Good word for something physical that's inexplicable

I'm looking for a word to describe something physical, something that you can tangibly and empirically feel, but cannot see, nor sense in any other way than touch, nor explain its imperceptibility. Does anyone have any ideas?

EDIT: If anyone can think of a single word for such a definition, that would be fantastic! :)

My suggestion:

Tangible phantom

Tangible: perceptible by touch. "the atmosphere of neglect and abandonment was almost tangible"

Phantom:

• a ghost. "a phantom who haunts lonely roads"

• a figment of the imagination. "he tried to clear the phantoms from his head and grasp reality" synonyms: figment of the imagination, delusion, hallucination, illusion, chimera, vision, fantasy, mirage;

• not real; illusory.

Some of the synonyms for phantom also works