Is Spacetime Infinitely Elastic or Does it Have an Elastic Limit?

• EskWIRED
In summary, spacetime gets stretched when massive objects are in motion. It is unknown if spacetime has an elastic limit, and it is possible for something called "cavitation" to happen if a sufficiently massive object rotates quickly.
EskWIRED
I understand that massive spinning objects drag spacetime along with their rotation, and that the inner region is dragged more strongly than the distant regions.

It would seem that spacetime gets stretched.

Does spacetime have an elastic limit, such that it could "break" at some point? Or is it infinitely elastic?

Could a sufficiently massive object, perhaps one that is configured like a propeller, cause something akin to cavitation of spacetime if it were to rotate sufficiently fast?

From what I understand, a black hole gets created when a strong enough force rips the fabric of spacetime and creates a hole of unknown depth. Here's a segment from wikipedia:

"In familiar three-dimensional gravity, the minimum energy of a microscopic black hole is 10^19 GeV, which would have to be condensed into a region on the order of the Planck length. This is far beyond the limits of any current technology."

http://en.wikipedia.org/wiki/Micro_black_hole

The "stretching" of spacetime is not like a rubber band. It does not break. Stretching, bending, and other descriptions are simply us trying to turn the results of a mathematical model into something that can be communicated in a few words instead of lots and lots of math. As such they don't always translate well.

Edit: EskWIRED, please don't delete posts after you've made them unless someone hasn't replied yet. I just spent a minute or two wondering why I couldn't quote a post, only to finally figure out that you deleted it!

Drakkith said:
The "stretching" of spacetime is not like a rubber band. It does not break. Stretching, bending, and other descriptions are simply us trying to turn the results of a mathematical model into something that can be communicated in a few words instead of lots and lots of math. As such they don't always translate well.

Thanks. I keep running into conceptual problems due to reading secondary sources which are full of imprecise metaphors.

Drakkith said:
Edit: EskWIRED, please don't delete posts after you've made them unless someone hasn't replied yet. I just spent a minute or two wondering why I couldn't quote a post, only to finally figure out that you deleted it!

Oops. I didn't do that intentionally.

Learning the math can help, yes. However sometimes you just have to ask the questions and get the answers, so don't feel bad. The only reason I know most of the stuff I know is because I've spent 3 years and had almost 10,000 posts on PF. I have very little formal education, and in fact, I just started up college 2 weeks ago as a freshman at the age of 29.

For sure, you need to know a lot of math to grasp the 'properties' of spacetime. Analogies just don't do it justice. Einstein insisted space and time are inextricably linked to gravity. That point has never been seriously disputed. Drakkith, you're too ancient to be studying math. You may injure yourself.

Chronos said:
For sure, you need to know a lot of math to grasp the 'properties' of spacetime. Analogies just don't do it justice. Einstein insisted space and time are inextricably linked to gravity. That point has never been seriously disputed. Drakkith, you're too ancient to be studying math. You may injure yourself.

No kidding... 6 hours of math homework last night, ugh.

EskWIRED said:
I understand that massive spinning objects drag spacetime along with their rotation, and that the inner region is dragged more strongly than the distant regions.

It would seem that spacetime gets stretched.

Does spacetime have an elastic limit, such that it could "break" at some point? Or is it infinitely elastic?

Could a sufficiently massive object, perhaps one that is configured like a propeller, cause something akin to cavitation of spacetime if it were to rotate sufficiently fast?

The "Fabric" representation of Space-Time is mainly used to simplify it's nature.

Space-Time "bends" in the presence of any mass, though supermassive/dense objects such as large stars, neutron stars, black holes, (quark stars?) have a more considerable effect.

This bending is known by almost all those who tackled the challenge of understanding astrophysics as Gravity.
The elasticity of the Univers is unkown hence we couldn't give you an exact answer, mainly because manifestation of pushing the Universe to the limits, also known as black holes, aren't very well understood when it comes for studying the exact singularity effect on space-time.

However we CAN say that the gravity of a black hole →∞, since the distrotion created also →∞, (the former star collapses indefinately hence it's volume →0, while it's mass retains a large value which increase overtime if the black hole is active[Not sure about the last statement, because what happens to matter inside a black holes is unkowns so we can figure out if it actually increase in mass] density →∞.

