Relativistic Soap Bubbles

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It is well known that the shape of soap bubbles is spherical because of the fact that a sphere is the least-area way of enclosing a given volume .
If we look to a soap bubble from a frame of reference that move at relativistic speed relative to the bubbles, then ,as a result of length contraction, we will see that the diameter of the bubble in the direction of our speed is decreased by gama factor...so the shape of the bubble is no longer spherical.
What is the reason that the least-aeea method is not successful in moving frames?
 

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  • #2
Hurkyl
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It is well known that the shape of soap bubbles is spherical because of the fact that a sphere is the least-area way of enclosing a given volume .
If you can say why "least-area" is relevant in the normal situation, you'll have your answer.
 
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If you can say why "least-area" is relevant in the normal situation, you'll have your answer.
If you give an answer it will be more useful than your If
can just two minutes be enough to answer a question in relativity you seem to be influenced by time dialation:biggrin:
 
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PAllen
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It is well known that the shape of soap bubbles is spherical because of the fact that a sphere is the least-area way of enclosing a given volume .
If we look to a soap bubble from a frame of reference that move at relativistic speed relative to the bubbles, then ,as a result of length contraction, we will see that the diameter of the bubble in the direction of our speed is decreased by gama factor...so the shape of the bubble is no longer spherical.
What is the reason that the least-aeea method is not successful in moving frames?
I wonder if you are aware the soap bubble will still actually look spherical, but rotated as it flies by at near c. If you carefully take light delay into account, you can derive that bubble is flattened in your frame, but that is not what you would see.

I don't know how that affects your issue.
 
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bcrowell
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A soap bubble minimizes its area because it has an energy due to surface tension that is proportional to its area.

Similarly, a wooden meter stick has a certain shape that minimizes its energy. Stretching or compressing it relative to its equilibrium length of one meter requires an input of energy. We could then ask why the usual way of computing its equilibrium length fails in a moving frame. In theory, you could calculate the behavior of the wood using a description of its electrons and nuclei in terms of QED, and the result would be as expected from SR. There is a discussion of this in W.F.G. Swann, "Relativity, the Fitzgerald-Lorentz Contraction, and Quantum Theory," Rev. Mod. Phys., 13, 197 (1941). Of course, QED didn't exist in 1941, and even today it's not practical to compute the properties of wood using QED, but Swann discusses the general physical interpretation of this sort of thing.

This kind of thing leads to the same philosophical and interpretational issues as Bell's spaceship paradox:
http://en.wikipedia.org/wiki/Bell's_spaceship_paradox ,
http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle.html [Broken]

I don't think any of this is trivial or obvious. Bell famously got a majority of physicists in the Cern cafeteria to make the wrong prediction about the spaceship paradox. Ohanian discusses this in Einstein's Mistakes on p. 283 and, in my opinion, gets it totally wrong -- but it does show that there can be controversy among people who are well versed in SR and have thought deeply about these issues.
 
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Mentioning soap bubbles makes me think that you are refering to the theory that says that space itself is made up of tiny bubbles. Spacetime dialates so that objects in it always travel at the same speed less than light.

Spacetime itself wouldn't have to be under the affect since it wouldn't be able to dialate so that an object traveling in it and the spacetime itself would also measure the same speed for light. So, space itself is immune to relativistic effects and has been said to be able to travel FTL itself. We will never have to worry about spacetime measureing the speed of light incorrectly as it warps to insure that everything else measures it at the same speed.
 
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I wonder if you are aware the soap bubble will still actually look spherical, but rotated as it flies by at near c. If you carefully take light delay into account, you can derive that bubble is flattened in your frame, but that is not what you would see.
Ahhh, the Terrell-Penrose effect. Yes, however that should have no effect on the gravitational or interial mass, yes?

GrayGhost
 

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