Markus Hanke

In Thai and Chinese, as well as some other Asian languages, verbs are not inflected at all, and pronouns are used only if absolutely necessary to avoid misunderstanding, ie if the information is not already implied by the context. So for example, in Chinese, 去 might mean “to go”, “I go”, “we went”, “you’ll go” etc, depending on context. These languages thus simply express the idea of “going from here to someplace else”, and leave the rest up to context. You can, of course, add specifics if you want to, but unlike in many European languages, those are optional. In Thai in particular, there’s quite some emphasis on not being specific, unless strictly necessary.

Yes, indeed. The ‘Self’ is an idea (which is one type of mental construct)…and as such it is manifestly real. But what the idea refers to…not so much. One can also say that the Self is a process, rather than a thing. Every moment of experience is made self-referential. We don’t generally experience objectively as in “there is pain”, “there is a visual impression”, “there is happiness”, but like “I am in pain”, “I see”, “I am happy”. It’s an on-going process of selfing.

I know very little about numerical GR, but from what I do know, this type of simulation is prohibitive expense in computational terms. It a shame that a model like GR, which is conceptually so simple, is so hard to actually solve! Yes, very true. A lot of investigative work still needs to be done here.

I don’t know an awful lot about philosophy, so I’m not qualified to comment on any “rights” or “wrongs”. It just seems obvious that in terms of phenomenology, all that is ever directly experienced is the presence of interconnected thoughts, thus we can safely conclude that there is a thinking process going on. The existence of an “I”-agent that is somehow “doing the thinking” is only inferred, but never empirically observed. Thus it seems suspect to state its presence as if it was an empirical fact. But that’s purely my own two cents about this topic.

I came across this by chance the other day, and felt that this is a particularly good explanation of the meaning of “metric” in the context of GR, so I thought I’d share it here for whoever is interested: Some nice visualisations in there. Also, the other GR-related videos on this particular channel are quite good. No particular point for discussion, I’m simply sharing this for all those who wish to learn more about this subject without having to dive too deeply into the abstract maths. Particular emphasis on comments from time stamp 19:40 onwards (on coordinate vs proper measurements), as that’s were all those many common misconceptions arise. EDIT: Apologies, I’m just after realising that there’s an open thread for posting YouTube science content: Moderators, feel free to merge my comment there, if necessary.

The extra effects here are highly non-linear, so there wouldn’t be any straightforward correlation - what it comes down to is that for some systems, it is in fact necessary to use exact solutions to the full Einstein equations, rather than linearised approximations, even though such systems are not ordinarily considered generally relativistic. To put it differently, within such systems, the error introduced by treating gravity as a linear perturbation of flat spacetime is much larger than is naively expected, due to additional non-linear effects in the full non-perturbative EFE. The big question is what characteristics must be present within a given system for this to be the case, and that question is still very much open. It appears that it being rotational may contribute to it, but it may also be down to other things. Within non-linear systems, it is very difficult to tell how much error margin you introduce (relative to the full non-perturbative solution) by linearising it locally, and then cutting off higher-order terms in the expansion to make it computationally accessible. Which is essentially what is happening here, since complex systems such as galaxies can only ever be simulated using simplifying approximations.

Except that it should be “There are thoughts, thus there is thinking”. The “I” is not part of the phenomenology here.

The distances are relevant for the original problem, being that galactic rotation curves flatten out at large radii, ie far from the galactic center. This is not what we’d expect based on ordinary Newtonian gravity, hence the ‘traditional’ need for Dark Matter. The deviation between weak-field GR and Newtonian gravity seems to arise specifically for rotational systems, at least that’s the kind of systems almost all of these papers investigate. This is to say that within such systems, one cannot naively equate the weak-field regime to simple Newtonian gravity - the difference between the two (according to some of the above papers) amounts to as much as 30%. IOW, there are circumstances were you can get very significant non-linear GR effects, even though the situation only deals with weak fields. Traditionally such systems have been treated as Newtonian, on the assumption that any GR effects would be minute and thus negligible; but now it might turn out that this was a fundamental error on our part. However, we need to be cautious here, because Dark Matter is also observationally relevant in systems without any significant rotation, for example the Bullet Cluster. So unless it can be shown that such weak-field non-linear effects also occur in more general systems, at least under some circumstances, then this whole thing may still not provide a good explanation for Dark Matter. But it’s an interesting line of research that’s well worth pursuing further. But it’s mathematically very challenging.