Which brings me to my point: According to my knowledge (if incorrect please post/correct me) the elasticity limit of the Universe isn't yet known and this brings two possible answers to your question, which one is right is unkown to myself:

-If the elasticity constant of the Univers is ∞: The Universe will always bend indefinately.
-If the elasticity isn't ∞: The Universe will break under the effect of a black hole and we can postulate that matter which enter a black hole will eventually "leak" out.

Thanks for reading, and hope I didn't go too far in explaining as it's my first time around here.

Edit: As stated above by the rest, you require immense mathematical tools to solve these questions, and I'm not sure if these mathematical tools exist yet.

Clairevoyance said:
-If the elasticity constant of the Univers is ∞: The Universe will always bend indefinately.
-If the elasticity isn't ∞: The Universe will break under the effect of a black hole and we can postulate that matter which enter a black hole will eventually "leak" out.

I am imagining a good sized Schwarzschild black hole, where the curvature of spacetime approaches infinity near the rather large event horizon. Now I'm imagining a similar black hole, with the most significant difference being that it is rotating at a fairly fast rate, causing significant frame dragging as a result.

Given that the curvature of spacetime approaches infinity in both cases, are there no additional stresses upon spacetime in the case of the frame-dragging, rotating black hole? Is curvature the only stress or deformation or force or aspect of spacetime that changes under the influence of both gravity and frame dragging?

If so, then I understand how and why the absence of an elastic limit near a black hole would preclude an elastic limit where frame-dragging is present.

And now for something (maybe not so) completely different:

I'm trying to figure out exactly what things would seem like in a frame-dragged environment. If one were to set up a lab in such an environment, it would seem that a rotating rod tangent to the ecliptic of a massive rotating sphere would get longer and shorter as it rotates. Indeed, the center of the rod would change as well, due to one end getting longer while the other gets shorter.

It also seems that clocks attached to the ends of the rod would get faster and slower depending upon the orientation of the rod. Is that correct?

What is the elasticity of 'nothing'? Space-time, to quote Einstein, does not possesses ponderable properties.

EskWIRED said:
I understand that massive spinning objects drag spacetime along with their rotation, and that the inner region is dragged more strongly than the distant regions.

It would seem that spacetime gets stretched.

Does spacetime have an elastic limit, such that it could "break" at some point? Or is it infinitely elastic?

Could a sufficiently massive object, perhaps one that is configured like a propeller, cause something akin to cavitation of spacetime if it were to rotate sufficiently fast?

General Relativity describes the motion of tiny "test masses." It says nothing about space. This "curved space" stuff is just an expression that is short for the curvature of the paths of test masses.

EskWIRED said:
I am imagining a good sized Schwarzschild black hole, where the curvature of spacetime approaches infinity near the rather large event horizon. Now I'm imagining a similar black hole, with the most significant difference being that it is rotating at a fairly fast rate, causing significant frame dragging as a result.

Given that the curvature of spacetime approaches infinity in both cases, are there no additional stresses upon spacetime in the case of the frame-dragging, rotating black hole? Is curvature the only stress or deformation or force or aspect of spacetime that changes under the influence of both gravity and frame dragging?

If so, then I understand how and why the absence of an elastic limit near a black hole would preclude an elastic limit where frame-dragging is present.

And now for something (maybe not so) completely different:

I'm trying to figure out exactly what things would seem like in a frame-dragged environment. If one were to set up a lab in such an environment, it would seem that a rotating rod tangent to the ecliptic of a massive rotating sphere would get longer and shorter as it rotates. Indeed, the center of the rod would change as well, due to one end getting longer while the other gets shorter.

It also seems that clocks attached to the ends of the rod would get faster and slower depending upon the orientation of the rod. Is that correct?

I'm far from an expert, but the so-called curvature of space is not at all infinite at the event horizon. Indeed there is LESS curvature at the event horizon the larger the black hole. Less massive black holes have MORE curvature at the event horizon.

You could say that the curvature was infinite at the center/singularity of any black hole. I would say that the curvature there is undefined.

Maths is abstract, leaving out the messy known unknowns, and the especially messy undefined unknown unknowns. If an object doubles its volume its radius increases by an amount less than the original radius, radial increases(shell depths) follow an idealised bell curve, allowing an unlimited number of additional equal volumes, but an inflated real object(bubble) would eventually burst if its volume kept on increasing by equal amounts. Compressing an ideally elastic volume also follows the abstract bell curve below the objects surface to its maximum compression which if exceeded turns the object inside out still following the abstract bell curve.

