Markus Hanke

This is a misconception which is as common as it false. SR is a model of Minkowski spacetime - it describes the relationship between any set of frames within this paradigm, irrespective of what their states of relative motion and acceleration are. In the special case of inertial motion, this relationship is simply a hyperbolic rotation in spacetime (=Lorentz transformation); if acceleration is involved, the relationship is a little more complicated, but nonetheless well defined: https://en.m.wikipedia.org/wiki/Acceleration_(special_relativity) There’s no “paradox” in the twins scenario that somehow needs resolution, it’s simply a straightforward consequence of the geometry of Minkowski spacetime, which has to do with the lengths of world-lines.

Given that you assume the theory of relativity to be valid, this will imply that an absence of time would also mean an absence of gravity between bodies. Clearly, this is not what we observe.

I understand Just as a side remark though, it is interesting to note that the EFE also admits cosmological vacuum solutions. An example is the Kasner metric; this kind of universe is completely empty (no energy-momentum and no cosmological constant), yet still not Riemann-flat in general, and metrically expands in an anisotropic manner. One can contrast this against the case of FLRW, and finds that it is precisely the presence of matter/radiation that enables an isotropic expansion. Obviously this is purely academic, but nonetheless instructive.

Of course I was very fortunate that I grew up in a part of the world were an excellent basic education is freely available to everyone. I consider myself lucky.

I was referring to the exterior metric, which has T=0 everywhere. The main point I am trying to make is that the EFE is a purely local constraint on the metric - but one must also account for sources that are distant in space and/or time, which happens via boundary conditions when solving the equations. To put it differently, the metric isn’t in general determined solely by local energy-momentum alone, but also by distant sources (and cosmological constant).

Careful here - the field equations emit many vacuum solutions without the presence of particles. For example, the standard Schwarzschild solution represents a spacetime that is everywhere vacuum (T=0 at all points), yet not flat. In general terms, the EFE states a local (!) equivalence between the Ricci tensor and a source term - but a vanishing Ricci tensor does not necessarily imply a flat manifold.

I think you’re forgetting that these distant objects are not just moving away from us, but also from each other. Metric expansion happens for all distances, not just those centred on Earth (which would be exceedingly weird). Furthermore, there’s a precise relationship between distance and recession velocity, irrespective of which direction you look. Be careful to place to much stock in a single observation - you have to remember that cosmological redshift is not the only data point available to us; there’s quite a number of different observations involved, and the Lambda-CDM model is currently (!) the one that best fits all the available data. It’s not just based on redshift.

Yes, don’t worry 👍 Yes, exactly. The key point is this - the most severe forms of autism aside for the moment, most autistics are perfectly happy and do not suffer if they are allowed to “live in their own world”, ie structure their daily lives according to their own needs, and have the ability to pursue their chosen interests. It is chiefly when we’re forced into environments, situations and pursuits that are fundamentally at odds with our psycho-neurological makeup that we get into distress, which triggers things like the need to stim, sensory overload, and autistic burnout. I think one possible way to help the autistic community at large, would be to exist within a system that provides some form of UBI (universal basic income). This would remove the pressure of having to somehow earn a basic living, while providing opportunities to contribute to society according to our strengths and abilities - and these contributions cannot always be measured in monetary terms. Needless to say, this would also benefit other groups whose contributions to society at large can’t be measured in money. Just my two cents Yes, that’s a good point. I think there’s no objective measure for this - normal is what accords to the general consensus of what constitutes normality, so it’s down to who is in the majority. It’s a numbers game. Yes, your absolutely right. As they say: judge a fish by its ability to climb trees, and it will never amount to anything. That’s often how it is with ND people.

