Cognitive dissonance in my physics

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Hi, 

Something I've been musing over recently.

E = M x C^2 and the fact that compressed springs have more mass than uncompressed springs .  Hot water will have more mass than cold,   etc etc....

How does this reconcile with conservation of mass ?

Both cannot be true.

PS: further reading gives me this 

"The conservation of mass only holds approximately and is considered part of a series of assumptions coming from classical mechanics. The law has to be modified to comply with the laws of quantum mechanics and special relativity under the principle of mass-energy equivalence, which states that energy and mass form one conserved quantity. For very energetic systems the conservation of mass-only is shown not to hold, as is the case in nuclear reactions and particle-antiparticle annihilation in particle physics."

Answered my own question there.

They aren't conservation of mass is in fact then wrong and only a approximation albeit a very good one for most circumstances .

Still interesting trying to visualise the way this all fits together , when your taught from an early age that conservation of mass is a thing and  you never question it .

TWS

1
 tcashmore 25 Feb 2020
In reply to Chive Talkin\':

I don't think there is a specific conservation of mass principle, I don't remember it from school ?   they don't teach it now at least from my daughter's gcse physics I've observed.   Is it something to do with chemical reactions specific to chemistry ?

Basic conservation laws in an enclosed system include momentum (including angular), energy, charge and certain quantum numbers i believe ?

Cheers

Post edited at 11:58
In reply to tcashmore:

> I don't think there is a specific conservation of mass principle, I don't remember it from school ?   they don't teach it now at least from my daughter's gcse physics I've observed.   Is it something to do with chemical reactions specific to chemistry ?

Yes for convenience it's taught in chemistry still. 

So on one hand we teach chemistry which includes conservation of mass ,  and then A level physics which teaches it's not a thing.

 Jamie Wakeham 25 Feb 2020
In reply to Chive Talkin\':

You have the right idea.  There is an implied conservation of mass in classical (ie pre-quantum and relativity) physics - we do it automatically, because we assume that when we heat up 1kg of matter, we still have 1kg at the end.  And it's built into things like balancing chemical equations.

Really, the thing that has to be conserved is mass-energy.  E=mc^2 shows you how to do that conservation.  For eample, you can have a photon do pair production and give you a positron-electron pair.  By knowing the mass of the position and electron, you can work out the energy required for the photon to be able to do it.

Of course, because the mass equivalent to one Joule is pretty damn small this only matters in circumstances when we look really closely, which is why classical physics holds up to describing everyday situations.

In reply to Jamie Wakeham:

> Of course, because the mass equivalent to one Joule is pretty damn small this only matters in circumstances when we look really closely, which is why classical physics holds up to describing everyday situations.

I started musing over this when wondering over the mass change in a electric battery between charged and uncharged over a 20  mile ride.   Which works out to be incredibly small as your dividing by c squared.

Post edited at 12:11
 Jamie Wakeham 25 Feb 2020
In reply to Chive Talkin\':

Yep, negligable.  To put it another way, a pretty big nuclear power station putting out 3GW at 35% efficiency is converting about 0.0001g of fuel per second.

If you want some real dissonance, compare that with the fact that the sun is losing mass at about 4 million tons per second...

Post edited at 12:33
 wintertree 25 Feb 2020
In reply to Chive Talkin\':

I increasingly think the teaching of physics by “diminishing approximations” or “diminishing deceptions” such as “mass conservation” is really a bad way of doing it, especially when those diminishing approximations derive not from the pedagogically ideal way of teaching physics but from the tortuous historical details of how we got to where we are now.  One could imagine a totally different set of diminishing deceptions where the intuition they develop aligns with where they’re going...

Conservation is a very powerful, as is geometry.  There’s really very little to classical physics apart from those two things, and they lie at the core of relativity.  Yet we explicitly teach them late on rather than as a precursor to physics which I think deflects the development of intuition and creates unaligned diminishing deceptions.

Post edited at 12:54
 wintertree 25 Feb 2020
In reply to Jamie Wakeham:

> If you want some real dissonance, compare that with the fact that the sun is losing mass at about 4 million tons per second...

