Markus Hanke

Yes - this often happens when people (consciously or unconsciously) adopt scriptural literalism as their mode of engagement with their chosen tradition, ie when they fail to distinguish the word from the message. When you allow this to happen, you essentially make it impossible for yourself to meaningfully consider other sources of information or modes of enquiry, resulting in a more or less filtered/distorted/one-sided view of the world.

The evidence for the existence of a gravitational attraction between masses is so overwhelming that it is entirely beyond any contention. Using the Cavendish setup, you can even perform experiments that show you this right at home in your living room. I recommend you give it a try - you can purchase DIY kits for this right off the Internet at a cheap price. Some of these come with spheres made of different materials - metal, stone, high-density plastics etc -, and some are even enclosed in vacuum chambers and Faraday cages, so that you can confirm yourself that these effects are not the result of any electromagnetic interactions, air movements etc. Gravity is very much real, and it is very easy to show that it is.

It depends largely on how exactly you define “actual present moment”, because the meaning of this is not at all clear. We are remembering a subset of whatever mental objects were present in consciousness at the instant the memory refers to. These mental objects are the result of the reality-model that the mind has constructed - this model takes as its input sensory data (“perception”), memories, and previously accumulated habitual processing patterns, which are then filtered and further processed in certain ways, and eventually output as mental objects that we can direct our attention to and be aware of. Phenomenological reality is a mental construct. It’s kind of like a graphical user interface on a computer - the operating system takes external inputs (user interactions, information stored in RAM, ROM and other storage media), processes these, and renders them graphically on a screen, printer, or other output device. The basic inputs and information storage units do not themselves contain GUI elements such as letters, windows, menus, dialog boxes etc etc (they are just electric potentials), but it turns out that these higher-order representations make for a useful “reality-model” for a computer to interact with its user. The specific form such reality-models take are strongly influenced by teleological concerns, ie the reason why the computer was constructed in the first place. But all of this aside, the basic issue is this - our memories contain what is by and large a structured and ordered sequence of remembered mind-moments. We remember perceptions from our childhood, and we remember our teenage years, and we recognise that one came before the other - in other words, we never remember the future, only the past. If the original input data does not already contain such a temporal ordering (ie there is no present moment), then why are our memories temporally structured in a self-consistent manner? A similar argument can also be made for any kind of non-sentient recording device that records a structured sequence of information based on external inputs. If there is no concept of present moment, it is very difficult to explain the emergence of this temporal structure.

What you suggest seems like an obvious solution, but unfortunately it does not and cannot work. Addiction is much more complex than just being a physical dependency on something. Yes, you could (ethical concerns aside for now) round them all up, put them in a camp, and forcibly put them through physical detox - the trouble with this is that it doesn’t actually address the underlying issue at all, because the dependency is in large part of a psychological, social and systemic nature. No one wakes up one morning and decides “I’m going to become a homeless addict…seems like a cool career choice!”. That’s not how it works. Most long-term addicts are in this situation because of multiple factors connected to their social environment, upbringing, past trauma, etc etc, many of which they have little or no control over. These are all complex issues that are not easily nor quickly fixed. It’s a common mistake to think that people remain addicts purely because of their physical dependency, and if we kick the physical dependency they cease to be addicts - that’s quite simply not true at all. So as for your proposal - you take them to your camp, forcibly put them through detox, and at some point will have to let them out again to re-join their families and social environments. What do you think happens then? I can pretty much guarantee you that within days or weeks almost all of them will be right back on their drug of choice, with perhaps the odd exception. Why? Because the underlying reasons for why they have begun to use substances in the first place have not been addressed. Addiction is a symptom of an underlying disease, not really the cause itself - just putting people through detox is like giving painkillers to a cancer patient; it alleviates the symptoms for a little while, but it doesn’t cure the disease. People don’t start off using because they are physically dependent, but for other reasons. It’s those initial reasons that need to be addressed. You cannot help an addict who doesn’t want to be helped - the impulse must always come from him/herself. People have to be ready to change, before therapy has any chance of success, and even then the relapse rates are still high. Forcing people into a treatment they are not ready for does not work. I don’t know if there are actual studies to show this (there probably are), but everyone who has ever actually worked with addicts knows that this is a basic fact. BTW, rounding up addicts and forcing them into rehab camps is what the Taliban in Afghanistan tried to do. Needless to say, it didn’t work. But it makes for an interesting case study if you want to research into it. So as for your proposal - it certainly has political appeal to those who don’t know much about drug addiction, but ultimately it does not and cannot work. It would just create a revolving-door kind of situation with people going in and out of camps, and the ones who ultimately profit will be the dealers and cartels, as always. Until we begin to treat homelessness and addiction as the social and health issue which it is, and stop criminalising something that the victims have little or no control over, no progress can be made on this problem. Criminalising the addicts and waging a “war on drugs” has never once worked, does not work now, and never will work. A complete re-think is needed.

So why can you remember it afterwards?

I myself am an ordained monastic in a Buddhist tradition of contemplative forest monks and nuns. The impulse to follow a contemplative and spiritual life - irrespective of what specific form this may take - need not at all run counter to science, as many who were simultaneously scientists and spiritual seekers have shown throughout history.

No, it’s silly because - as I have already shown you - it directly follows from the principle of least action (as well as other principles, as pointed out by several contributors here), so it makes no sense to claim that it is “wrong”.

It depends what you mean by “problem”. You were asserting in your OP that F=dp/dt isn’t the correct formulation of Newton’s 2nd law, so I tried to provide you with the bigger picture of where this relation comes from. My point was to show you that it isn’t just made up (and thus potentially wrong), but that it follows from more general principles. It’s essentially a special case of the principle of least action. F=ma then is in turn a special case of F=dp/dt - it works well for many simple systems (which is why we all learn it in school), but its domain of validity is limited. F=dp/dt is more general, and also works in some cases where F=ma doesn’t. And then of course there are systems where neither of these work (as joigus has pointed out), and then you have to use the full Lagrangian formulation of mechanics. This isn’t to say that F=dp/dt can’t be derived in other ways too, which is what studiot is trying to show you. Either way, just claiming that F=dp/dt is wrong and must always be replaced by F=ma - which is what you seem to be saying - is silly, because that’s manifestly false.

Newton’s second law in the form F=dp/dt (which is equivalent to F=ma iff m=const) isn’t just made up, but follows directly from the principle of least action, and is thus mathematically derivable in a self-consistent manner. I suggest for starters you might take a look here. Your claim that this is “wrong” somehow is thus pretty meaningless.

No, it wouldn’t. This is purely a SR problem, and all it involves is comparing the lengths of the two world lines, which is a straightforward (though not always easy to evaluate) line integral: \[\tau =\int _{C} ds=\int _{C}\sqrt{\eta _{\mu \nu } dx^{\mu } dx^{\nu }}\] wherein C is the path in question. Now, even without having to consider any specific numbers, we can work out the differential ageing between the two. Suppose we have two events in spacetime, A and B, which we connect via two different paths (the two twins) - we assume for simplicity that the two events have the same spatial coordinates, and differ only in time; this would correspond to (eg) one twin remaining stationary and inertial somewhere, and the other one travelling away and returning again, so that they both start off together at rest, and finish together at rest. This is the simplest possible twin scenario. Let’s use a coordinate system that has its origin at event A, and a metric with sign convention (+,-,-,-). The inertial twin then simply traces out a world line of length \[\tau_{1} =\int _{A}^{B} ds=\int _{A}^{B}\sqrt{\eta _{00} dx^{0} dx^{0}} =\int _{A}^{B} d\tau\] The other twin, the one that is travelling away and returning, on the other hand traces out a world line of length \[\tau_{2} =\int _{A}^{B} ds=\int _{A}^{B}\sqrt{\eta _{\mu \nu } dx^{\mu } dx^{\nu }} =\int _{A}^{B}\sqrt{( d\tau )^{2} -( dx)^{2}}\] wherein dx depends on the spatial path of that travelling twin. Since we know from the extremal value problem in variational calculus that the inertial traveller always maximises the path length between given events (using this sign convention in the metric), and since the two paths in this scenario are not identical, we can immediately conclude that it must be the case that \[\tau _{1} >\tau _{2}\] This also implies that the path of the travelling twin can never be a geodesic, so it cannot be everywhere inertial.

