Physics Discussion Thread

[GuruPrabhu]

Wouldn't this imply that the correlation between the potential equation and the physics it represents is arbitrary, and therefore incidental (or coincidental, if you will)? It just so happens that a particular form of an equation represents a particular physics i.e. ax^2 + bx^4 represents Higgs potential.

Whether it is incidental/coincidental or not does not address the root question of why *any* equations should describe physical phenomena? In this case, not only does this arbitrary equation satisfy the need for the physics, no other simple equation seems to work (at least to the extent that folks have explored other simple forms for the potential).

So, the question that troubles me is this: why do simple equations work in describing physics? Or, why do seemingly complex phenomena find explanation in simple mathematical equations?

Take the solar system for example. The planets have complex orbits so at first glance it looks like a complicated phenomenon. However, it is elegantly described by Newton's law of gravitation. The potential is exactly 1/r, not 1/r^1.1 or 1/r^0.9 -- why?

Similarly, the electrostatic potential is also 1/r. Is that a coincidence?

To me, there is something deep which science has not yet fully grasped.

[brihaspati]

The 1/r potential can be shown to be an approximation at "large" distances from point source, corresponding to solutions of equations of motion in curved spaces. For example a simple starting point of setting the Einstein tensor proportional to the energy-momentum tensor, and using a spatially isotropic curvature - in spherical coordinates - would add a term to the flat space metric tensor, that would be proportional to 1/r approximately at large distances.

If one compares this metric with a corresponding flat space approximation using Newtonian gravitational mechanics, one can see that the terms coincide for large distances.

Thus in this case, a rather simple assumption that space-time curvature is proportional to the energy-momentum tensor at that point, leads to a set of differential equations under some simplifying assumptions [isotropy for example] that reproduces the classical Newtonian potential. The particular mathematical form for that potential follows as a mathematical solution to an initial "model" which is however not really "mathematical" or "arbitrary", that is the curvature \propto energy-momentum [R_{ij}+0.5g_{ij}R =KT_{ij}, R_{ij} is the Ricci tensor, R the scalar curvature, g_{ij} the metric tensor, T_{ij} the energy momentum tensor]. The left hand side of the equation is the homogenized curvature tensor, while the right hand side is the energy-momentum. It is just expressing the physical concept that space-time gets more curved if more "energy" is concentrated at that point.

There are extensions of this principle to derive the Electric potential too - by adding torsion to curvature terms. There are similar more modern theories that extend by adding (1) dimensions [a 5D model was used early on to derive both the grav and elec potential] (2) adding torsion terms (3) and extending the underlying algebra from real to quaternions/octal etc.

Much of the "quantum" potentials are similarly modeled by establishing an equivalence of the metric in ordinary space to tangential operator space. For example consider the flat space metric in Euclidean/Minkowski notation x^2+y^2+z^2-c^2t^2=0 [describing light ray]. Replace each x with \partial/\partial x, etc, and you get Laplacian \phi -c^2[\partial^2/\partial t^2]\phi =0. Solve for time-independent or stationary case, and you get the classic Newtonian potential for \phi. If instead of 0 we use proportional to a non-zero constant, we get another interesting potential - one connected with mesons. Similarly trying to write the above equation as a bilinear form - an inner product of two linear terms, forces us to go for a matrix algebra that gives rise to the Dirac \gamma operators [one anti-commuting and others commuting].

But they are all starting out with ideas expressing physical models, but given in mathematical form. Hence they produce corresponding "values" which appear to fit uncannily observed reality.

[Bade]

GP, Bji

I had always thought at least the 1/r nature of the potential for both electrostatics and gravity comes out of Gauss's theorem, where a surface integral of the flux is equated with the volume integral of source and sink, which is essentially a conservation law of flux lines. Wiki also has a reasonable writeup on it.

http://en.wikipedia.org/wiki/Divergence_theorem

But the case of the Higgs potential as a polynomial limited to terms of 2nd and 4th order is very adhoc. One could perhaps view it as an approximation of the series expansion of trigonometric functions of cos(x) if you will. But what does that mean ? Also it is an even function by choice, if not and had the choice been powers of 3rd and 5th (as in sin(x) expansion), then the continuous choice of values for the minimum would not exist (no mexican top hat form), and hence no spontaneous symmetry breaking possible.

