What is the design of these shelves? Are they commercially made or fabricated by the contractor. I agree that rebar is not a good idea. It will be hard to get everything looking plumb and they will bend down under load. Also, 14" is incredibly deep for a cantilevered load like this.

I installed some nice Ikea shelves that were about 43" and 74" long and they were 10" deep. The support design was a steel bar that ran almost the full width of the shelf, and had two 9" posts welded on that stuck straight out. The bar was lag bolted to the studs and the shelf had two holes in it that slid over the posts. Once mouted, the hardware was not visible and the back of the shelf was flush with the wall. It was incredibly well engineered. Ikea said it could handle about 33 lb of load, but I'm sure it could have taken much more given the length of lagbolt I used.

If you are intent on using the shelves you have, I suspect you're going to be unhappy unless you add a support system of some kind.

Here is a link that might be useful: LACK Shelf

Please describe a "floating shelf." I have no idea what you are talking about.

Eric, its a horizontal slab/shelf attatched to the wall only at its back edge, with no visible means of support.

The most effective way to make floating shelves is to create a torsion box with a pocket in the back edge.
A ledger strip is then attached solidly to the framing in the wall (3 inch #12 screws at every stud).
The pocket in the back of the torsion box slides over the ledger and enough fasteners are added through the top and bottom of the box into the ledger to secure the shelf.

There are metal brackets that appear on the market from time to time that faster to the wall and have a metal post sticking out that enters a pocket on the back of the shelf.
The tend to have problems with securing the metal brackets to the wall solidly enough.

Hollw wall anchors will not work for thses shelves.
The shelf creates a large withdrawal load on the fasteners and will pull anchors right through the wall.
You might be OK for a small shelf with light loads, but not books or heavy items.

Rebar would be fine as a support, but it would need to be driven into a hole in the studs or glued in using epoxy to fill ang gaps (while making sure it stays level).

Using rebar to support a shelf will work fine if the shelf is never overloaded, but if the load is too large, the rebar will split the wooden stud into which it has been inserted. You could prevent this outcome by scribing a large written warning on the shelf, clearly visible, but I doubt that the homeowner would accept that feature. It seems to me that a "floating shelf" ought to be regarded as decoration or art, something to be looked at but not used to carry a load. For example, you could use this type of shelf to display your christmas cards.

If your going to put heavy items on this you will need to bolt metal flat stock to the associated studs. Welded to these flat bars will be square stock protruding out from the walls connected to each other at the ends. The shelf will slide around this metal frame to the wall. A couple of screws will hold it in place.
Have the frames fabricated at a welding place.
Ron

Sorry I haven't gotten back over here, it's been a tough week. This is just one of the areas my contractor has been a mess. He's about a day from being fired.

So the shelves are solid ply, not a torsion box...he ordered them. The wall's already been closed up and painted, so there's not a chance in hel! he's going to go in there with special hardware bolted to the stud. And the whole POINT was to store pots, pans, a microwave and wine. Not picture frames. He knew that.

Advice - should I prevent him from hanging these shelves?

Thanks in advance, you all have been great.

If by "solid ply" you mean they are simply sheets of plywood, then yes, stop him; there's no way he can mount them as floating shelves. I do think it's possible to build floating shelves that could carry such loads, but it sounds like your contractor may not be up to the job.

The saga continues...

GC comes in today to install them, and finds that they are 3 feet (FEET, MIND YOU) too short. They've been sitting in my garage for 5 weeks waiting to be installed, could he have maybe sometime in the last 5 weeks measured them? No indeed.

He going to mount them to the wall (with prefab floating wall mounts) and the ceiling, with bars running down through all three. Not a bad solution, I think...but probably still not a good idea to have solid ply versus a lighter torsion box, right?

So then I explain what a torsion box is to him (thank you, Wikipedia) and he says, "OK, we can do that. I'll have it ready by Monday.

Let's just say...I'm calling around to carpenters independently, this is clearly beyond his reach.

Seriously. What the? I asked him at the outset whether I should just go with traditional uppers or shelves and he said "oh, I like the shelves better." One would think that meant he knew how to build and hang them, right? Right?

Well, "shelves" implies one sort of thing, and "floating shelves" another. He may be more comfortable with the former than the latter.

Torsion box construction is a way of providing a structure that is particularly light and rigid. It may or may not be necessary, depending on factors such as how many ceiling-mounted supports are used.

FWIW, I'm not all that comfortable dismissing your current contractor's abilities based on what's been said here. If the plan is to add some ceiling-mounted support bars, then we're no longer talking about floating shelves and the whole installation has become much more forgiving.

Make sure the support bars are tied into the joists with at least 3 inch #12 screws in correctly sized holes in the wood.
Loading fasteners in withdrawal is the worst direction (minimum strength).
Heavy loads on ceilings are often mounted to the sides of the joists (now the fasteners are in shear, the strongest direction) and then the ceiling repaired.

I just installed a floating shelf today. The specs said it could handle 15 pounds. I made sure at least on screw went through a stud. The rest were installed with Molly anchors, which are used if you want more weight load. They are similar to butterflies. They pull into the wall and have wings, so it's tight against the wall. We have thin wood panelling, so before I put my espresso machine on it, I'm doing a streas test. I weighed 15lbs woth of books using a poatage scale and will leave it for about a day to see if it collapses. I hope yours work out for you. They are neat!