Interesting paper from back in July (how did I miss this?), co-authored by Giorgio Immirzi, one of the foremost experts on GR and quantum gravity: https://arxiv.org/abs/2207.04279 This is just the latest paper within an increasingly large body of work that indicates that ‘dark matter’ as a separate phenomenon may be entirely superfluous. The basic idea here is that, under certain specific circumstances, even in the weak-field and low velocity regime, there may be non-negligible GR effects that aren’t found in Newtonian gravity. Hence, sometimes Newtonian gravity is not a valid approximation to GR in the weak field domain - which is the very assumption from which the idea of dark matter arises in the first place. What’s more, it turns out that under certain circumstances not even weak-field approximations of GR (such as GEM for example) are valid - specifically, this appears to be the case for rotating systems. In other words, within this paradigm, dark matter would neither be some new exotic form of particulate matter, nor is it a modification of the laws of gravity; it’s quite simply an artefact of us not having applied standard GR correctly, because the assumption “weak field”=“Newtonian” does not always hold. Small selection of other papers along the same lines: https://arxiv.org/abs/2207.09736 https://link.springer.com/article/10.1140/epjc/s10052-021-08967-3 https://www.worldscientific.com/doi/abs/10.1142/S0218271808012140 https://arxiv.org/abs/astro-ph/0610370 https://academic.oup.com/mnras/article-abstract/496/2/2107/5850386?redirectedFrom=fulltext https://arxiv.org/abs/1509.09288 https://arxiv.org/abs/2112.04116 https://arxiv.org/abs/2109.13515 https://arxiv.org/abs/2102.11282

When I look at the history of even just the 20th century, I cannot help but disagree. But that’s really not the point of this thread. That’s true, but unfortunately we cannot speculate on what kind of ethical standards - if any - an alien civilisation may adhere to. It’s easier to speculate about technology. I mentioned it as one of the many possible solutions to the Fermi paradox, so I think Dark Forest is perfectly entitled to appear on a science forum, especially since it is a direct consequence of game theory. The original impetus for this was the idea that an alien species being advanced and civilised must necessarily imply them being benevolent and moral - while I very much hope for this to be so, there is really no evidence that such an implication necessarily holds true. Please remember that Dark Forest is not my idea - it’s the mathematical result of some basic assumptions, plus game theory. We can’t just dismiss this only because we don’t like it on moral grounds. You cannot know this. This discussion wasn’t about us and our survival specifically; it was sparked by the Fermi paradox, and the question as to the probability of us being visited by alien spacecraft (UFOs and all that). I never suggested that we should attack anyone - the question as to what should be done if we ever did detect an alien civilisation is a different conversation. I simply suggest that it might be unwise to advertise our presence and location too loudly, until we have a better idea what the consequences of such an act might be. I do not think that is unreasonable or paranoid.

You’ll need to enclose both enumerator and denominator separately to make it look even better, like “\frac{\displaystyle{}}{\displaystyle{}}. It’s a bit of a pain, but it does make a difference to the way the output looks. As for proper vertical alignment and sizing, I haven’t figured this out myself yet (any ideas @studiot?).

Try wrapping both parts of the fraction in “\displaystyle{}”: \[\displaystyle{v=\frac{a_{0} t}{1+\displaystyle{\frac{a_{0} L_{n}}{c^{2}}}}}\] I’m not sure how to fix the equation being too tall, and not vertically centred on the equal sign.

Very interesting point! +1 And what about the compatibility problem in all its facets - would a very advanced civilisation even be recognisable as such by other species, or would they just blend into their natural environment so well that it would be really difficult to detect their presence at all, even from close by? We always imagine alien structures to look overtly like a piece of manufactured technology, but really, there’s no guarantee that this must be so.