[brihaspati]

Bade ji,
Agreed that potential looks arbitrary and "shop-order" to fit predictions. But if you think of it, any potential that is a radial function, say U(r), cannot be odd - since by isotropy then U(r) must be 0 everywhere. [U(r)=U(-r)=-U(r)]. However, with the Higgs - the problem becomes that of phase-changed potentials and hence comes into the complex field with symmetry restrictions. So renomalizability imposes quadratic terms, leading to the square and fourth powers. However, the Higgs potential is still debated - and all its terms are a matter of splitting heads.

As for Gaussian divergence, yes it does - but that is the now-classical explanation. The space-time curvature concept gives a slightly more elegant, and in the case of gravity a more accurate system of equations of motion for point masses. Moreover this provides a means of coupling together grav and EM from a single theory - which is not possible in the Gaussian divergence approach. In fact the strings/M are simply working on this curvature approach in higher dimensions to derive the all various interactions as manifestation in 4D.

[GuruPrabhu]

I had always thought at least the 1/r nature of the potential for both electrostatics and gravity comes out of Gauss's theorem ...

Bade Saar, one can keep assigning deeper mathematical justifications to a physical measurable. But, the bottom line question was about *why* any of them should work. IOW, what is the stranglehold of math on physics?

But the case of the Higgs potential as a polynomial limited to terms of 2nd and 4th order is very adhoc. One could perhaps view it as an approximation of the series expansion of trigonometric functions of cos(x) if you will. But what does that mean ? Also it is an even function by choice, if not and had the choice been powers of 3rd and 5th (as in sin(x) expansion), then the continuous choice of values for the minimum would not exist (no mexican top hat form), and hence no spontaneous symmetry breaking possible.

This is technical stuff deviating from the main topic, but the basic point is that the potential has to respect SU(2)xU(1) symmetry. This limits the choice of possibilities. This is a bit OT, but a good model should predict cos(weinberg angle) = Mass_W/Mass_Z. Only one potential does that (unless one extends to super-potentials).

All this is OT and we can have a discussion on the frontiers of particle physics, but the topic at hand is about the role of math in the context of physical phenomena.

[brihaspati]

It is not mathematics that determines physical reality - and hence there is no particular overruling role of mathematics. The starting point for all these derivations is always a statement that describes a particular assumption on physical reality. I mentioned the curvature momentum assumption specifically to show that it is a description of a physical reality model which when stated in mathematical terms leads to a "potential" term of 1/r - it does not start out by assuming anything on that potential mathematically.

Mathematics should be seen as a condensed logical derivation procedure. The physical model is always the starting point, not maths.

There are many competing theories that try to predict the Higgs potential. The various physical realities assumed on the underlying model when formulated or expressed in mathematical terms leads to corresponding derived mathematical forms. It is the physical assumptions that determine where the maths will lead, and not the maths that determines the initial physical assumption.

[SriKumar]

So, the question that troubles me is this: why do simple equations work in describing physics? Or, why do seemingly complex phenomena find explanation in simple mathematical equations?

Take the solar system for example. The planets have complex orbits so at first glance it looks like a complicated phenomenon. However, it is elegantly described by Newton's law of gravitation. The potential is exactly 1/r, not 1/r^1.1 or 1/r^0.9 -- why? Similarly, the electrostatic potential is also 1/r. Is that a coincidence?

Given the fact that the physical causes of forces (IMHO, potential is a surrogate for forces, a quantity that is measurable) in electrostatics and gravity are different and yet they show identical qualitative trend, I would lean towards calling this the definition of coincidence. I dont want to get hung up on semantics but rather, the point I want to make is that the basic physics to explain the forces of attraction between two electric charges is very different from that of two masses due to gravity. However, we see a correlation/similarity merely because the measured observations in the two phenomena (i.e. forces between two masses, and, forces between two charges) have the same kind of relationship , i.e. forces are inversely proportional to the square of the distance, and directly proportional to the product of masses (or charges). IMHO, the equation is a merely a statement of an experimental observation, nothing more.