Chronos said:
Drakkith, you're too ancient to be studying math. You may injure yourself.

Well, I'm 56 and retiring in 10-15 years at which time I plan to finish my physics degree from being my minor (only lacked three hours from making it a dual major, but I needed a job) and take it as far as I can (masters and PhD, if possible).

I've always hated math, but, over the years, it has begun to fascinate me.

You're never too old, unless you tell yourself you are.

dichotomy58 said:
Maths is abstract, leaving out the messy known unknowns, and the especially messy undefined unknown unknowns. If an object doubles its volume its radius increases by an amount less than the original radius, radial increases(shell depths) follow an idealised bell curve, allowing an unlimited number of additional equal volumes, but an inflated real object(bubble) would eventually burst if its volume kept on increasing by equal amounts. Compressing an ideally elastic volume also follows the abstract bell curve below the objects surface to its maximum compression which if exceeded turns the object inside out still following the abstract bell curve.

Maybe I should have said, shell depths follow a curve of similar shape to a bell, (not statistics bell shaped curve). Shell depths are given by the original radius times cube root (1+x) - cube root(x). The google search bar draws a graph of f(x) = (1+x)^(1/3) -x^(1/3). Remember if air is removed from an inflated balloon it eventually turns inside out!

dichotomy58 said:
Maybe I should have said, shell depths follow a curve of similar shape to a bell, (not statistics bell shaped curve). Shell depths are given by the original radius times cube root (1+x) - cube root(x). The google search bar draws a graph of f(x) = (1+x)^(1/3) -x^(1/3). Remember if air is removed from an inflated balloon it eventually turns inside out!

As an object contracts into a singularity, maybe some of its particles turn inside out, forming new antimatter, which upon bumping into unconverted particles change into gravitons, (gravity has to get in and out somehow).

dichotomy58 said:
As an object contracts into a singularity, maybe some of its particles turn inside out, forming new antimatter, which upon bumping into unconverted particles change into gravitons, (gravity has to get in and out somehow).

Antimatter is not simply normal matter "turned inside out". Also, gravity is the curvature of the metric of spacetime and as such it does not need to "get out" of the black hole since the black hole is also the result of the curvature of the metric.

Drakkith said:
Antimatter is not simply normal matter "turned inside out". Also, gravity is the curvature of the metric of spacetime and as such it does not need to "get out" of the black hole since the black hole is also the result of the curvature of the metric.
Thanks Drakkith, the volume of material making up the balloon does not change either, its the air pressure around the balloon that changes, causing it to inflate or deflate, or even turn inside out. Maybe as you point out, a particle that displaces a closed volume of space remains unchanged, as its displaced spacetime , surrounding it, varies.
you may like to try the graph for (1+1/sin(x))^(1/3) -(1/sin(x))^(1/3) looks like fingers & nails.

What do you mean by "displaced spacetime"? Mass and energy alter the metric but nothing is displaced.

Drakkith said:
What do you mean by "displaced spacetime"? Mass and energy alter the metric but nothing is displaced.

Please see,Crank link deleted", which examines the mathematical possibility that spacetime displacements may cause a mass effect. Objects are made of molecules, atoms, and subatomic particles, which dont stay still, probably. The spacetime inside(a probability of position, determined by their standing waves) is of a different kind, to their outside surrounding spacetime, could one type displace the other?

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dichotomy58 said:
Please see, crank link deleted, which examines the mathematical possibility that spacetime displacements may cause a mass effect. Objects are made of molecules, atoms, and subatomic particles, which dont stay still, probably. The spacetime inside(a probability of position, determined by their standing waves) is of a different kind, to their outside surrounding spacetime, could one type displace the other?

I'm sorry, that website is not a reputable source of good information. PF rules only allow discussion of mainstream theories, of which that is not.

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Drakkith said:
I'm sorry, that website is not a reputable source of good information. PF rules only allow discussion of mainstream theories, of which that is not.

