A couple of questions about singularities

[twistor]

Which is the difference between a cosmological and a gravitational singularity? Is there any mathematical tool that relates them? Do they REALLY exist or are they of a nature that simply escapes GR? How can the Big Bang and flatness of space coexist? Could the Big Bang be a local event? How does QM relate to singularities? Why didn't black holes form in the early universe?

 

[jtbell]

I count seven questions, not two (a "couple").

 

[Mordred]

I count seven questions, not two (a "couple").

lol

Which is the difference between a cosmological and a gravitational singularity??

A cosmological singularity is a time when our mathematics can no longer describe the dynamics. Prior to 10^-43, we cannot desribe as the math involved no longer makes sense, to many infinities and processes. A Gravitational singularity such as a black hole is a point like singularity said to have infinite density. We do not know for sure as their is no way to measure beyond the event horizon of a black hole.

Is there any mathematical tool that relates them?

Their are a variety of mathematical methods to describe them, for a BH google Shwartzchild metric, For the Cosmological singularity its more involved in the thermodynamic equations of an ideal gas, and symmetry metrics

Do they REALLY exist or are they of a nature that simply escapes GR?

Black holes do exist, see the previous on Cosmological singularity

How can the Big Bang and flatness of space coexist?

Your obviously thinking of the big bang as some explosion. This is wrong, the big bang only describes a hot dense beginning, not some super particle that pop media programs would have you believe.

Could the Big Bang be a local event?

no the big bang occurred throughout all the universe. However the volume of the universe was smaller, we do not know if the universe was infinite or finite at that time, nor do we know the size now. We only know the observable portion of the universe.

How does QM relate to singularities?

QM has a minimum size, length and energy level called Planck units. As a consequence some of the infinity issues are avoided.

Why didn't black holes form in the early universe?

Primordial black holes did form in the early universe, how early we do not know for sure. This is a consequence of more material due to a denser intergalactic medium

 

[twistor]

lol



A cosmological singularity is a time when our mathematics can no longer describe the dynamics. Prior to 10^-43, we cannot desribe as the math involved no longer makes sense, to many infinities and processes. A Gravitational singularity such as a black hole is a point like singularity said to have infinite density. We do not know for sure as their is no way to measure beyond the event horizon of a black hole.


Their are a variety of mathematical methods to describe them, for a BH google Shwartzchild metric, For the Cosmological singularity its more involved in the thermodynamic equations of an ideal gas, and symmetry metrics


Black holes do exist, see the previous on Cosmological singularity


Your obviously thinking of the big bang as some explosion. This is wrong, the big bang only describes a hot dense beginning, not some super particle that pop media programs would have you believe.
no the big bang occurred throughout all the universe. However the volume of the universe was smaller, we do not know if the universe was infinite or finite at that time, nor do we know the size now. We only know the observable portion of the universe.



QM has a minimum size, length and energy level called Planck units. As a consequence some of the infinity issues are avoided.



Primordial black holes did form in the early universe, how early we do not know for sure. This is a consequence of more material due to a denser intergalactic medium

Thank you a lot!

 

[Matterwave]

I'd like to point out that parts of Mordred's post which referenced some minimum time or minimum units are really only educated guesses. The singularity for both the cosmological case, and the gravitational case occur only at one point (at t=0 for the cosmological case, and at r=0 for the gravitational case), it's just that we do not expect our physics to work well sufficiently close to these singularities (in physics we don't like to have true infinities in physical observables as would be the case if singularities really existed). The minimum time or minimum units are really just educated guesses on at what scales our currently understood physics will break down (where the "correct" physical results would be significantly different than our currently predicted results), and we have to apply new physics.

 

[Frank Weyl]

hv = E = m(c^2)
hv = m(c^2)
Planck's constant multiplied by the frequency, divided by square of the speed of light (in a vacuum), gives the mass of the virtual/real particulate.
The highest frequency (v) available in quantum mechanics is defined by the Hansen constant as: sqrt[ C^5/(h-bar)G] which is 10^43 Hz.
In our 4-dim continuum and, because this number is derived from constants, this is absolute.
This posits that, at this frequency, mass and energy are in 'transit-phase' or metathesis.
The 'Hidden variables' that caused (as causality) the plenum to expand is, at this moment in time, more conjecture than theory.
String theory 'suggests' (within the math) that the plenum was a 'Planck-like' quantum object, of 10^-33 cm diameter, and not, as misused, a singularity.
A singularity is a dimensionless point (in space) Apart from the fact that there was not any space, in which a singularity could exist at the plenum,
(Space-time was created due to the expansion)
A quantum object with, almost vanishing size but not zero, appears to be the correct interpretation of a substantial 'singularity' within the meaning of the word used in the above context.
The 'BB' appears to have been an expansion not an explosion. Explosions throw their debris into something. There wasn't anything to explode into at the plenum.
Space-time was created with the expansion.

 

[Mordred]

Not sure if your aware of how to post math in Latex, Frank makes it easier to read for complex forms. This link explains how to do so
https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

 

[Frank Weyl]

Not sure if your aware of how to post math in Latex, Frank makes it easier to read for complex forms. This link explains how to do so
https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

Now, I didn't know that!
I shall be having a field day once I get the hang of it.
Nice to find you here Mordred.
Seems as if QM is wrong about superposition in the macro-world.
We CAN be in 2n places at once!
Thanks for the latex thread.
I thought it prudent to reiterate my explanation I gave on the other forum.
I added a couple of lines to comply with the essence of the question/discussion.