Ultimately, I see 1/r, or rather F = K /R^2 merely as a description of the two phenomena. The description could well have been verbal. The mathematical description is powerful because it can be manipulated via mathematical rules into other forms which could potentially (no pun intended) tell us more about a system. (But do all mathematical predictions pan out correctly?). I am sure you've heard of rhetorical algebra. This describes what I mean by saying that math is a script and a means of description of nature which needs to be checked/tested at every step.
http://jwilson.coe.uga.edu/emt668/emt66 ... eline.html

[GuruPrabhu]

Ultimately, I see 1/r, or rather F = K /R^2 merely as a description of the two phenomena. The description could well have been verbal. The mathematical description is powerful because it can be manipulated via mathematical rules into other forms which could potentially (no pun intended) tell us more about a system.

This is the crux. You are saying that the description could well have been "verbal", and that the only advantage math brings with it is the power to make predictions. However, this is not a minor advantage. Math can predict unobserved phenomena! No amount of verbal deduction could do that -- there are countless examples!

The case of Higgs is analogous, but really quite different. The potential in that case is that of a self-interacting field [nuclear interactions also do that, albeit, in a confined way - the potential is restricted to very short distances]. There is no "force" to be observed directly, so there is no verbal way of describing it strictly. Of course, if the Higgs is discovered, one can imagine studying its self-interaction at accelerators. So, just like the Dirac example, this is a case where math precedes observations.

[Vayutuvan]

The potential is exactly 1/r, not 1/r^1.1 or 1/r^0.9 -- why?

Similarly, the electrostatic potential is also 1/r. Is that a coincidence?

To me, there is something deep which science has not yet fully grasped.

Guru Prabhu ji

Interesting question I had been ruminating on for sometime. On what basis are we sure that it is exactly $1/r$ and not $1/r^{1+-\epsilon}$ where $0< epsilon << 1$? Is it possible that we are unable to measure that accurately?

[Rahul M]

the exact value does not matter all that much in this case because the 1/r potential function for newtonian gravity is a special case approximation of the more general GTR field equations.

[GuruPrabhu]

On what basis are we sure that it is exactly $1/r$ and not $1/r^{1+-\epsilon}$ where $0< epsilon << 1$? Is it possible that we are unable to measure that accurately?

There are several ways of addressing this. The age-old method is a torsion pendulum technique which has become incredibly sophisticated over the years. Here is a link that explains this:

http://en.wikipedia.org/wiki/Cavendish_experiment

These experiments try to pin down G. Here is a modern one:

http://www.physicscentral.com/explore/a ... search.cfm

However, departure from 1/r^2 falls into an interesting new category of research. There have been several modifications to gravity proposed for small scales. Some of these involve extra dimensions (at least two more -- one more is ruled out). I googled and found an article that seems to summarize things quite well:

http://www.livescience.com/8789-gravity ... stery.html

Here are technical review papers (if you want details) from the world's leading group in this research:

http://www.npl.washington.edu/eotwash/

Another method that is now becoming feasible to search for Graviton production at colliders like the LHC. There are two models, named after their authors ADD (Arkani-hamed, Dvali and Dinopolous) and RS (Randall and Sundaram). Then there is the modified Kaluza-Klein model. You can google those key words to see the latest. Here is the Wiki to help get started:

http://en.wikipedia.org/wiki/Large_extra_dimension

[Amber G.]

WRT to Matrimc's comment about "epsilon" ...

..I had always thought at least the 1/r nature of the potential for both electrostatics and gravity comes out of Gauss's theorem...

FWIW: People mau already know but 1/r nature (coulomb's law that force goes as 1/r^2) is equivalent to Gauss theorem..(If you assume one, you can prove the other).

It also gives an excellent (practical) way to experimentally verify the coulombs law ( or 1/r potential) to a very high precision. One simply measures field inside a charged metal sphere... absence of the field will verify Gauss's law, and this method is much more precise than, say, actually measuring the force and distance(s)...

Historically Cavendish IIRC, with is torsion balances and all, was sure that that inverse square law is (experimentally) correct to about 1% ( IOW the power of '2' is between 1.99 and 2.01) .. Maxwell's time the experimental uncertainty was less than .000001 but now a days with fairly simple techniques we can verify that the factor 2 is correct within about 10^(-16).

[Amber G.]

I see that there was no clear answer to my "sound" problem. Well...the effect is quite real and well known..
Interesting that we talked about light refraction etc.. and the main phenomena is due to refraction of sound.

