# Balloon vs SR

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#### neila9876

When I was a kid, I liked to play balloon.
If a balloon moves very fast away from us, accoding to Lorenzt transformation, we consider that the size of the ballon in the along direction will contract, while the size of the balloon in the cross direction will not change.
Because we consider that the volumn of the ballon lessened, the mass of the air inside the balloon increased, so the density of mass of the air inside the balloon increased.
What interesting is: should we consider that the balloon will contract in the cross direction too due to the increase of mass density of the air inside the balloon?
Thank you.

#### topsquark

Forum Staff
When I was a kid, I liked to play balloon.
If a balloon moves very fast away from us, accoding to Lorenzt transformation, we consider that the size of the ballon in the along direction will contract, while the size of the balloon in the cross direction will not change.
Because we consider that the volumn of the ballon lessened, the mass of the air inside the balloon increased, so the density of mass of the air inside the balloon increased.
What interesting is: should we consider that the balloon will contract in the cross direction too due to the increase of mass density of the air inside the balloon?
Thank you.
For the first part you are absolutely correct. The air will be denser according to a stationary observer.

For the second part, remember that the balloon in it's reference frame still looks like the balloon when it was at rest. So if the size of the cross section changes for the stationary observer then it would also have to happen in the frame moving with the balloon and that isn't going to happen. (The contraction is only in the direction of motion.)

It's a good question!

-Dan

#### neila9876

balloon vs balloon

@dragon:
Change a method to research:
1. The semi - tramp kicks the balloon off, then the mass density of the air inside the balloon increases. According to dragon's opinion, the size of the balloon will not contract in the cross direction.
2. The semi - tramp puts the balloon into a refrigerater too cool it down, also the mass density of the air inside the balloon increases. But he finds that the size of the balloon contracts in all directions.
The "increase of mass density of the air inside the balloon" is one event, why two different results? Logic splits in nature?

#### Woody

accelerating or freezing the balloon,
Two different actions, two different results.
I don't see were you are leading.

#### neila9876

two vs four

@Woody:
Good question! It's so nice to see Professor Woodpecker here...haha
Next, the semi - tramp has to do a drudge ...
He hugs the balloon and dives deep into the sea bottom. The mass density of the gas inside the balloon increases and the size of the balloon contracts in all direction.
He flys into the the cosmos and observes a big balloon (sun) collapse (white dwarf). The mass density increases and the size contracts in all direction...
What Relativity describes is true contraction of physical space, not just a game of math. Then when the balloon moves very fast, according to that dragon's opinion, the balloon will becomes very thin and "bang"...While in the reference frame of the balloon, it will not...

#### Woody

Ah,
So for a balloon moving relative to an observer at relativistic speeds
The observer would see a higher density within the balloon, than an observer traveling with the balloon.
which must imply that the material properties of the fabric of the balloon
must also be different for the two observers in order to prevent the balloon from bursting for the relativistic observer.

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#### neila9876

Traditional Lorenzt transformation in SR considers only the element of moving speed of the object while the physical structure of the object is realistic...the balloon should contract too in the cross direction so that it will not "bang"....

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#### neila9876

Lorenzt vs pig

Logically, the Lorenzt transformation will not cause contraction in the cross direction does not mean other factors will not do it either.
The equation for Lorenzt transformation of length contraction is: L’ = L/γ
The mass – speed equation is M = γM0
Then, ML’ = M0L so, L’ = M0L / M motion element eliminated
Because M0 and L are constants, then: L’ ∝ 1 / M. This might be called the “mass – space equation”.
Mass M is a scalar, so the equation reflects the contraction of size in all directions due to the increase of mass.
It seems that the “mass – space equation” is a derived one. But its components “mass” and “space” are most basic physical elements. Actually, it should be a more basic equation than the equation for Lorenzt transformation of length contraction and the mass – speed equation. It describes more basic natural rule.
During the course of exploration, people often touch the leaves of a tree first, then the sticks, and so on the stock, at last the root. But for a tree, the root is the most basic.
From the angle of the physical substance of the object itself, the research might be more indepth and sufficient.

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#### neila9876

round vs thin

Actually, the mass – space equation can evolve to be L’ ∝ 1 / ρ where ρ is mass density.
Only the contraction of cosmos is able to render ρ trend to infinite and so space trend to zero: it will be a singularity. “Interaction” will disappear and so will the “existence”. It is in conformity with Woody’s great philosophical opinion about “interaction - existence”.

#### neila9876

mostly worthy to read is here, but I failed to attach file.
Assume a part of stable DC circuit with the shape of “L” rests in inertial frame S: section 1 horizontal; section 2 vertical; wire cutting face square a × a for convenience.

Another inertial frame S’ moves rightward at velocity u.
First, analysis resorts to traditional Lorentz transformation.
In frame S:
For section 1, I1 = n1qv1; for section 2, I2 = n2qv2
(Here take the moving direction of electron as the direction of current for convenience, n is the density of free electron in the wire, q is the charge carried by electron, v is the moving velocity of free electron.)
I1 = I2, n1 = n2 = n, v1 = v2 = v
In frame S’:
For section 1, △x’ = △x / γ , (γ = 1 / √1 - u²/ c² ) , △y’ = △y , △z’ = △z
V’ = △x’△y’△z’ = △x△y△z / γ = V / γ , V’ is volume in frame S’, V is volume in frame S
So, n1’ = γn1 = γn
Lorentz transformation of velocity:
v1’ = (v1 - u) / (1 - u v1/c² )
I1’ = n1’qv1’ = γnq (v1 - u) / (1 - u v1/c²)
For section 2, also V’ = V / γ
So, n2’ = γn2 = γn
Lorentz transformation of velocity:
v2’ = v2 / γ(1 - u v1/c²)
I2’ = n2’qv2’ = γnq v2 / γ(1 - u v1/c²) = nq v2 / (1 - u v1/c²)
I1’ ≠ I2’
Physics rule is not equally applicable in inertial frame S’.
Next, resort to the space contraction in all directions which is disclosed by the Mass – Space equation.
In frame S’:
For section 1, n1’ = γ³n1 = γ³n
v1’ = dx’ / dt’ = (v1 - u) / (1 - u v1/c² )
I1’ = n1’qv1’ = γ³nq (v1 - u) / (1 - u v1/c²)
For section 2, n2’ = γ³n2 = γ³n
v2’ = dz’ / dt’ = dx’ / dt’ = (v1 - u) / (1 - u v1/c² )
I2’ = n2’qv2’ = γ³nq (v1 - u) / (1 - u v1/c²)
I1’ = I2’
Physics rule is equally applicable in inertial frame S’.

Li Qiang Chen
July 17, 2019

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