Can Singularities Be Modeled as a Conventional Field?

In summary, The conversation discusses the possibility of having a field with discrete Dirac delta functions, where these singularities are interrelated through a conventional field. However, this concept of "various magnitudes of all the singularities" is questioned as a contradiction. The response explains that the Dirac delta function only picks out a particular value of any function that is integrated, and in quantum mechanics, the integral of the product of two functions acts as an inner product in the algebra of those functions.
  • #1
Loren Booda
3,125
4
Is it possible to have a field f([pard](x)) - fractal or otherwise - where [pard](x) are discrete Dirac delta functions, and f interrelates the various magnitudes of those singularities as a conventional field would for points over a continuum?
 
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  • #2
I think the phrase "various magnitudes of all the singularities" is a contradiction in terms. a δ doesn't have a value until it's integrated, as in ∫f(x)δ(x-a)dx = f(a).
 
  • #3
selfAdjoint,

Couldn't local Dirac singularities in my proposed field represent also various magnitudes obeying their point-by-point (distribution) normalization through overall integration?
 
  • #4
Loren, go back and look at the integral I posted, notice that f(x) in there. It could be anything. What the Dirac δ does is to pick out a particular value of any function that you integrate. Dirac modeled it on the finite case of a vector like (0,1,0). If you inner multiply that by any arbitrary vector (a,b,c) you get
(a,b,c)(0,1,0) = 0*a + 1*b + 0*c = b
(so it picks out the second component, and if you used a 1 in a different place you would pick out a different component. Now in QM math the integral of the product of two "functions" is an inner product in the algebra of those functions, so δ(x-a) in the integral picks out the "a-value component" of the function.
 
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What is a field of singularities?

A field of singularities is a mathematical concept that describes a region in space where a physical quantity, such as energy or velocity, becomes infinite or undefined. It is often used in the study of black holes and other extreme phenomena.

How are field of singularities formed?

Field of singularities can be formed through various physical processes, such as the collapse of a massive star or the collision of two black holes. In these situations, the immense gravitational forces cause the space-time fabric to become infinitely curved, resulting in a singularity.

What are the implications of a field of singularities?

The existence of a field of singularities has significant implications for our understanding of the laws of physics. It challenges our current theories and suggests that they may break down in extreme environments. It also raises questions about the nature of time and space in the presence of a singularity.

Can a field of singularities be observed?

Currently, there is no way to directly observe a field of singularities since they are surrounded by an event horizon, which prevents anything, including light, from escaping. However, scientists can study the effects of singularities, such as gravitational waves, to gain insight into their properties.

Is it possible to travel through a field of singularities?

According to our current understanding of physics, it is not possible to physically travel through a field of singularities. The intense gravitational forces would tear apart any known object. However, some theories, such as wormholes, suggest that it may be possible to traverse a singularity through exotic means.

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