Candle in an open container spinning in a centrifuge
So here we have a physics puzzle to tease you a little bit. The idea is simple. You put a candle in an open container (let us say a glass, like in the restaurants). You attach the container to a centrifuge, with a long arm, and you make the centrifuge spin at high speeds.
The big question is: what happens?
This is sometimes the flavor of big physics questions. One puts a couple of ingredients together, sometimes in a lab, and sometimes as a theoretical exercise, and one is supposed to come up with a detailed description of what happens. In this problem there are many ingredients, and it is not obvious what is important and what is not. This is what makes these problems fun. This problem was suggested to me by Nick Warner a couple of weeks ago. I thought it would be good to release it with some picture.
Shores of the Dirac Sea 
The flame will point inwards.
The rest frame of the container is accelerating inwards (centripetal acceleration). By Einstein’s Equivalence Principle, this is equivalent to an inertial frame with a component of the gravitational field pointing outwards.
The hot gases in the flame are less dense than the surrounding air, so by Archimedes’ Principle, are buoyant and will experience a force in the opposite direction of the gravitational field and so are pushed towards the centre of rotation. QED.
Here’s another, if you’re interested.
The candle falls over. Real Physicists want to calculate whether the wind from the open top blows out the flame before or after the candle falls over, so we know whether the lab burns to the ground before we do the experiment.
Bouyant candle flame or tethered helium balloon, if it is constrained to angularly accelerate it points in the “up” direction – toward the hub. However, put a clock on the accelerated inner rim and it keeps hub time. Release a photon toward the hub and it is not red-shifted when it arrives. Transverse Doppler effect is not gravitation.
Phys. Rev. 129(6) 2371 (1963)
Now, the fun part! Instead of releasing a photon from the angularly accelerating rim toward the hub through vacuum… have it traverse a medium. Does the photon arrive at the hub red-shifted after it exits the medium? Will the results be different from low refractive index media (e.g., Fomblin Z-DOL 4000 oil RI = 1.296 or Teflon AF 2400 RI = 1.290) and high refractive index media (e.g., cubic zirconia RI = 2.15 to rutile RI = 2.60)?
A Beckman Coulter Optima Max-XP ultracentrifuge pulls 1,019,000 gees. That allows a very compact Pound and Rebka Harvard Tower experiment (22.6 meters becomes 22 microns).
If it were a closed container, it would be pretty easy to figure out what happens. But with an open container, I’m not quite sure what happens with the air flow, although my guess is that the flame not only leans towards the center but also opposite the direction it’s moving, with a weaker flame due to lower pressure.
Hi Andy:
That was a cute puzzle. It is amazing how the jars of containers have to take all that added pressure.
What if you replaced the candle in a jar apparatus with a black body cavity. How would the photon gas (quantum mechanical object, not the hot gases) behave in response to the accelerations (which would perturb the classical object, the cavity walls)?
So the hot air stays near the center of the wick and moves upwards so one could imagine a sort of chimney effect with a taller narrower flame.
Physics puzzle will really going to make your brain sweat.
Hi Andy, I must agree the puzzle is cute.