How Does the Balloon Analogy Explain the Expansion of the Universe?

[jv11]

TL;DR

Using balloon analogy of universe to calculate big bang singularity?

Here is quick explanation :

The Balloon as Space-Time:
The balloon's surface is analogous to a two-dimensional representation of our three-dimensional universe, where space and time are interwoven (spacetime).

Dots as Galaxies:
The dots on the balloon represent galaxies, which are not actually moving across the surface of the balloon, but rather being carried apart by the expansion of the balloon's surface itself.

Expansion of Space:
The inflation of the balloon signifies the expansion of the universe, where the fabric of space itself is stretching and causing galaxies to move away from each other.

No Center of Expansion:
A key point the balloon analogy illustrates is that there is no single "center" from which the universe is expanding. Just as every point on the balloon's surface sees other points moving away, every point in the universe sees all other points receding.

Limitations:
The balloon analogy is a simplification. Our universe is three-dimensional, and the analogy only represents it as a two-dimensional surface. Additionally, the balloon analogy doesn't account for the acceleration of the universe's expansion, which is a more complex aspect of the Big Bang.

I am aircraft maintenance engineer.

I have a question :

Can we try to calculate dimension of big bang singularity by using this balloon analogy?
Balloon (secured to ground) is inflated by pressure Po of air.
The pressure Po is acting on balloon wall and make the radius R bigger.

Any balloon has two radiuses:

1)
Rs-the smallest sphere - radius of balloon where pressure inside is zero
and elastic forces in the ballon wall
are smallest but still curve the ballon wall material in to the sphere.

2)
Rb- the biggest sphere- radius where pressure inside ballon is maximum.
The elastic forces are biggest.
If ballon is inflated beyond Rb radius- the wall of balloon ruptures.
The wall of balloon has a tensile strength(S).
The specifics tensile strength(Ss) is
Ss=S/D- density of balloon wall.
Ss is constant (depends only on temperature).
S=F/A
F- force acting on balloon wall
A- cross section area of material force acting on.(Radius of balloon).
The universe can be seen as a wall of balloon.
Gravity is the force pulling the balloon wall towards the center .
Dark mater and energy are pushing the wall of balloon outwards.
The wall itself is made of electromagnetic fields.The electromagnetic fields are either squished or pulled (they are material the balloon wall is made of).
The null energy condition, a concept in general relativity, places a theoretical limit on the specific strength of any field, including electromagnetic fields. This limit is approximately 9 x 10^13 kNm/kg.
Ss=9x10^10^16Nm/kg
This is Ss- specific tensile strength of
balloon wall.
Radius of balloon wall is size of visible universe:
Rb=4.4x10^26m
Ab=6*10^53
The current density of the universe is close to the06.8% Dar4.3% Da
critical density, which is estimated to be about 9 x 10^-27 kg/m'This density is a combination of ordinary mat-ter, dark matter, and dark energy.
D=9x10^-27kg
From formula
Ss=S/D
Tensile strength of ballon wall is:
S=Ss*D
S=9*10^16*9*10^-27
S=8.1*10^-10Pa
This is the pressure of forces acting on the in and out of balloon wall.
they are in balance .
From formula S=F/A
F=S*A
F=8.1*10^-10*10^53
F‎ = 8.1×10⁴³N
To calculate big bang balloon size or
radius Rs we have to go back to Planck epoch of big bang .
The Planck force Fp=1.21*10^44N is the force acting on the the “inside “Of the balloon.
The force F (of today)is very similar to Fp.
If force F is constant during inflation
From formula
S=F/A
Po=Sb=Planckpressure
Po=Sb=4.6x10^113Pa
From
intensity 1/intensity 2=d2^2/d1^2
We can see that tensile strength S of balloon wall follows the inverse square law with distance .
D=m/Vp
m=MASS OF UNIVERSE
m=10^54
D=10^54/4*10^-105
D=2.5*10^158kg/m3
Specific tensile strength for big bang is
Ssb =Sb/D
Ssb =4.6*10^113/2.5*10^158
Ssb=1.84*10^-45Nm/kg
The temperature during Planck epoch is:
tb=10^32 C
Ss specific tensile strength depends on temperature.
The temperature of universe is
t=-270 C
From :
tb/t=N1 and Ssb/Ss=N2
N1‎ = 10^32/-278‎ = -3.597×10²⁹
N2=9*10^16/1.84x10^-45=4.89*10^61
From N1 and N2 we can see that amount of Ss(specific tensile strength) drops with increase of temperature following inverse square law.


Could it be that Planck length is the size of big bang singularity?

Tx

 

[phinds]

https://www.physicsforums.com/insights/balloon-analogy-good-bad-ugly/

Could it be that Planck length is the size of big bang singularity?

That doesn't even make sense.

 

[PeroK]

A singularity is not a physical thing. It's where the mathematics breaks down.

 

[jv11]

Imagine taking all the matter and energy in the universe and squeezing it into a point of zero volume. That's essentially the idea of the Big Bang singularity. It's the moment when the universe as we know it began, but it's also a place where our current physics can't explain what happened.
This is big bang singularity in time t=0 sec.
In Planck epoch- t=10^-43sec- this is Planck size sphere - the laws of physics do not do not apply.
Could we call this big bang singularity?
The Planck size sphere fits perfect to be smallest size sphere with Rs of universe balloon analogy.

 

[renormalize]

In Planck epoch- t=10^-43sec- this is Planck size sphere - the laws of physics do not do not apply.
Could we call this big bang singularity?

No, because a "Planck size sphere" by definition has a very small but finite size. The big bang singularity has zero size.

 

[berkeman]

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