Why is Maxwell’s Theory so hard

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Why is Maxwell’s Theory so hard

#1  Postby newolder » Jan 05, 2019 5:06 pm

An essay (5 pages-ish) by Prof. Freeman Dyson on the reticence of Maxwell and the similarity to the later development of quantum mechanics.

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Re: Why is Maxwell’s Theory so hard

#2  Postby laklak » Jan 05, 2019 5:27 pm

Well, it's not easy to find a silver hammer.
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Re: Why is Maxwell’s Theory so hard

#3  Postby newolder » Jan 05, 2019 5:37 pm

The song that broke the Beatles is unlikely to Help! here, I fear.
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Re: Why is Maxwell’s Theory so hard

#4  Postby romansh » Jan 05, 2019 6:09 pm

I thought that was a neat essay.

A few years back I noticed that (in our meso world) pressure had the same units as energy density. (I understand Dyson is not referring to our meso world here). Strange thing is I don't recall ever having being taught that pressure can be seen as energy density, though it seems intuitively obvious.
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Re: Why is Maxwell’s Theory so hard

#5  Postby Evolving » Jan 05, 2019 7:59 pm

romansh wrote:A few years back I noticed that (in our meso world) pressure had the same units as energy density.


I think it's customary to define a pascal as a newton per square metre: 1 Pa = 1 N/m2. Pressure is the force exerted on a two-dimensional area: say the force exerted by the air in a balloon on the rubber skin, or the force exerted by the plasma in a star on a shell (centred on the centre of the star) contained within the star's volume.

Certainly you can multiply numerator and denominator by m and get 1 Pa = 1 Nm/m3 = 1J/m3. I was going to go on to say that I was not sure how helpful it is, and ask rhetorically what in the real world corresponds to this volume represented by m3. But on reflection it is interesting to consider that when a gas exerts a force of 1 newton on a square metre of balloon skin or shell contained in a star, this corresponds to 1 joule of energy per cubic metre of the gas.

That is, obviously, not to say that there really is a joule of energy in each cubic metre of the gas: that energy density is only given in the layer of gas that is actually exerting the pascal of pressure on the two-dimensional area, and it may fall off or increase the further away from that area you measure. The energy density seems more likely to be constant throughout the gas in the case of a balloon than a star.

Interesting.
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Re: Why is Maxwell’s Theory so hard

#6  Postby Evolving » Jan 05, 2019 8:04 pm

newolder wrote:An essay (5 pages-ish) by Prof. Freeman Dyson on the reticence of Maxwell and the similarity to the later development of quantum mechanics.

Starts with Modesty is not always a virtue


That link won't open for me. Is it because I'm not user tong?

EDIT: I've searched the DAMTP website and on this page

https://search.cam.ac.uk/web?tag=alldamtp&query=Dyson%20Maxwell&inst=DAMTP&x=14&y=13

the Dyson Maxwell article is listed. Can't open it there either, though. Maybe it's me.
Last edited by Evolving on Jan 05, 2019 8:09 pm, edited 1 time in total.
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Re: Why is Maxwell’s Theory so hard

#7  Postby Macdoc » Jan 05, 2019 8:08 pm

Correct me if I'm wrong ...brownian motion keeps the pressure constant in a balloon but a star is constantly producing energy via fusion so there will be wildly changing pressure gradients against gravity - these would be conveyed by plasma flows of varying temperatures??
Some with enough energy to produce a CME to fry our electronics?
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Re: Why is Maxwell’s Theory so hard

#8  Postby Evolving » Jan 05, 2019 8:11 pm

Yes: the pressure within a balloon will normally only be changing while you're blowing the air into it, and once you've stopped doing that and tied the balloon up, one would expect the pressure to be pretty much constant throughout the balloon. In a star, as you say, the pressure is constantly being fuelled by fusion which takes place at differing rates at various depths of the star.
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Re: Why is Maxwell’s Theory so hard

#9  Postby Macdoc » Jan 05, 2019 8:41 pm

Thanks I can usually visualize processes without having the underlying math.
Had a good discussion on another forum about the important of visuals in explaining concepts - he was absolutely fixed on "you must have the math" and the visuals were immaterial and several of us disagreed.

After all it was thought experiments that led Einstein and THEN he did the math to prove it. I figure you need the math to use a concept but necessarily to understand one.
ie images or even animated illustrations of processes in a nuclear plant are very useful and understandable but the math exceedingly complex.

So I can visualize what's going on in balloon or star without being to quantitize it....if that makes sense.
I find some of the animated explanations of physical principles fascinating and in particular complex systems like AGW/Atomosphere processes benefit understanding more than

Net Radiation = Q* = total in - total out
Image

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Re: Why is Maxwell’s Theory so hard

#10  Postby romansh » Jan 05, 2019 8:45 pm

I think we are talking about two different things here.

