Physics Discussion Thread

[negi]

The answer is yes, there is no "drag" in vacuum, unless you believe in Higgs field. As for "eternity", IIRC, the limit on the lifetime of the proton is >10^34 years.

Thanks, what does one mean by lifetime here ? How is this figure arrived at ?

[Rahul M]

naveen, about the problem. look up earnshaw's theorem.

[GuruPrabhu]

Thanks, here is the problem again.

Problem for Jingo's:

What happens to a positive charge particle (say a proton) at the origin, surrounded by 6 fixed equal positive charges which are at the same distance from the origin in north-south, east-west, up-down position? Of course, due to symmetry, the charge will be at equilibrium, but is it stable equilibrium? (that is, if you disturb the charge just a little, will it stay at the origin or will run away?)

(Hint: If you just take two charges (say east-west or x-axis) the proton in the middle will escape in y-axis (or z-axis) if it is disturbed a little in that direction)

As Amber has hinted, reduce the problem to one dimension because the other two are symmetric. Let us say that the distance to each charge is D and let us imagine a small deviation x in one direction. The potential in that dimension will be:

V = 1/(D+x) + 1/(D-x), after eliminating constants.

Minimizing this with x, gives the minimum at x=0.

To see if this is stable, take the second derivative and evaluate at the point of minimum. (left as an exercise). Just for fun, replace the charge in the middle with a negative charge and see how it changes.

[GuruPrabhu]

The answer is yes, there is no "drag" in vacuum, unless you believe in Higgs field. As for "eternity", IIRC, the limit on the lifetime of the proton is >10^34 years.

Thanks, what does one mean by lifetime here ? How is this figure arrived at ?

It is a lower limit on the lifetime. It says that if you watch a proton for 10^34 years, the probability is 67% that it would not have decayed.

Of course, that is not how the experiment is done. A better way to do it is to watch 10^34 protons for one year, ensure that none have decayed, and set the limit. In practice this is done nowadays with large water detectors like Super-Kamiokande.

India's Kolar Gold Field experiment was a pioneer in this field. Unfortunately, the team from TIFR did not understand neutrino backgrounds very well and claimed a positive result back in the 80's, which brought unnecessary egg on their faces. In their defense, there was no large scale computing available back then and they did not have a way of simulating the neutrino interactions.

[negi]

Thanks Rahul.

Seriously man I am a gand@ #1 I should have googled for the theorem in question.

Anyways guys so after having whined for years I have managed to send an email to NCERT folks to restructure the XIth and XIIth class syllabus ; I mean how does one explain teaching Newtonian mechanics in XIth standard physics without introducing the differential calculus to students ? (How is one supposed to mathematically explain a student what does one mean by 'rate of change of a quantity with respect to time' ?), similarly how does one expect students to grasp concepts like Gauss's theorem without introducing 'integral calculus' to the kids ?

I see they have the syllabus structured in the exact same way as before (when I did my XIIth) i.e. teach Electrostatics in chapter-I in physics while introduce Differential Calculus in mathematics only in chapter-5 and integral calculus is covered in the part-II; seriously is it just me or everyone who studied using NCERT course-ware feels the same ?

No wonder parents have to send their kids for tutions.

[GuruPrabhu]

Thanks Rahul.

Seriously man I am a gand@ #1 I should have googled for the theorem in question.

I just did and find that my explanation above is incomplete

[brihaspati]

Seems more likely! There are similar debates on distribution of gold.

Hmm.. Gold, actually sinks (Experimental result.. no debates).. unlike U or Th..

One simple pointer should be that the gravitational forces should on an average tend to cancel off the closer you go to the centre of a massive ball [for all practical purposes can neglect the GR singularity problem]. So the gravity argument will not explain differential sinking if all the elements were present in current quantities right at the beginning of the process of accretion.

