Hello, I have been wondering if according to the relativity theory if something could be truly flat.

The geometry of our spacetime is non-Euclidean, so two objects can't have as short a distance between them  as two objects in a hypothetical Euclidean space. The paths are always curved.

Thank you very much StringJunky

In SR a flat plane in any inertial frame is a flat plane in all others, is it not?

35 minutes ago, J.C.MacSwell said:

In SR a flat plane in any inertial frame is a flat plane in all others, is it not?

It's a question for GR. Gravity is pertinent. Any path has to follow a geodesic and they are not Euclidean straight. I'm not, and the OP is not, talking about locally flat. They said "truly" flat, which I take means no arc over any distance. If you care to elaborate, I''m all ears.

41 minutes ago, StringJunky said:

It's a question for GR. Gravity is pertinent. Any path has to follow a geodesic and they are not Euclidean straight. I'm not, and the OP is not, talking about locally flat. They said "truly" flat, which I take means no arc over any distance. If you care to elaborate, I''m all ears.

Yeah. I don't think it holds for GR. Maybe approach it locally or where gravity has limited effect, but I can't see it over any distance under that definition of flat.

1 hour ago, J.C.MacSwell said:

Yeah. I don't think it holds for GR. Maybe approach it locally or where gravity has limited effect, but I can't see it over any distance under that definition of flat.

Maybe a flat plate that symmetrically divides the Universe into two identical halves? (stab in the dark)

1 hour ago, J.C.MacSwell said:

Yeah. I don't think it holds for GR. Maybe approach it locally or where gravity has limited effect, but I can't see it over any distance under that definition of flat.

MacSwell is correct, 'flatness' is a local property of the manifol;d under GR.

SR is flat anyway at all scales.

I am defining 'flatness' as synonymous with zero curvature.
That is it is a point function with a value at every point of the manifold.
However it should also be noted that there is more than one curvature (direction or degree of freedom) for a 3D manifold.

Since we do not know the shape of the manifold we cannot say for certain that the answer to the OP is yes or no.
This is because the value of the curvature at some points in some manifolds can be zero for example saddle points in 3D.
If our universe has such points then the answer is yes something could be truly flat.
If it does not then no.

Edit

Another thought. Since (the disposition of) matter is responsible for the curvature and matter is always moving about in our universe I can conceive of a situation where the local curvature reverses and thus passes through zero at some point or interval in time.

Edited September 17, 20178 yr by studiot

If, by flat, you mean having no thickeness, everything that falls into a black hole becomes flat on the surface of the event horizon and stays there for a long long time due to time dilation. Since the EH is a sphere, I suppose that you could say that there is an infinitesimal amount of curvature to the flatness.

If you want an example of the least amount of curvature, IDK, how about an electron on the surface of the largest SMBH in the Universe.

1 hour ago, TakenItSeriously said:

If, by flat, you mean having no thickeness, everything that falls into a black hole becomes flat on the surface of the event horizon and stays there for a long long time due to time dilation. Since the EH is a sphere, I suppose that you could say that there is an infinitesimal amount of curvature to the flatness.

If you want an example of the least amount of curvature, IDK, how about an electron on the surface of the largest SMBH in the Universe.

Flat does not refer to thickness (nor length nor breadth, nor width.)

It refers to the way distance is measured between one point and nearby points.

2 hours ago, studiot said:

Flat does not refer to thickness (nor length nor breadth, nor width.)

It refers to the way distance is measured between one point and nearby points.

Ahh, I see, you mean as in space where gravity from all bodies cancel out to zero. seems posible but it seems impossible to measure which is kind of like saying its analogous to a Heisenberg state.

Since Gravity reaches us from the observable Universe, then it would seem like position and momentum vectors would loose meaning in a local non-inertial frame if taken  in the context of the observable universe frame. Just like it does in the quantum scale as we observe it in the context of the human domain. 

Therefore it would be impossible to say with any certainty..

 

edit to add:

Its interesting to note however that this is similar to the problem of finding the primality of large numbers where the complexity becomes too great to predict in any meaningful amount of time due to the scale of the domain of large numbers which makes the universe look like the quantum scale though probably not literally.

However, I did find a way to find primality of large numbers which should work in near real time once the data is compressed and saved.

so who knows?

.

Edited September 18, 20178 yr by TakenItSeriously

Special relativity is indeed flat because it is a theory of moving systems in the absence of gravity.

 

What may help is looking into flat land and then investigate the implications of higher dimensions - you might find a gem of knowledge in it.

4 minutes ago, Dubbelosix said:

Special relativity is indeed flat because it is a theory of moving systems in the absence of gravity.

 

What may help is looking into flat land and then investigate the implications of higher dimensions - you might find a gem of knowledge in it.

This doesn't preclude the possibility of 'flat spots' in systems with gravity as I already noted.

Well you can argue gravity is never absent in the universe. So special relativity isn't fundamentally correct at the core

 

''We have all seen footage of astronauts floating freely in space, performing twists and turns that seem to defy gravity. As a result of these portrayals, many people believe that there is zero gravity in space. However, this statement could not be further from the truth. Gravity exists everywhere in the universe and is the most important force affecting all matter in space. In fact, without gravity, all matter would fly apart and everything would cease to exist.''

 

http://www.yalescientific.org/2010/10/mythbusters-does-zero-gravity-exist-in-space/

But yeah, think about when protons get flattened in high energy scattering as an example of fundamentally flat systems, at least by all practicality. 

6 minutes ago, Dubbelosix said:

Well you can argue gravity is never absent in the universe. So special relativity isn't fundamentally correct at the core

 

''We have all seen footage of astronauts floating freely in space, performing twists and turns that seem to defy gravity. As a result of these portrayals, many people believe that there is zero gravity in space. However, this statement could not be further from the truth. Gravity exists everywhere in the universe and is the most important force affecting all matter in space. In fact, without gravity, all matter would fly apart and everything would cease to exist.''

 

http://www.yalescientific.org/2010/10/mythbusters-does-zero-gravity-exist-in-space/

But yeah, think about when protons get flattened in high energy scattering as an example of fundamentally flat systems, at least by all practicality. 

Not sure if that was a response to my post, but it was not what I meant.

I know. I was just adding some things.

On 10/1/2017 at 9:36 AM, Dubbelosix said:

Special relativity is indeed flat because it is a theory of moving systems in the absence of gravity.

 

What may help is looking into flat land and then investigate the implications of higher dimensions - you might find a gem of knowledge in it.

I believe the OP was referring to General Relativity, not Special Relativity.

Special Relativity is a theory about relative inertial frames of constant velocity.

Gravity can be treated as curved local space in GR, but it can also be modeled as local accelerated non-inertial frames in terms of the Equivalence Principle.

Another words SR is about relative constant velocity while gravity is about relative local acceleration.