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AccidentalFourierTransform
AccidentalFourierTransform
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Refer, "The classical theory of Fields" by Landau lifshitzLandau&Lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of light). Since velocity is perpendicular to radius vector, Radius does not change according to the observer at rest. But the length vector at boundary of disk, parallel to velocity vector will experience length contraction . Thus, $\dfrac{radius}{circumference}>\dfrac{1}{2\pi}$$\dfrac{\text{radius}}{\text{circumference}}>\dfrac{1}{2\pi}$ , when disc is rotating. But this violates rules of Euclidean geometry.

What is wrong here?

Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of light). Since velocity is perpendicular to radius vector, Radius does not change according to the observer at rest. But the length vector at boundary of disk, parallel to velocity vector will experience length contraction . Thus, $\dfrac{radius}{circumference}>\dfrac{1}{2\pi}$ , when disc is rotating. But this violates rules of Euclidean geometry.

What is wrong here?

Refer, "The classical theory of Fields" by Landau&Lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of light). Since velocity is perpendicular to radius vector, Radius does not change according to the observer at rest. But the length vector at boundary of disk, parallel to velocity vector will experience length contraction . Thus, $\dfrac{\text{radius}}{\text{circumference}}>\dfrac{1}{2\pi}$ , when disc is rotating. But this violates rules of Euclidean geometry.

What is wrong here?

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seeking_infinity
seeking_infinity
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Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of light). Since velocity is perpendicular to radius vector, Radius does not change according to the observer at rest. But the length vector at boundary of disk, parallel to velocity vector will experience length contraction . Thus, $\dfrac{radius}{circumference}>\dfrac{1}{2\pi}$ , when disc is rotating. But this violates rules of Euclidean geometry.

What is wrong here?

Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of light). Since velocity is perpendicular to radius vector, Radius does not change according to the observer at rest. But the length vector at boundary of disk, parallel to velocity vector will experience length contraction . Thus, $\dfrac{radius}{circumference}>\dfrac{1}{2\pi}$ , when disc is rotating. But this violates rules of geometry.

What is wrong here?

Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of light). Since velocity is perpendicular to radius vector, Radius does not change according to the observer at rest. But the length vector at boundary of disk, parallel to velocity vector will experience length contraction . Thus, $\dfrac{radius}{circumference}>\dfrac{1}{2\pi}$ , when disc is rotating. But this violates rules of Euclidean geometry.

What is wrong here?

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seeking_infinity
seeking_infinity
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Euclidean geometry in non-inertial frame

Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of light). Since velocity is perpendicular to radius vector, Radius does not change according to the observer at rest. But the length vector at boundary of disk, parallel to velocity vector will experience length contraction . Thus, $\dfrac{radius}{circumference}>\dfrac{1}{2\pi}$ , when disc is rotating. But this violates rules of geometry.

What is wrong here?