Sorry, physics wise, this makes no sense..can you explain further.. after all if you drop a heavier object in ocean .. it sinks. Period. ..Crust/mantel may be much more viscus but over long time heavier elements will tend to "sink" ... (specially if they were present in current quantities right at the beginning).. By "sink" I mean, the if the matter is heavier than its surrounding it will tend to go towards center of the earth .. .. if all other things were same ...As GP said.. the reason for U, and Th is not gravity alone...

(Hint: Mn, NI, V, Fe ..Pt, Au, Pd etc ... all "sink"...
While U, Th,... Zr, and W .. do not ...)
BTW, W and Au has almost the same density.
.

The earth does not appear to be a homogeneous ball, but as long as it is say a sphere with even concentric spherical shells differing from each other in density etc, a point at the centre has all the gravitational forces due to all point masses within the sphere - canceled. Try out a simple calculation and will see that closer you get towards the centre of a massive ball [below the GR singularity limit] the gravity will go towards zero. However, inhomogeneities, or how the layers formed, pressure at that point within the sphere etc all will have effects. I think in astronomy/astrophysics a similar concept exists for points in space - the Lagrange points?

[GuruPrabhu]

del

[Amber G.]

I was trying to solve AmberG's puzzle on a positive charge sorrounded by 6 other positive charges (from outset looked like a straight forward coloumb's law related problem); so I figured that the charge will be in a state of stable equilibrium until the destabalising force is strong enough to push it outside the imaginary box formed by the 6 point charges.

However in doing so asked myself following questions; please bare with my silly questions :

1. How does the setup behave if one were to somehow simulate this in a lab experiment ? AmberG explained it is possible to replicate this in lab. To substantiate when the destabilizing force (I presume again a negative/positive charge) will be removed will the charge come back to it’s position and stop or it will enter into an oscillation which will decay gradually (due to inertia)?

I first heard the problem from an IIT prof, and the result (I did the calculation and result surprised me a little) is very interesting. In one dimension (that is if the charge in question is restricted to move in x-axis only and there are only two other fixed charges) the equilibrium is stable, and indeed there will be small oscillations around the equilibrium point..)

But in higher dimensions (two or three) ..it is an unstable equilibrium. So the minute disturbance will make the charge go flying..*very* non-trivial question is in which direction? (good exercise, if you want to use your calculus and find (vector) derivative of the gradient of the potential..).. As I said, intuitively it is hard to guess the answer in three dimensions (6 charges).

As Rahul suggested (I did not know of the name of the theorem).. if one looks at it that way one can know that it will not be a stable equilibrium without doing all that math.
(I actually did the calculation, then realized yes.. of course..ityadi and the point of the prof's method)

The calculation is not hard, though a little more complicated (but not much more) than what GP wrote down.. as one has to calculate V(r) where r is a vector displacement...

[Amber G.]

One simple pointer should be that the gravitational forces should on an average tend to cancel off the closer you go to the centre of a massive ball [for all practical purposes can neglect the GR singularity problem]. So the gravity argument will not explain differential sinking if all the elements were present in current quantities right at the beginning of the process of accretion.

Sorry, physics wise, this makes no sense..can you explain further.. after all if you drop a heavier object in ocean .. it sinks. Period. ..Crust/mantel may be much more viscus but over long time heavier elements will tend to "sink" ... (specially if they were present in current quantities right at the beginning).. By "sink" I mean, the if the matter is heavier than its surrounding it will tend to go towards center of the earth .. .. if all other things were same ...As GP said.. the reason for U, and Th is not gravity alone...

(Hint: Mn, NI, V, Fe ..Pt, Au, Pd etc ... all "sink"...
While U, Th,... Zr, and W .. do not ...)
BTW, W and Au has almost the same density.
.

The earth does not appear to be a homogeneous ball, but as long as it is say a sphere with even concentric spherical shells differing from each other in density etc, a point at the centre has all the gravitational forces due to all point masses within the sphere - canceled. Try out a simple calculation and will see that closer you get towards the centre of a massive ball [below the GR singularity limit] the gravity will go towards zero. However, inhomogeneities, or how the layers formed, pressure at that point within the sphere etc all will have effects. I think in astronomy/astrophysics a similar concept exists for points in space - the Lagrange points?