Yes, absolutely. But remember the context of this discussion - the claim was made that autism is a disease that’s due to blood toxicity, and can be cured on that basis. This of course is utter nonsense, and as an autistic person myself I’d really wish there was a way to rid us of such snake oil salesmen (and there are many of them). Autism - like other forms of neurodivergence - isn’t a “disease”, it’s a difference in brain physiology that has genetic, developmental and environmental factors involved. It cannot be “cured” in the classical sense, for that reason. It manifests across a range of areas - social, cognitive, executive functioning etc -, and impacts a person’s quality of life anywhere on a spectrum from very mildly to extremely severely. Succinctly stated, neurodivergent people tend to have support needs - we must live in a world that is fundamentally designed for neurotypicals (both culturally and evolutionary), but because we aren’t neurotypical, some expectations can be hard for us to meet and some situations difficult to handle, and we need support and accommodations to manage them. Some of us need only a little (or no) support and accommodation, others need a lot, and for some it’s debilitating, and they need 24/7 support and care. So in my personal opinion, it’s not about “curing” autism - which fundamentally suggests that we’re somehow deficient and need fixing, which is a questionable stance to hold. Rather, it’s about recognising that autistics may need extra supports and accommodations in certain areas, and being willing to offer those. There are also meaningful interventions available for at least some of the more severe and debilitating manifestations of autism, and I completely agree that these should be offered so long as the aim is to improve quality of life, and not just to make people “less autistic” and “more normal”. That’s an important difference. We will never be neurotypical, but with the right help we can become less dependent on external supports. There’s another thing I’d like to mention, which is not so often talked about - some commonly held life goals and values that are normal and generally unquestioned in the neurotypical world may not be shared by all autistics. For example, wanting and needing to be social and around others, wanting to acquire possessions and material goods, wanting to have family and procreate, conforming to gender norms, following generally accepted blue prints for how life should be lived, ideas around what has value and what doesn’t, concepts of what gives us meaning and joy in life etc. While this is of course very individually different, not all of us autistics share these goals and values, so we end up in a situation where we are forced to try and fit into a society and culture that feels fundamentally alien to us. We can’t be our real selves, but must train ourselves to wear a certain mask and act a role so that we might appear to be able to meet the expectations of a neurotypical society, simply because it’s practically and logistically very difficult to exist outside that system. We feel like we don’t have a choice, so we live a life that’s at odds with who we are. This creates a lot of suffering and struggle. So at least part of our suffering isn’t due to autism itself, but due to demands and expectations placed on us by others to “be a certain way”. Such behaviour - called stimming - causes us no suffering. On the contrary, it feels soothing and comfortable, and dissipates the perceived pressure of sensory overload. I do it by (gently) pressing certain places on my hands for example, and it helps me to self-regulate. Who are others to say that this is wrong and needs fixing? I would suggest that the problem here isn’t this particular behaviour pattern itself, but how it is perceived by others. From a neurotypical point of few it appears meaningless, odd and not normal, and it is tacitly assumed that the one engaged in it does it only because he feels compelled to do so, and thus suffers. But it’s not like that - it’s a self-regulation tool, like people take a painkiller when they have a headache. Both help increase well-being. The problem is only that society has deemed taking painkillers to be acceptable behaviour, but not flicking your fingers. If you stop an autistic person from stimming, or shame them into hiding the behaviour, you aren’t acting to promote their overall welfare, even if as a result they might appear “more normal” and supposedly fit in better. I would suggest that training autistics to appear less autistic is generally not in our overall best interest, unless we ourselves specifically ask for such interventions. This is a difficult ethical question, particularly for severely autistic children - there’s ways and training methods to make them appear less autistic, so they can function better in neurotypical society. The price they pay of course is that they’re forced to be something they’re not, that they’re forced to play a part in a story they themselves haven’t read or understood. Are you really doing them a favour, are they really suffering less afterwards? Most people in the autistic community who underwent such childhood interventions seem to say that no, it wasn’t in their best interest, even if it did enable them to function better in society. The general consensus is that providing supports and accommodations on an individual basis if and when needed, is probably the best way for most of us. Sometimes that means we need a lot of support, and that’s the measure of a modern enlightened society - how it relates to their weakest members, who perhaps can’t contribute in traditional ways. Caveat: if the behaviour is dangerous, or injurious to one self or others, as sadly sometimes is the case, then of course intervention is necessary regardless.

You might have, had you met me in person Though I generally mask quite well, so even IRL it may not be immediately obvious to people. Autistic people very often develop intense interests in certain topics, and sometimes hyperfocus so much on those that they become quite knowledgeable and proficient in them, even though they aren’t formally trained experts in their chosen field. It should be noted though that - contrary to the commonly imagined stereotype - this is not always in an STEM related subject. It can be anything from art, history, music, politics etc, to something very specific like trains, jeans, or Elvis Presley. One may also have a hyper-interest in more than one thing at a time, and sometimes those interests can change over time. We are as different from one another as any other group of people, and the idea that all autistics are math geniuses is a common but inaccurate misconception. On another note, autism is not the same as savant syndrom - these are distinct diagnoses.

The solution is for people who are not themselves autistic, and who evidently don’t understand what autism even means, to stop proposing “solutions”. I am autistic, and I am not a problem that needs to be solved.

I’m probably forgetting something obvious but…what are you referring to by “types”? Do you mean the Weyl tensor, Ricci tensor, and Ricci scalar?

Not the AT specifically, but I’ve done a few of the long-distance trails around Europe. Meant to do the Continental Divide Trail a few years back, but had to cancel due to Covid. Agree with everything @TheVat said, especially the bits about water. One can’t be careful enough, there’s nothing more miserable than a stomach bug on trail. Personally I’m partial to my good old Sawyer Squeeze filter, has served me well for many a trail!