! Moderator Note Thread moved to the ‘Speculations’ section, since this isn’t mainstream physics.

No, that’s a common misconception. GR only comes into play if there is non-negligible gravity involved; the case of acceleration in a flat spacetime is handled perfectly well by SR. We already have plenty of direct evidence from particle accelerator runs that accelerated particles behave exactly like SR says they do. Perhaps the best demonstration of this is Fermilab’s “Muon g-2” experiment, where unstable muons are introduced into the ring and accelerated to a \(\gamma\) of ~30. And as expected, their average life time really increases by the expected amount as compared to a reference sample that remains stationary in the lab frame. And this is only one example - literally every accelerator run we do demonstrates the reality of time dilation and length contraction, in exactly the way SR predicts it will.

No. What I mean is that the metric of spacetime itself becomes time-dependent here, in such a way that it appears to a far-away stationary observer as if the EH was oscillating with a quadrupole moment, even though the “position” of the horizon remains constant locally in a small neighbourhood. So what oscillates here is the relative separation between events, but not the coordinate position of the events themselves. This is somewhat similar to what’s called the “ring-down” phase at the end of a BH merger, where energy-momentum is dissipated away via gravitational radiation.

I think this would depend. In principle both EM radiation and G radiation should propagate along the same geodesics, so for “ordinary” objects like stars etc and “ordinary” G waves the deflection angle should be nearly the same since any non-linear effects are negligible. However, if the wave length of the G radiation becomes very large, and/or the background field is very strong, I would imagine there might be situations were such effects cannot be neglected, and the deflection angles differ. I’m not sure though. This may be relevant: https://arxiv.org/abs/2001.01710

Same here…welcome to my world

Oh yes, they are. The Lorentz transformation leaves the metric invariant: \[g_{\mu \nu } =\Lambda _{\sigma }^{\mu } \Lambda _{\rho }^{\nu } =g_{\sigma \rho }\] Rewrite this in matrix notation: \[\Lambda ^{T} g\Lambda =g\] Take determinant on both sides: \[det\left( \Lambda ^{T}\right) det( g) det( \Lambda ) =det( g)\] Since none of these determinants is ever zero, and since the determinant of the transpose equals the determinant of the original matrix, you get: \[det( \Lambda )^{2} =1 \] which implies that \(\Lambda\) is always invertible. Thus, inertial frames related via Lorentz transformations are always symmetric. ! Moderator Note It is against the rules of this forum to post personal theories into the main physics section, let alone onto an existing thread. If you wish to discuss this, you must open your own thread under “Speculations” and explain your thoughts there (don’t just give links).

Yes, they do “carry” energy-momentum. That’s an interesting question (I never really considered sources of directional g-radiation), the answer to which I am not sure about. There are two main issues here that make this situation somewhat different from Newtonian mechanics: 1. The energy-momentum in a gravitational wave cannot be localised, and 2. There is no global law of energy-momentum conservation in curved spacetimes of this sort. Point (2) is to say that yes, energy-momentum is conserved everywhere locally in small neighbourhoods that can be considered approximately flat; but there is no such conservation law for larger, curved regions. Take careful note here of the difference between a conservation law being violated, and no such law existing in the first place. In the absence of meaningful energy-momentum conservation (in the Newtonian sense), it is not at all clear to me whether or not a source of directional g-radiation would receive an impulse in the opposite direction. I’d say before even considering this issue one what have to first ascertain whether such a thing as a directional beam of g-radiation can even exist, which is in itself not clear. I’m very careful to commit to any definite answer on this, as this is one of those scenarios where ordinary Newtonian intuition can very quickly lead one down the wrong road. The best I can say is that it would be necessary to actually do the maths, which would be highly non-trivial.

