emil's black space-time

[Emil]

If there is an Einstein's curved space-time, then it must be another space-time, which is not curved, relative to which Einstein's curved space-time is curved.
I named this space-time, which is not curved as "emil's black space-time".
Now depends where you live.
If you live in Einstein's curved space-time, then you don't notice the curvature of space-time, in which you live, but you notice the curvature of "emil's black space-time".
To notice the curvature of Einstein's space-time , you really need to live in "emil's black space-time".

 

[przyk]

Er, no, it's possible to characterise curvature intrinsically in GR - i.e. without reference to an external higher dimensional spacetime, and in fact that's the standard way to do it. If you're living in curved space or spacetime, you have all sorts of measurable effects that differ from a flat space, that you can use to characterise the geometry. For example, the internal angles of triangles don't necessarily add up to 180 degrees, parallel lines can meet or diverge, and so on.

That said, you can do the mathematical exercise of viewing a curved space as being contained in a higher dimensional flat space. In Riemannian geometry this sort of thing is called an "embedding". An issue raised in another thread a while ago prompted me to Google this up in the case of GR. If I recall correctly, the result was that you could generally do the embedding, but in the worst case you might need a flat spacetime of up to 87 spatial dimensions and 3 timelike ones to contain the curved four dimensional spacetimes GR is capable of predicting.

 

[Emil]

Er, no, it's possible to characterise curvature intrinsically in GR - i.e. without reference to an external higher dimensional spacetime.....

I do not deny this possibility, I only say that it is much easier and accessible, for analysis, from "emil's black space-time" reference frame.
"emil's black space-time" isn't a higher dimensional spacetime.
It is just a curved reference frame , relative to Einstein's space-time.
So, the two curvature annihilated each other and becomes flat.

For example, the internal angles of triangles don't necessarily add up to 180 degrees, parallel lines can meet...

I do not understand why you say "paralle" if they can meet?
What is your definition for "parallel"?

 

[AlexG]

What is your definition for "parallel"?

Two lines such that a connecting line can be drawn between them with all four interior angles of 90 degrees.

In a flat, Euclidian geometry, such lines would never meet. In a curved, non-Euclidian geometry, such lines do intersect.

 

[Emil]

Two lines such that a connecting line can be drawn between them with all four interior angles of 90 degrees.

More simple : "Two lines in a plane that do not intersect or touch at a point are called parallel lines." (Two lines that never meet.)

In a curved, non-Euclidian geometry, such lines do intersect.

Only in the limit at infinity.

What is the relationship between Einstein's curved space-time and non-Euclidian geometry ?

 

[Emil]

Even this design

of space-time curvature is made from the perspective of "emil's black space-time".

 

[AlphaNumeric]

If there is an Einstein's curved space-time, then it must be another space-time, which is not curved, relative to which Einstein's curved space-time is curved. I named this space-time, which is not curved as "emil's black space-time".

Einstein's work covers both curved and flat space-times. It's based on Riemannian geometry, which covers all sorts of weird and wonderful, as well as mundane, space-times. Riemannian curvature flat space is Euclidean. Riemannian curvature flat space-time is Minkowski. Ricci flat space covers black holes, Calabi-Yau manifolds and the FRW space-time of cosmology.

If you live in Einstein's curved space-time, then you don't notice the curvature of space-time, in which you live, but you notice the curvature of "emil's black space-time".

So we notice the curvature of your flat space-time? Well done on contradicting yourself.

To notice the curvature of Einstein's space-time , you really need to live in "emil's black space-time".

I think you need to stop living in fantasy land, never mind 'emil's black space-time'.

What is the relationship between Einstein's curved space-time and non-Euclidian geometry ?

Here's a thought, why don't you learn something about geometry before making ignorant claims about it?

Non-Euclidean geometry is the geometry of spaces which aren't Euclidean, which is most. Einstein's work is based on Riemannian geometry which covers every possible space-time you've ever heard of. I say you because those space-time constructs it doesn't apply to are unknown to you. But then so are most standard space-times....

Even this design of space-time curvature is made from the perspective of "emil's black space-time".

No, it isn't. It's a half truth graphical representation of concepts which are not actually in relativity at all. Relativity doesn't say space-time bends actually like that. However, it isn't possible to draw the geodesics properly and yet get across their non-Euclidean structure due to spherical symmetry of the SC metric.

You're insufficiently familiar with the relevant material and thus you're reading too much into simple analogies aimed at lay persons. Actual Riemannian geometry is not that but you don't know it and it would seem you have no desire to know else you'd have done some reading before shooting your mouth off.

I hate to break it to you but you haven't got any insight into this stuff.

 

[przyk]

I do not deny this possibility, I only say that it is much easier and accessible, for analysis, from "emil's black space-time" reference frame.

The experience of people working in general relativity, and more generally with Riemannian geometry, is that it isn't easier to do it that way. Once you know how to handle the geometry intrinsically, that turns out to be the most convenient way to do it.

"emil's black space-time" isn't a higher dimensional spacetime.
It is just a curved reference frame , relative to Einstein's space-time.
So, the two curvature annihilated each other and becomes flat.

Then I have no idea what any of what you're saying is supposed to mean.

I do not understand why you say "paralle" if they can meet?
What is your definition for "parallel"?

Things are a bit more subtle when it comes to the notion of "parallel" in curved spaces. There are a couple of different but related ways of defining what I said more precisely, but the result is the same in any case: the properties of "parallel" lines aren't the same in curved spaces as they are in flat spaces, and this is something potentially measurable to someone living in such a curved space.

Even this design

of space-time curvature is made from the perspective of "emil's black space-time".

That's a pop science diagram. Nobody seriously uses it in general relativity.