Velocity of sound in air depends on air's temperature, and sound travels slower in cold air and thus bends just like light when it goes from one medium to other... and what you hear is very much similar to mirages in desert... Check out sound refraction (or acoustic shadow etc) in any good book/source...( When it comes to volume of sound, it is not important whether the sound travels slow or fast. Important point is when there are difference in layers.. sound waves bend)
For example, a well know example, (and an article in Nature) at Queen Victoria Funeral, cannon sound was heard hundreds of miles away (in Scotland) while the sound "skipped" some localities just outside London. Another well known example, historians talk about, Gettysburg battle, signal fires, where sounds which at times were heard in Pittsburgh ( >100 miles).. were missed at a distance of about 10 miles!

In the day air near the ground is warm (and gets warm fairly soon after sunrise) and air above is cold(er).. sound waves bend "upwards" and do not reach ground locations far away..

Basically when ground get cold (land gets cold fairly fast after sun goes down) air near ground is colder.. sound waves bend .. (almost like total reflection from the upper layers..)... and they hit the ground far away.

[kasthuri]

It is not mathematics that determines physical reality - and hence there is no particular overruling role of mathematics. The starting point for all these derivations is always a statement that describes a particular assumption on physical reality. I mentioned the curvature momentum assumption specifically to show that it is a description of a physical reality model which when stated in mathematical terms leads to a "potential" term of 1/r - it does not start out by assuming anything on that potential mathematically.

Mathematics should be seen as a condensed logical derivation procedure. The physical model is always the starting point, not maths.

There are many competing theories that try to predict the Higgs potential. The various physical realities assumed on the underlying model when formulated or expressed in mathematical terms leads to corresponding derived mathematical forms. It is the physical assumptions that determine where the maths will lead, and not the maths that determines the initial physical assumption.

1. Pure mathematicians have least regard for mathematical logic.
2. The logicians are confused why they aren't called mathematicians.
3. Pure mathematicians don't find any joy in the beauty of physics.
4. The physicists are really happy in their world. They consider pure math as a separate world of abstraction and the relevance of math in explaining the world is at best - a tool. It is just an epsilon world.
5. Both physicist and mathematicians have a total disregard and disrespect for biology/molecular biology. Having a satisfactory theory of Relativity and not so satisfactory QM marks the end of their world. The central dogma of molecular biology is just a dogma!
6. For biologists, the word "science" essentially means biochemistry, molecular biology and genetics and never physics and math, leave alone logic.

Now I am left wondering what it all means by "physical reality"? Can it be at least defined "statistically"?

[Amber G.]

Added later: For those who want to understand the refraction of sound.. any good book/source would do. Here are a few short links (from google):
(A single page doc)
http://paws.kettering.edu/~drussell/Dem ... fract.html

(From this:

s when the temperature is coolest right next to the ground and warmer as you increase in height above the ground. Since the temperature increases with height, the speed of sound also increases with height. This means that for a sound wave traveling close to the ground, the part of the wave closest to the ground is traveling the slowest, and the part of the wave farthest above the ground is traveling the fastest. As a result, the wave changes direction and bends downwards. Temperature inversions most often happen at night after the sun goes down when the ground (or water in a lake) cools off quickly, while the air above the ground remains warm. This downward refraction of sound is why you can hear the conversations of campers across the lake, when otherwise you should not be able to hear them. (remember that they can probably hear you too!)

or
http://www.pa.op.dlr.de/acoustics/essay ... ng_en.html
And here are some war stories due to this effect..
http://www.acoustics.org/press/136th/ross.htm
At the first soviet atom bomb test, due to similar refraction effect there were few unexpected deaths far away from the location because some buildings far away blew up...

[SriKumar]

You are saying that the description could well have been "verbal", and that the only advantage math brings with it is the power to make predictions. However, this is not a minor advantage. Math can predict unobserved phenomena! No amount of verbal deduction could do that.

Agreed, with the caveat that some predictions might not have panned out (but I cannot think of a concrete example here .... usually failure of predictions tend to get buried in the depths of time). This brings us to the question of what is the sanctity of mathematical rules of manipulation e.g. differential of cos(x) is -sin(x), for e^x, it is e^x, etc. Why are these rules 'sacred'? This seems important because any predictive capability that math has arises from following specific rules of manipulation that were determined independently of physics. Not sure I can comment much about this. (Could there be an alternative definition of the differential of a given term?)

