studiot

Well think again Sorry the graphs are to do with manifolds more generally.

Indeed so, or at least nearly so as I have said to several members, several times in the past. This fact also has implications for the thread about 'time travel', which I have been trying to bring out, but others seem to have abandoned that thread. Note that whilst a line may have zero Gaussian/Riemannian curvature, it may still have torsion, which is a similar but different thing. A to the question of are all 1D manifolds flat, that was the point of my figures A and B. A is a plot of a second order differential equation - that of the rate of a chemical reaction - the reciprocal of concentration is plotted against time - one axis is non linear B is a plot of a first order differential equation - that of radioactive decay - log(activity) is plotted against time - again one axis is non linear

Tomatoes.

With regard to 'flat' this post was wasted in Marius' threads but is highly pertinent here, So I will reproduce it in full. It is important to distinguish the measure and the measurand in all circumstances. That is the ruler is not the same as that which is being measured. Failure to do this leads to much misunderstanding. Here are two 'straight line' graphs. Or are they ? Straight is the one dimensional version of not curved or zero curvature ie flat. I would be interested in your response to the question.

Yes, but this is what I mean by not mixing up the measurand and the measure. The appropriate variation should be applied to one or the other, but not both. As an aside it is worth considering the origin of the word 'Frame'. One to two centuries ago measurements were made with rigid rods and surveyors extended these by using metal chains. There was even a unit of measure called the chain. So it became common to imagine a coordinate system as a rigid metal framework extending in all directions from the body of interest and marked with grid marks of the measure. This metal 'Frame' always moves along with the body, where its origin is located. So measurements in this frame are taken against the grid marks inscribed on it. Originally frames were referred to as rigid frames. Since the numbers are preinscribed and number is a relativistic invariant in both SR and GR, all observers will observe the same number of grid marks. It was the genius of Einstein that led us to realise that we must therefore adjust the comparison between the grid marks on the rigid frames for different observers in some way to accomodate this, since in general each observer will see the measure between these marks as different from the ones in his own rigid frame. This matchng can be done in one of two ways. Either by transformation (SR) or by applying a 'metric' (GR)

I missed that late last night. Another well thought out post thank you. +1 Thank you both for a good discussion about current particle physics. +1 As an applied mathematician, my formal study of pp ended in 1970 and I have only followed it sporadically for interest since. My work went in other directions. One thing that leads to many misunderstandings is the difference in terminology between Mathematics and Physics, especially for such fundamental 'objects' as Field, Vector, Tensor, Particle and Space. It is therefore important not to mix up physical objects such as a physical fields and mathematical fields, as not all properties are interchangeable/applicable in both disciplines.

Thank you for this clarification. So we are talking about fibre bundles ? In fact not about physical 'space' at all, but some abstract (mathematical ), space, inhabited not by physical objects but by mathematical ones. Good point, +1

Since you seem to want to discuss gravity effects in particular, I'm not sure how you want to apply these in the 'internal space of particles' or even what you mean by this. Compared to other effects, gravitational effects are very small at short range, such as inside particles, but come into there own at galactic distances. Are you looking for effects such as the grazing incidence of starlight passing the Sun showing up in EM radiation passing the nucleus in the otherwise empty atomic particles or ?

We don't have subthreads here, but I have put a comment into that thread you refer to since it also discusses curvature. Meanwhile I look forward to your 'many answers' here. Even though you don't have a question we need something specific to discuss as the topic of the thread. This something does not have to be a question.

It is important to distinguish the measure and the measurand in all circumstances. That is the ruler is not the same as that which is being measured. Failure to do this leads to much misunderstanding. Here are two 'straight line' graphs. Or are they ? Straight is the one dimensional version of not curved or zero curvature.