 

[Emil]

Einstein's work covers both curved and flat space-times. It's based on Riemannian geometry, which covers all sorts of weird and wonderful, as well as mundane, space-times. Riemannian curvature flat space is Euclidean. Riemannian curvature flat space-time is Minkowski. Ricci flat space covers black holes, Calabi-Yau manifolds and the FRW space-time of cosmology.

No, my space has clear characteristics that I described above and is unique.
You only have to read it, but I have serious doubts that you will understand.

So we notice the curvature of your flat space-time? Well done on contradicting yourself.

This is your level of understanding. I spelled it out:

If you live in Einstein's curved space-time, then you don't notice the curvature of space-time, in which you live, but you notice the curvature of "emil's black space-time".
To notice the curvature of Einstein's space-time , you really need to live in "emil's black space-time".

I do not expect that you understand.

I think you need to stop living in fantasy land, never mind 'emil's black space-time'.

Look who's talking! Who lives in Einstein's curved space-time !

Here's a thought, why don't you learn something about geometry before making ignorant claims about it?

Again your wrong perception of reality.
You really don't know what it means, at the end of a sentence, a question mark?
You really don't know what is the difference between question and claim?

...before shooting your mouth off.

I didn't even open my mouth! You have a habit of talking in the meantime, you type the keyboard buttons?

I hate to break it to you but you haven't got any insight into this stuff.

I warn you that I will fight for my right to choose any frames of reference, which I think makes it easy for me, according to the first postulated.
"The laws of physics are the same in all inertial frames of reference."
If you want to take my right, with pirate methods, I will change the name of "emil's black space-time" in "our dark space-time" and I will call all to fight for our right to choose any frames of reference!

 

[AlexG]

Nothing Emil has posted in this thread makes any sense at all.

 

[Emil]

@przyk,

If you don't like my "emil's black space-time", not use it.This is mine. If you want, I borrow it to you but if you did not need it, I do not mind.

 

[Emil]

Nothing Emil has posted in this thread makes any sense at all.

Practical things are beyond you, huh?

 

[AlexG]

Practical things are beyond you, huh?

I am hampered in my ability to understand you by a physics education.

Let me know when you've read up on Euclidean and non-Euclidean geometry, then we'll see if your posts improve.

 

[Emil]

I am hampered in my ability to understand you by a physics education.

Let me know when you've read up on Euclidean and non-Euclidean geometry, then we'll see if your posts improve.

Seriously, think about how you notice (observe) that something is curved or straight.
You really need a "standard" for straight.
But if this "standard" is curved due to curvature of space?
You will not be able to notice (observe) this curvature.
You must get out of this system, to get a new system where you have a new "standard" for straight.
Compared to the new "standard" for straight, the old system is curved.

 

[AlphaNumeric]

No, my space has clear characteristics that I described above and is unique.

You haven't said anything unique or interesting or even valid. Flat space-time is a standard concept. It's a special case of Riemannian geometry. Your interpretations of even simple lay person pictures are wrong.

If you're able to understand some Riemannian geometry why don't you define your space properly. Give its metric. You do know what a metric is, right?

You only have to read it, but I have serious doubts that you will understand.

I'm absolutely certain I understand this stuff more than you. Simply stringing together words you don't understand does not a space make. But what would I know, it's not like I researched novel geometries for several years or anything....

This is your level of understanding. I spelled it out:

I do not expect that you understand.

You clearly don't understand the concepts of intrinsic and extrinsic geometries. Hardly my fault. The fact you're so innumerate that you can't define what you're talking about properly isn't other people's fault.

For example, if I were going to define a space I wished to talk about the first thing I'd do is give its metric. Failing that I'd give the homology structure or the immersion, if it's an immersed space. You've given none of those, I doubt you even know what they mean.

Look who's talking! Who lives in Einstein's curved space-time !

I can't help but feel you're wailing against things you don't understand. Previous relativity related discussions you've been involved in have served to highlight how little you grasp of even basic bookwork, never mind have novel ideas.

AI didn't even open my mouth! You have a habit of talking in the meantime, you type the keyboard buttons?

Are you really that dull or are you trolling by being deliberately obtuse?

I warn you that I will fight for my right to choose any frames of reference, which I think makes it easy for me, according to the first postulated.
"The laws of physics are the same in all inertial frames of reference."

None of which has anything to do with your claims.

If you want to take my right, with pirate methods, I will change the name of "emil's black space-time" in "our dark space-time" and I will call all to fight for our right to choose any frames of reference!

I can only conclude you're descending into deliberate nonsense, as the alternative is you're actually detaching yourself from reality.

 

[Emil]

@AlphaNumeric,

I have once explained to you ! You have a very limited "obtuse" understanding of reality !
You have no idea how to notice (observ) a straight line or a curved line.
This is physics and not mathematics. You would need to limit yourself to mathematics.

 

[AlphaNumeric]

So you cannot properly define what you're talking about. At least have the honesty to say so. As for maths and/or physics, neither one of them are you even remotely familiar with.

 

[Emil]

So you cannot properly define what you're talking about. At least have the honesty to say so. As for maths and/or physics, neither one of them are you even remotely familiar with.

Take your hands off my reference frame, from "emil's black space-time".
If you are polite and courteous then I borrow it to you, otherwise take your hands off.
You only have to make your own reference frame and don't try to take the others reference frame.

 

[AlexG]

Is it my imagination, or does the previous post completely disconnect with any kind of reality?:wtf:

 

[Emil]

Is it my imagination...

Yes, finally you've found your own reference frame. Congratulations! :bravo:
Now you should give it a name. What about "AlexG's imagination"? :scratchin: