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Showing content with the highest reputation on 09/28/20 in all areas

  1. 1 point
    Do you mean the observer who is at the same place as the blinking light? Yes indeed, for him the interval is simply whatever he reads on his clock. It would seem to me that Y will be spatially removed, i.e. up in orbit above the tower...? Perhaps I misunderstood. I can't give you a straight answer to this without having done the numbers, since this scenario mixes relative motion with a curved space-time background, so calculating the geometric lengths of their respective world lines isn't trivial. Z isn't a geodesic, because he is launched up, so he undergoes acceleration. Yes, indeed. The maths here aren't overly complicated, but they are definitely tedious. I am not sure I follow you. Are you essentially saying that, if you somehow introduce a gravitational source into a scenario that was hitherto flat spacetime, then the spacetime interval will be affected by this? If so, then you are correct. Both is correct The interval is usually written as a line element, which is an infinitesimally small section of a world line: \[ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}\] This is a local measure, and it is covariant under appropriate changes in coordinate system. The obtain the geometric length of some extended world line C in spacetime, you integrate this: \[\tau =\int _{C} ds=\int _{C}\sqrt{g_{\mu \nu } dx^{\mu } dx^{\nu }}\] This is a standard line integral, and it can be shown that it is also a covariant measure. Hence, all observers agree both on the line element, as well as on the total length of some given world line. There are always infinitely many possible world lines between any two given events, in any spacetime. Generally speaking though, only one of them will be a geodesic (unless the spacetime in question has a non-trivial topology). Yes, it is a function of the metric, see expression above. I think I lost you here, I am not sure what you are meaning to ask...? In SR, there will be one unique geodesic connecting two given events (that's an inertial observer travelling between the events), and then there are infinitely many world lines that are not geodesics (corresponding to observers who perform some form of accelerated motion between the events). Yes. When performing coordinate transformations, the components of a tensor can change, but the relationships between the components do not, meaning the overall tensor remains the same. I see what you are saying, and whether or not this is a mathematically rigorous deduction is a good question. This is probably better posed to a mathematician. I am hesitant to commit myself here, because I can think of other quantities where this is not true - for example, energy-momentum (in curved spacetime) is conserved everywhere locally, but not globally across larger regions. The geometry of spacetime near a binary system is not stationary, and the overall spacetime isn't asymptotically flat either, because of the presence of gravitational radiation. The geometry will be slightly different each time the binary stars complete a revolution. There really isn't any way to define a consistent (!) notion of 'gravitational potential' that all possible observers could agree on.
  2. 1 point
    The element hidden in several of the replies is creativity, or the lack thereof. In my experience, collaborative teams where several members are very creative, especially if they have different skill sets, produce amazing results (because they tend to build on each other's inspirations). But-- one good engineer, if sufficiently creative, can outperform a group that lacks creativity.
  3. 1 point
    I suggest some research, even Wiki, of the Greece-Turkey tensions and conflicts, especially the Cyprus situation. It has briefly turned 'hot' a few times, but it is exactly because both are members of NATO ( Turkey is NOT EU ) that pressure could be brought to bear and hostilities stopped ( but tensions remain ). Similarly if Canada were attacked, the UK is duty bound ( NATO treaty ) to come to our aid, along with the US, France, Germany, Italy, Spain, and the rest of the 30 odd member states, including Poland, Hungry, Greece, Turkey and all of the former Yugoslav states. And no, Hungary was not part of NATO in 56, but of the Warsaw Pact. Australia and New Zealand, on the other hand, belong to SEATO, to which the US and UK were also signatories, but it hasn't been as successful' as NATO; it doesn't have its own headquarters/command and member states like French Indochina and Pakistan have dissolved or left. I would stress that NATO ( and to a much lesser extent SEATO ) is the military alliance since shortly after WW2, while the EU grew out of economic ( strictly ) European alliances that were formed during the 50s, and which C DeGaulle tried desperately to keep the UK out of ( until the 70s IIR ). It is NATO that has contributed to the peace; an attack on any member state is an attack on all of them. You don't think it was the EU that stopped Russian expansion of the Warsaw Pact ( more accurately Warsaw Occupied Possessions ) westward, do you ? The UK, as an independent state, will continue its downward spiral to irrelevance ( along with the other former European Great Powers ) in the face of competition from other resource rich states, like Russia, China, India, Brazil, and the North America block. A United Europe, though, has clout, power, and can't be pushed around by anyone. The UK could have remained a part of SOMETHING, instead you guys voted to become irrelevant, and go begging to others for trade deals. I can't wait until Prometheus has an opportunity to vote on re-joining the EU; hopefully the rest of you come to your senses in sooner than 20 years.
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