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5

This seems to be called the eternal-time-machine spacetime, and I believe the original paper was Morris 1988, which is available online and not paywalled. On p. 1447, they claim: ...at late times by traversing the wormhole from right mouth to left, one can travel backward in time (i.e., one can traverse a closed timelike curve)... The question says: ...


1

This is exactly the source of energy exploited by the fission of high-mass nuclei (i.e. nuclear power). You start with a heavy nucleus (say $^{235}\mathrm{U}$) and add a neutron. What you get out is two lighter nuclei (often, but not always, krypton-92 and barrium-141) and several neutrons: $$ ^{235}\mathrm{U} + n \to ^{92}\mathrm{Kr} ^{141}\mathrm{Ba} + ...


0

This effect was originally predicted in special relativity, time slows for an object undergoing acceleration compared to the observer, but Einstein's big leap to general relativity was realising that gravity is an acceleration - standing on the surface of the Earth or sitting in a rocket accelerating at 9.8m/s/s are (as far as the time dilation go) the same ...


1

There is a simple thought experiment that you can use to show this. Consider a rocket accelerating in space, and consider a clock at the top of the rocket, and a clock at the bottom of the rocket. If we do this, we'll note that, if the rocket is going away from us, then the clock at the front of the rocket will have sent light to us at a time when the ...


2

It's a fundamental principle of both special and general relativity that the line element, $ds$, given by the metric: $$ ds^2 = g_{\mu\nu} x^\mu x^\nu \tag{1} $$ is an invariant. That is, all observers in any coordinate systems will calculate the same value for $ds$. It's this fundamental symmetry that is responsible for time dilation, along with all the ...


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Yes, because what slows down clocks is acceleration, whether by gravity or by centrifuge, if you like. It doesn't matter how fast the airplane is, but how high it is, because gravity is stronger at lower elevations.


1

What you read is correct. I am not sure if those were the exact words of your teacher but according to the general theory of relativity, sun doesn't "attract" the photon (or any other body for that matter). In fact gravity is not even a real force. Let me briefly state what the theory of relativity has to say about gravity without going into the complicated ...


6

To properly understand what is going on you need to understand general relativity. Massless particles, like photons, travel on null geodesics and mass bends spacetime so the null geodesics are not straight lines. The problem is that neither you nor your teacher understand general relativity so this isn't a very convincing argument. But here is an argument to ...


1

In Feynamn lectures, he shows in a rather straight-forward manner, taking the example of a charge moving parallel to a wire, that a complete electromagnetic description is invariant to the inertial frame of reference, i.e. electricity and magnetism taken together are consistent with Einstein’s relativity. So in cases, such as your example, you must always ...


3

The unified formula used in General Relativity is $$d\tau=\sqrt{\sum_{\mu=0}^3\sum_{\nu=0}^3 g_{\mu\nu}dx^\mu dx^\nu},$$ which by Einstein's notation (summation over doubly repeating indices is implicit) is also written as $$d\tau=\sqrt{g_{\mu\nu}dx^\mu dx^\nu}.$$ Here $d\tau$ is the proper time "felt" or measured by particle moving in the spacetime, for ...


2

The time dilation due to velocity and due to spacetime curvature can't be separated. Both are derived from the metric. There isn't a general formula for this because it depends on the metric in question. For example in my answer to the question A clock in freefall I calculate the time dilation for an observer falling from infinity towards a black hole, but ...


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It's a perfectly valid interpretation. If you have a look at the question How long would it take me to travel to a distant star? you'll find it's quite possible to cover a distance greater than $ct$ in an elapsed time $t$. But this doesn't mean special relativity is wrong - indeed the calculations done in that Q/A were done using special relativity. The ...


0

One can in principle travel a given distance along a ruler in arbitrary short time. The relevant velocity definition is proper velocity: the distance measured by an observer at rest with respect to the ruler, divided by the time passing on the wristwatch of the traveller. Note that proper velocity deploys a mixture of reference frames, whereas ordinary ...


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There is geometrical significance. You are sooo close. You are in Euclidean space, but you should be in hyperbolic space. As @fqq points out, you have stumbled upon rapidity, a parameter in hyperbolic geometry that is the analog of angle in Euclidean geometry. In Euclidean geometry an angle (in radians) is a parameter that measures the Euclidean length ...



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