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What is Space made of?


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When discussing coordinates sytems and metrics is is important to realise that they are independent concepts.

A space can have a metric but no coordinate system and vice versa.

References to topological spaces have been made.

Topological spaces do not require coordinate systems and some topological spaces do not require a metric.

What is required for GR is continuity for the equations to make sense and the tensors to exist at all.

Mathematics now separates continuity into several allied concepts ( coincidentally all beginning with C) and I did promise Joigus a thread on the subject.

I suppose this is now becoming urgent.

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observable i'm using a new interpretation(that i made up) that means only thing observable by the human eye exist in it   and black holes basically suck light it "prevents" it escaping but i

I guess the answer is science doesn't know. Why guess?

Nope , you are now confusing 'science' and 'technology". Despite popular opinion, the two have nearly nothing to do with each other. And sometimes , 'technology' helps 'science' a bit forward. Bu

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10 hours ago, Markus Hanke said:

Spacetime is a mathematical model, it is not any kind of physical substance or object

 

6 hours ago, MigL said:


(IOW, space-time has no actual 'fabric' that bends )

Agreed, that's the way I see it also....In case I did confuse anyone when I said 

23 hours ago, beecee said:

All are essentially real: Space is expanding and the source of what we know as Dark Energy. Time is essentially interchangeable with space and is a variable quantity. Spacetime can be bent, warped, curved, lensed in the presence of mass.   

 It is our models that are real, and have best and accurately  described what we observe as close to reality as is possible. Something does not have to be physical to be real imo.

I'm an old bugger too. 

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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?

 

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Mordred has probably gotten busy with 'real life', and doesn't have as much free time to devote to forums.
We all await his return.

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17 hours ago, MigL said:

Maybe my idea of a metric is not the same as yours Markus, and if not please elaborate so that we may all understand better.

Well, in a pure mathematics context, the metric has a pretty abstract definition in terms of something called the “first fundamental form” - which essentially boils down to defining the notion of an “inner product” on your manifold. Physically, this means that a metric enables you to quantify lengths, areas, volumes, angles etc - so it makes it possible to relate physical laws to real-world measurement outcomes. More specifically in GR, it is used to quantify the separation between events in spacetime. Given a connection, this determines all the various curvature tensors etc.

I must reiterate that it is not my intention to deny that some coordinate system needs to be chosen in order to actually perform the calculation - however, the point is that the physics aren’t in the coordinate system itself, they are in structure of the metric, i.e. in how the components of the metric tensor (in a given coordinate basis) are related to one another. This is an invariant property, unlike the value of the components themselves. I meant it in this sense. 

12 hours ago, studiot said:

A space can have a metric but no coordinate system and vice versa.

Indeed, that’s pretty much what I am attempting to point out, with the addition that in the context of GR, the metric is the more fundamental object.

12 hours ago, studiot said:

What is required for GR is continuity for the equations to make sense and the tensors to exist at all.

Indeed.

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18 hours ago, studiot said:

What is required for GR is continuity for the equations to make sense and the tensors to exist at all.

Is that the same thing as differentiability?

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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.

 

 

 

7 minutes ago, geordief said:

Is that the same thing as differentiability?

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.

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1 hour ago, geordief said:

Is that the same thing as differentiability?

It should be noted that a differential manifold does not mean the manifold is differentiable.
It means that at least some functions defined on that manifold are differentiable.
It does not mean that the coordinate system is differentiable - that has no meaning eg the statements x, y or the x - y plane are differentiable are meaningless by themselves. They are short form for functions lying in the x - y plane are (or are not) differentiable. The x - y plane itself is quite indifferent to whether some function is differentiable.

A similar point can be made of continuity, but it is more complicated.
Functions are 'continuous' or not as the case may be.

Continuity for the space in which they lie has been broken down into lesser concepts of which connected is probably the nearest.

Topologically a circle may be 'continuously' deformed into a wiggly loop.
No metric or coordinate system is necessary for this.

Topologically we talk of transformations rather than functions, although they are very similar.

 

 

 

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17 hours ago, Col Not Colin said:

However, denying that a co-ordinate system exists is a completely different thing. 

Yes, that’s not what I am trying to do - though I do think it is possible to a large extent to talk about gravitational physics without making reference to coordinates. But of course, you need a suitable choice of coordinates to extract numerical predictions from the model, I wouldn’t deny that at all.
What I am attempting to emphasise is merely that the coordinate system doesn’t encode the actual physics on your spacetime, anymore than street names on a map encode the layout of a city; so while it might be necessary in practical terms, it isn’t fundamental as such. The physics are found in the metric and the connection. This is ultimately (in a physical sense) why one is free to change coordinate basis without affecting any physical prediction the model makes.

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Surely the basic Physics comprises the 'invariants' of the Theory ?

