geordief

I have heard that ,in relativity (and QM?) the (sentient) observer and the mechanical mechanism are equivalent. This comes up from time to time but not as often as I might expect. Is that because it is a mundane observation (ironically ) or is there more to be mined from it (perhaps my lack of intellectual curiosity has not kept me abreast with current thinking around this) ? For example is it related to questions such as why we cannot "get outside" of the universe and look at it as a whole (in the mind's eye) but are forever condemned to be looking at ourselves (through a special part of the anatomy possibly) ,which seems like a logical contradiction to me.

Have to admit ,I am out of my depth....

Can it be said that the speed of light is an example of the maximum speed of propagation of information and as such is measured by all observers as the same value? (I am fairly sure though that this maximum speed is observed/posited rather than proved logically) Can it also be said that all inertial observers will measure the rate of relative motion between 2 other bodies when account is taken of the spacetime interval : ie when apparent relative movement is adjusted for "real" relative movement ?(it is a question, I am not sure of this)

Maybe the present is an illusion( it sure is fleeting,are you sure it was there? )

Does not the observer also "observe" him or herself too? The observer (human ,ie brain) can be considered to be made up of components with the useful illusion of being one thing when in fact it is a system. The speed of information applies within the system ;even the speed of light applies although it is unmeasurable in that context. For an observer to observe any event "in vacuo" is impossible,I think. edit: I also feel there is no boundary between the observer and the observed, so apparently that Wheeler graphic applies to my predisposition ,although the "universe" I have in mind is not cosmological but fundamentally neighbouring or local.

Yes,that was what I was thinking of (the mistake I was making,) So what relation does the Cotangent Space have to the Tangent Space? I appreciate that it is its Dual but is it related in any other way? Is there any significance in the fact that the Tangent and the Cotangent are inverse of each other in regular geometry? Are these two spaces somehow also inverses of each other? It is not the case,is it that they are related by means of a 90 degree rotation about a common (0,0) vector?** **edit: I think I have learned elsewhere just now that this can not be the case

Suppose we have two hotels in an earthquake zone. Each hotel has an observer inside that uses the hotel he/she is in as their local coordinate system ie Observer A uses the different room levels to indicate the value of z and points along the sides of the walls to indicate the values of x or y . After an earthquake , one of the hotels is pushed up on its foundations with the result that Observer B's coordinate system is tilted by ,say exactly 45 degrees in each of the x,y,z directions .... (Faulty Towers ) Is Observer B's coordinate system (vector space) now the Dual of A's ? Vectors in his coordinate system do indeed "pierce" the coordinate planes of those of Observer A. Do I now understand the idea behind the Dual Space?

Well to go with this 2 dimensional surface embedded in the 3-space I think I have a very clear picture of the Tangent space.To describe it it would be as if I was one of those circus performers spinning plates at the end of a stick. I,the performer am vertical (normal) to the surface and the plates ,hopefully are spinning in the Tangent Plane. And ,yes I think I would describe that tangent plane as a 2d subset of the 3-space But where is the Cotangent plane,? Not representative by one of the other circus performers doing cartwheels from what you seem to be saying (and as I was imagining it) I thought it was a plane orthogonal to the Tangent Plane, very much like the z=0 plane is orthogonal to the x=0 plane If that is not the correct plane then I am stumped. Perhaps I am getting mixed up with the terms "plane" and "space" Is the "Tangent plane" the same as the "Tangent space"? I am grasping at this. Is it ,with covectors as if , instead of running x,=,y = and z = lines across the 3d space and measuring the vectors against them ,with covectors we are ,instead drawing parallel surfaces (e.g. x=0,×=1....y=0,y=1.....z=0,z=1 ...z=n) and measuring how many surfaces the covector passes through? With the distance between surfaces being perhaps arbitrary or perhaps corresponding to that used on the ordinary framework used by the normal vectors. Is that why I am reading about parameterization and linear functionals at the moment (either reading around the subject or going in circles )

Is the Cotangent Space not perpendicular to the Tangent space then ? If it is not then it seems I have my wires crossed I thought it was a space defined by/including a vector that was erected normal to the point p on a manifold (I was thinking of a 2 dimensional surface) Perhaps you are telling me that it is simply the dual space of the Tangent space and there is no visually geometric representation of it (as there seems to be with the Tangent space) I am not really familiar with the concept of the Tangent space of a line .....

Would the Tangent space at x be a plane above and along the line and the the Tangent space any one of any number of those vertical "revolving doors" you go through going into e.g. a hospital? That "revolving door" is centred at x. If you take the Tangent Plane and "swing it" 90 degrees ( about a fulcrum at x) you also get one of the Cotangent planes(set those planes "revolving" and you get any number of them.) Does that make sense?

Well I have come across the geometrical representation of the Tangent space as a kind of group of all the vectors at a point of a Surface that are tangential to the surface Visually they look a bicycle wheel with very many spokes lying flat on the surface with the centre of the wheel situated at the point on the surface Now ,the Cotangent Planes I view visually as an open book with many,many pages and with the spine of the book following a direction that is perpendicular to the point on the surface of the surface. So I picture the first plane (the Tangent plane) as geometrically perpendicular to the Cotangent Planes I see them as very similar but mutually perpendicular. Have I got a correct picture of the Cotangent plane(s)?