The energy density of a star in part could be analogous to how pressure (energy density) changes with depth in water, ~100 kPa with each 10 m.

I could be wrong, but I would surprised if the energy density changes significantly on a moment by moment basis in a star (our Sun), though at some point in a hopefully distant future all bets are off. I have read it takes hunderds of years for a photon to escape the core of our sun ... at least on average.


Having said I think Dyson is referring to quantum phenomena ... and this is definitely beyond my pay grade.
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Re: Why is Maxwell’s Theory so hard

#11  Postby newolder » Jan 05, 2019 9:05 pm

romansh wrote:I thought that was a neat essay.

A few years back I noticed that (in our meso world) pressure had the same units as energy density. (I understand Dyson is not referring to our meso world here). Strange thing is I don't recall ever having being taught that pressure can be seen as energy density, though it seems intuitively obvious.

The essay is excellent. One of the highlights for me is how the mode of discussion was seen to change at least twice in the development of Maxwell’s EM theory and later quantum mechanics.

The ideas of measurable quantities like pressure and mechanical motions were replaced with ideas about field intensities that were manifestly mathematical abstractions - the unit of electrical field intensity is the square root of a joule per cubic metre and only the square of such an abstraction yields a measurable energy density.

Similarly, the two ‘layers’ of quantum mechanics are the abstract wavefunction, equivalent matrix elements or state vectors that are either squared or are the product of two abstractions to give the probabilities of measurement outcomes.

Maxwell’s EM is seen best as a theory of fields rather than mechanical levers and pulleys and the language of quantum mechanics is that of geometry rather than words alone. Is what I took away from the read. :smile:
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Re: Why is Maxwell’s Theory so hard

#12  Postby Macdoc » Jan 06, 2019 1:54 am

I could be wrong, but I would surprised if the energy density changes significantly on a moment by moment basis in a star (our Sun), though at some point in a hopefully distant future all bets are off. I have read it takes hunderds of years for a photon to escape the core of our sun ... at least on average.


But plasma can be compressed and water cannot ( mostly apparently ). So you can have a plume of very hot very dense plasma rise through the sun and emerge as a CME ....

but I could be wrong and CMEs might be compressed by the magnetic fields at the surface. :scratch:

Came across this

http://news.mit.edu/2014/a-river-of-pla ... e-sun-0306
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Re: Why is Maxwell’s Theory so hard

#13  Postby romansh » Jan 06, 2019 4:59 pm

Macdoc wrote:
But plasma can be compressed and water cannot ( mostly apparently ). So you can have a plume of very hot very dense plasma rise through the sun and emerge as a CME


I am having a hard time seeing what the ability to be compressed has to do with roe g h?
Air pressure is independent of elevation?
Hot water does not convect?

And if it takes photons centuries to escape the core of the sun?
I am not saying the plasma does not move around … it plainly does.
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Re: Why is Maxwell’s Theory so hard

#14  Postby Macdoc » Jan 06, 2019 5:37 pm

But plasma at difference densities is the point.

Energy density is the amount of energy stored in a given system or region of space per unit volume.


So a super hot and super dense plume of plasma surely has a changing energy density "moment by moment" and given there is constant production of energy/heat with thermonuclear reactions I'd say it varies wildly moment by moment.

Team creates high-fidelity images of Sun's atmosphere - Phys.org
https://phys.org › Astronomy & Space › Astronomy
Jul 18, 2018 - Team creates high-fidelity images of Sun's atmosphere. July 18 .... "We should expect steep fluctuations in density, magnetic fluctuations and reconnection ... Explore further: STEREO maps much larger solar atmosphere than .

https://phys.org/news/2018-07-team-high ... phere.html

Air pressure is independent of elevation?

Yes - it can be compressed, and air pressure at sea level changes all the time within bounds.

Hot water does not convect?


Yes but pressure doesn't change significantly the way a gas does and it is entirely temperature dependent - very hard to compress further unlike a gas or a plasma.

That a photon takes a long time "on average" to reach core to surface I don't see as relevant but I'm willing to be illuminated :whistle:
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Re: Why is Maxwell’s Theory so hard

#15  Postby Cito di Pense » Jan 06, 2019 6:00 pm

Macdoc wrote:
Hot water does not convect?


Yes but pressure doesn't change significantly the way a gas does and it is entirely temperature dependent - very hard to compress further unlike a gas or a plasma.


Well, actually, pressure does change, so you probably meant to type 'volume' instead of 'pressure'. Maybe you've experienced clearing your ears when SCUBA diving or even just bobbing around in a swimming pool. Liquids are mainly incompressible, which means that their volume does not change much with pressure or temperature, but compressibilities and thermal expansivities are not negligible for many specified sets of working conditions.