While this is true, the problem here is that what constitutes a “real-life standard” is relative to the technological development of the civilisation in question. Back in 1800, the idea of travelling from New York to London in ~7 hours using a jet-powered, pressurised, heavier-than-air flying machine at altitudes of ~30.000ft would have been so ludicrous that you’d have been laughed out of town, had you brought it up. Nowadays it’s so trivial that no one even thinks about it anymore. And that’s just 200 years. Now, what will the real-life standards of a civilisation that is - say - 2 million years ahead of us be like? Today, we can accelerate electrons and protons to energies on the order of ~TeV, which is very close to the speed of light. To do the same (proportionally) with a block of solid metal the size of the Empire State Building (and that’s probably all that is needed) requires nothing more than a scaling-up of already existing technology, as well as lots and lots of energy, and some kind of suitable guidance system to make sure you hit your target. Obviously ludicrous to us at present, but probably not ludicrous to someone 2 million years ahead of us in technological terms, who is able to harness the necessary amount of energy. I do not find this inconceivable at all. Besides, there might be other ways to bring about the desired result; the relativistic projectile was just the most straightforward method that came to mind, since it doesn’t require speculative technologies, just lots of lots of energy. Also, real-life standards go both ways. If you look at the data we actually do have available, being the set of all the different species that have evolved on Earth, then it would seem to me that different species co-existing peacefully and cooperatively is most definitely not the norm we see (though there are examples of symbiotic relationships that are mutually beneficial). Rather, the overall real-life standard here seems to be one of competition over scarce resources, as well as predator-prey dynamics. I can only hope that the addition of higher intelligence changes this, but there are no guarantees of that being the case. So in the absence of more data, I would argue that the equation “intelligent”=“benevolent and peaceful” should be treated as suspect. It may hold - but then again, it may not. Until we know for sure, it may be a wise policy to not advertise our presence and exact location all too loudly. You never know who might be listening.

That’s because it is irrelevant, since the effect coming from metric expansion is many orders of magnitude greater than any net effect from gravity wells. Metric expansion does not happen within gravitationally bound systems on very small scales such as the distance Earth <> Sun. It’s not mentioned because the relative velocity between us and those bodies is small, so the amount of Doppler redshift is minuscule. It certainly does not contribute in any way to cosmological redshifts. The very first thing you have to do is actually understand current physics - you need to know exactly where we stand at the moment, both so far as large scale physics is concerned (GR, cosmology), as well as high-energy physics (quantum field theory, Standard Model). If you just reject the current paradigm without knowing exactly what it is you are arguing against, then no one is going to ever take you seriously. And herein lies the issue - the three biggest problems with what you are posting here are that 1. The idea of a massive photon is entirely incompatible with the Standard Model as we know it, and 2. You haven’t demonstrated that photons having rest mass is a concept that is actually able to replicate the phenomenology of dark matter, and 3. There are serious gaps in your understanding of current models You haven’t addressed point (1) at all, even though it has been pointed out to you. For point (2) you have offered only speculations that don’t even begin to address how massive photons are a viable explanation for dark matter. As for point (3), it’s kind of obvious that you really don’t know much about the basic models underlying current cosmology - for example your comment that, because light is deflected, it must have mass; or that mass is the source of spacetime curvature (both of these are inaccurate). So no, you don’t have to accept the Lambda-CDM model - but you are expected to thoroughly understand it in all its facets, before anyone will take you seriously. I see little evidence of that, to be honest (not intended as ad hominem, but simply a statement of fact based on your posts here). You also appear to forget that massive photons as explanation for dark matter is an old idea (“heavy light”), that has already been considered in detail by a number of physicists. But once you put some actual maths around this, it becomes obvious very quickly that it simply doesn’t work; even a photon with rest mass doesn’t have the right kind of properties to accurately account for the observed effects of dark matter. This general-reader type of article might be of interest: https://bigthink.com/starts-with-a-bang/heavy-light-dark-matter/ Hence, I maintain what I said earlier - interesting as a speculation, but a complete non-starter as a serious DM model.

The mass can be small-ish, because it isn’t the mass itself the creates the destruction, but its kinetic energy from moving at high-relativistic speeds. The critical bit is getting the speed just right, because you wouldn’t want it to just punch through the target without expending its energy - the sun will be length-contracted into a flattened disk in the rest frame of the projectile. Exactly.

No. The issue is, rather, that the concept of photons having rest mass is a pretty old idea, and has already been extensively tested in numerous high-precision experiments. Here’s the current status for both mass and charge for photons: https://pdg.lbl.gov/2020/listings/rpp2020-list-photon.pdf As you can see, the currently applicable upper bound is on the order of \(m<10^{-26}eV\), which is way too small by many orders of magnitude to account for the observed dark matter effects. It has also been pointed out already that a massive photon would have other consequences within the Standard Model, none of which we observe in the real world. Thus, as things stand at the moment, the idea is a non-starter from the beginning.

