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location Kolkata,India[91-33-25514464]
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visits member for 3 years, 1 month
seen Mar 27 '13 at 12:06

Author/Teacher from India. Interested in General Relativity and other areas of physics


Sep
21
comment Newton's Law of Gravitation, Gauss Law and GR
(in continuation)The speed of light is independent of its source. The idea of speed in the said formulation is different from the spatial part of four velocity ie from proper speed (or celerity).Proper speed can exceed the speed of light without hurting or violating relativity. But the three velocity concept plays an important role in the construction of relativity itself though it is not of a covariant form
Sep
21
comment Newton's Law of Gravitation, Gauss Law and GR
Well,the four acceleration of a test particle following a geodesic is zero[all components are zero].This is in conformity with the fact that gravity is not a force.But this four acceleration is different from the acceleration we perceive in the physical world,for example the acceleration of an apple falling from a tree.The non covariant form of acceleration is important for understanding physics.But the covariant form has a different type of elegance in so far as the transformation rules are concerned.An interesting analogy would be the concept of the classical three velocity
Sep
7
comment Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
$\frac{\partial E}{\partial t}=\frac{\partial E}{\partial \psi}\frac{\partial \psi}{\partial t}$Or,$\frac{\partial^2 E}{\partial t^2}=\frac{\partial^2 E}{\partial \psi^2}(\frac{\partial \psi}{\partial t})^2+\frac{\partial E}{\partial \psi}\frac{\partial^2 \psi}{\partial t^2}$Similarly:$\frac{\partial^2 E}{\partial x^2}=\frac{\partial^2 E}{\partial \psi^2}(\frac{\partial \psi}{\partial x})^2+\frac{\partial E}{\partial \psi}\frac{\partial^2 \psi}{\partial x^2}$ We finally have$\frac{\partial^2 E}{\partial t^2}-\frac{\partial^2 E}{\partial x^2}=0$ for points where mass=0.
Sep
7
revised Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
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Sep
7
comment Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
As the $\psi$ wave passes through a point the values of energy and momentum(determining the spacetime curvature) can change in a specific manner as given by PDE(2) if we are to stay on the "coordinate shell"
Sep
7
revised Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
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Sep
7
revised Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
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Sep
7
comment Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
I have used the term analogue/counterpart in the sense that the variables get interchanged,for example E<-->t;p(x)<---->x etc. We get the wave equation[speed=c=1] with the variables interchanged.
Sep
7
asked Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
Sep
1
awarded  Enthusiast
Aug
27
revised On the Discretization of Energy Levels
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Aug
27
revised On the Discretization of Energy Levels
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Aug
26
comment On the Discretization of Energy Levels
We may write directly,$F(E,P)=\int_{\infty}^{-\infty}\int_{\infty}^{-\infty}f(x,t)e^{ia(Et-px‌​)}dxdt$ and use the facts $\frac{\partial F}{\partial x}=0$ and $\frac{\partial F}{\partial x}=0$ to arrive the results in the previous comments.
Aug
26
comment On the Discretization of Energy Levels
Regarding Relation B in the scond last comment:(1) It satisfies the Klein Gordon Relation. (2)For the invariance of the exponential part the Lorentz transformations are a suitable candidate provided "a" is a universal constant.(3)Energy and momentum are suitable choices for E and p if Et and px are dimensionally identical.(4)The psi indicated by relation (B)is periodic nature associated with a probability picture.
Aug
26
comment On the Discretization of Energy Levels
Relation (A) becomes the Fourier transform when both x and t tend to infinity.Using (B) in (A) and allowing x and t to tend to $\infty$,we obtain:$F(E,p)=Const\times \delta(E-E_0)\delta(p-p_0)$ Integration of the last formula on the (E,p) domain counts the number of (E0,p0) modes present.If we divide this by the total number of possible modes we obtain a probability picture
Aug
26
comment On the Discretization of Energy Levels
$F(E,p,x,t)=\int_{-\infty}^{x}\int_{-\infty}^{t}f(x,t)e^{ia(Et-px)}dxdt$----(A).‌​$\frac{\partial F}{\partial x}=\int_{-\infty}^{x}\int_{-\infty}^{t}(\frac{\partial f}{\partial x}-ipxf)e^{ia(Et-px)}$ Again $\frac{\partial F}{\partial x}=\int_{-\infty}^{x}\int_{-\infty}^{t}(\frac{\partial f}{\partial t}-iEf)e^{ia(Et-px)}$. If $\frac{\partial F}{\partial x}=0$ favors $\frac{\partial f}{\partial x}-iap=0$ =>$(x,t)=Ae^{iapx}$. Again, $\frac{\partial F}{\partial x}=0$ should favor $f(x,t)=Be^{-iaEt}$. Finally we obtain $f(x,t)=Ae^{-ia(Et-px)}$--(B)which is a solution of the Klien Gordon equation.
Aug
25
comment On the Discretization of Energy Levels
A Relevant Paper:independent.academia.edu/AnamitraPalit/Papers/1889577/…
Aug
22
revised On the Discretization of Energy Levels
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Aug
21
comment Pseudo-Superluminal Motion and the Synchronization of Clocks
@RonMiamon:Observers at A and B agree that the speed of light locally is "c" : that is OK. But if you think of a light ray passing over a finite distance from A to B the average speed of light measured by the observer at A (or at B) = distance of separation(physical)/Time measured by his own clock. And this value may be different from "c"
Aug
21
accepted Pseudo-Superluminal Motion and the Synchronization of Clocks