A few words in favor of verbal deduction: they give rise to new models to explain phenomena. Is it not true that Einstein's theory of relativity came about through 'thought experiments' he did, in terms of what happens when things travel at the speed of light. Atleast, the explanations in physics text books are presented in those terms. Similarly, would it be fair to say that string theory is an alternative model to explain the behavior of matter from a fundamental level (a different approach from the standard model) and would have arisen from thought/imagination rather than math.

[SriKumar]

It also gives an excellent (practical) way to experimentally verify the coulombs law ( or 1/r potential) to a very high precision. One simply measures field inside a charged metal sphere... absence of the field will verify Gauss's law, and this method is much more precise than, say, actually measuring the force and distance(s)

Could you please give a link (if available) that gives details of the experimental equipment and procedure? Thanks.

[Amber G.]

^^^ Probably any good source (or google search) will do..
for example see pp 756 (Chapter 24.6) of this:
Experimental verification of Coulomb's law

[brihaspati]

[...]
1. Pure mathematicians have least regard for mathematical logic.

Sure? I mean there are bad apples and constipated ones. But most do follow "mathematical logic". It could also be a case of people not really being consciously aware of all the steps that they condense into compact theorems.

2. The logicians are confused why they aren't called mathematicians.

Probably its a matter of scope and focus.

3. Pure mathematicians don't find any joy in the beauty of physics.
4. The physicists are really happy in their world. They consider pure math as a separate world of abstraction and the relevance of math in explaining the world is at best - a tool. It is just an epsilon world.

There are some interested in both. Physicists in pure maths and pure mathematicians into physics. I guess the source of confusion arises primarily with those mathematicians engaged in number theoretic disciplines. But even there considerable overlaps exist. Some pure mathematicians have openly and primarily drawn inspiration from physics, like Connes in his work on non-commutative algebra - and area where physicists have contributed to maths and mathematicians into physics.

5. Both physicist and mathematicians have a total disregard and disrespect for biology/molecular biology. Having a satisfactory theory of Relativity and not so satisfactory QM marks the end of their world. The central dogma of molecular biology is just a dogma!
6. For biologists, the word "science" essentially means biochemistry, molecular biology and genetics and never physics and math, leave alone logic.

Maybe, but again there are many who work cross-discipline. "Algebraic statistics" is for example little to do with "algebra" or "statistics" per se but a combination of concepts derived from various areas of pure maths and probability, applied to biology and first launched by mathematicians.

Now I am left wondering what it all means by "physical reality"? Can it be at least defined "statistically"?

A tricky question. But at least for "macro-phenomena", some degree of clarity exists in the concept of "reality" - it is the QM average/Expectation in a statistical sense of a state of the system.

[brihaspati]

In fact topology, number theory and algebra on general number fields are very closely linked to physics now. Many researchers work in both or work in one and are guided by needs of the other. Molecular biology, especially protein 3D-structures are increasingly coming into interactions with pure maths. There is actually increasing pressure on "pure" mathematicians to be relevant for other disciplines. This would be actually a good thing though. The feverish early modern era maths activity was stimulated directly by practical problems and observations in navigation, engineering, ballistics, military and health sectors.

[Amber G.]

Okay Another sound/noise puzzle this time the physics text book ref I just gave had this puzzle..

...Some railway companies are planning to coat the windows of their passenger
trains with a very thin layer of metal in response to increasing rider complaints about
other passengers talking loudly on their cell phones. The metal layers will be thin enough
to be transparent....

How a thin layer of metal is going to help?

[vina]

However, it is elegantly described by Newton's law of gravitation. The potential is exactly 1/r, not 1/r^1.1 or 1/r^0.9 -- why?

Similarly, the electrostatic potential is also 1/r. Is that a coincidence?

That is so because the the circle and it's 3d revolution, the sphere is described perfectly mathematically. The math behind that is exact. The Stoke's theorem, Green's Theorem and the Gauss theorem are mathematically exact. Hence any physical phenomenon that is described by that has to be exact!

[vina]

Interesting question I had been ruminating on for sometime. On what basis are we sure that it is exactly $1/r$ and not $1/r^{1+-\epsilon}$ where $0< epsilon << 1$? Is it possible that we are unable to measure that accurately?