No it is not. As has already been explained multiple times now, the two observers do not use the same notion of time when they are discussing in-fall time in their respective frames - hence you are not comparing the same quantities, and thus there can’t be a contradiction. Let’s be explicit here, so we can put this baby to bed once and for all. Suppose we have a particle in Schwarzschild spacetime starting out at rest at some initial radial position \(r_0\), which we can take to be far from the black hole, so that it initially corresponds to a far-away stationary Schwarzschild observer. It is then released and begins a radial free fall towards the horizon at \(r_S\). For the Schwarzschild observer (stationary and far away), the time it takes for the particle to reach the horizon, as measured on his own clock is (in natural units): \[\Delta t=\int _{r_{0}}^{r_{S}}\left(\frac{dt}{dr}\right) dr=-\int _{r_{0}}^{r_{S}}\frac{1}{\sqrt{2\left( 1+\frac{M}{r}\right)\left( 1-\frac{r_{s}}{r}\right)}} dr\ \rightarrow \infty\] This is coordinate in-fall time, since we’re integrating the ratio dt/dr, the expression for which follows from the equation of radial motion. On the other hand, the in-fall time as measured on the falling particle’s own clock is \[\Delta \tau =\int _{r_{0}}^{r_{S}}\left(\frac{d\tau }{dr}\right) dr=\frac{1}{3}\sqrt{\frac{2}{M}}\left(\sqrt[3]{r_{0}} -\sqrt[3]{r_{S}}\right)\] which is the proper in-fall time, and it is very much finite, as you can hopefully see. This expression comes straight from the metric. In order for there to be a contradiction, it would have to be the case that the length of the world line of the in-falling particle takes on different values for different observers; however, this is not the case, since \(\Delta \tau\) is a rank-0 tensor, so it is generally covariant, and thus all observers agree on it. To sum up: \(\Delta \tau\) is the length of the in-falling particle’s world line in spacetime, and the same for all observers \(\Delta t\) is not in general the length of the in-falling particle’s world line in spacetime, and explicitly depends on which observer is chosen These just simply aren’t the same physical quantities. Thus \(\Delta \tau \neq \Delta t\) isn’t a contradiction, but a necessary consequence of being in a curved spacetime, since time here is a local quantity. You can’t compare apples and oranges, and then claim there’s a contradiction because they don’t look the same. You have to compare apples to apples instead: In the frame of the falling particle, the length of its in-fall world line in spacetime is \(\Delta \tau\). In the frame of the distant stationary observer, the length of the particle’s in-fall world line in spacetime is also \(\Delta \tau\). It’s precisely that world line and its geometric length that your God-observer would see. No contradictions to be found anywhere - quite the contrary actually, since both observers are in perfect agreement about the length of that world line! PS. Why is it then that the far-away stationary observer never visually sees the particle reach the horizon? That’s because in-fall geodesics aren’t the same as outgoing geodesics. A photon originating close to the horizon can only escape to infinity via a trajectory that’s “flattened” tangentially to the horizon; the relative angles as seen by Schwarzschild and shell observers are related via \[\tan \theta _{shell} =\sqrt{1-\frac{2M}{r}}\tan \theta _{Schw}\] The closer to the horizon one gets, the more tangential the escape trajectories become, and at the photon sphere the angle is so small that nearly all photons become trapped into unstable orbits. Below this point, from the horizon down, the photon must fall in. This is why the Schwarzschild observer never visually sees anything reaching the horizon - because the closer one gets to the horizon, the fewer photons manage to escape back out to reach that observer, resulting a “dimming” of the object as seen by the outside observer (they are also red-shifted, resulting in further dimming). Once the photon sphere is reached, nearly all emitted photons are either captured into orbits, or must fall in, so the object becomes essentially invisible to outside observers. Only under very special circumstances can individual photons escape from here. Once the horizon itself is reached, no escape is possible at all, not even for photons, because null geodesics are everywhere perpendicular to the radial direction (the horizon is a null surface). Due to the symmetries of Schwarzschild spacetime, the coordinate time of a distant observer is defined such that it reflects precisely this difference between ingoing and outgoing null geodesics - it diverges to infinity precisely because no photon can ever reach this observer from the horizon, so nothing is ever visually seen to be reaching that point. This is in contrast to ingoing geodesics, which can be perfectly radial everywhere. Thus there is no contradiction, because ingoing and outgoing null-geodesics simply aren’t the same, not even in this highly symmetric spacetime.

Just aim at the central star then, instead of the individual targets. It will take a larger mass and higher speeds, but it’s still doable.

