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The color of the photon is related to its frequency $f$, which can be related to the energy of the photon by the expression $E = hf$, where $h$ is Planck's constant. Thus the different colors of the emitted photons describes their different energies. The next step is to determine why specific elements emit certain colors. This has to do with the different ...

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On page 68 the paragraph headed Calculating displacement given a time and acceleration includes the text: Assume that you’re on your traditional weekend physics data-gathering expedition. Walking around with your clipboard and white lab coat, you happen upon a football game. Very interesting, you think. In a certain situation, you observe that the ...

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The redshift of very distant galaxies is mainly due to the expansion of space whilst the light has been travelling towards us. The basic relationship (at non-relativistic speeds) is that $v = H_0 d$ where $v$ is the velocity implied by the redshift and $d$ is the distance. The constant of proportionality $H_{0} \sim 70$ km/s per Mpc. That is, a Galaxy ...

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Doppler shift distance measurements are only useful if the expansion velocity is much greater than the peculiar velocity of the galaxy, so that the latter can be neglected. As the expansion velocity is proportional to distance, we can only use Doppler shift if the measured redshift is high, that is, the galaxy is very far (as an estimate, I've seen $D\ge ... 0 What you are missing is that the size and the distance between two objects perceived by human eye turns out to be false due phenomena of diffraction at very large distances.You see, the limit of resolution of human eye is small. To know what I mean, consider 2 points of paper very close to each other. Move your head away from paper until what you see is ... 1 If I'm understanding the question properly, the actual distance (represented in the diagram by$D$), is very different to the distance that we roughly 'see' with our eyes (represented by$E$). In general, the 'actual' distance will be much greater than the 'apparent' naive distance. There are, of course, much larger problems with trying to use your method ... 3 In an expanding universe, the farther away an object is, the faster is it's recessional velocity relative to an other object at distance$r$: $$v_{rec}=H(t) \cdot r$$ with$H(t)$as the current Hubble parameter. On the other hand, for every given distance there is also an escape velocity $$v_{esc}=\sqrt{\frac{2\cdot G\cdot M}{r}}$$ If you want your 2 ... 0 Well, in your very ideal system and from the classical point of view, yes the dices (considering they as an electromagnetic neutral system) will be in touch at some time independent of where are they at the beginning. 3 I read a few lines about general relativity and [... an equation for] the eigentime of a time-like curve. I suppose that this is referring to an equation similar to $$\tau A_J^Q := \int_0^1~dt~\sqrt{g[~\dot\gamma, \dot\gamma~]},$$ where$A$denotes a particular participant ("material point", "principal identifiable individual"), the quantity being ... 1 Exactly as an ideal clock at rest with the observer (here pictured as a timelike curve) measures the proper time of the observer, ideal rulers at rest with the observer measure the distances in the rest space of the observer. Mathematically these rulers are pictured as an orthonormal basis made of$3$vectors normal to the unit tangent vector to the ... 0 In GR the notions of space and time are no longer different, they are combined into spacetime. Points in spacetime are labelled by coordinates, which can be arbitrarily chosen, and can in the special case of Minkowski space be the familiar x, y, z and t. The only physically meaningful quantity however is the line element:$\$ds^2 = g_{\mu \nu} dx^\mu ...

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The proper time of a time-like curve is its length.

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