Brihaspatiji - As said before, in the context of which we were talking ..this still makes *no* sense to me. Sure, at the center of the earth gravitational force is zero..but whether you are at the surface of the earth or inside a mine (even many miles deep) gravitational force is towards the center of the earth.. You will fall down.. and metal coin will sink if you put it in a bucket of water.. ityadi.... Can't see much relevance, at least in this context, about Lagrange points or GR singularity...

As for a point inside earth (assuming spherical symmetry)...one may show that all the gravitational force due to OUTSIDE spherical shell (that is all the mass deposit closer to crust/surface) may cancel out.. not due to all the mass which is inside of that spherical shell.
What (if anything) am I missing?

[Amber G.]

GP - Thanks for posts... About the tree, you are, of course, correct. It gives IR (although not as much as us but still some - in IR photographs trees can be seen quite clearly). And yes, if you ever camped outside in open and want to avoid your sleeping bag getting moist in the morning tree's IR can help. (Though there may be some blocking of the view, if you are looking at the stars..)

[Rahul M]

exactly, the problem becomes 'interesting' only when you take it to more than 1 dim. of course, practically there is no way to restrict the test charge along the line joining the other 2 charges.

one simpler way to see this, without going the whole hog to 2D or 3D, is using a similar construct to which GP used. just allow the test charge to move in any direction, as in real life.
move the test charge by a small amount in a direction other than the joining line. for simplicity take the direction to be perpendicular to the joining line (you can always resolve any movement along other directions into one along the joining line and one perpendicular to it. we have already established that movement along joining line gives stable equilibrium.)
pretty easy to see the outcome even intuitively without calculations.

Amber ma'm, about the theorem, it's there in griffiths IIRC.

[Bade]

Griffiths as well as Berkeley Physics course, but need to check. I vaguely remember this being one of the pop quiz questions for 1st sem during UG as part of electrostatics. There were some killer problems and the highest scored was 11/25 in the class.

[Bade]

I suppose that you are talking about US budget for science. Yes, it has shrunk in constant $$ terms. But, at close to a billion $$ per year for HEP alone, it is still by far the largest program in the world. These are not the signs of a "bankrupt" economy as such -- your claims of "no hopes for increasing prosperity" is debatable, but OT here.

In any case, my point was that countries like India and China will bankroll the ILC.

Why would India and China do that unless ILC is located in either of the countries ?

No hopes of increasing prosperity in the short-term is clear, long-term it is someone else's show and why care onlee ?

[Amber G.]

exactly, the problem becomes 'interesting' only when you take it to more than 1 dim. of course, practically there is no way to restrict the test charge along the line joining the other 2 charges.

Rahulji, IMO, actually if one wants to demonstrate experimentally, it is easier to "restrict" the movement in one dimension (just put the charge in a long very thin horizontal tube ) or two dimensional (put it on a -low friction - table)... with gravity and all it is harder (relatively) to do it in three dim... This may be OT for theorists..

one simpler way to see this, without going the whole hog to 2D or 3D, is using a similar construct to which GP used. just allow the test charge to move in any direction, as in real life..

FWIW - The problem, (this approach to actually calculate how the field varies) I saw in a recent graduate level MIT homework problem (as Bade said it is a fairly common pop-quiz type problem) ... sort of becomes a little messy (( here the 'distance' from all the charges is not that simple looking and no easy way to get around it)..the second and third derivatives of V comes out to be zero.. and you have to go up to fourth derivative ..

move the test charge by a small amount in a direction other than the joining line. for simplicity take the direction to be perpendicular to the joining line (you can always resolve any movement along other directions into one along the joining line and one perpendicular to it. we have already established that movement along joining line gives stable equilibrium.)
pretty easy to see the outcome even intuitively without calculations.

