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  1. mitochan

    I A problem with the solution to the ladder paradox

    May I interpret you as one of the sketches attached ? The string will not be broken when the doors move in a synchronized way, i.e. the two door operators do the same procedure watching their clocks one at the front wall and the other on the back wall of the barn. Of course the two clocks...
  2. mitochan

    I The Universe filled with a "homogeneous perfect fluid"

    You may be able to regard matter and radiation fill the universe though they are not homogeneous. For an example the space is filled with cosmic background photons. quantum field of particles extends to all the universe.
  3. mitochan

    Integral of 1 / (x^2 + 2) dx ?

    Then \int \frac{dx}{x^2+2}= \frac{1}{\sqrt{2}}\int\frac{d\frac{x}{\sqrt{2}}}{(\frac{x}{\sqrt{2}})^2+1}=...
  4. mitochan

    Integral of 1 / (x^2 + 2) dx ?

    Please take a look at attached calculation.
  5. mitochan

    I Black hole inside of a black hole... can it be done?

    The primitive deduction, A BH as well as an ordinary body has a timelike line in our spacetime. The center of BH has its timelike line also. The singularity of BH lies in its center. Thus singularity of BH is on a timelike line would have one or more errors that I cannot point them out clearly.
  6. mitochan

    I Black hole inside of a black hole... can it be done?

    I draw a sketch for better understanding at attached.
  7. mitochan

    Determining if series converges or diverges

    An orthodox way is to investigate |\frac{a_{n+1}}{a_n}| is greater or less than 1.
  8. mitochan

    Integral of 1 / (x^2 + 2) dx ?

    If you can integrate \int \frac{1}{x^2+1} dx you are not far from the answer.
  9. mitochan

    I Black hole inside of a black hole... can it be done?

    When two blackholes collide to one, in some time in a merging process are there two singular points within a merged blackhole? PS In time reverse one black hole spit into two blackholes. It seems prohibited so such a BH merging should be an irreversible process.
  10. mitochan

    B Photon in a box

    Say the box has side lengths a,b and c. QM says energy states of photon are E_{mnl}=\frac{\hbar^2}{4}\{\frac{m^2}{a^2}+\frac{n^2}{b^2} +\frac{l^2}{c^2}\} This holds for adiabatic change of a,b and c. Whether the box undertakes change of perimeters depends on the conditions of box we set. In...
  11. mitochan

    I If gravity is not a force, what is holding us down?

    Say a ball falls and bounce back from the floor to make a reverse motion. Falling ball is along a geodesic and the going up ball is along another geodesic because momentum is given from the floor and free motion is interrupted then. This shows that reverse motion is not going backward along...
  12. mitochan

    I If gravity is not a force, what is holding us down?

    Not one way, reverse process is possible. Say you throw a ball upward, it goes slower, stops at the top, goes down faster and comes back to your hand. All through the trajectory is geodesic and called free fall even when it is going upward, or called, more properly I think, in free motion.
  13. mitochan

    I If energy is relative, is the rest mass also relative?

    Because we have convention that mass is energy measured in a special frame of reference called COM frame of reference.
  14. mitochan

    B Energy-mass equivalence

    Mass is defined as energy measured in COM frame of reference where total momentum is zero. If such COM system does not exist, there is no defined mass but energy, e.g. a photon. An electron and a positron pair, we may say they are matter, is generated from two photons. These photons have...
  15. mitochan

    Which lamp is dimmed in the circuit?

    Kirchhoff's law does not care they are series, parallel or neither. That is the reason why it is used.
  16. mitochan

    Which lamp is dimmed in the circuit?

    Say ##I_A## is current through A I_A=I_D I_B+I_O=I_A+I_C where ##I_O## is current through wire parallel to B with no lamp. I_O >> I_B because of scarce resistance of wire.
  17. mitochan

    Magnet repulsive force -- how long does it last?

    Statistical mechanics say it is the factor of e^{\frac{-E_g}{k_BT}} where E_g is an energy gap to overcome potential peaks to other states.
  18. mitochan

    Magnet repulsive force -- how long does it last?

    The law of entropy increase in statisc or thermal mechanics would work here. The ordered spins of molecules tend to be randomized which leads zero magnetic field. The ordered motion of charges e.g. electric currents in wire would be dissipated which also leads to zero magnetic field.
  19. mitochan

    I Length contraction and time dilation

    Not for answering your question but for showing extraordinary of relativity, say you switch on flashlight. Light goes everywhere to make a sphere light sphere expanding with speed constant c. You observe it sphere. Your brother driving a car also observe it a sphere shape. How is it...
  20. mitochan

    I Length contraction and time dilation

    Hello. As you deduce no shrink takes place on the arms of interferometer that stays still in our IFR. Lorentz hypothesized that light speed along the arm change in go and return. In order to meet his hypothesis and the result of no interferometry he has to conclude that the arm shrinks. But...
  21. mitochan

    I Length contraction and time dilation

    World interval is invariant under transformation between IFRs, i.e. s^2=c^2t^2-x^2-y^2-z^2=c^2t'^2-x'^2-y'^2-z'^2 You can deduce some results from it.
  22. mitochan

    A Calculate the distribution of energies from momenta

    By author's definition \int \int p(E_j,E_k)\delta(E-E_j-E_k)dE_jdE_k = \int p(E_j,E-E_j)dE_j=1 By your defnition \int \int p(E_j,E_k)dE_jdE_k = \int \frac{Numerator(E_j,E-E_j)}{Denominator}dE_j=1 So it depends on how the normalization is defined.
  23. mitochan

    A Calculate the distribution of energies from momenta

    Your last formula with the relation E=E_j+E_k says LHS: spherical shell in 3N dimension p-space RHS: spherical shell in 3N_j dimension * spherical shell in N_k dimension, p-spaces RHS is cut of sherical shell in two sub spaces. so RHS should be integrated to be right one wrt LHS as...
  24. mitochan

    Bar magnet made from smaller opposing bar magnets

    If magnets gather in a place with same NS direction, their magnetic flux enhances to produce larger magnet. If magnets gather in a place with random NS direction, their magnetic flux kill each other to show zero magnetic field in total.
  25. mitochan

    Molecular size surprise

    You teach me that CO2 molecule is made of three atoms and smaller in size than O2 which is made of two O atoms with no C. Interesting!
  26. mitochan

    Waves -- How does increasing tension affect frequency and period?

    If you pull gut of violin or guitar tighter so with higher tension the scratch sound gets higher pitch so higher frequency. Period T is inverse of its frequency f, T=1/f.
  27. mitochan

    Trying to understand electric and magnetic fields as 4-vectors

    \vE¯∥=\vE∥,\vE¯⊥=γ(\vE⊥+\vv×\vB⊥)I am sorry to say my post #1 was wrong. Electric fields and magnetic fields from electromagnetic tensor comes from E_{i}=cF_{0i},\ B_i=-\frac{1}{2}\epsilon_{ijk}F^{jk} I wonder whether it is same as your formula in post #1 and what are ##E^0## and ##B^0##?
  28. mitochan

    Trying to understand electric and magnetic fields as 4-vectors

    The formula without ##\gamma^2## terms seem correct Lorentz transformation. How do you estimate these terms necessary ?
  29. mitochan

    Stability of a Driven Pendulum

    Is there any condition on ##T_d##? Say ##T_d=\infty## the inverted pendulum is unstable.
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