gen·e·sis
(j
n
-ss)n. pl. gen·e·ses (-s
z
) 1. The coming into being of something; the origin. Not all of us are really sure what path we are following , but most of us are happy that we are going someway . This can be in case of decisions , interests , selfishness and to some extent whats 'standard'. Consider the same in case of technology . Even speaking 'Technology' doesnt make you feel 'technical' , its like 'Technology' like 'Science' is as broad as the latter. Now being an Engineering Student , I am not sure of my path , but I certainly know that If I do what is told to me ( maybe by the professors , elders and other old people who think they have a bit more grey matter than us....(students)..) .. I would certainly yield a fruitful result , that would give me a comfortable lifestyle , 'standard' lifestyle and a bit more than I require ...
But...its not always that simple , passing out of a good institute with the 'degree' you got through your entrance examination , wont make you an expert in that field , even if you end up doing a PhD. in that field . It doesn't end here , guys like 'Mani Shankar' , a chemical engineer from BITS ending up as a movie producer ...who knew?? ... So you might be one of those who might end in a completely different scenario/field as of now , so whats best is follow the well known "Wait and Watch" strategy..
Last week , I came from Delhi where I went as part of the BITS team for St.Stephen's , Delhi Science Fest . Many of the Science Talks and Summits were really penetrating , going by what one of the Genetics gentleman spoke "A Stephenie who will be giving a noble lecture in some topic he never studied at St.Stephens ....it wasn't even his branch" ... presented in front me a perfect example of a guy who passed out with a degree from one of the best science colleges of the country , started gaining interest in something he didn't even remotely study in his science college.
So...it goes on .. think ... we are all at the mercy of a degree , 'not-so-obedient' puppets in the hands of 'not-so-authoritative' intellectuals ... But it goes without saying that to feel the truth ,
you have to seek inside yourself . So thats what I did ...
I felt a slowly developing interest in basic Sciences while preparing for IIT examination , maybe the company of a roommate (who is now at IITK ) catalyzed it. But it was always an internal interest I never let out in public , because I knew engineering was the way , and above all , I never found handling technical things or dealing with mathematical paradigms difficult, but always a bit more interesting than fundamental Sciences. But then the path I chose , always had two directions , one which I would end up with , and one end which would travel with me . It was difficult but then God has his (with respect to all females..) own ways . I am now pursuing a dual degree , one in basic sciences and one in engineering . Consider it anything you want , but this came naturally somehow from somewhere , uncalled for , unasked for ...just given away..
So , when I went to the Fest at Delhi , I presented a paper on my all time favorite topic of 'Gravitational Wave Theory' (..sorry for the coughs you got..) which I have been studying on my own , even without knowing much about Einstein's GR paper of 1915, I was doing something he presented in his paper . The satisfaction on presenting such a paper was far too enticing , the story doesn't end here , God has flown in for more adventures,more pains and not too forget far more surprises which I will cease to mention over here , but there's a 'sweet' story in the making ...
"This is how things work , each one of us have a "Genesis" of our own "
Interesting indeed. But, I don't find it surprising that there are people who go beyond their "degree". But, I find it confusing that many don't - "we are all at the mercy of a degree " as you say.
ReplyDeleteHaving said that, may I know what did you do in GR ? And what text did you use for your self-study ?
My paper was on studying the 'Sources of Gravitational Wave Theory,along with Detection Techniques" , for this I referred Wikipedia.org , University De Licci,Italy Journal and a General Relativity Library Reference...and some general knowledge too.. :)
ReplyDeleteP.S it would be better if you reply with a name rather than remaining 'anonymous' ... :)
Hmm, couldn't locate the De Licci reference - can you be a bit more specific ? ( can you give me a link, for example ? ) So do I understand correctly, if I say that you did a review on various astrophysical sources of gravitational radiation ?
ReplyDeleteP.S.: The probability that you would know me is almost zero. Hence, I am afraid even my real name might not convey much information. :D
P.P.S. : I'm just a physics student who came across your blog through "the Omniscient" Google. You can address me by my pseudonym "tom".
Well , if you are 'so' interested in the paper reference , I can email you the pdf format of that paper...
ReplyDeleteYes I did a review of the sources , and the 'condition' which is required for any celestial object to emit GW's , also a bit of technologies (upcoming n used) , which have been introduced to detect these GW's..My paper also included some mathematics for the Earth-Sun System GW power commutation using a formula given in the same Italy University Journal..Thought there were several loopholes in my paper as the judges there said...I am still working ...
I generally dump all my knowledge here:
http://kobolit.blogspot.com
..in case you were curious enuf!
P.S Tellin me yr name/location/education wont harm ;)
Ok, sir, I've bowed in to your inquisitiveness. This is my original name :)
ReplyDeleteAs I had already told you, I would be very surprised if you've even heard this name before.
".. I can email you the pdf format of that paper..."
Even an online link would do.But, you can mail me at moc.liamg@mayagan (read it in reverse).
"..the 'condition' which is required for any celestial object to emit GW's"
Hmm, if the gravitational fields are assumed to be small, so that you can linearise Einstein's equations, the the condition for radiation is that the second time derivative of quadrupole moment of a mass distribution should be non-zero. Is this what you are referring to ? Or do you have a more general/specific condition in mind ?