Although mass-energy equivalence isn’t material to the issue, the mass balance question that unsettled me is that of the mass of the Earth.  There’s no agreement on if the planetary mass balance is negative or positive.  That bothers me.

 Robert Durran 25 Feb 2020
In reply to Chive Talkin\':

> Compressed springs have more mass than uncompressed springs .  Hot water will have more mass than cold,   etc etc....

Presumably something else lost mass/energy while doing the compressing and the thing that heated the water lost mass/energym (?)

In reply to Robert Durran:

> Presumably something else lost mass/energy while doing the compressing and the thing that heated the water lost mass/energym (?)

Yes of course. 

In reply to Jamie Wakeham:

> Yep, negligable.  To put it another way, a pretty big nuclear power station putting out 3GW at 35% efficiency is converting about 0.0001g of fuel per second.

No wonder nuclear weapons are so powerful .

> If you want some real dissonance, compare that with the fact that the sun is losing mass at about 4 million tons per second...

Incredible . 

 wercat 25 Feb 2020
In reply to Chive Talkin\':

if E = MC^2

does that equate to Mass times the square of the hypotenuse of  a lightspeed right angled triangle?

so if you charge a battery how does that affect time?

In reply to wercat:

> if E = MC^2

> does that equate to Mass times the square of the hypotenuse of  a lightspeed right angled triangle?

> so if you charge a battery how does that affect time?

You tell me ;-D

 wercat 25 Feb 2020
In reply to Chive Talkin\':

the title of the thread sounds as if it should be a late 80s song

 Dave Garnett 25 Feb 2020
In reply to wintertree:

> I increasingly think the teaching of physics by “diminishing approximations” or “diminishing deceptions” such as “mass conservation” is really a bad way of doing it, especially when those diminishing approximations derive not from the pedagogically ideal way of teaching physics but from the tortuous historical details of how we got to where we are now.  

In which case E=mc^2 is itself an over-simplification that ignores momentum.

As I discovered recently as a result of this very forum! 

cp123 25 Feb 2020
In reply to wintertree:

Teachers have always taught through 'lies to children' because quite simply young children do not have the ability nor experience to think in complex abstract ways.  Building up a set of rules which may be oversimplified to start with but can be followed allows experience to be built and upon further discoveries can be model be more complicated. Teach the simple stuff first and add complexity in a layered way works everywhere, from Physics, to driving, to teaching novice climbers belaying.

Furthermore, the historical route generally is a good approximation of the pedagogical way - it was only as human beings got better at science did we start to notice the areas where our simpler models broke down. 

For example Newton's laws and gravitational attraction explain all of mechanics up to GCSE, its only at A-level where some of the areas where it breaks down are explored. 

Adding complexity such as: 'There is no such thing as gravity, its just 4D spacetime warping in the presence of energy locked up as mass' when first introducing weight causing acceleration is not going to help matters.

Conservation is very powerful and teachers do teach it, any sort of balancing equation in chemistry or biology uses it.  However, understanding what to conserve, and how to conserve it are quite high level skills.

1
 bigbobbyking 25 Feb 2020
In reply to wintertree:

> I increasingly think the teaching of physics by “diminishing approximations” or “diminishing deceptions” such as “mass conservation” is really a bad way of doing it

I often think one of the strongest lasting impressions my physics education left on me was the ability to decide when a particular approximation is appropriate and when it's not. So I disagree: I think this is a really useful skill that Physics/science teaches. Your theory/model may work in situation X, but there is a limit to the applicability of your model, and you should be aware of where that point is.

Even for those conservations that we believe right now to be fundamental may turn out not to be.

 bigbobbyking 25 Feb 2020
In reply to Chive Talkin\':

You could also add that there's no such thing as 'conservation laws' just symmetries that are obeyed and you can derive all the conservation laws from them. But I'm not sure that's going to help a GCSE student.

In reply to bigbobbyking:

> You could also add that there's no such thing as 'conservation laws' just symmetries that are obeyed and you can derive all the conservation laws from them.

Noether's theorem

> But I'm not sure that's going to help a GCSE student.

Very unlikely probably wouldn't even know what you where talking about.

 wintertree 25 Feb 2020
In reply to Dave Garnett:

> In which case E=mc^2 is itself an over-simplification that ignores momentum.

