Col Not Colin

Laboratory rats is something that comes to mind. You have a collection of forums here, people making and replying to comments from others all the time. I cannot imagine how many times these people and posts have been analysed and even directly manipulated and interacted with for the purposes of someone's research. That might very well be some experiment in Psychology, a study on how the internet is used, or something similar. It's quite kind and ethically minded of you to let people know why you're asking for the thing you want. I wouldn't recommend deliberately starting a false discussion or manipulating the forums but browsing through all those threads that already exist here seems like fair game. This is a public forum and people should know their comments can be read by anyone. Sadly, I don't think you'll find those letters between attendees of the fifth Solvay conference you were looking for. Well, maybe with a lot of digging and after twenty years have passed so that you can see which people or ideas did become significant. Public forums tend to attract people with time to spare, something to shout out about and then also tend to cultivate cliques and self-appointed experts. Active scientists, going to a modern Conference, don't have the time for a forum like this. I'm new here, with little experience of this forum and not pointing any fingers at anyone, that's just how it is in many other public forums. Anyway, I'll have another read through all you've written and see if I can think of anything useful that fits your requirement. The trouble is I'm new here and attaching, scanning and or even just seeing if I can drag-and-drop in formulae is something that will take me an hour. To anyone reading this ---> Why isn't there a simple equation editor at the top of the toolbar? If you are designing a new interface for this thing, Slomobile, please put one in.

Maths person here, not trained in Psych. stuff. I've just done a brief survey of "special interest" as applied to individuals with Autism on the internet. Do you want comment by an untrained layman? Also, I'm only here because of the unusual situation at the moment. Covid-19 lockdowns forcing discussion onto the internet etc. If you're doing research on internet forums beware of biased data at the moment.

I hope this isn't another topic left abandoned by the OP. Started 8 December with this question - Can infinites exist in nature? What if the answer is yes BUT only if you consider mathematical objects that may not have any meaning in the real world. Classic Example: Send an object at a fixed speed from a start line to a finish line. Count the number of times the distance to the finish line can be halved. For example, at the beginning the distance was d. A bit later the distance to the finish line was d/2. Then it would become d/4, later it would become d/8... etc. You might say it was halved infinitely many times and eventually the distance to the finish line was 0. Was that something that happened an infinite number of times? Also, did it happen in only a finite amount of time, that being the total distance d divided by the constant speed s? Generally we (human beings with some liking for science and maths) say yes to those questions. An infinite sequence of events can happen in a finite amount of time. There are bucket-fulls of other examples you can consider. However, the event or thing that happened is usually dependant on some mathematical construction - the halving of the distance in the first example I gave. If you decided that space wasn't the continuous thing we thought it was but instead it was discrete or quantised then halving the distance isn't something you could always do. Let's say that the planck length may be the smallest little chunk of distance that you can have in the real world. Then you could only half the distace when there were an even number of planck lengths to start with. You have to approximate the division by 2 otherwise. There was a large BUT FINITE number of planck lengths from the start line to the finish line, so there was only a finite number of spatial configurations (approximate halvings of the distance) that could have occurred. There are a number of scientists working on the idea that space (and time) is discrete not continuous and if this seems valid and useful then the things you mentioned - Many Worlds theory (Quantum Mecahnics) and the Big bang (Cosmology and GR) are going to get a good re-think and re-formulation anyway.

Not sure but you may want to fix the spelling of it-nerest in the title.

