Is True Virtual Reality Possible?

There are many Virtual Reality (VR) devices sold today but they only provide video and sound.
What I mean by true VR is The Matrix type where it is almost impossible to distinguish from the real world.
So not just vision and hearing but all senses must be provided realistically.

First issue is whether computers today have enough power for it or not.
Answer depends on whether the VR world(s) need to be realistic physics simulations
running at atomic scale or not. (Quantum scale is already beyond our computing power.)
I think just providing solid/fluid/gas simulations could be enough, just like in computer games, instead of realistic atomic level physics simulation.
So computing power shouldn't be a really big problem.

Second/real issue is Brain-Computer Interface (BCI).
I think none of existing technologies are really anywhere near what is needed.
Clearly the perfect solution would be a device that can read/write any/all neuron(s) in human brain in real time.
Also clearly it needs to be non-invasive.
Because any surgical operation on brain/nerves is a huge risk.
Not many people, besides of people who cannot move, would want to take such a risk I believe.

So the main problem is whether it is possible to create a device that can write (force/suppress its firings) a selected neuron,
and also can read it (detect its firings), in a non-invasive way.
I think there maybe only two possibilities to investigate.
One is by focusing ultrasound and other is by focusing radio waves.
Also even if write operation is possible (which should be easier), there is no guarantee read operation also will be.

Realize that if only write is possible then VR experience will be like a replay of memories of a person.
For a person to be able to respond/interact with VR world, read operation would be necessary.
But even having only write operation could allow applications like education/training.
(Imagine you first create a recording of someone going thru pilot training and later replaying that (fast and multiple times) using VR.)