The Tunnel Under the World by Frederik Pohl, Science Fiction, Fantasy

"The Tunnel under the World" was first published in 1954 in Galaxy magazine.
On the morning of June 15th, Guy Burckhardt woke up screaming out of a dream.
It was more real than any dream he had ever had in his life. He could still hear and feel the sharp, ripping-metal explosion, the violent heave that had tossed him furiously out of bed, the searing wave of heat.
He sat up convulsively and stared, not believing what he saw, at the quiet room and the bright sunlight coming in the window.
He croaked, "Mary?"
Pinching yourself is no way to see if you are dreaming. Surgical instruments? Well, yes -- but a mechanic's kit is best of all!