Hi Markus (and everyone else). Worry not, I think we all realise spacetime supports mathematical structure that we can call a co-ordinate system. I appreciate that you may prefer to sneak your co-ordinate system in through the back door by tweaking some of the requirements you previousy mentioned. Others, like myself and MigL, may put it front and centre by demanding that spacetime is a differnetiable manifold. You can have a +1 for your latest comment. I don't have a copy of MTW and my library is closed during a covid lockdown, so I won't be looking through it anytime soon. From what I can recall, not using any specific co-ordinate system is one thing and, of course, it is possible to use any arbitrary co-ordinate system satisfying a few requirements (as you mentioned earlier). However, denying that a co-ordinate system exists is a completely different thing. Just to be clear on what I mean by a "co-ordinate system": Spacetime is a manifold, it has an atlas with charts covering the manifold and then given any point in the manifold, there exists an open neighbourhood and a chart providing a 1-to-1 and smooth (or at-least C^p differentiable) correspondance to R^4. That local correspondance to R^4 is all we really need and that is what we can consider as our (local) co-ordinate system ("need" is also a stronger term than required, it's there and it's a non-negotiable part of the definition, whether we need it or not). Extending that local co-ordinate system to a global co-ordinate system should also be possible, since a manifold is usually defined as something that has a MAXIMAL consistent atlas (and every point in the manifold is in the domain of at-least one chart). There may be some unusual cases with things like a disconnected manifold where maybe a local co-ordinate system can not be uniquely extended to a global co-ordinate system - but I wouldn't be too worried. I'm not sure Mordred wanted to identify the most general object ever imaginable as spacetime. Indeed the type of manifolds that I'm considering are necessarily open sets in the topology induced from R^4 by the charts - but I've seen that it is quite possible to consider closed sets, often called manifolds with boundary and build a functional object we can consider as spacetime with that, if you wanted to. Anyway, what was that thing you mentioned earlier, Subjective Phenomenology, I'm going to go and look that up. I've got some time to spend while the lockdown continues. Sounds like a sociology thing but I could use a break from science for a moment. I might also catch up on a few YouTube videos, apparently there's some new evidence in support of MOND (Modified Newtonian stuff). Best wishes to everyone, I'll check up on the discussion later. Hi geordief. Do you want a Mathemtican's view? People often say continuity when they mean some degree of differentiability. Differentiability is a stronger requirement. For a simple model that we can call General Relativity, we assume everything is as differentiable as required. As regards the original context of the quote you sighted: The equations need to make sense, there needs to be "sufficient continuity for the equations to make sense". One Tensor involved is the Riemann tensor which is calculated by taking derivatives of the metric, so the implication was that there would be sufficient differentiability of the objects. I didn't write those original comments. That is only what I chose to understand by it. Bye and best wishes.

Hi Beecee, Joigus, Studiot, Dimreepr, MigL, Markus. For those who sent internet acronym definitions, I believe the response is ty, tyvm. I'm still waiting a day to see if the OP writes anything. Anyone know this Mordred person?

Hi MigL. I'm an old person, we used assembly language on a computer not modern internet acronyms. Does IOW = in other words? Anyway, I don't especially want anyhting. I'm not sure what the thread wants or what the OP wants. I consider myself a scientist, although my background is mainly in Mathematics. I almost agree with what you said about how science works. I, personally, wouldn't model physical space any other way. However I do have an interest in what space is actually physically made of, in addition to what physical and mathematical properties it must have - but that's not the main point, what does this thread or the OP want? For the sake of starting what may be a new discussion: There are other ways you could model the physical universe. See, for example, the work of Stephen Wolfram who uses ideas from computation. I do NOT mean programming a computer to find numerical solutions to some Mathematical model but instead modeling the universe as if it is governed by some simple, small algorithms from which he does seem to identify some emergent structure which can be recognised as General Relativity. I'm NOT an expert on any of this and I may have mis-represented his work but the essential idea is that it is not like building a mathematical model as we would understand it. Late Editing: I'm an idiot, sorry. MigL was probably talking to the OP.

