Is it better to place the food in the center of or on the edge of a microwave turntable?

There are resonate standing waves inside the microwave. A microwave works at 2.4 GHz. The wave length of 2.4 GHz is 4.92 inches or just under 12.6 centimeters. This is a sinusoidal wave, so half of that wavelength distance is in the trough and half is in the hump of the waveform. These high frequency photons are bouncing around in a Faraday cage made of metal. Their pattern inside the metal box is fixed. The magnetron is off to one side and emitting the radio light from a fix position. As the waves of light bounce around inside, they tend to align into standing wave patterns. Some of the waves cancel out while others work together to amplify little extra energetic spots.

If part of your food is effectively stationary, like at the turntable center of rotation, there is a chance that a dead spot in the radio light wave pattern will form in that region and will not transfer energy to the food. The more the food is offset, the more it should cross points of radio light. So it is always more effective to offset the dish as much as possible.

If the bowl you are heating is smaller than the radius of the microwave's glass-platter, then no problem, you can offset it to touch the outside of the platter and miss the centrepoint.

If the bowl is larger than the radius, I usually heat for half the time with one side of the bowl touching the outside of the platter, then slide the bowl to touch the opposite side of the platter, and then heat for the other half the cook time.

Even heat dispersion generally.

Fun experiment: take your turntable out, place in a large plate with pieces of the shittiest American cheese slices. We are talking kraft single serves. Splay them out, no deeper than one layer thick is needed, but make a full cover of the microwave bed (on top of the plate though. You will make a mess if not). Then you simply cook the shit out of it. You will see the cheese bubble and burn in the microwave wave peaks and you will see cold cheese in the wave troughs.

And then you pull out a ruler and measure how far apart the middles of the bubbles are. Look up the frequency of your microwave and then use that to calculate the speed of light with nothing but fucking cheese, a microwave and a ruler.
- Is that you, Brian Cox?
Chocolate chips are easier.
This is a fun experiment, but it's not precisely the peaks and troughs of the actual waves themselves that you're seeing, it's the maximums and minimums of the amplitude from those waves interfering with their reflections. You see the interference pattern, not the waves.

The turntable is there because the microwaves bouncing around inside the unit don't do so completely evenly; there will be spots that don't get heated as much. Moving the food around inside the unit makes it so one of those cold spots isn't consistently in one place in the food.

So with that as a context, if a cold spot is at or near the center of the turntable, it's not going to get moved around in the food when it rotates. So better to put the food away from the center.

My guess is that the edge or center is relative to the design of individual units, but after starting using the edge it seems to be more even so I've kept with it because the level of effort is basically zero.

Doing lower power for longer has far more impact on even heating if you aren't making something that needs max power like popcorn.

Doing lower power for longer has far more impact on even heating

This! It took me forever to suppress my impatience enough to learn that, but it's been life changing.

This varies by microwave as not all microwaves perform the same way, but in my case, for more even heating there are benefits to placing the food just off-center. When the food is placed in the center it doesn't heat as evenly, which is to do with standing waves forming inside the microwave, which leads to hot and cold spots.

I've seen the best results when I stack or pile food around in a doughnut shape, and center the hole of the donut shape on the turntable.

In my newish place there is a built in microwave without rotating plate. Do modern microwave ovens use technological innovations to spread out the waves somehow clever or is it just a stupid modern microwave?

Those are actually the better microwaves. They use a rotating piece of metal to scatter the microwaves across the chamber, offering a better saturation than the regular turn table variants.
- Oh that's a nice surprise. Thanks.

The more movement the better. That's why I only put live food in there /s

Edge of if I can.

There are always dead zones or lower power zones in a microwave. As the tray goes back and forth it turns around in circles it takes care if the problem. By going in and out of the zones.

I find it varies a bit to bit based on the microwave, but on average I get the most success by putting the plate in the middle of the microwave and arranging the food in a "donut" on the plate, it seems like the outsides of the plate if it's in the middle do the best, probably because they get more rotation than the center.

Rotation is good. It makes sure the food gets bombarded by microwave particles on all sides. If it's on the edge of the turntable, though, the side facing the table would be colder because the microwaves take more effort to hit it, much like how the moon has a dark side because it's tidally locked around the Earth.

Im of a "hill of beans" mindset on this.