> As I discovered recently as a result of this very forum! 

Don’t feel too bad, someone at NASA neglected relativistic momentum when proposing a much lampooned magic space drive last year...

 wintertree 25 Feb 2020
In reply to cp123:

I wasn’t rallying against deminishing deception, just suggesting that we don’t often use the best ones.  I also would happily see the process of so teaching better qualified to students earlier on as what it is.

> Furthermore, the historical route generally is a good approximation of the pedagogical way - it was only as human beings got better at science did we start to notice the areas where our simpler models broke down. 

I don’t think they are always.  As a counterpoint if we explained flux, geometry and conservation, Newton’s law more or less emerges naturally from Gauss’ law just as electrostatic forces do.

Its not about the simple models, it’s about the way they are built and presented.  I’m not suggesting raising mass energy at school I’m suggested the way we build our diminishing deceptions could be better aligned with where they’re going.

> Conservation is very powerful and teachers do teach it, any sort of balancing equation in chemistry or biology uses it.  However, understanding what to conserve, and how to conserve it are quite high level skills.

I never said it wasn’t taught; I said it’s taught “explicitly” late on.  It’s used as a tool from almost the beginning.

 wintertree 25 Feb 2020
In reply to bigbobbyking:

> You could also add that there's no such thing as 'conservation laws' just symmetries that are obeyed and you can derive all the conservation laws from them.

That’s a bold statement on the chicken and the egg, but it’s my point - eg starting with conservation and symmetry for a Gauss’s law arrival at the diminishing deception of Newton’s law aligns better with where it’s going than teaching Newton’s law “as is” then banging on about symmetry and conservation like they’re something new later on.

 Keep in mind that the subset of this stuff taught at school is almost totally non vocational so the learning outcomes should be flexible and should in my view be aligned to to that which develops people the best for further study in the field.

Post edited at 15:01
cp123 25 Feb 2020
In reply to wintertree:

> I don’t think they are always.  As a counterpoint if we explained flux, geometry and conservation, Newton’s law more or less emerges naturally from Gauss’ law just as electrostatic forces do.

Newton's law of gravitation is taught in year 13 often in parallel with electrostatics, with the parallels explicitly pointed out (if you have a good physics teacher )  Guass' law is more elegant, but far more abstract and requires vector calculus or surface integrals, mathematical skills 99% of A-level pupils do not have.  So we either try and teach them these maths skills now, and remember they are still learning 1D calculus and vectors, so good luck bringing them together that takes 80% with you, or we hold off teaching gravitation, electrostatics and fields until university which has all sorts of implications.

 

> I never said it wasn’t taught; I said it’s taught “explicitly” late on.  It’s used as a tool from almost the beginning.


Fine, but again, symmetry leading to conservation laws is abstract.  The conservation of momentum coming from Galilean invariance is an abstract idea, and is beyond most year 10s which is where momentum is often taught.  Sure, include it as 'hinterland' so the more able in the room can think about it, but it will wash over 90% of pupils as they don't have the experience nor capacity to think in such abstract ways.

Anyhow, a good teacher will be adding this extra stuff in, so the subject is enriched with more knowledge.  I'm not convinced that teaching it this way hinders intuition, and the example you gave doesn't add weight to your argument.

 wintertree 25 Feb 2020
In reply to cp123:

> Newton's law of gravitation is taught in year 13 often in parallel with electrostatics, with the parallels explicitly pointed out (if you have a good physics teacher )  Guass' law is more elegant, but far more abstract and requires vector calculus or surface integrals, mathematical skills 99% of A-level pupils do not have. 

I disagree - presented right it's no more abstract than flux from a light bulb, and you can use it to build a pathway to Newton's and Coulomb's law without any vector calculus or surface integrals beyond knowing the surface area of a sphere which I presume they know... then both laws are presented not "as is" but "for a reason" that itself is strongly intuitive.  This also allows you do not plant the false misconceptions that come with teaching N + C "as is", e.g. that (1) separate charges (mass or electric) interact/exchange information/momentum/energy directly with each other, and (2) that they do so instantly.  