Quite likely that I missed the key points.. I will think about it, if you have time perhaps you can expand it ...
My problem, if you are saying what I think you are saying is ... in 3 dim, movement along joining line (of two fixed charges) does NOT give stable equilibrium ( unlike when there are 2 charges only - somewhat counter intuitive).. and the line (x=y=z) does give stable equilibrium...

(If anyone like to check the result, the x-component of the Electric Field comes out something like = kx (x^2-9y^2-9z^2)+ higher order terms ...)
>>>>
I did not know the name of the theorem . .. Thanks.
>>>>

Way I like to explain it (in intuitive sense) as to look at the 'lines of force' (do people remember physics lab when one used small compass to draw magnetic lines of force .. or that used to be in pre-historic times onlee? .

Forget about the middle charge (no middle charge)..just field lines.., now consider a small volume near the center, to be stable equilibrium, look at the surface of this small volume ...all lines of force must be pointing "inwards" (other wise, a charge placed there will flyaway outwards.).. but that's impossible because there is no charge inside that small volume. .. (lines of force converge only at charges..)

[GuruPrabhu]

Why would India and China do that unless ILC is located in either of the countries ?

Two points:

1. Why does India support LHC?
2. What makes you think that ILC will not be located in Tibet?

[GuruPrabhu]

Griffiths as well as Berkeley Physics course, but need to check. I vaguely remember this being one of the pop quiz questions for 1st sem during UG as part of electrostatics. There were some killer problems and the highest scored was 11/25 in the class.

My brain is too rusty for these clever problems etc. I scraped through the exam hurdles in life and I don't look back. Real life is very different and the problem it throws up are challenging in a different way.

I view physics education as accidents of history. Given that my mobile phone has more power than any equation for solving problems without symmetries, what is the point of equations except as a curious educational tool?

For example, you can solve all electrostatic problems via the relaxation technique on a computer in microseconds. Given an arbitrary set of boundary conditions, a software package will be able to infer the potential in an arbitrarily large 3-D space. So, what is the worth of Laplace's equation today? In fact, if Laplace had a computer in his days, would he have bothered with inventing equations?

This is actually a deep question -- is mathematics more fundamental than a tool when it comes to physical reality? I don't know. The example of Dirac's equation is compelling, as are Lorentz transforms. And then there is Shroedinger . Are these accidents or are they telling us something deeper about the mysteries of the universe?

[Rahul M]

Amber ma'm, I said something much simpler, to consider (infinitesimal) movement in the transverse direction too and see what happens. it gives us an indication about why the arrangement is unstable.

GP, IMHO an exact equation reveals much more about the physics of a problem than a brute force solution by computation. the later gives you only the solution.

[GuruPrabhu]

GP, IMHO an exact equation reveals much more about the physics of a problem than a brute force solution by computation. the later gives you only the solution.

An exact equation gives exact results for unphysical problems (e.g., try arranging those 7 charges in this problem on a lab bench).

Brute force gives reasonable answers for realistic problems.

Which is more useful?

[Beyond usefulness, I seriously doubt that there is any place for exact symmetries in the universe today. Most interesting phenomena arise from broken symmetries, which broke as the universe evolved. If symmetry ruled the world, we would not exist. There still a few unbroken symmetries remaining like charge conservation, rotational/translational invariance etc.]

[Amber G.]

I said something much simpler, to consider (infinitesimal) movement in the transverse direction too and see what happens. it gives us an indication about why the arrangement is unstable.
.

Rahulji - I still don't get what is "movement in transverse direction"?.. If there are only two charges, then the line perpendicular could be thought .. and any small movement in that direction would be intuitively unstable. (Indeed in the original problem, I gave that as a hint).. Ditto for 4 charges on the plane (movement perpendicular to that plane). But when there are 8 charges, it is not obvious what is this "transverse direction" ...(Simply because, you can't select any such transverse direction - such that you get further away from all the charges..) ..

[Amber G.]

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..)

[ramana]

Air density changes due to temparture?

[Bade]

Why would India and China do that unless ILC is located in either of the countries ?