I have read that the Tangent space and the Cotangent Spaces are Duals of each other. Why is this so? I can understand that both are vector spaces and so "qualify" on that account but are they uniquely qualified to be Duals of each other ? Is the fact that they have a vector in common (the point p on the surface) important*? Can the Tangent space be Dual to any other vector spaces or is the Cotangent Space the only possibility? *important in making them Dual Spaces

Assumption is a dangerous quality.I assumed I would be more or less happily welcomed into Canada as I was from the UK. But I answered the totally unexpected "have you ever taken drugs?" question truthfully and was refused entry (from the USA). Many years ago... I also would assume that members of the Royal family would be especially persona grata in Commonwealth countries but perhaps this is not so now(if it ever was) Still I agree that ,as a representative of the Queen he should fit the bill although perhaps some Canadians might prefer to keep a distance from that sort of an entanglement and might feel that a ceremonial Queen is enough. Certainly in the UK the term "hangers on" is quite easily applied to outer members of the Royal family.

Sure,your description of her "house rules" does sound a little maniacal but on the one hand her private life (and that of her household ) is of no real interest to me personally or hopefully to anyone else immune to prurience. And secondly I cut her slack on account of the strange conditions she lives in - that I would like to a kind of prison environment. I think she is a class act because she copes with her harsh conditions without real complaint when the rewards are hard to discern (apparently she considers that she has a duty to the country-I think she is deluded but I respect her fortitude ) The issue of Monarchy versus other forms of self government is what concerns me most -the rest is incidental.

We Brits don't like the Monarchy (well , 'lisabeth is a class act) Would you have room for any more boarders?

That and gaining more power when no one from the Repubs objects.Divide and conquer

Yes, a better search doesn't bring up anything at all to back that up. Had there been anything in it at all I would have found it very interesting ...but no news is no news.

Does GR have anything to say about particle physics? When two particles collide is it just a case of going through the debris and looking for new objects or are there simple collisions where it is possible to predict when the initial conditions are known? I am reading through Einstein's Popular Exposition and have come across this quote "The only statements having regard to these points which can claim a physical existence are in reality the statements about their encounters. In our mathematical treatment, such an encounter is expressed in the fact that the two lines which represent the motions of the points in question have a particular system of co-ordinate values, x1, x2, x3, x4, in common" https://www.bartleby.com/173/27.html which seems to describe the "collision" of two world lines... (I am also learning that AE was a strong user of hallucinogenetic drugs and am quite astonished not to be aware of this until now https://vocal.media/futurism/11-things-you-may-not-know-about-albert-einstein I researched this when I came upon his introduction of the "reference-mollusk" description in his book and thought "hold on a second here....what?" https://www.bartleby.com/173/28.html "This non-rigid reference-body, which might appropriately be termed a “reference-mollusk,” is in the main equivalent to a Gaussian four-dimensional co-ordinate system chosen arbitrarily" and thereafter )

I am going through this section of Einstein's Popular Exposition of Special Relativity https://www.bartleby.com/173/10.html#txt1 "In the first place we require to determine the points Aand B of the embankment which are just being passed by the two points A'and B' at a particular time t—judged from the embankment. These points A and B of the embankment can be determined by applying the definition of time given in Section VIII. The distance between these points A and B is then measured by repeated application of the measuring-rod along the embankment" and have two questions I seem to need help with 1) What might be a rigorous set up of an experiment to show this scenario?(I am struggling with synchronizing the passing of the 2 points wrt to the observer's FOR) 2) Suppose we have an object moving at a relativistic speed wrt an observer.... This object emits a light signal which is both transmitted directly to the observer and is also reflected immediately **off another object which is at rest wrt the observer. Which signal does the observer see first? Do they both arrive simultaneously except for the retransmission time involved in the reflection process? **ie the spatial distance between the moving object and the reflecting object in the same FOR as the observer is vanishingly small.

Is it possible to indicate what other factors might contribute to uniquely determining the local geometry? (no one factor is the unique determinant if I have understood correctly)

Is the distribution of mass/Energy in the universe synonymous with the gravitational field? By that I mean ,if we attempted to visualize the gravitational field would we end up just using the arrangements of the galaxies and stars and say "that is what the gravitational field looks like.You are looking at it" (because some people seem to say the gravitational field is just a model -or a set of measurements, and others seem to say "no,it is as physically real as anything else ")

No,I have given up* on that idea ( that there was a point that could be identified as the origin of spacetime allowing some kind of a privileged frame of reference) But I am still wondering whether the gravitational field** can be said to increase (or decrease) in extent over time in the same way that the universe itself is said to have expanded (and inflated) Did/does the magnetic field expand with the universe even if not from an "origin" as I wrongly suggested before ? *because it has been shown to be untenable. **am unclear whether we can talk about one gravitational field(They are after all supposedly infinite in extent)

Is it possible/reasonable to assume that ,as Gravity first established itself (around T + zero seconds?) it came with a Gravity Field as part of the package ?(that Gravity and the Gravity Field were the same thing) So did the newly formed Gravity Field start off small and expand along with everything else? Does the analogy of the expanding cake in the oven apply to the Gravity Field(I have taken the raisins in the dough to represent Galaxies etc but could they equally well represent the Gravitational Field? ) Also , although it seems impossible to talk about mass in isolation from the global Gravitational Field does "global" there just mean "non-local" and so we can (if that is a sequitur) talk about different Gravitational Fields even though they are all interconnected?

So it is not just the "singularity" that is a roadblock? This is a period where measurements ,if possible would be finite?

Apparently spacetime was established first (At T+10^-43 seconds if I have that right) and em radiation came next. I am wondering have any simulations or discussions been done as to the evolution of spacetime (ie gravity?) during this epoch ,as it it probably referred to. Apologies if this question makes little sense but I have just come on upon this topic and would not know how to go about researching it or if there would be any point in doing so.