I agree. This is the main reason why I suggested the OP focuses on this. It is far more difficult to explain what space is physically made of and the best answer may be "don't know, don't care, it's not required knowledge for GR". Space and Spacetime must have this Mathematical structure (and present a list of requirements similar to Markus) but that is all. I've also had a bit more time to think about what the OP (I believe that stands for Original Poster) was trying to do and where the collection of comments have gone since then. I've had enough time that I might even retract my own earlier statement There isn't much need to focus on what mathematical structure spacetime should have. That's already clearly explained and set out in any text-book. What Markus has done is slightly more interesting: We may be able to shuffle the requirments around and demand some types of mathematical structure instead of others and there should be a minimal set of requirements (although, I'm sorry to say that I'm not convinced Markus' list is that minimal set because I cannot see how we are going to get a co-ordinate system out of that list of structures and properties). However, defining spacetime by the minimal set of mathematical structure that is defined upon it and/or the minimal set of mathematical properties it has, is probably only of interest to people who favour Mathematics. Studiot seems to be representing the viewpoint of a more general scientist and not a pure mathematician. Defining spacetime as a Mathematical structure does not explain what it is, only how it behaves. He also goes further and states that Physical reality is the key and Mathematical representation is not. Beecee seems to have a similar interest in defining what space is based on physical reality and if I've understood the essence of his comments correctly, there is another useful idea contained within: Start from Special Relativity and add just enough to model gravity as curvature. Which raises another minor challenge for Markus: Do we really need item 4 in your list - the conservation of the stress-energy tensor? Are you (Markus) talking about the Binachi identities, the field equations with zero curvature (all zero Rieman Tensors), or something else? If our goal was JUST to model gravity as curvature then do we need anymore than the geodesic equation and an assumption that particles travel along geodesics (I suppose we could summarise both of these by saying that we require a least action principle)? Perhaps having the Einstein Field Equations is not a required goal. Your other requirements (such as 1 and 3) imply that the metric has already been given, or at-least is assumed to exist, and so we don't necessarily need the Einstein Field Equations to determine the metric. Don't worry, Markus, I saw your last line about "GR as opposed to other models of gravity", I appreciate that what I've just described is not a full model of GR as we know it. The main point is, until the OP or the audience make it clear what it is and exactly how much they need explained, we can't be sure what the minimal amount of structure required will be. There was a person called dad who posted in February 2020 and said something that actually seems sensible enough to me: (I don't seem to be able quote that one too well... the above was an answer to Mordred's original question "What is space made of"). I don't know the full context of dad's post but it was hated and got a -3 score. The only thing I would have added to it was ...because it doesn't matter, it's not required knowledge for GR. Obvioulsy I think we can and should discuss the issues otherwise I wouldn't be here but dad's post doesn't seem that silly to me. I'm going to put a +1 score on that. Anyway, is the OP still producing an article describing what space is made of? Is it time to focus on what space is actually physically made of instead of worrying about the mathematical structure it must have? What are we doing here and what is the purpose of this "thread" (that's what they used to call a collection of forum posts in the old days)? Returning to Studiot's comments. What is it that most people end up discussing in all those other threads entitled "what is space?" If the OP no longer has any direct goal and this thread stays open, what kind of definition or explanation is it that people want?

Hi Markus. Thanks for your comments. You may be right in your collection of requirements. However, there is some over-lap in the properties that they explain and will require and it is obviously possible to identify alternative criteria that are sufficient. I hope you'll forgive me if I take a moment to determine if the total collection of requirments you presented really is sufficient structure for GR. There were some earlier comments about requring a co-ordinate system and I would be a bit relunctant to let them go. Text-book definitions of the structure required in GR do seem to utilise charts, an atlas, diffeomorphisms mapping the manifold to/from R^n etc.. Such a definition also has the advantage of providing your requirement no.1 automatically. There is a topology induced on the manifold from R^n (specifically R^n with the usual metric on R^n). There doesn't seem to be an obvious way to extract a co-ordinate system from the set of requirments you have listed. I would say a co-ordinate system is essential for what is defined as Spacetime in GR, otherwise what you have is a perfectly interesting object (a topological space with some extra structure) that may exhibit properties that are in some sense similar to spacetime and GR but it's not what we can define as Spacetime. Hi Studiot. Thanks and I'll get to your coments later. I've got stuff to do for an elderly relative first. Please advise me if non-scientific personal stuff should be kept off the forums. I'm also not too interested in scoring points but I'll look into how I can award points to others later if that's important to everyone else.

New User here. Hi everyone. Please advise me where to go and what is appropriate, my apologies in advance for getting it wrong so far. 1. Thanks for pinning this post to the top of the board, it seems like a good one for newbies to start with. 2. It would help if the original creator(s) posted an update, so that we could see what the article looks like after 4 years of comments and editing. I've only had a scan through all the comments and that took a whole day. 3. Are you sure people often ask "What is space made of"? Have you got any surveys or other evidence for that? In my limited experience, most are happy to assume it's an empty vaccum. However, I do agree that people are quicky and frequently mis-lead into thinking that space is a stretchy fabric. I also agree with many of the later comments about quantum foam and vaccum energy that you could try to incorporate into your definition of space. If you are determined to incorporate QFT then I suppose spacetime does have to have fields in it. The problem is being certain that you have covered everything in your attempt to say what space is made of or even what mathematical objects must be supported and exist in space. There is almost no way of future-proofing the idea. Early General Relativity only really considered simple particle theories. It's unlikely anyone knew that anything like QFT, dark energy or vaccum energy could be added later. It's amazing that GR still seems to hold so well given that we have incorporated so much more into it than it was originally designed to model and we would be extremely optimistic to assume that nothing more will ever be added. As a consequence, I suspect the original creator would be better off not trying to tell people what space is actually made of - but instead focuses on what is the least amount of structure required for GR. Therefore, his/her definitions of spacetime as a (pseudo) metric space seem the better way to go. It is an ambitious target to try and describe all the (intangible) objects, like fields, that may be inferred or required to exist in space.