The Physics arXiv blog has praised a paper called “On the weight of entanglement” and claimed that the author, David Edward Bruschi, found a new link between quantum mechanics and general relativity. Unfortunately, the paper is mostly wrong, and that what isn’t wrong isn’t new.
It is well known that quantum particles too must have gravitational fields and that measuring these gravitational fields would in principle tell us something about the quantization of gravity. Whenever you have a state in a superposition of two position states, its gravitational field too should be in a superposition. However, the gravitational field of all particles, elementary or composite, that display quantum properties is way too small to be measured. Even if you take the heaviest things that have yet been brought in superpositions of location you are still about 30 orders of magnitude off. I have done these estimates dozens of times.
The only way you can find larger effects is if you exploit secondary consequences of models that are not just perturbatively quantized gravity. For example the Schrödinger-Newton equation that assumes that the gravitational field remains classical even though particles are quantized can have odd side effects like preventing particle dispersion, or reducing the Heisenberg uncertainty. These effects can be somewhat larger, but they are still much too small to be measurable. The problem is always the same: gravity is weak, really weak. Nobody has ever measured the gravitational field of an atom. We measure gravitational fields of large things: balls, mountains, planets.
In the new paper, the author argues that entanglement “has weight.” By this he seems to mean that the full entangled state couples to gravity. It would be more surprising if that wasn’t so, but the treatment in the paper is problematic for several reasons.