> So we either try and teach them these maths skills now, and remember they are still learning 1D calculus and vectors, so good luck bringing them together that takes 80% with you, or we hold off teaching gravitation, electrostatics and fields until university which has all sorts of implications.

Like I said I think - actually know and have done - that you can lay a pathway to N+C's laws based on the idea of fields and Gauss' law without the maths.  As well as building a a picture of field theories as underpinning these forces if you continue teaching this way you also do with the silliness that is "deriving" various fields from "test masses" or "test charges" which tends to further misconceptions that fields are just tool for solving problems and that drivers a further artificial wedge between E and B fields.

> > I never said it wasn’t taught; I said it’s taught “explicitly” late on.  It’s used as a tool from almost the beginning.

> Fine, but again, symmetry leading to conservation laws is abstract. 

Yes - but I never said symmetry should be taugt at school as leading to conservation laws (that was comments from other posters, one of which I replied to).  I said that symmetry can be front and centre in getting to Newton's and Coulomb's law for example.  This can done with nothing more then a description of flux emanating from a charge and spreading over the surface of a sphere, and the symmetry boils down to it being evenly spread over the surface as there is no "special" or "preferred" direction to space.  3 identical lightbulbs and 3 paper spheres of different radiuses make this physical and tangible in minutes, as do analogies of uniformly spreading a fixed amount of paint over the different spheres.

> Anyhow, a good teacher will be adding this extra stuff in, so the subject is enriched with more knowledge.  I'm not convinced that teaching it this way hinders intuition, and the example you gave doesn't add weight to your argument.

As you see above I disagree and I think my example does add weight as I've now spelt out in a bit more detail. 

Why do we teach any of this at school level?  It's not vocational - it should be about expanding the mind so I'm all for finding ways to make the more intuitive/physical content accessible rather than excusing it as being beyond the kids - potentially less could be taught but with a more solid understanding that aligns with where it's going.

Post edited at 18:47
 BusyLizzie 25 Feb 2020
In reply to cp123:

> For example Newton's laws and gravitational attraction explain all of mechanics up to GCSE, its only at A-level where some of the areas where it breaks down are explored. 

My daughter, a canny soul, was distinctly pissed off when she realised that after GCSE the teachers say ok, we were lying, here's how it really is.

(I know that's not really how it is, but her indignation  was v funny).

 wintertree 25 Feb 2020
In reply to BusyLizzie:

> My daughter, a canny soul, was distinctly pissed off when she realised that after GCSE the teachers say ok, we were lying, here's how it really is.

And the joke is - they're still lying!   Well the good ones are qualifying that it's the next step down the diminishing deceptions.

cp123 25 Feb 2020
In reply to wintertree:

I think one of the joys of teaching is you get to do things you're way, as long as you get the results and your class performs well in their public exams.  If you reckon you can add insight by touching the surface (no pun intended) of Guass' Law when teaching your lot fields then that's good. Personally I'm not convinced and don't think anything is wrong with keeping it simple but also add richness in other ways, for example scalar potential and path independence or not in the case of friction.

By the way objects do interact at a distance (I'm doing it now with the earth, even though a chair is separating us) and there is no need to say it happens instantly, gravitational waves are a excellent relevant, interesting example that they don't.

Guass' Law still breaks down at large energies, hence Einstein's Field Equations, and if you are getting that far in your physics you have no doubt been exposed to the maths required to do Guass properly and so mathematical intuitions are already established. Non mathematical intuitions are to be steered clear of, think QM or special relativity, or even Newton's first law, all areas where intuitions are to be guarded against.

However the fact we are both spending far too long discussing the point means I would quite like to be in your class, as you clearly care about teaching your lot. After knowing your stuff, which you clearly do, caring is the most important thing.

Cheers

cp123 25 Feb 2020
In reply to BusyLizzie:

If they sold it as lies they are doing a pretty crap job, it should be sold as delving deeper into the physical world and hitting the boundaries of knowledge.

Was it a Chemistry teacher per-chance, as they have the biggest change from GCSE to A-level?

 wintertree 25 Feb 2020
In reply to cp123:

> I think one of the joys of teaching is you get to do things you're way, as long as you get the results and your class performs well in their public exams. 

