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Markus Hanke

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Everything posted by Markus Hanke

  1. Photons always propagate at c locally, so do not experience proper acceleration anywhere, and hence they satisfy the geodesic equation - pretty much by definition. They cannot in fact do anything else, as they wouldn‘t be photons otherwise.
  2. SR is model of Minkowski spacetime, i.e. of the relationships between events in the absence of gravitational sources. It is a special case of General Relativity, for cases where gravitational effects are negligible. The specific form that Maxwell’s equations take is a consequence of relativity, not its cause.
  3. SR is a model of Minkowski spacetime, i.e. an empty vacuum spacetime devoid of gravitational sources, including electromagnetic fields. It is thus not an “offshoot” of EM. One can use Minkowski spacetime as a background for field theories, so long as the gravitational effect of those fields is negligible - this leads you to quantum field theory and the Standard Model. This framework is perfectly well capable of describing particles and forces that do not carry electric charge, and are not of EM origin. This is not a valid line element, because it isn’t an invariant.
  4. ! Moderator Note I think this topic is better suited to the Speculations section of the forum - thread moved. While there are a lot of similarities (but also lots of differences) between gravity and EM in the Newtonian domain, you need to remember that Newtonian gravity is only an approximation in the low velocity, weak field regime. The full model of gravity - General Relativity - is quite unlike Maxwell’s electromagnetism, so you cannot really compare them in this manner.
  5. Quarks have the same status within the Standard Model as all the other fundamental building blocks - whether you detect them with particle-like properties or with wave-like properties depends solely on your experimental setup. This is not an ontological question (the nature of the entity is either one or the other, or both, or neither), but an epistemological one - what can the experimenter know about the system in question? What information about the system is made available through a specific, given setup? So essentially, whether something appears as a wave or a particle is more an expression of the relationship between the quantum system and the observer, than it is a statement of the nature of the entity itself. This is true for all of the particles within the Standard Model.
  6. The reasons are of a mathematical nature. When you formulate the theory, there are two basic requirements that need to be fulfilled - it needs to be internally consistent, and it needs to describe the correct particles (with correct properties etc) which we empirically find the in the real world. It turns out that these requirements are fulfilled only if there are more than 4 spacetime dimensions, otherwise the model doesn’t work.
  7. QFT can be generalised to curved space-time backgrounds, so we do know quite a bit about this. Did you consider the fact that the dynamics of gravity are highly non-linear? Gravitational fluctuations do not superimpose linearly, as (e.g.) EM waves would.
  8. Yes, you could run the maths on it, though potentially this isn’t a straightforward calculation (especially in the case of the Alcubierre metric). My understanding (though I’m no expert on this particular solution) is that there is no horizon, but a narrow region of extreme tidal gravity. The two regions remain causally connected though. Again, I don’t know the answers to this straight off the bat, but of course one could sit down and do the actual maths (definitely not a trivial calculation!). The relationship between clocks here would be well defined, and can be calculated. My intuition is that causality would remain preserved in all cases that are actually physically realisable (and there is a big question mark in that regard, so far as the Alcubierre solution is concerned). Wormholes connect potentially distant regions in spacetime, so in principle they span intervals of both space and time. In principle, yes. “Now” is always a local notion - it would be very difficult, perhaps meaningless, to try and define a notion of simultaneity in a spacetime with a topology that is multiply connected. This is a very complex question, not just because this spacetime is multiply connected, but also because the existence of a wormhole does not necessarily imply causal connections (i.e. information may not be able to propagate through that wormhole, depending on its exact geometry). Interesting question though!
  9. It’s similar to a wormhole in the effect it has - i.e. providing a “shortcut” between widely separated regions -, but the geometry of spacetime is quite different. No exotic matter or any other special constructs are needed to create a stable, traversable Krasnikov tube; just lots of energy in the right configuration.