Two points:

1. Why does India support LHC?
2. What makes you think that ILC will not be located in Tibet?

1. Indian participation in LHC sustains the minimal activity needed to keep minds busy and talent pool occupied within the field. So it could be a buildup to the next level of projects in HEP. The hardware for LHC built especially by CAT at Indore has other spin-offs for India outside of HEP.

2. I like your idea of the site location for the ILC in Tibet, primarily for the terrain feature.

[Bade]

AmberG, the trivial reason would be more traffic in the evening hours, 5-7 pm as there is always lot of local traffic in addition to regular commuters. It is hard to take this out of the equation for your problem.

But air can be more dispersive in the evening with more pollutants at lower levels of the atmosphere, gaseous and particulates and hence increases refraction of sound waves.

Air temp is always higher later in the afternoon than in the early hours which affects speed of sound but the speed itself should have no bearing on the amplitude as detected by the ears as it is the same energy reaching the detector in the ear.

[negi]

GP ji when Maxwell and Gauss mama formulated their laws they already knew vector calculus; unless there is a more concise and unambigous way to articulate these laws without the associated math; how can one introduce these concepts to a 12th standard student to a level that he be able to apply this to problems ?
Computer simulations while are more effective tools to help one visualise such problems they achieve that 'abstracting' the math (in form of a algo in the simulation programme) from an individual.Point being the guy who writes the simulation prgramme would need to know the relevant math, no ?

[Rahul M]

I said something much simpler, to consider (infinitesimal) movement in the transverse direction too and see what happens. it gives us an indication about why the arrangement is unstable.
.

Rahulji - I still don't get what is "movement in transverse direction"?.. If there are only two charges, then the line perpendicular could be thought .. and any small movement in that direction would be intuitively unstable. (Indeed in the original problem, I gave that as a hint).. Ditto for 4 charges on the plane (movement perpendicular to that plane). But when there are 8 charges, it is not obvious what is this "transverse direction" ...(Simply because, you can't select any such transverse direction - such that you get further away from all the charges..) ..

well, I didn't see the original problem, but guessed what it was from negi's reply.
the word transverse is frequently used in the sense of perpendicular, I don't get why perpendicular is understandable and transverse is confusing.

anyway, we seem to have said similar things without understanding each other.

[Rahul M]

GP, without knowing/understanding the underlying mathematical basis someone armed with a computer would be reduced to tackling each particular problem individually.

[Amber G.]

...the word transverse is frequently used in the sense of perpendicular, I don't get why perpendicular is understandable and transverse is confusing.

Indeed no coufusion between perpendicular and transverse, but my question was how do you get to "perpendicular/transverse" direction when you have eight charges??

[Rahul M]

I think I made it clear I was talking of the 1D case.

[Amber G.]

AmberG, the trivial reason would be more traffic in the evening hours, 5-7 pm as there is always lot of local traffic in addition to regular commuters. It is hard to take this out of the equation for your problem.

Indeed, that's why I asked if others have noticed it? This could also be a good way to teach kids scientific method to do controlled experiment (rule out other causes like more traffic, background local noise etc)..

If you think about it (go back in your memory), (or do the experiment..) mornings are indeed "quieter" (for distant noises). For example, we noticed, when we lived near a beach, surf sounds clearly noticeable ( half a km away) in evening but almost never in the morning.. For , TV reporters covering a war, or people in the war-zone ...you hear more gunfire in the evening..If you live near a train station. train whistles seem to go further in evening than in the morning ... ityadi...

So question is the phenomena real? If so why?

[Amber G.]

I think I made it clear I was talking of the 1D case.

Thanks.

[brihaspati]

Brihaspatiji - As said before, in the context of which we were talking ..this still makes *no* sense to me. Sure, at the center of the earth gravitational force is zero..but whether you are at the surface of the earth or inside a mine (even many miles deep) gravitational force is towards the center of the earth.. You will fall down.. and metal coin will sink if you put it in a bucket of water.. ityadi.... Can't see much relevance, at least in this context, about Lagrange points or GR singularity...