That didn't answer what you want to discuss about them ? With regard to Feynman's calculations. I don't have access to the observational data necessary to check them. But given the pedigree of the author I would start from the premise that they are accurate. They are the sort of observations and calculations that allow determination of intrinsic curvature in an N-dimensional manifold from within the manifold. (3 in this case). Note however that in the space of the universe the curvature varies from point to point, (ie is local), according to the nearby distribution of mass.

your actual question here is Unfortunately the answer here is that nobody really knows. It is empircal. That is appears to be an observed fact in the face of the unavailability of alternative hypotheses that do not contradict other existing observations. Read my last sentence very carefully because alternative and accepted hypotheses have been overturned in the past on the basis that they predicted something that does not happen by observation. The most spectacular such overturning is probably the discovery of oxygen when it was held that if a substance burned it lost something (which seemed very reasonable at the time), but when all the products of combustion were first collected and weighed their weight was always found to exceed the original substance weight so in fact the only tenable hypothesis was that the substance gained (combined) with something unknown.

This could be an interesting thread. It has a title but no point of discussion. One question. Do you want to discuss just 3D space or 4D spacetime or both or none of these ?

How is this time travel ? How is travelling forwards in time in any way consistent with the OP which specified travelling backwards ? Are you going to address my comments in response to your previous post? Happy New Year.

This is the sort of 'time travel' that is not physically possible, in the spacetime manifold that we observe around us.

Edit Yes, look carefully at my train manifold and you will see the beginnings of the model. In essence, yes. See my earlier posts.

Nothing stops you from pulling the trigger. I already explained that neither you , nor your trigger can 'travel in time' the way described. However if folks want to discuss why 'time travel' is impossible we should really do this in another thread.

This is exactly one sort of situation I had in mind when I said that the commonly understood time travel scenario is impossible. The twins demonstrate another form of time travel. The killing your father sort is impossible so no paradox arises.

I mean that the in particular the time sub manifold of the spacetime manifold is the wrong shape. (Shape is defined by the relationship between the points of a manifold) There is only a direct relationship between 'adjacent' points in the time sub manifold. (That is a definition or another way of saying there is only one time dimension). Conmsider another one dimensional manifold - a single tack railway. How would an express train pass a slow train on such a track ? It may be possible for microscopic quantum objects to do this but not for macroscopic material ones. Immaterial waves also have this capability.

Well I don't agree that time travel ( as you and Moontanman appear to envisage it) is possible within the universe as we know (observe) it. The spacetime manifold is the wrong shape to allow this.

Computability is a branch of Mathematics, it is not about IT in general or any sort of 'Computer Engineering' Note that not all computing technology is based on 'logical systems', there are for instance such things as analogue computers which work on entirely different principles. Swansont has probably the most relevant comment There is a heirarchy of systems of logic, known as First Order, Second Order and so on. The most commonly referred to is First Order Logic which basically corresponds to the popular idea of systems based on black and white, one or zero, high voltage or low voltage, True or False... etc. Associated with FOL is something called 'The Law of the Excluded Middle' This declares that every possible result is either a 1 or a zero or whatever. Or as the name suggests there is no middle or third option. This works very well for logical systems that can be broken down into simple enough parts. But many systems have compound situations and FOL can fial in these cases leading to such paradoxes as "Nick the Greek says that all Greeks are liars" Second Order Logic dispenses with the Law and can overcome these paradoxes. But there are many other variatios of the theme, both in the 'hardware' (physical implementation) and the 'software' (rules) of logical systems.

You are actually asking about two different things. 'Computability' and 'Logic'. In the UK the definitive books is https://www.amazon.co.uk/Computability-Logic-Fifth-George-Boolos/dp/0521701465 (Boolos is the principal author) Earlier editions can be had for a few quid.

Thanks all for you input. SJ in particular I am not ignoring you, I just wanted to go to bed. Interestingly I don't get the problem on my trusty old Dell P4 optiplex with Windows XP, that I use for serious work.

Update. I got a X to 'close' in the top left corner of the latest one. When I clicked close I got a Ads by Google notice replacing the original ad When I clicked to 'not see this again' I got three questions as to why not Can't see why they think I( am ever going to take an Expedia holiday or buy cushions for my non existant flat or other such rubbish.

Windows 10 with edge.