My reading is that the compressibility of plasma is to first order related to the Mach number of the flow. At M < .3, the flow may be considered incompressible. FWIW, densities in stellar interiors are much higher than those of normal liquids. My further reading is that stellar interiors are in hydrostatic equilibrium when not transitioning off the main sequence or undergoing some other cataclysmic event at the end of a stellar lifetime.
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Re: Why is Maxwell’s Theory so hard

#16  Postby newolder » Jan 06, 2019 6:08 pm

Evolving wrote:
newolder wrote:An essay (5 pages-ish) by Prof. Freeman Dyson on the reticence of Maxwell and the similarity to the later development of quantum mechanics.

Starts with Modesty is not always a virtue


That link won't open for me. Is it because I'm not user tong?

EDIT: I've searched the DAMTP website and on this page

https://search.cam.ac.uk/web?tag=alldamtp&query=Dyson%20Maxwell&inst=DAMTP&x=14&y=13

the Dyson Maxwell article is listed. Can't open it there either, though. Maybe it's me.

I missed this one - apologies. I have no idea why a link to a pdf won't open for you. What browser are you using? Does it require a pdf reader plug-in that you may not have installed? :scratch:

How do you normally access pdfs in the arXivs?
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Re: Why is Maxwell’s Theory so hard

#17  Postby newolder » Jan 06, 2019 6:25 pm

Macdoc wrote:Thanks I can usually visualize processes without having the underlying math.
Had a good discussion on another forum about the important of visuals in explaining concepts - he was absolutely fixed on "you must have the math" and the visuals were immaterial and several of us disagreed.

After all it was thought experiments that led Einstein and THEN he did the math to prove it. I figure you need the math to use a concept but necessarily to understand one.
ie images or even animated illustrations of processes in a nuclear plant are very useful and understandable but the math exceedingly complex.

So I can visualize what's going on in balloon or star without being to quantitize it....if that makes sense.
I find some of the animated explanations of physical principles fascinating and in particular complex systems like AGW/Atomosphere processes benefit understanding more than

Net Radiation = Q* = total in - total out


The essay describes how, initially, Maxwell tried to describe EM radiation in 'familiar' terms that required a medium for EM transmission. This idea had to be abandoned when the constancy of the speed of transmission was observed to be constant. The correct understanding requires the mathematics of fields that were relatively new to Maxwell but well known by the time Einstein was working.

Similarly, the development of QM as described in the essay required an abandonment of the tenets of local realism and the adoption of more abstract ideas underlying any measurement outcomes.

The essay points to our future understanding of, say, quantum gravity, where again new methods will undoubtedly be required and developed. They may be stringy ideas or combinatorics or a mixture of both or something other but the idea that human intuition will clear the path is probably no longer true.

I have no problem with your discussion of stellar interiors using EM theory but I think it should be in a more specialised topic that this. Just saying.
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Re: Why is Maxwell’s Theory so hard

#18  Postby Evolving » Jan 06, 2019 6:56 pm

newolder wrote:I have no problem with your discussion of stellar interiors using EM theory but I think it should be in a more specialised topic that this. Just saying.


Fair enough. I only brought up stars in order to contrast them with balloons. Romansh pointed out a connection with energy density, which I picked up on and thought that, on the whole, it was an interesting point, but wanted to point out that this arithmetic connection with the pressure strictly only holds with respect to the layer of the gas that is immediately adjacent to the surface in which the pressure is being exerted. In the case of a balloon it probably holds, in fact, with regard to the whole of the gas (because the pressure will be broadly constant all the way across the gas), but in the case of a star it certainly doesn't, because the pressure is definitely not constant across the star.

I didn't say that the pressure was changing with time.
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Re: Why is Maxwell’s Theory so hard

#19  Postby Evolving » Jan 06, 2019 6:59 pm

newolder wrote:
Evolving wrote:
newolder wrote:An essay (5 pages-ish) by Prof. Freeman Dyson on the reticence of Maxwell and the similarity to the later development of quantum mechanics.

Starts with Modesty is not always a virtue


That link won't open for me. Is it because I'm not user tong?

EDIT: I've searched the DAMTP website and on this page

https://search.cam.ac.uk/web?tag=alldamtp&query=Dyson%20Maxwell&inst=DAMTP&x=14&y=13

the Dyson Maxwell article is listed. Can't open it there either, though. Maybe it's me.

I missed this one - apologies. I have no idea why a link to a pdf won't open for you. What browser are you using? Does it require a pdf reader plug-in that you may not have installed? :scratch:

How do you normally access pdfs in the arXivs?


I don't know why it wouldn't open. I was trying on my work PC. I'll try on my personal Mac later, but my daughter is using it with the Just Dance app!
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Re: Why is Maxwell’s Theory so hard

#20  Postby Macdoc » Jan 06, 2019 7:48 pm

newolder wrote:
I have no problem with your discussion of stellar interiors using EM theory but I think it should be in a more specialised topic that this. Just saying.


That's fine ...the thread was being a thread ...wandering hither and yon a bit :whistle:

A ballon I get....interior of a star ...nah. :shock:
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