In SR the invariant intervals form a network that requires no coordinate system whatsoever.
In fact the addition of any coordinate system adds restrictions that are not present in the physics, in the similar way that the introduction of coordinate geometry restricts the geometry of Euclid.

For GR the invariants are different and still being worked on to this day.

https://en.wikipedia.org/wiki/Curvature_invariant_(general_relativity)

https://link.springer.com/article/10.1007/BF02726036

 

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17 hours ago, studiot said:

Surely the basic Physics comprises the 'invariants' of the Theory ?

In SR the invariant intervals form a network that requires no coordinate system whatsoever.
In fact the addition of any coordinate system adds restrictions that are not present in the physics, in the similar way that the introduction of coordinate geometry restricts the geometry of Euclid.

For GR the invariants are different and still being worked on to this day.

https://en.wikipedia.org/wiki/Curvature_invariant_(general_relativity)

https://link.springer.com/article/10.1007/BF02726036

 

Precisely. +1

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  • 2 weeks later...

In my aforementioned Murphy's law applied to e8 Vacuum Fluctuations thread, the m-brane portion of the model dictates that di-branes overlap it is like combining mathematical infinities, can't be done, so instead we must reduce the space between them in increments equal to their radii (the planck length) per transformation (which represents a planck time).

You can measure distance in three dimensions of direction. The time is change in these reductions in space created as the m-branes overlap

Sorry just apart of a potential thesis paper. Maybe I'll write it maybe I won't. Depends on which decision will get me what I want. Apparently it's neither decision, or both, or just dependent on the judge.

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On 12/8/2019 at 8:28 PM, studiot said:

 

 

How is this possible without an underlying coordinate system ?

 

I can't agree with this since the sticks (intervals) have a clearly defined measure.

And clearly there exists a stick between each pair of events in the set.

Even if the set includes every number in  RRRR

 

Spacetime is a concept mostly arising from the theory of Relativity. Phenomenologically speaking , either time does NOT exist ( almost implied within QM ) or there is an essence or entity or whatever truly existing by the name of "time" which fundamentally goes against the grain of Space. Space cannot be intrinsically grafted onto Time to provide for Relativity a hybrid by the name of Spacetime or Timespace. 

They are two differing entities not even hypothetically mathematically capable of merging together the way Minkowski wanted them to. Even worse was Dr Einstein's arbitrary adopting them into his own theory of Relativity through the artificiality of having a Riemannian ambience. I suggest reading most of the critique made by Prof Henri Bergson on Einsteinian mannerism of dealing with Time and Spacetime. 

These catastrophic events of going from the flat space of the much laboriously worked-on special theory of relativity to the queer curvature of spacetime in General Relativity are still affecting us in dealing with yet other problematics such as dark matter, dark energy, black holes, worm holes, negative energy, etc, etc... pushing us to be coerced into focusing hundreds or even thousands of much-energy-taking articles and books on yet another grotesque being by the name of Quantum Gravity. 

Then, come in the issues of pair-production threshold for gamma rays and of the photon-production threshold(s) for cosmic rays even when at Planck-Scale effects might be perceived as new paths for modern physics. Here even departures from Lorentz symmetry can take place,, and a very valuable type of particles physics processes to be brought in here are the ones that are totally forbidden in a STANDARD special-relativistic setup. I personally believe there is every reason why we should name all of the abovementioned processes "anomalous". 

 

I am doing my best not to go further and further into the noxious consequences of accepting spacetime (curvature). We have even had to dilate and contract time when this hinges onto the fixed speed of light. There many other anomalies, too. But enough of it all FOR NOW.            

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54 minutes ago, Prof Reza Sanaye said:

I am doing my best not to go further and further into the noxious consequences of accepting spacetime (curvature). We have even had to dilate and contract time when this hinges onto the fixed speed of light. There many other anomalies, too. But enough of it all FOR NOW.            

!

Moderator Note

You don't get to do this in ANY mainstream section. We have a Speculations section for challenges to mainstream science. Open a thread there if you think you can support your extraordinary claims, but don't hijack other threads with unsupported assertions. It's against our rules.

 
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17 minutes ago, Phi for All said:
!

Moderator Note

You don't get to do this in ANY mainstream section. We have a Speculations section for challenges to mainstream science. Open a thread there if you think you can support your extraordinary claims, but don't hijack other threads with unsupported assertions. It's against our rules.

 

Very Dear Moderator

Many many thanks for your hint. I feel now quite free to open and distend this topic in even better format (elsewhere) .......

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1 hour ago, Prof Reza Sanaye said:

Very Dear Moderator

Many many thanks for your hint. I feel now quite free to open and distend this topic in even better format (elsewhere) .......

I have started a new thread here for your convenience,

containing my answer to your comments

 

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