I suspect this is in reference to the BH thread you had started, and the supposed contradiction due to different observers disagreeing on in-fall times. I remind you once again that the two reference frames in question do not deal with the same premise, because they do not share the same notion of ‘time’. To cast it into the terms used here, the P belonging to the frame of the in-falling particle is not the P belonging to the frame of the distant stationary observer - you are comparing proper and coordinates times, but those are very different things. To make a valid comparison, you need to choose a physical premise that does not depend on your choice of observer - in this case the obvious choice is the length of the in-falling particle’s world line, ie proper in-fall time. For the in-falling observer, this world line is of finite length; for the distant stationary observer, this same world line is also of finite length. They both agree that the particle reaches the horizon, if you use the correct premise. The only difference is that the distant observer never sees this happening (which should be obvious, pardon the pun), whereas the infalling observer does. This is why it is important to grasp the very crucial difference between ‘global’ and ‘local’.

Yes, that was precisely the problem I was getting at.

Unfortunately I have yet to find good literature on this topic that is accessible to the general reader. Most papers about this spacetime out there are quite mathematical, including the one you quoted. If I can find anything, I’ll post it here on the forum. Generally speaking, the Vaidya solution is a generalisation of Schwarzschild in that spacetime isn’t assumed to be empty, so it is one of the simplest non-vacuum solutions to the field equations. It’s basically the kind of geometry you get for a spherically symmetric, non-charged, non-rotating body immersed in uniformly ingoing or outgoing matter or radiation. As a result, the parameter M in the metric now depends explicitly on time, so this is can be used as a toy model for a growing or evaporating black hole.

Well, it would be like being confined to a perfect sensory deprivation chamber that is somehow able to completely suppress all external inputs. All that remains than are internal inputs, ie thoughts, memories, dreams, etc etc. Most people will probably consider this the highest form of torture. I can’t really answer these questions, also because this is not my area of expertise. Out of all the current attempts to explain consciousness, Integrated Information Theory seems to make the most sense to me, in which case the precise nature of the physical substrate underlying consciousness really isn’t relevant. Neurons are an extremely efficient solution, but in principle at least a network of machines that work in similar ways should do the job just as well. And yes, if IIT holds any water at all, then there should be degrees of consciousness, depending on complexity and structure of the network in question. In the future there might be ways to experimentally test this, but right now I think it’s pretty much all conjecture.

Precisely! +1 No such observers physically exist. The closest you can come to it is to describe the situation only in terms of generally covariant quantities, ie quantities that do not depend on the choice of observer at all - meaning all physical observers must necessarily agree on them. That’s pretty much a God’s eye view on the situation. Mathematically, this means tensors (and spinors) of any rank will be used to describe the physics. For the situation at hand, the obvious choice would be the length of the in-falling particle’s world line (which is by definition equal to proper in-fall time) - which is finite and well defined, and as being a rank-0 tensor everyone agrees that it is finite and well defined. There’s also another issue - coordinate in-fall time diverging to infinity is valid only in Schwarzschild spacetime, which relies on a number of boundary conditions, most notably asymptotic flatness. In other words, to get Schwarzschild spacetime, you need to assume that the universe is everywhere completely empty so that spacetime far from the black hole is approximately flat. Obviously, in the real world, this only ever holds at most as a rough approximation - in reality, there will be stuff orbiting or falling into the black hole, and other gravitational sources at various distances. If you account for in-falling matter and/or radiation, but retain all other symmetries, then you end up with a different kind of spacetime, called Vaidya spacetime - and here even the coordinate in-fall time as measured by a distant observer is quite finite (though much longer than the proper in-fall time in the particle’s frame).

No, not really. I was just aiming at the question of how to define “conscious”, as opposed to a machine that merely appears to be conscious. The difference between these is surprisingly hard to define. As for the nature of consciousness itself, I would conjecture that it probably arises as a global property of a complex system such as the brain, so I would think it resides in the global connectome and signal timings of the brain, rather than the nature of the individual building blocks. So if you were to replace all the neurons with machines that process inputs and outputs in the same manner, and are connected in the same way, then that new machine brain should be just as conscious. But of course, that’s purely conjecture - perhaps I’m entirely wrong on this. Yes, I did mention that we need to provide sensory channels, or else the results will be unpredictable. It would also be an ethical issue - imagine finding yourself conscious as a disembodied brain with all sensory channels turned off? Not good.