As for a point inside earth (assuming spherical symmetry)...one may show that all the gravitational force due to OUTSIDE spherical shell (that is all the mass deposit closer to crust/surface) may cancel out.. not due to all the mass which is inside of that spherical shell.
What (if anything) am I missing?

(1) we were talking of "heavier elements" necessarily "sinking" towards the centre
(2) I also mentioned before that it would depend on what was the nature of the "fluid" in space within which you initially place the "heavy" element. If earth had already solidified to a certain extent, any accretions coming from outside - like star-burst [novae] would deposit material on the surface and it would tend to sink towards the centre, but as it goes further inside [an approximate smaller spherical shell of diameter less than the outer surface of the semi-molten" earth] the "net" gravity "towards the centre" will become lesser, but pressure of material "above" will increase. This will have other effects, like raising the melting point perhaps but will also tend to stabilize the heavy metal at that mid-way range along the radius but which will appear as having sunk from the surface towards the centre - in a relative sense.
(3) But the situation would be different if the heavy metal was present throughout the "molten fluid" right from the beginning. Even "agglomeration" combined with rotational or angular momentum will tend to have a rather well distributed nuclei of heavy elements through out.

One illustration should be to think of what has happened in our solar system. Our sun still has not gone to the stage where it is generating "heavy" elements. Which means most of the heavy metals we get were gifts from other starbursts. In that original soup, [by the current model of gravitational condensation of "dust" and gases until temperature rises sufficiently to ignite the Hydrogen] by the "move" towards centre argument - we should not have a spontaneously "combusting" ball of lightest elements at the centre! But a solid core of iron/Uranium/gold etc.

Ignore my ref to the GR limit. The spherical schwartzchild solution should give a singularity at a certain radius for all "massive" objects, which for earth will be negligible. The normal physics gets screwed up at that limit so I simply mentioned it in case anyone nitpicked on it.

[SriKumar]

For example, you can solve all electrostatic problems via the relaxation technique on a computer in microseconds. Given an arbitrary set of boundary conditions, a software package will be able to infer the potential in an arbitrarily large 3-D space. So, what is the worth of Laplace's equation today? In fact, if Laplace had a computer in his days, would he have bothered with inventing equations?

Correct me if I am wrong but is it not true that the relaxation technique is a numerical solution for the Laplacian equation? I suspect you are indirectly referring to the solution method rather than a mathematical formulation of the problem. In other words, when you can get a numerical solution with ease, why bother about a close-formed solution. At the end of the day, you still need the Laplacian formulation of the behavior of the physical system (charges, heat eqation) so you can atleast start to get a solution. I agree that numerical solutions are easier on the head than close-formed solutions, and for real-world problems where symmetry does not exist numerical solutions are the only option.
However, i) we need the equation to describe the phenomenon, and ii) with a mathematical statement of the problem you can truly understand the system behavior for simple systems which can serve as a guide in more complex cases (non-symmetry, odd boundary conditions, odd-shaped domains).

This is actually a deep question -- is mathematics more fundamental than a tool when it comes to physical reality? I don't know. The example of Dirac's equation is compelling, as are Lorentz transforms. And then there is Shroedinger . Are these accidents or are they telling us something deeper about the mysteries of the universe?

First thought would be 'is the tool not based on mathematics' but indulge me here. I am not familiar about the subtleties of universe and how well the above equations describe them but I have thought a bit about the topic in general. I think that having an equation that can describe the physical behavior of a system is truly a piece of good luck, especially if the equations are tractable. I dont think a physical system has to perform according to a predictable law, but many (thousands) of systems do (heat conduction, wave propagation, population growth, economy, revenue, etc), and to that extent, we call them predictable and can estimate the result with some accuracy before a test is performed and observations taken. I almost agree with your statement that the equations describing a (any) system is a bit of a 'coincidence', because there are many forms of equations and only one fits (linear, quadratic, etc.) the natural behavior- meaning that the rest do not, by definition. And also, there are many cases that the equation does not fully or completely describe the phenomenon (so what do you do....you add more terms and constants to the original equation and get to publish another paper saying 'we have better predictions now with our sooperior, high-tech, math equation' and apply for more funding and if you are lucky, the eqn. gets named after you ).