Totally agree.  But that doesn't mean we should just assume that the standard approach to teaching things, arrived at by historical chance, is the best way.

> By the way objects do interact at a distance (I'm doing it now with the earth, even though a chair is separating us)

What I said is that teaching Newton's and Coulomb's laws as-is implies they interact at a distance *directly*.  This is exactly what I mean by the wrong diminishing deceptions building false mental pictures rather than ones intuitively aligned to where things are going.  My interaction with the moon is not direct but is mediated by each of us exchanging information/energy/momentum/whatever with the gravitational field.  Establishing fields as a key if invisible part of the system radically changes the intuitive view of the interactions as well as allowing the key laws to emerge from rather less "trust me it just is" than otherwise.

> and there is no need to say it happens instantly, gravitational waves are a excellent relevant, interesting example that they don't.

Nothing does.  Information in all the fields propagates at lightspeed (or below).  However, when you look at Coulomb's law you see instant interaction.  Trying to explain the propagation time of the information about the location of one charge to the other without having a concept of fields is a hiding to confusion.

> Guass' Law still breaks down at large energies, hence Einstein's Field Equations, and if you are getting that far in your physics you have no doubt been exposed to the maths required to do Guass properly and so mathematical intuitions are already established.

Sure - I wouldn't claim otherwise.  But using a basic version of Gauss' law to lead students to the inverse square laws lays the basis for field theories.  There are weak analogies to Gauss' law linking mass energy and curvature within relativity too.

> Non mathematical intuitions are to be steered clear of, think QM or special relativity, or even Newton's first law, all areas where intuitions are to be guarded against.

Again - no surprise I'm sure - I disagree!  The wrong intuition is to be steered clear off, but it's possible to lay down an intuitive pathway without the mathematics that nevertheless aligns with the coming mathematics, rather than building barriers in people's heads that hinder them later on.  When I get the time one day I hope to play through some of the various games (e.g. Quantum Minds) being developed to try and build a quantum friendly intuition.  What makes something "intuitive"?  Learning it at the right time in the right way.  The unhelpful intuitions you allude to are partly intuitive through early formative experiences and I would argue through accident of the way we teach.  If things like Quantum Minds can shift this, it's massive.  Our education system is almost set up to delay beyond usefulness that spark that used to allow minds far younger than mind to make key leaps in theory (especially in maths) through intuition.  Although this is more of a concern in mathematics where young age seems to an almost critical factor in discoveries.

> However the fact we are both spending far too long discussing the point means I would quite like to be in your class, as you clearly care about teaching your lot. After knowing your stuff, which you clearly do, caring is the most important thing.

Thanks!  I don't thing too long can be spent discussion this sort of stuff.  

 Dave Garnett 25 Feb 2020
In reply to wintertree:

> Don’t feel too bad, someone at NASA neglected relativistic momentum when proposing a much lampooned magic space drive last year...

Really?  I think even I would have thought 'magic space drive' was a clue.

 Jamie Wakeham 26 Feb 2020
In reply to BusyLizzie:

> My daughter, a canny soul, was distinctly pissed off when she realised that after GCSE the teachers say ok, we were lying, here's how it really is.

Yep, I've dealt with that indignation many times!  I reckon one of my favourite parts of the teaching year is that bit where you describe firing electrons* through the double slit experiment, and that the interference pattern comes out. 

Of course students are angry when they realise that what we've been telling them about electrons is 'not true', but then you have the opportunity to talk about models, and how different models are appropriate to different situations (exactly what bigbobbyking is talking about).  I frequently admit at this point that my job is telling lies to children, but I don't get sacked because I know which children to tell which lies to...

* today I learned that we've observed the double slit pattern with molecules of 810 atoms!  That factoid is definitely going into my description of the phenomenon.

 wintertree 26 Feb 2020
In reply to Jamie Wakeham:

> * today I learned that we've observed the double slit pattern with molecules of 810 atoms!  That factoid is definitely going into my description of the phenomenon.

If you haven't seen it, Yves Couder demonstrated the double slit experiment with oil droplets about 1 mm in size.  A purely classical realisation of a coupled particle/wave system akin to pilot wave theories in QM -  youtube.com/watch?v=W9yWv5dqSKk&


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