It absolutely has to be 2 and only exactly 2. That is because of Gauss theorem or the 2d case of Green's theorem, which reduces any anything to a sphere/circle, which is described exactly by math.

[vina]

Anyway .. here is another problem --

We live in a quiet neighbor-hood but there is a highway not too far from us. In the morning (or day time) we don't hear any noise but in the evening (when we take a walk) we often hear traffic noise from the high-way?
What possible could be the reason? .. (Do others have similar experience? Sound from far away places, much clearer in the evening than in the day or morning..)

Could be multiple reasons. One plausible one could be this. In the morning, there is usually dew on the ground, the air on the ground is usually of lower temperature (the sun needs to burn through multiple layers and reach and warm up everything). So what happens is that the atmosphere is not one homogenous medium, but rather stacked up as different layers of slightly higher density each.

Now when this happens, sound can if conditions are right propagate only in those particular channels and get totally internally reflected at the boundaries and not penetrate the adjacent layers of different density (sort of like optic fiber) and propagate massive distances. The thing is if you are in one of the other channels in which the sound is not propagating (if you are in a higher density channel) , you will not hear it .

In the evening , the sun has been shining all day, there is no temperature gradients of consequence, the atmosphere is homogenous and you will be able to hear.

In fact in underwater warfare/acoustics this is very important. Submarines hide in those kind of thermal layers and if your sonar is not dunked right into it, you would be able to detect it. On the other hand, if you are in that layer, the noise gets propagated hundreds of miles very easily and you can detect from very large distances. In fact , whales can communicate over hundreds of miles using this phemonemon.

Gosh. I cant believe it. I still remember this vibrations and acoustics stuff after all these years from the Madrassa.

[GuruPrabhu]

However, it is elegantly described by Newton's law of gravitation. The potential is exactly 1/r, not 1/r^1.1 or 1/r^0.9 -- why?

Similarly, the electrostatic potential is also 1/r. Is that a coincidence?

That is so because the the circle and it's 3d revolution, the sphere is described perfectly mathematically. The math behind that is exact. The Stoke's theorem, Green's Theorem and the Gauss theorem are mathematically exact. Hence any physical phenomenon that is described by that has to be exact!

What do you mean by "exact"? Please scroll up and look at test of this exactness. Who guarantees "exact"? And how?

[GuruPrabhu]

Okay Another sound/noise puzzle this time the physics text book ref I just gave had this puzzle..

...Some railway companies are planning to coat the windows of their passenger
trains with a very thin layer of metal in response to increasing rider complaints about
other passengers talking loudly on their cell phones. The metal layers will be thin enough
to be transparent....

How a thin layer of metal is going to help?

Faraday shielding?

[vina]

Now I am left wondering what it all means by "physical reality"? Can it be at least defined "statistically"?

I hope you dont. Then it gets in to tragi-comic world of e-Con-O-Mix and then it will be over to the likes of Super Comprehension to describe the universe . Facts and real life experience be damned.

[GuruPrabhu]

This brings us to the question of what is the sanctity of mathematical rules of manipulation e.g. differential of cos(x) is -sin(x), for e^x, it is e^x, etc. Why are these rules 'sacred'? This seems important because any predictive capability that math has arises from following specific rules of manipulation that were determined independently of physics.

Now you and I are talking the same language. Why indeed are these rules sacred?

[vina]

What do you mean by "exact"? Please scroll up and look at test of this exactness. Who guarantees "exact"? And how?

The math is exact. Now if you want to describe that physical phenomenon (whatever it is , grativity, elecrostatics.. whatever) using that set of math , then it is exact. If you say 1/r^2.025 , it no longer remains the inverse square law. It is not a "statistical" law, but an exact law. That is all there is to it.

[GuruPrabhu]

The math is exact. Now if you want to describe that physical phenomenon (whatever it is , grativity, elecrostatics.. whatever) using that set of math , then it is exact. If you say 1/r^2.025 , it no longer remains the inverse square law. It is not a "statistical" law, but an exact law. That is all there is to it.

Fine, I have no problem with math being exact. In fact, I agree. The problem is that physical reality depends on number of dimensions. How does math "know" how many dimensions there are? Answer is that it doesn't.

[Amber G.]

^^^ Of course, (the numerical part of the problem asks the student to calculate, how thick the metal ( certain properties of gold/ silver are given.. and RF frequency of cell signal is given ..) film has to be to be ityadi ....