Bottomline, I see mathematics i.e. equations, as a script that can define physical behavior (though purists would argue that math does not need the crutch of reality/nature to justify itself). The advantage of this script is that it can be easily manipulated (try differentiating a sentence 'the rate of outflow is directly proportional to the height of the water level) to give us a solution (prediction) of the behavior of the system. Between a numerical and a close-formed solution, close-formed solutions are for simpler cases obviously, but it can be very powerful to help understand new, unfamiliar systems quickly.

[GuruPrabhu]

Wow, a lot of responses to the thread on the role of mathematics. Regarding Laplace equation etc, perhaps I was not clear. In the curriculum today, first the Laplace equation is introduced and then the student spends a lot of time solving simplistic symmetric problems by using all forms of cute tricks of differential equations, e.g., asymptotic Bessel's functions, Legendre Polynomials and what not. It is the latter that I was questioning. IMO, in a 60 minute lecture, one can introduce Laplace's equation *and* give a tutorial on a good software package and be done. The student would understand the "funda" and also have gained the ability to solve problems.

Instead, in a typical curriculum, even a graduate student spends weeks on this stuff and is still clueless when faced with a simple real world problem like how to design an electron gun.

[GuruPrabhu]

I almost agree with your statement that the equations describing a (any) system is a bit of a 'coincidence', because there are many forms of equations and only one fits (linear, quadratic, etc.) the natural behavior- meaning that the rest do not, by definition.

I didn't say anything about a "coincidence". Maybe you misunderstood what I meant by "accident".

My point was to ponder why equations have predictive power, i.e., why can they create new realities. That is why I mentioned Dirac, Shroedinger etc. It is not a simple matter about the "form" of the equation, but the invention of new variables.

[GuruPrabhu]

Indian participation in LHC sustains the minimal activity needed to keep minds busy and talent pool occupied within the field. So it could be a buildup to the next level of projects in HEP. The hardware for LHC built especially by CAT at Indore has other spin-offs for India outside of HEP.

Is there no other way to keep the minds busy? If the "buildup" simply leads to more "mind busy" activity in the west, then what was gained by India?

[Bade]

If the bare minimum in numbers is getting "trained" on the LHC it is still worth time and money spent. If it remains a training activity with little to show in terms of gains for India, naturally the program will be wound down soon. But it has not, so some gains are there as decided by DST/DAE.

Question then is what does India plan to do with expertise gained by LHC participation ? Or is it going to be a limited TIFR group sustenance in HEP activities. Even if it is just the latter then it has limited merit, since we do not plan to scale up efforts in basic sciences in the immediate future.

If there are no proposals from the scientific community in India to build ILC there, then the expectations from such participation are limited.

[rsingh]

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..)

Had such experience. In day time noise is canceled by other noise much closer to you. In evening or early morning not much noise near you. Heavy overloaded truks make "puuuuuuuuuur" noise which can be overheard for kilometers......if surrounding is calm.

BTW one question for gurus..........do the data stored in devices as usb key or cd has weight?

[Bade]

rsingh, you ask questions which are more difficult to give straight answers than AmberG.

The above will require an experiment to see the effects of coupling of the gravitational force (mass) and electromagnetic force. The current textbook understanding of when unification of such forces happen or coupling is comparable enough to have a sizable effect (changed mass/weight as data gets stored on device) is far from achievable as the energy required is large.

[negi]

^ Well won't the answer be 'NO' ? As the USB device when not connected is inherently a 'closed system'. Unless we are talking about inertial mass the weight should not change for a solid state storage media at rest at a given point .

Infact on a CD I would say it's mass should reduce after it gets written as the laser would etch 'pits' on the optical coating to create a series of zeros and ones.