In my fictitious universe, a god like entity ( which is an amalgam of all individuals , scientific understanding , capabilities , and tech of a type 3.5 civilization ) produces a sun with the same mass of our own , and a habitable Dyson sphere around it.
My question is : What movement or mechanism would be necessary to cause shifts in seasons inside of such a Dyson sphere?
Your Dyson needs to move around the sun the same way a hula-hoop does around the person spinning it around their waist. If this happens then some parts of your sphere will be closer of further from the sun than others, and "seasons" (changes in temperatures) will occur.
The radius of this "sphere" will need to be slightly bigger than 1 AU, thus making the diameter slightly bigger than 2 AU, which will allow movement without bringing one part of the sphere so close to the Sun that it fries.
The exact size would be based on how far away the Earth ever gets from our own Sun.
Niven's original RingWorld (which is somewhat similar to a Dyson Sphere) had an inner ring containing sunlight blocking plates which cast shadows upon the inhabited surface to simulate day and night. In his novel, the spaces in between the plates were empty and allowed full daylight to shine through, but there is no reason that these empty spaces couldn't be semi-transparent and varied so that different amounts of sunlight gets to the surface at different times of its "Year".
Also, since you are going for a sphere, the thickness of the atmosphere contribute to seasonality. The air will be thickest along the equator relative to the sphere's rotation and thinnest near the axis upon which it spins. If the upper parts of this atmosphere was composed of light-absorbing gases, there might be a relatively permanent seasonal distribution of temperatures between the equator and the axis, with the average temperature climbing higher as you traveled towards either axis. Not an annual schedule of changing seasons but a differentiation of climates across the available land mass.
Now add a few super oceans into the mix in the higher realms where the air is thin and the sunlight hottest and you could create some enormous storm systems, rotating moisture down towards the equator and simulating seasons, not from the distance from heat/light source (which would be constant), but using super-dense cloud cover instead.
Axial tilt is the reason we have seasons on Earth however you would not necessarily want to do that. Look at it this way. The only thing you would get out of it would be your seasons. I would put an inner sphere in my Dyson Sphere and cover it with a solar film that I could adjust over whatever areas I wanted to give me both power and whatever seasons I wanted. Just think what kind of political fallout you could create over control of the film. You could control who was a first world or third world country and furthermore everyone would be always fighting wars for control of the film! What fun!
A rigid completely enclosed Dyson with 1g internal-face gravitational acceleration build at a radius of around 1 AU (thus requiring magic-like technology) would be incredibly bright, with an temperature following the formula:
$T=[E/(4 \pi \eta \sigma r^2)]^{(1/4)}$
where $\eta$ is the emissivity (=1 for a blackbody), $\sigma$ the constant of Stefan-Boltzmann's law ($5.67032e-8 Wm^2K^{-4}$)and E the total energy output of the star measured in watts.
All the energy of the sun hits the Dyson, which has an Earth-like albedo of 0.37. It's gonna be hot.
Earth is cooled by its rotation, reducing the flux in half effectively, and by its spherical shape resulting in light hitting it as shallow angles. The Dyson does not have this features.
A back of the envelope Wolfram Alpha calculation suggests that at about 1AU with a sunlike star, the sphere would have an equilibrium temperature of about 400 K.
Not sure about seasons, but you can easily boil eggs. Or people.