This would be contributions from distant sources, as opposed to local ones, as well as contributions from any non-zero cosmological constant. Basically anything that stops spacetime from being completely flat before you account for any local energy-momentum. I agree, in this type of scenario you have clear causation in an operational sense. However, I was really thinking more of an isolated system where all parts remain in free fall at all times. Energy-momentum is locally conserved (the divergence of the tensor vanishes) - but then so is curvature (Einstein tensor). You cannot locally create nor destroy Einstein curvature, any more than you can create or destroy energy-momentum. You can only shift these around, and have them change form - so which ‘causes’ which? Not directly, but it contains energy density.

While these comments are certainly true, I think the relationship isn’t as trivial as it might appear; after all, a vanishing Einstein tensor doesn’t necessarily imply a flat spacetime, so these equations form only a local constraint on geometry, but they don’t uniquely determine it. Any background geometry is as much considered to be a ‘source’ as is local energy-momentum, when it comes to working out the particular form of a metric at a certain event. Furthermore you have the non-linearities of the constraint itself, which, in some sense, might also be considered a ‘source’. But those contributions of course don’t explicitly appear. Personally, I just think of spacetime as pure geometry - the only difference between vacuum and non-vacuum is how the Riemann tensor decomposes (Weyl and Ricci curvature), so I envision it purely geometrically all the way. In that way of thinking, no question of causation arises, you just have ever-shifting geometries. But maybe that’s just weird old me

That’s because mass never appears in the GR field equations - what is generally called the source term here is the energy-momentum tensor. One must also remember what these equations actually say - they state a local equivalence between a certain combination of components of the Riemann tensor (the Einstein tensor) and the energy-momentum tensor. Nowhere does it claim a ‘causative relationship’, but instead it says that these two are the same thing (up to a constant of course); neither one comes first and ‘causes’ the other.

Indeed. Just wanted to mention this again quickly in case other readers find it helpful to have some geometric intuition what the various aspects of curvature - Riemann, Weyl, Ricci - actually mean.

Another way to say this is that, in this kind of spacetime and under geodesic motion, shapes (ie angles) are preserved, whereas volumes and surfaces are not.

This short document might help, particularly chapter 3: https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/first_order_approximations_in_general_relativity.pdf

Sorry, I have not been able to keep up with these discussions over the last few days, as I’m busy with a large RL project. What was the question here? deSitter spacetime has non-zero Riemann tensor, so it’s not flat.

In fairness, I think this misrepresents what KJW is trying to say. How does a freely-falling test particle under the influence of gravity move? It follows a geodesic in spacetime, which is a particular solution to the geodesic equation. This equation is itself a particular form of the principle of extremal ageing, ie the tendency will be for the test particle to move such that a comoving clock will record an extremum of proper time between any given pair of events along the trajectory. When you actually perform this variational problem, of course all components of the metric are technically involved. However, when you are dealing with situations that are in some sense close to being Newtonian / not too relativistic, such as Earth for example, the tt-component of the metric will be much larger than the rest of the metric, by a factor of ~c^2. It will dominate the calculation - meaning time dilation plays a much larger role than tidal effects. In that sense, it is indeed almost exclusively time dilation that gives rise to our daily experience of “downward gravity” here on Earth. Of course, this would not be true in other situations, like near the EH of a solar mass BH, where tidal gravity plays a major role. This doesn’t mean that the source of gravity isn’t energy-momentum and curvature, it just means that under certain circumstances the tidal components don’t play a major role, leaving mostly just time dilation as the dominating effect.

The kind of wavelengths you get would depend on the specifics of the setup - it’s conceivably possible to get visible light too. For a stationary charge supported in a gravitational field, the result I am familiar with from the literature (see link further up in the thread) would indicate that a comoving detector would not detect any radiation, but another detector freely falling past the charge, would. Good point. But I think given enough charge and enough acceleration, it should be detectable. I must admit I’m not sure what the actual numbers are like, I never looked at this in that much detail.

AFAIK (and can remember) it comes basically from the general definition of the Hamiltonian, with the potential field \(A_{\mu}\) plugged in. I’m a bit pressed for time these days (involved in a big project here at the monastery), so I wasn’t able to immediately find a proper textbook reference; but the second-to-last answer on this PSE thread outlines what I mean: https://physics.stackexchange.com/questions/283519/derivation-of-electromagnetic-stress-energy-tensor-in-curved-spacetime I’ll have to dig through my notebooks when I get a chance, I know I’ve got a proper reference on this somewhere.

Sure - isn’t that already a suitable model for the situation at hand? The charge is seen to radiate in some frames but not in others. Ok - this doesn’t sound like too hard of a test to perform, I wonder if this has been done? I remember having seen this done, so I’m aware of the concept. What problem do you see with this?

But we’re not giving up covariance, are we? We’re simply considering how the EM field - a covariant object - decomposes in a particular frame. Is this not a form of non-locality? Basically you’re saying that whether or not a charge radiates in some local region depends on the existence of potentially distant sources (=external field). I need to think about this one first