  10. That’s true, though technically speaking - and I know I’m nitpicking here - they are not a means of FTL travel, since everything happens at subluminal speeds. On a purely practical level, my main issue with wormholes would be not so much their stability, but the fact that - at the time of their creation - there is no way whatsoever to control where/when the other end of the passage will form, not even in principle. This makes them rather useless for practical purposes. Still, if for the sake of argument it could be made to work somehow, the possibilities would be fascinating - The sci-fi author Dan Simmons has explored this concept in his Hyperion Cantos, with his “farcaster” device. A very interesting read, so far as sci-fi goes. I would like to briefly mention another - lesser known - topological construct, which could in principle be created in the real world, given enough energy: the Krasnikov Tube. It’s a permanent, stable distortion of spacetime that can be left behind in the wake of a correctly configured spacecraft moving at close to the speed of light. Any subsequent craft travelling that same route will find its trajectory shortened, much like in a wormhole, but without the need for exotic energy. This is theoretically feasible, and avoids all the issues of warp travel and wormholes, but does require a lot of energy to put into practice, at least for the first journey when the tube is created.
  11. I agree, though I have never studied it in any great detail.
  12. Personally I think there is a great mathematical beauty in String Theory, and a number of important advances in both mathematics and theoretical physics have emerged from the study of this model. However, “it’s beautiful” is not a scientific argument, and no indicator as to its value as a valid model of quantum gravity. One of the main problems I see right now is this - String Theory doesn’t actually produce GR in the classical limit, it produces GR plus a large number of scalar fields. There is no evidence for any of these scalar particles in the real world, nor is there any known way to mathematically remove them from the theory. This is an awkward problem, and I don’t see it being discussed very often in the ST community. Furthermore, we don’t actually know whether or not ST is even capable of reproducing all the particles of the Standard Model (plus their interactions and symmetries) in a self-consistent manner. My take on this is - String Theory certainly warrants further research, but it is at best unclear whether or not it can produce a workable model of quantum gravity. There are a lot of fundamental problems associated with this model, which would need addressing.
  13. I do not see how a hexaquark - or any multi-quark system for that matter - would fail to electromagnetically interact with its surroundings (i.e. absorb/emit light), which is a basic property of DM.
  14. I think it is fair to say that FTL travel is a concept that will always be of interest to us as a species. Nonetheless, there are good reasons to conjecture (based on currently known physics) that FTL travel is not a valid concept, due to various fundamental issues with it. Firstly, I am very sceptical of this, as the Casimir vacuum does not represent a “true” negative energy density in the physical sense; it is not exotic matter. Secondly, even if it does fulfill the requirements of the Alcubierre solution, it still wouldn’t be of practical use, since the Casimir effect cannot easily be scaled up to the size of an entire spaceship.
  15. The other fundamental issue I see is that, even if one was able to generate an Alcubierre bubble somehow, it would be entirely useless for all practical purposes. For starters, there is no practical way to control how this construct propagates - you couldn’t change its direction of propagation after it has been created, or even slow it down and bring it to a halt relative to some external reference point, by any means I can think of (excepting perhaps non-linear interactions with strong background curvature, which isn’t practical). The other awkward problem is that the “walls” of the bubble would constitute a region of extreme curvature, so anything entering or exiting the warp bubble would be ripped to shreds by tidal gravity. Lastly, once created, I don’t see any way of collapsing such an Alcubierre bubble again; effectively, any ship in the interior would end up being trapped forever. One must also wonder what the vacuum in the interior of the bubble, and especially around the walls, would look like from a QFT perspective - Unruh radiation? All in all, it is an interesting concept from a purely academic point of view, but wholly impractical as a means for FTL travel.
  16. As I attempted to explain, GR (which is the block universe model) is a model of gravity, and nothing else. It makes no predictions as to how much mass is in the universe. Also, since you are saying that you are not changing anything about GR, then that means you obtain the same solutions to the same equations, yielding the same dynamics. So you are either changing GR, or you are contradicting existing observational data as to the average energy density of the universe.
  17. “Spacetime” is a pseudo-Riemannian manifold of dimensionality 3+1, endowed with a connection and a metric. An “event” is a single point on that manifold. A “coordinate” is a unique label that identifies the event - its “name”, if you so will. The specific choice of coordinate system is arbitrary, so long as it is consistent across the manifold. ”Photograph” and “memory” are not terms that are used in this context. And yet that is exactly how GR models gravity, and it does so very successfully. Whether you can accept it or not, it works very well. In the context of GR, there is no such thing as an “object” - there is only a set of events along with information on how these events are related, and together these make up spacetime. What we conceive of as a macroscopic “object” is simply a set of world lines, each of which in turn is a specific set of individual events that are related in specific ways. The only difference between a region of spacetime that is merely vacuum, and a region of spacetime that we think of as the “interior” of some energy-momentum distribution, is its geometry - the former is Ricci-flat, the latter is not. That’s all there is to it. In this picture, you simply have events, and their geometric relationships in spacetime, and nothing else. Crucially, this entire construct is static - nothing “moves” anywhere, neither in space nor in time. The question as to why the human mind only perceives a future-oriented succession of space-like hypersurfaces within that spacetime, is outside the scope of the theory of GR - which was designed only to provide a model for gravity, and nothing else. I think this is really important to remember - GR is a theory of gravity, not an attempt to explain the nature of time and/or space.
