Understanding of the theory of relativity

In summary: Originally posted by pellman1. How can the unknown be forgotten and who'd assume it's unimportant?2. How?1. Usually, people forget about unknown (not yet discovered) things because they are unknown. This is a simple explanation why unknown things are usually forgotten to be taken into consideration. How is it related to this thread?2. What do you mean by "how"? I do not understand what you are asking me about. Please be more clear.InstantonIn summary, a singularity in spacetime represents an infinite space-time curvature and signals a breakdown in any theory. This breakdown is due to the existence of particles in free fall ending or beginning at some finite time and is classified as
  • #1
maximus
495
4
a vauge question:

i am, admititly, far from a complete understanding of the theory of relativity and special relativity but could someone humor me by explaining exactly why the T.ofR. perdicts its own break down at a singularity.
 
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  • #2
because in the spherical case of a black hole, the singularity is located in the center, and represents infinite gravitational curvature.
 
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More precisly the existence of singularity on spacetime means there is a region of spacetime that physical theory doesn't apply. So, you have a theory that is suppose to be applied everywhere in spacetime, that predicts regions where it can't be applied.

Instanton
 
  • #4
Originally posted by instanton
More precisly the existence of singularity on spacetime means there is a region of spacetime that physical theory doesn't apply. So, you have a theory that is suppose to be applied everywhere in spacetime, that predicts regions where it can't be applied.

Instanton
Even more precisely GR defines the Universe (except
fot the particles ) as a single continuous geometrical
entity. However, if the mass in a singularity is
infinite then space-time has a "hole" in it, and
that kin'na ruins the "suit"...:wink:

Live long and prosper.
 
  • #5
A singularity is an infinity - in this case, an infinite space-time curvature. Usually when a theory predicts an infinite value it is interpreted as a failure of the theory in that case, e.g., the infinite self-energy of an electron in classical EM. Thus we say, that the theory "breaks down" inside a black hole.
 
  • #6
Originally posted by maximus

...could someone humor me by explaining exactly why the T.ofR. perdicts its own break down at a singularity.

The phrasing of your question hides the issue because singularities by definition signal a breakdown in any theory. But to answer the intended question, there are theorems in GR predicated on very reasonable assumptions proving that singularities are a generic feature of realistic cosmologies since realistic distributions of mass-energy will develop black holes.

Originally posted by instanton

...[GR] is suppose to be [but can't be] applied everywhere in spacetime...

No, GR is not required to be applicable everywhere.

Originally posted by instanton

...[GR] predicts regions where it can't be applied.


Originally posted by pellman

A singularity is an infinity - in this case, an infinite space-time curvature.

We currently have no completely satisfactory way of characterizing GR singularities since they indicate a breakdown in spacetime and thus cannot be ascribed location. In fact, geometrical pathologies like the blowing up of curvature scalars or bad behaviour of curvature or metric components can never classify the infinite variety of spacetime singularities, and global methods where singularities are viewed as bounding spacetime don't work either. By far the most satisfactory tool - and in fact the one on which the aforementioned singularity theorems are based - is "geodesic incompleteness" which captures the intuitive idea of the existence of particles in free fall ending or beginning (like entering or exiting a black hole singularity for example) at some finite time. Depending on the behaviour of curvature along such geodesics, the corresponding singularities may be classified as scalar curvature, parallelly propagated curvature, or non-curvature singularities.
 
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Originally posted by steinitz

No, GR is not required to be applicable everywhere.

Well I never said it is. Read the original question more carefully.

Instanton
 
  • #8
Originally posted by instanton
More precisly the existence of singularity on spacetime means there is a region of spacetime that physical theory doesn't apply.

So, you have a theory that is suppose to be applied everywhere in spacetime, that predicts regions where it can't be applied.


Instanton

Both of these remarks are misleading as I've indicated. With someone else I might have ignored the second remark. But you claim to be a graduate student and I therefore expect more precision from you.
 
  • #9
Originally posted by steinitz
Both of these remarks are misleading as I've indicated. With someone else I might have ignored the second remark. But you claim to be a graduate student and I therefore expect more precision from you.

Maybe I should've been more precise. What I meant was following. The original question was about the statement we often hear "exactly why the T.ofR. perdicts its own break down at a singularity." In my opinion the statement implies GR suppose to be applied in whole spacetime, but predicts the region which it can not be. It is just my interpretation of the statement Maximus quoted, not my blided belief on classical GR.

Now, you pointed out I read more carefully of the original question and I realize I do not really know what the statement exactly means. As you said singularities are characterized by geodesic incompleteness. What precisely is wrong with that? It maybe weird, but I can not really think of any concrete reason. Maybe you have better idea.

Instanton
 
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Originally posted by instanton As you said singularities are characterized by geodesic incompleteness. What precisely is wrong with that?

What is wrong with what?
 
  • #11
Infinities indeed are usually the indicators that something is forgotten to be taken into consideration (often not known yet phenomenon which is nevertheless important).

In case of gravitational singularities it can be angular momentum (of black hole), or minimum allowed by math angular momentum, or quantum nature of gravity, or vacuum fluctuations, etc
 
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  • #12
Originally posted by Alexander
1. Infinities indeed are usually the indicators that something is forgotten to be taken into consideration (often not known yet phenomenon which is nevertheless important).

2. In case of gravitational singularities it can be angular momentum (of black hole), or minimum allowed by math angular momentum...

1. How can the unknown be forgotten and who'd assume it's unimportant?

2. How?
 

1. What is the theory of relativity?

The theory of relativity is a scientific theory developed by Albert Einstein in the early 20th century. It consists of two main theories: special relativity and general relativity. Special relativity deals with the laws of physics in non-accelerating frames of reference, while general relativity deals with the laws of physics in all frames of reference, including accelerating frames. It is a fundamental theory that explains the relationship between space and time, and how they are affected by gravity.

2. What are the key concepts of the theory of relativity?

The key concepts of the theory of relativity include the principle of relativity, which states that the laws of physics are the same in all inertial frames of reference, and the constant speed of light, which is the maximum speed that any object can travel in the universe. Other important concepts include time dilation, length contraction, and the equivalence of mass and energy (as described by the famous equation E=mc^2).

3. Why is the theory of relativity important?

The theory of relativity has had a significant impact on our understanding of the universe and has been confirmed by numerous experiments and observations. It has revolutionized our understanding of space and time and has led to the development of technologies such as GPS and nuclear energy. It also provides a framework for understanding the behavior of objects at high speeds and in the presence of strong gravitational fields.

4. How has the theory of relativity been tested and confirmed?

The theory of relativity has been tested and confirmed through various experiments and observations. For example, the famous Michelson-Morley experiment in 1887 demonstrated that the speed of light is constant, regardless of the observer's frame of reference. Additionally, observations of the bending of starlight around massive objects, such as the sun, have confirmed the predictions of general relativity. Other tests include the measurement of the slowing down of time for objects moving at high speeds and the verification of the equivalence of mass and energy through nuclear reactions.

5. Are there any practical applications of the theory of relativity?

Yes, there are several practical applications of the theory of relativity. One of the most well-known is the use of general relativity in the development of GPS technology. The theory also plays a crucial role in the development of nuclear energy and has been applied in the fields of astronomy, cosmology, and particle physics. However, many practical applications of the theory are still being explored and developed.

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