, the professor skipped any explanation and launched into an inscrutable series of lectures. “That entire semester I didn’t learn a single thing from the course,” said Van Raamsdonk, who’s now a respected theoretical physicist at the University of British Columbia.

 

[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.