  18. Same here! That was a great machine back in the day, happy memories
  19. There are at least four different notions of time (in this context) that I am aware of. The block universe is an example of eternalism, which corresponds to John McTaggart’s “B-Time”. The obvious alternative to this is what is called presentism, i.e. the notion that only the present moment has ontological status, which corresponds to McTaggart’s “A-Time”. Then, there is the “growing block universe” interpretation, which essentially posits that past and present exist in the same way as in the standard BU model, but the future does not - so the block “grows”, in a manner of speaking. Lastly then, there is the idea that time is merely an emergent phenomenon in the statistical sense, and not at all fundamental to the universe. All of these ideas have been debated (and continue to be debated) in depth from all angles, both in the philosophy and physics communities. All four of them have pros and cons associated with them, and all of them have certain problems that remain hitherto unsolved. From a physics point of view though, B-Time appears to yield quite a successful model (GR) for the large-scale dynamics of gravity, so it is very useful in that regard. But I would be hesitant to give it any ontological status in itself.
  20. Don’t forget though that GR as a model does not stand in isolation - the large-scale physics of the universe need to remain compatible with the small-scale physics of the Standard Model. Unfortunately the QFD and QCD parts of the Standard Model Lagrangian are not scale invariant, so you cannot replace a universal expansion with a contracting observer, without breaking some crucial physics in the process.
  21. This isn’t just true for electromagnetism, but for all laws of physics, once written using the correct formalism. For example, the Standard Model of Particle Physics - including all parts that are not EM related - is fully Lorentz invariant. As is relativistic fluid dynamics. And relativistic mechanics. And so on. The point is that all inertial observers experience the exact same laws of physics, not just the same propagation of light.
  22. Not that I am aware of, since the calculation requires in-depth knowledge of how to handle systems of non-linear partial differential equations, which goes far beyond what most amateurs would be familiar with. There are of course textbooks that explicitly go through this, but none of them is aimed at amateurs (they are usually at post grad level). Normally, spacetime curvature would not be a given quantity, you need to find it first. In order to do so, you have to first solve the Einstein equations for the physical scenario in question; and the quantity you solve it for is the metric (more accurately - the components of the metric tensor). Once you know the metric, you can then calculate spacetime curvature with it, which is - in the most general case - described by the Riemann curvature tensor. To find the metric outside a body, you solve the vacuum equations \[R_{\mu \nu}=0\] For the metric in the interior of the body, you need to find a solution for the full Einstein equations \[R_{\mu \nu } -\frac{1}{2} g_{\mu \nu } R=\kappa T_{\mu \nu }\] where the stress-energy tensor on the right describes the distribution of energy-momentum inside the body. You then match these two solutions at the boundary, i.e. you ensure that the metric remains smooth and continuous at the body’s surface, by appropriate choices of integration constants. This will essentially give you one metric that covers the entire spacetime, interior and vacuum. The Riemann tensor then follows from this accordingly.
  23. The mind does not have direct access to the “external world” (for lack of a better term - you know what I mean here), it only has access to a filtered and pre-processed version of whatever data the sensory apparatus delivers. As such, there is always a “mechanism” involved in any observation; whether this is mechanical (i.e. lab apparatus) or biological (i.e. sense organs) in nature, the underlying process is the same one in both cases, so there is no difference.
  24. Very interesting. Thanks for posting! This immediately begs the question of how a full GR treatment of tachyon propagation would look like. Given non-locality, how would one describe their world lines (if that’s even meaningful)? How do they couple to background curvature? How would they behave around event horizons, and regions of geodesic incompleteness? Etc.
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