Personally I think it is silly to block the signals...

[vina]

It depends on number of dimensions. How does math "know" how many dimensions there are? Why does it pretend to be "exact" if it has no clue about reality?

Math is complete in itself. It is exact. That is the beauty of it. In fact, Srinivasa Ramanujam thought that every equation he wrote was a reflection of the Goddess in Namagiri (his family originally was from Namagiri) thoughts. In fact. Math in his opinion was God.. perfection. It is "swayambhu" if you want.

Now all that happens is that YOU use math to describe things we see/understand in the physical world. The incompleteness or "reality" or lack of it is only our perception/maya/whatever. Math couldn't be bothered with it.

[vina]

^^^ Of course, (the numerical part of the problem asks the student to calculate, how thick the metal ( certain properties of gold/ silver are given.. and RF frequency of cell signal is given ..) film has to be to be ityadi ....

Personally I think it is silly to block the signals...

Was my answer to the sound problem correct ?

[GuruPrabhu]

Folks,

I am impressed by how much traffic has been generated in this thread. What I find amazing is that a lot of postors are very sure about their physics. I wonder what is the reason for this certitude.

Real life physicists are all confused beings. Most don't know what is going on and are working hard to derive some sense out of outrageous phenomena and coincidences.

My 2 cents.

[GuruPrabhu]

Now all that happens is that YOU use math to describe things we see/understand in the physical world. The incompleteness or "reality" or lack of it is only our perception/maya/whatever. Math couldn't be bothered with it.

Yes, math can't be bothered ityadi. But, please go back and read the thread to get to the crux of the problem. If not, please accept my Pranaam and leave me alone. Thank you, Saar.

[GuruPrabhu]

^^^ Of course, (the numerical part of the problem asks the student to calculate, how thick the metal ( certain properties of gold/ silver are given.. and RF frequency of cell signal is given ..) film has to be to be ityadi ....

The skin depth at 2.4 GHz (typical cell phone carrier frequency) is available on google. It is probably micrometers.

[Bade]

In the context of 1/r potential discussion above, if there are extra dimensions indeed, one can see already that simply assuming 3 spatial dimensions and doing Gauss's theorem in this space will only give an incomplete solution to the true nature of the potential.

[GuruPrabhu]

In the context of 1/r potential discussion above, if there are extra dimensions indeed, one can see already that simply assuming 3 spatial dimensions and doing Gauss's theorem in this space will only give an incomplete solution to the true nature of the potential.

Thank you, Saar!

[kasthuri]

Brihaspatiji,

1. "following mathematical logic" or using classical logic to prove theorems will not fetch us too far. One may argue that we have so many wonderful theories in physics due to the standard logic, but it is my humble opinion that unless some sort of axiomatization of physics is explored using other logics (non-standard models, para-consistent etc.) we may not be able to completely reconcile gravity and quantum effects. Hawking's lecture titled "Godel and the End of Physics" rightly points in this direction. Btw, I am aware of Hilbert's failed program for axiomatizing physics.
As far as I have come across, mathematical logic is often taught in philosophy departments than on math. And in fact, CS departments have shown more interest on logic than math folks. In a nutshell, logic matters more now than ever, be it cs, math or physics.
2. I don't see why "meta-mathematics" is not mathematics in the first place.
3 and 4. Math to a large extent is shaped by physics and vice-versa. I simply don't see the reason why they should be separated at all. Almost all legends in either field have contributed to the other. And it is my belief (I don't have any justification) that for any physical phenomena that we see there should be a corresponding mathematical/mental construct and vice-versa. This belief of mine correlates well with the Vedantic viewpoint that physical world is a manifestation of the mind in its complete glory.
5 and 6. I feel that "physics envy" often reduces the reality into the world of atoms and universe. There is whole world of biology out there which physics have no clue about. The phenomenon of transcription and translation is unexplainable in any mathematical term. QM is not an answer for what happens inside a gene. Gene is not a quantum phenomena.

Therefore, the word "physical reality" should really mean "reality as explained using the principles of physics". Biological realities such as gene regulation, cell cycle, signal transductions are macroscopic yet they aren't "covered" by physics so far.

[GuruPrabhu]

hope this is useful for Amber's problem