Oops sorry, but in fairness you did ask about displaced spacetime, which I read about on that website. Anyway heres another fun graph for sin(x+1)^(1/3)/pi -(sin(x)/pi)^(1/3)

dichotomy58 said:
Oops sorry, but in fairness you did ask about displaced spacetime, which I read about on that website. Anyway heres another fun graph for sin(x+1)^(1/3)/pi -(sin(x)/pi)^(1/3)

Please note, the graph of (x+1)^(1/n) -(x)^(1/n), only continues for negative values of "x", for compressions below the objects initial volume, when the roots, of value "n", are whole, odd, real numbers. When I tried googles graph drawing aid, the even whole numbers and even plus or minus fractional numbers of "n", stopped at "x=0". Maybe this graph is an example of why its possible to turn a three dimensional shell like volume inside out, although not the shells two dimensional surface?

dichotomy58 said:
Please note, the graph of (x+1)^(1/n) -(x)^(1/n), only continues for negative values of "x", for compressions below the objects initial volume, when the roots, of value "n", are whole, odd, real numbers. When I tried googles graph drawing aid, the even whole numbers and even plus or minus fractional numbers of "n", stopped at "x=0". Maybe this graph is an example of why its possible to turn a three dimensional shell like volume inside out, although not the shells two dimensional surface?

Maybe of the four spacetime components making up an event happening to an object, three of them are observed along each of the objects, volumes, three " real " dimensions, while the fourth component, along an imaginary dimension, accounts for the objects, volumes, motion through an observed amount of time. Rotating objects may change the position of points of reference on an objects volumes surface, over time, eventually returning to the point of first observation, maybe spacetime only gets dragged once per revolution?

Please don't speculate. Different effects of spacetime, including frame dragging, are fully described by General and Special Relativity and the two theories have passed all tests so far.

Drakkith said:
Please don't speculate. Different effects of spacetime, including frame dragging, are fully described by General and Special Relativity and the two theories have passed all tests so far.

I am still learning relativity, is it really possible that the distortions of a triangle on a two dimensional surface, captures all the information contained by three real mutually perpendicular dimensions, plus one time dimension. Graph for ((x+1)^(1/3)-x^(1/3))*sin(3.142*x)*cos(3.142*x-pi/2) ripples

Pythagoras theorem, establishes the base line(hypotenuse between the previous pair of axis), of the next right angled triangle, the next axis being perpendicular to this base line, is then used to establish the next base line, and so on, provided that the planes that the triangles sit on are not undulating (convex or concave).

dichotomy58 said:
Pythagoras theorem, establishes the base line(hypotenuse between the previous pair of axis), of the next right angled triangle, the next axis being perpendicular to this base line, is then used to establish the next base line, and so on, provided that the planes that the triangles sit on are not undulating (convex or concave).

Right triangles, base lines, s1 = (x^(2) + y^(2))^1/2, s2 = (s1^(2) + z^(2))^1/2, s3 = (s2^(2) - (ct1)^2)^1/2. Taking a square of paper, fold across one corner from the y-axis towards the x axis, the paper should bend upwards to a point on the new perpendicular z axis, the fold represents base line s1, then fold the opposite way to represent the base line s2, the perpendicular paper edge representing (ct1). Looking end on spacetime looks a bit like letter "z" reflected in a mirror.

1. What is the Elastic Limit of Spacetime?

The Elastic Limit of Spacetime is the point at which spacetime can no longer stretch or bend without breaking. It is the maximum amount of stress or deformation that spacetime can withstand before undergoing a permanent change.

2. How is the Elastic Limit of Spacetime measured?

The Elastic Limit of Spacetime can be measured through various experiments and observations, such as gravitational lensing, the behavior of matter and light near black holes, and the detection of gravitational waves. These methods help scientists understand the maximum amount of stress that can be applied to spacetime before it breaks.

3. Why is the Elastic Limit of Spacetime important?

The Elastic Limit of Spacetime is important because it helps us understand the fundamental nature of the universe. It also plays a crucial role in theories of general relativity and the behavior of gravity, as well as in the study of black holes and other cosmological phenomena.

4. Can the Elastic Limit of Spacetime be exceeded?

According to current theories, the Elastic Limit of Spacetime cannot be exceeded. If spacetime were to be stretched beyond its elastic limit, it would result in a permanent change in its structure, leading to significant consequences for the fabric of the universe.

5. How does the Elastic Limit of Spacetime relate to the Big Bang Theory?

The Elastic Limit of Spacetime is an essential concept in the Big Bang Theory. According to this theory, the universe began as a singularity, a point of infinite density and spacetime curvature. As the universe expanded, the Elastic Limit of Spacetime prevented it from collapsing back in on itself, allowing for the formation of galaxies and other structures we see today.

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