In particular, say you are given the quadrupole moment Q_{ij} of a source defined by
Q_{ij}(t) = ∫ ρ(x,t) [ x_i x_j - 1/3 * δ_{ij} x^2 ]
Where the integral is done over the whole source(ρ is the mass density of the source). Then the Einstein formula for the power emitted by the source is
Power emitted = G/(5c^5) * Σ_{ij} d^3/dt^3[Q_{ij}] * d^3/dt^3[Q_{ij}]
where the symbol Σ_{ij} denotes a sum over i,j=1,2,3 . Is this the formula you were referring to ?
that first 'italics' condition is very right.. I theoretically defined this condition for an object to emit GW :
ReplyDelete"I think changing quadropole moment , can be thought of a change in Inertia , or to say , change in distribution of mass through an imaginary plane , containing the axis of rotation (of the object) as a line in its plane . "
This line summed up quite a lot of mathematics for me..
and for the Power emitted formula , it was of similar form as the one given by you , but it was as a function of a harmonic 'n' , which depends on the elliptic curve of the binary system , n=1 for a perfectly elliptic binary system , which I assumed Earth-SUN SYSTEM TO BE...
so r u a student , where??
ReplyDelete"I think changing quadropole moment , can be thought of a change in Inertia , or to say , change in distribution of mass through an imaginary plane , containing the axis of rotation (of the object) as a line in its plane . "
ReplyDeleteHmm, this is not always necessary - for example consider two equal masses falling towards each other, they will emit gravitational radiation roo.(See below for the calculation, if you're not convinced.)
Now, in this case, what is the axis of rotation ? What is the plane containing that axis and how is the mass distribution changing in that plane ? The "definition" you've given simply doesn't make much sense in this situation !
Calculation of power emitted as Gravitational waves when two masses fall towards each other
ReplyDelete(Skip the following if you understood the argument given above)
Consider two equal masses falling towards each other, as shown below, starting from rest.
m--->---.---<---m
Let r be the distance from the center of mass(which I've denoted by a dot above and I choose it to be the origin). Take the common axis to be z-axis.
Hence the position of two masses are respectively (x,y,z)=(0,0,r) and (0,0,-r)
To the zeroth approximation, Newtonian mechanics tells you that
d^2/dt^2 [r] = - Gm/(2r)^2
(We neglect the effect of gravitational wave on the masses)
Assuming that the masses are small in size, the components of quadrupole moment in this case are
Q_{zz}= m(r*r - 1/3*r^2)+ m((-r)*(-r) - 1/3*r^2)= 4/3*mr^2
Q_{xx}=Q_{yy} = m(0*0 -1/3*r^2)+ m(0*0 -1/3*r^2)= -2/3*mr^2
Q_{xy}=Q_{yx}=Q_{zx} =... = 0
Now to calculate the third time derivative, we first calculate
d^3/dt^3 [r^2]
= 6 d/dt [r] * d^2/dt^2 [r] + 2r * d^3/dt^3 [r] ----- By Chain rule
= - Gm/(2r^2) * (dr/dt) ------ By Newton's Law
Hence, we get
d^3/dt^3 [Q_{zz}]= - 4/3 * m * Gm/(2r^2) * (dr/dt) = - 2/3* Gm^2/r^2 * (dr/dt)
and
d^3/dt^3 [Q_{xx}]= d^3/dt^3 [Q_{yy}] = 2/3 * m * Gm/(2r^2) * (dr/dt) = 1/3* Gm^2/r^2 * (dr/dt)
All the other components are zero.
Substituting this into the Einstein's formula which I quoted in a previous comment, the total power radiated comes out to be
Power emitted = G^3/(15c^5) * m^2/r^4 * (dr/dt)^2
which is terribly small in most cases.But, the point is that it is non-zero.
Now, I don't know whether you've heard it already, but, Mass Quadrupole moment is closely related to the total moment of inertia of a system. In fact, if you think of moment of inertia as a matrix I_{ij}
ReplyDeletethen
Q_{ij} = I_{ij} - 1/3 * δ_{ij} Trace[ I ]
Trace[ ] denotes sum of the diagonal elements.
So, Mass quadrupole moment is just Moment of Inertia with its trace removed . That is, you take the moment of inertia matrix and subtract a specific constant from each of its diagonal elements so that the sum of diagonal elements in the new matrix is zero.
"and for the Power emitted formula , it was of similar form as the one given by you , but it was as a function of a harmonic 'n' , which depends on the elliptic curve of the binary system , n=1 for a perfectly elliptic binary system , which I assumed Earth-SUN SYSTEM TO BE..."
Hmm, different harmonics are just different frequencies (which occur
when you fourier-transform Q_{ij} (t) ). And I don't think it has anything to do with Elliptic curves, Ellipses may be. :D
And, to answer your last question, I am a graduate student at TIFR. Now, it's my turn to ask - What about you ? What is the basic science+Engineering degree that you 're doing at BITS ?
I am doing B.E(Hons) Electronics and Instrumentations wuth MSc(Hons).Physics , 5 yr dual degree , I am in my second year now :)
ReplyDeleteCorrection there , not elliptic curves but ellipses , elliptic curves
ReplyDeleteare the 3 degree curves(homogeneous??) , as compared to the simple 2D Euclidean Gemoetry we deal with..I meant simple Ellipses..