I am autistic indeed, and in the very fortunate position that my own personal autistic profile is such that for me the advantages of being on the spectrum far outweigh the challenges (which exist, but may not be obvious here). Unfortunately this is not true for many other - perhaps even the majority of - autistic people, a large proportion of whom suffer significantly from their autistic traits and common comorbidities, and above all from the failure of the wider neurotypical world to understand, respect, accept and accommodate these traits. Ultimately whether or not the “D” belongs in there is very much a matter of personal circumstance and experience - for me personally, I do not consider my autism to be a “disorder” in any way, and wouldn’t choose to change it even if given the opportunity; however, other autistic people may think about their own situation very differently, and this absolutely needs to be respected too. Everything considered, I am not a very “typical” representative of the autistic community. And for those of you who aren’t aware - English is also not my native language; my real-world vocation has nothing to do with science; and I am not university-educated. The foundations of physics are simply a matter of personal interest to me, so it’s all self-taught. And rest assured that if I’m among real experts on these subjects matters (e.g. among some of the regulars over on PhysicsForums), I’m also left feeling ignorant and dumb Which is why I’m mostly just a silent reader there. But for me this is rarely a negative experience, since I consider ignorance to be an opportunity to acquire new understanding, which is never a bad thing. PS. To give perhaps a better insight into the subject matter of this thread - when I respond to posts, my entire focus is always 100% on understanding better how the world works. That means when I see a statement that doesn’t gel very well with the current scientific consensus on the matter at hand, I’ll simply say so - social considerations never come into it for me at all. I don’t set out to intentionally hurt or belittle people, but neither do I go out of my way to mollycoddle others’ feelings (unless they are obviously vulnerable in some way). The social aspect just simply isn’t on my radar at all. A verbal or mathematical statement is either a good description of some aspect of the world, or it isn’t - that’s all there is to it for me. This is also how I roll in the real world - I am very focused on concepts, insights, and values, and have little to no interest in social or cultural conventions. That get’s me in trouble sometimes, since most other people appear to be reifying socio-cultural conventions into some sort of universal truths or standards. I’m just not everyone’s cup of tea I guess

There is no known physical mechanism that can “shield” gravity in this way, so no reflection - in the sense that term is used for light e.g. - can happen. It is, however, possible to deflect gravitational waves, i.e. change their principle direction of propagation via interaction with background curvature, or other gravitational waves. Yes they can, and in full theory of GR that is a highly non-linear process (but linear approximations can sometimes be used to describe this). Yes, the Einstein equations emit solutions - both in vacuum and in so-called null dusts - which can be physically interpreted as the equivalent of standing waves. I don’t know about the amplification bit, since this is a non-linear situation, so one would have to run the maths on it. This should theoretically be possible I think, though again, one would have to do the maths (which wouldn’t be trivial at all) to be absolutely sure. I don’t understand this question…can you explain further?

Good point, this never occurred to me +1 Very different indeed. In fact, based on GR in 2D, the only gravity that could exist in such a world would be found in the interior of mass-energy distributions - there could be no gravity at all in vacuum.

Does the forum software here support the ability to number posts within a thread? If so, wouldn’t it make sense to turn that function on? More than once now have I had to refer back to what someone said earlier on a thread, in a way that just can’t be done easily using the quote function. There are just situations where it is easier to simply refer to a post number (“You made this claim in post #…”). Thoughts?

Yes, precisely +1. The basic twin scenario is simple, I don’t understand why people feel the need to add so many extra complications to it that do nothing to illuminate the underlying physics. This seems to be a problem with SR in general.

Ah ok…I can see how someone might be tempted to look at it in this way. That didn’t even occur to me. Thanks for pointing it out. Obviously though, since there is exactly one geodesic (=extremal) path connecting any pair of events in spacetime, there must always be at least one local section of the journey where the two travellers are not related via a Lorentz transformation. Yes, perhaps you’re right and it’s that simple.

