We will use a carton of eggs in the grocers dairy fridge packaged for retail sale.
This needs empirical data to answer factually, and I do not have any eggs at hand at the moment, and do not know how to simulate various Richter-scale seismic results.
IMHO as a home cook, any earthquake that would generate sufficient shaking to cause an egg to scramble in the shell would also cause the eggs to impact a floor-like surface where they would be broken before the yolks could actually scramble in situ. Also, yolks, even when scrambled in controlled kitchen conditions, generally require at least some degree of purposeful puncturing of the membrane to scramble. And lastly, an egg’s contents have very little air space allowing minimal movement inside the shell for the violence that would be required for scrambling.
I wasn’t able to find anything online about chicken-egg transport, but I did find an article about transport of kiwi and emu eggs. Apparently accelerations of up to 2 g’s don’t have a significant effect on embryonic development, which (I assume) means that the yolk would not break under such an acceleration. Only a few earthquakes have exceeded 2 g at peak acceleration, so you’re going to need a mighty strong earthquake to scramble your eggs in the shell. My guess would be that there hasn’t been an earthquake recorded that was strong enough to do it.
Ok. That’s disappointing.
Disappointing, reassuring. Tomato, tomahto.
Not scramble, addle. Scrambled eggs have been cooked.
Given the lack of air space and the lack of a untensil to pierce membranes and stir things around, I can’t imagine any realistic way to apply enough force to scramble/addle the eggs without breaking the shell.
This can be an easy ‘n’ fun experiment.
- Buy a carton of eggs
- Tape them up really well so the carton doesn’t fly open.
- Go to the hardware store. Put the eggs in the paint shaker.
- Start at low speed, then take out one egg to see if it scrambled.
- Repeat at higher levels until you finally get an egg to scramble.
if ultrasonic vibrations could be applied to the shell (in a manner without breaking it, like a fluid bath) that might mix the contents given enough time and the right egg.
earthquake test might be simulated with a paint mixer.
either would make a fun experiment.
You do realize that if you can determine the earthquake energy required to scramble eggs in the shell, and actually do it, there would be no one alive to actually eat them. I mean, what a waste of eggs!
- Now that we know what it takes to scramble an egg in a carton, try it with the egg inside a chicken.
I have some tentative figures here, but they only apply to spherical chickens in a vacuum.
While “scrambled eggs” refers to cooked eggs the verb scramble can be used in a generic way to refer to anything that’s been “mixed together confusedly” (dictionary.com). Not that it needs to be since we have perfectly good alternatives in whisk or mix.
The online dictionary also does not confirm your use of addle, which it defines as “to make or become rotten.”
It’s definilty possible to break the yolk in an egg by shaking it hard and long enough by hand. I’m not sure how long it would take to get it mixed enough to be considered scrambled, though.
How do you calibrate the paint shaker to the Richter scale?
The freshness of the egg is an important variable.
Would those figures also work for a spherical chicken on a treadmill in a vacuum? 
You could insert an empty syringe via hyperdermic needle and rapidly pump and withdraw air (pressure) from the yolk/egg interface.
Probably the most efficient way of scrambling an egg invoves not only a pure linear shaking, but introduces some rotation. For instance if you shake an egg with a slight wrist motion, the rotation will cause high shear stress in the albumen, breaking the various internal membranes holding the yolk and eventually breaking the yolk membrane itself. Then a linear shaking should do well to mix the yolk and albumen that have different densities.
Put a seismograph in the paint shaker?
You don’t, as MikeS pointed out the key reading here is peak acceleration, which doesn’t always correlate to magnitude in a straight line fashion. For example the September 2010 Canterbury earthquake had a magnitude of 7.1 but lower peak acceleration than the February 2011 Christchurch earthquake: