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(There's a couple of these questions kicking around, but I didn't see anyone give the "two boosted copies" answer. Generically, I'd say that's the right answer, since it gives an actual causality violation.) In your scenario, the two planets remain a hundred thousand light years apart. The fact is, you won't get any actual causality violations with FTL that ...

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Calculating the power emitted as gravitational waves is relatively straightforward, and you'll find it described in any advanced work on GR. I found a nice description in Gravitational Waves: Sources, Detectors and Searches. To summarise an awful lot of algebra, the power emitted as gravitational waves by a rotating object is approximately: $$P = \frac{32}{... 19 It is true that general time-travelling violates conservation of energy. If you transport yourself into yesterday, you appear twice in the universe for that day, which means twice your rest energy, which is a lot of energy. It may mean that time-travelling is inconsistent and therefore impossible. But not necessarily. In general relativity, it is very hard ... 19 Gödel's rotating universe solution does allow for time travel (closed timelike curves), but it has nothing to do with wormholes--in such a universe one could travel into one's own past just by taking a rocket on a long-term looping path through space, from any starting location. This page discussing Gödel's solution includes a spacetime diagram showing how ... 15 Conservation of energy/mass is the result of a symmetry called time shift symmetry, and if this symmetry is broken energy/mass will no longer be conserved. It is far from obvious that time shift symmetry would be preserved if closed timelike curves were possible, so you can't use conservation of energy as an argument that time travel is impossible. 14 Time travel is difficult to prove or reject, even by using a formula (at this time there is no decisive proof for or against it). There are solutions of Einstein's equations which allow closed timelike curves, like Gödel's universe, Kerr black holes, wormholes, etc. As mentioned in other answers, chronology protection conjecture, grandfather paradox and ... 14 No, because Hubble expansion has negligible effects on very small systems (such as human beings). Here is an answer which explains the maths behind it : Can the Hubble constant be measured locally?? 13 Shortly, no, this is not correct. Here's why. Hubble's law gives us that for a distance of one megaparsec, that space expands by approximately 70 km/s (the data varies, but it's somewhere between 60-80 km/s - it doesn't matter, and you'll see why). Now, how tall is your average human? Let's be generous and say your time traveler is 2m tall. Now, how many ... 12 The problem is that if you had two such wormholes, you could still end up in your own past light cone. For example: suppose I took a wormhole trip to Alpha Centauri, leaving in the year 2050 and arriving in 2049 (according to some fixed inertial reference frame). Since Alpha Centauri is 4 light years away, this doesn't take me into my past light cone. But ... 12 A short answer to your question is yes. If you were to hover a short distance above the event horizon for short time, a very long time would pass for asymptotically flat observers. Let's do some calculations! If you were to hover say distance h\ll r_s above the event horizon, then the time dilation factor \gamma that you would feel would be of the form ... 11 No, conservation of energy is for the entire system. If you can travel from time A to time B then both time A and B are parts of the same system as far as conservation of energy is concerned. Even if you assumed that despite travel being possible the times were separated, time travel would simply require the transfer of equal energy from in the reverse ... 10 Consider that most elevators have a counterweight to store energy. The counterweight isn't perfect, but it reduces the overall energy needed to move the carriage. As the elevator moves up, the counterweight moves equally down. Likewise, a time machine would have to overcome the energy deficit/surplus caused when moving from one point to another, but it ... 9 I think it's worth expanding a bit on Hal's answer to try and make it a bit less technical. We denote a point in spacetime as (t, x, y, z) i.e. both the position x, y, z and the time t. In the absence of time machines we can only pass through a spacetime point once. Of course you can go back to the point in space x, y, z but only at a later time so ... 9 To know what a closed timelike curve looks like, you just do like every spacetime metric. You compute geodesics and field equations and all of that. Unfortunately, things start getting complicated. Closed timelike curves have a lot of weird behaviours, especially when it comes to matter fields upon them. They may not have a properly defined Cauchy problem, ... 8 I'm unsure if you're specifically asking about the Gödel spacetime or if your question is a more general one of whether time travel can exist. So let me try to give a general answer that addresses both. Einstein's equation tells us how the geometry of spacetime is related to the distribution of matter and energy. Leaving aside the vexed issue of quantum ... 8 There will be spoilers if you keep reading Firstly, he is shown surviving inside black holes. From where did he got oxygen? Perhaps from oxygen bottles. But, in an intense gravitational pull, how he survives? He would have got torn apart! am I right? The popular press says the word black hole and it is a bit vague what they mean because there are some ... 7 Well, the most trivial one is "Where the hell are all the time travellers from the future today?" 7 One additional nice feature to consider in rejecting time travel is global entropy of the universe. As far as it is known today, in the past universe had lower entropy and it is impossible to reduce the entropy of the system without dumping the "excess entropy" (plus, whatever additional entropy created in the process) elsewhere. The same consideration ... 7 If you define "now" to be all those points in space and time that have hypothetical, pre-synchronized, stationary clocks that read the same time as your clock, then there "currently" exists a hypothetical observer somewhere, who is moving relative to us, for whom "now" includes Earth, circa 1900. But these notions of "now" are different for the two ... 7 If you have a look at my question Does someone falling into a black hole see the end of the universe? the answers demonstrate that an observer falling into a black hole doesn't see into the arbitrarily distant future. This question assumed a freely falling observer, but even if you have a rocket motor to hand it doesn't make much difference. Once inside the ... 7 The closest thing in mainstream theoretical physics is "closed timelike curves", paths along which you can travel and thereby return to the same place and time as you started, provided your velocity varies as the path requires. (Shortcuts through spacetime called Einstein-Rosen bridges or "wormholes" can be a part of the setup.) Whether such paths exist ... 7 When using formulas in physics it is important to keep in mind the assumptions that the formula is based on. In this case T_0 is the time on a clock in its rest frame. It is doubtful that tachyons exist, but if they do then they are not at rest in any inertial frame, so the time dilation formula simply does not apply. However, the Lorentz transform does ... 6 To change the past you require a closed timelike curve. Stephen Hawking proved that closed timelike curves cannot be created in a finite system without using exotic matter. I think the proof was in his paper on the Chronology Protection Conjecture but I don't have access to the paper at the moment. This far we have a reliable grasp on whether causality can ... 6 You and your friends line up. You sit down, you spend some time synchronizing your watches. And you make a plan. You measure that you are all a meter apart. And you have 299,792,458 friends. You plan out how to do a wave. You plan it so when you stand up the person next to you stands up a little later and the person next to them a little later and so on ... 6 This is a good question and more philosophical in nature: Philosophy SE may be a better home for this question (there are indeed solid and knowledgeable physicist who loiter at that site). Essentially you are talking about the Eternalist or Perdurist conception of time - if you've not heard these terms before they may give you some terms to search by. Famous ... 6 For a spherically symmetric object the relative rate that time flows is given by:$$ \frac{d\tau}{dt} = \sqrt{1 - \frac{GM}{c^2r}}  where $G$ is Newton's constant, $M$ is the mass of the object (the Sun in this case), $r$ is the distance from the object and $c$ is the speed of light. The mass of the Sun is $1.989 \times 10^{30}$ kg and the radius of the ...

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As a general rule, the second law is used to rule out physical theories; if your physical theory allows you to circumvent the second law then the problem is with your theory, not the second law. This is summed up in a famous quote by Sir Arthur Stanley Eddington: The law that entropy always increases holds, I think, the supreme position among the laws of ...

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