For me personally, it’s fair to say that I’ve been concerning myself with the theory of relativity for quite some time, and while I’m not an expert by any reasonable metric, I still dare say that my knowledge of the subject is above the average one would find in a group of randomly-chosen members of a (reasonable well-educated) public. Yet, even after all these years, I am still failing to understand why so many people consider these scenarios “paradoxical”? I get that the outcome of such experiments can appear surprising at first glance, but that’s not the same as calling it “paradoxical”. I’m not being condescending, sarcastic or whatever else, it’s a genuine question. I just don’t get it. Analogy(!!!): It’s a little bit like flying from, say, New York to London - you can fly eastbound, and follow a suitable geodesic (i.e. a great circle segment, ignoring vertical motion for simplicity now, all other factors being equal), and get to London in a certain amount of time. Or you can choose to fly westbound, and likewise follow a geodesic, just in the opposite direction. Or you can choose some other route that isn’t a geodesic at all, so long as they all start at the same place and terminate at the same place. No one would be surprised by the fact that for these three cases, the onboard clocks read different elapsed times - I mean, it’s rather obvious that there is exactly one, and only one, route that minimises the total in-flight time. Any route that diverges from that flight path will necessarily be of different duration, assuming all other factors remain equal. It’s no different for a path in spacetime, that is traced out by different travellers between the same two events. In topologically trivial Minkowski spacetime (which is the stage against which this is set), there is precisely one - and only one - path between any pair of given events that extremises (minimises or maximises, depending on sign convention) its own length, which is by definition equal to the proper time recorded on a clock that physically travels this path through spacetime. Any path that varies from this one choice must necessarily be of different length, ie a physical clock travelling along it will record something other than the extremal value. If you set this up as a variational calculus problem, you unsurprisingly end up with the geodesic equation - the extremal path between any pair of events here is a geodesic of Minkowski spacetime, which physically corresponds to a traveller moving inertially. The reverse of this statement is just as true - in singly-connected Minkowski spacetime, any path between given events, the length of which differs from the extremal value obtained from the variational calculus problem, is necessarily non-inertial at least within some small region along it, since the extremal path is a unique solution to the equation. Why is this considered “paradoxical”? I struggle to even consider it “surprising”, since it seems entirely obvious to me that this is what will happen, just like in the analogy of the planes above. You can’t - in general - take two different routes between the same points and reasonably expect them to have the same lengths (unless you cheat by introducing non-trivial topologies etc). Note that this isn’t about why SR is what it is (ie hypothetical underlying mechanisms etc), but simply about why this result should be considered surprising or paradoxical. To me it isn’t, unless I am missing something so basic that I can’t even see it - in which case I’d be grateful if someone could point it out to me. My other issue is that I’ve seen the original scenario amended such that the travellers involved do not actually connect the same pair of events. What meaningful physical conclusion - in terms of elapsed times - would one hope to arrive at by comparing paths that don’t connect the same events? I don’t get this either. It seems even less surprising that - again in general - you get different results if you compare paths between different events.

A physical paradox can arise only if there is an inconsistency in transformations between frames. Here’s what I mean by this. Say you perform a Lorentz transform to get you from frame A to A’ - by doing so, lengths and times in A’s choice of coordinates will change, since a Lorentz transform is nothing other than a combination of hyperbolic rotations and boosts. A linear transformation, in other words. But what happens if you perform a second Lorentz transformation, identical to the first one, only with a negative argument (-v instead of v)? The already transformed lengths and times associated with A’ will transform again - since this new transform is the same one as the original one, only in the opposite relative direction, one should recover the original frame A. If one doesn’t, the situation is not internally self-consistent. So, consistency in this context means (L denotes Lorentz transform): L(v)A -> A’ L(-v)A’=L(-v)L(v)A -> A A applies L, and arrives at A’. Likewise, A’ applies L, and arrives at A. There is perfect symmetry between these frames. In a situation where such consistency holds, it is not possible to construct any physical paradoxes based on this linear transformation alone, because any pair of inertial frames will always agree on how they are related to one another. So, in order to show that one cannot construct physical paradoxes in Minkowski spacetime based on the axioms of SR, it is sufficient to show that every Lorentz transformation has a unique and well defined inverse, such that \(L L^{-1}=I\), wherein I is the identity element. Suffice to say that this is indeed the case, and if you want I can present the formal proof here (or you can just Google it yourself).