The Man Who Awoke, a 1975 fix-up novel by Laurence Manning, which was also the answer to the old question A man builds a suspended animation machine to visit the future; originally published as a 5-part serial in Wonder Stories (1933), reprinted in Famous Science Fiction (1967–1968) as follows (links to the Internet Archive):
"The Man Who Awoke" in Famous Science Fiction, Summer 1967
"Master of the Brain" in Famous Science Fiction, Fall 1967
"The City of Sleep" in Famous Science Fiction, Winter 1967/1968
"The Individualists" in Famous Science Fiction, Spring 1968
"The Elixir" in Famous Science Fiction, Summer 1968
The complete novel can be borrowed (for free but registration required) from the Internet Archive.
The first part of the saga, the novelette "The Man Who Awoke" a.k.a. "The Forest People", was anthologized several times, notably in Before the Golden Age edited by Isaac Asimov.
Wikipedia plot summary:
After the disappearance of Norman Winters, his son, Vincent, questions the servants working on his New York estate. After receiving a suspicious answer from the groundskeeper Carstairs, one of his father's most loyal workers, Vincent threatens to turn him in to the police. Preserving his freedom, Carstairs presents Vincent with a letter from his father detailing his whereabouts.
In the letter, Norman explains his collaborations with various scientists to determine how to build a chamber which will shield him from cosmic rays[a] and a coma-inducing drug. Norman constructs an underground chamber with six-foot leaden walls impervious to the outside radiation's influence on his cells. Once in the chamber, Norman will use the sleep-drug to fall into a coma where he “shall not awake until [he is] again subjected to radiation,” which will be provided by an X-ray lamp (similar to what one finds next to any dentist's chair) set to power on after five thousand years. In hopes of awaking to a Utopian future, Norman encourages Vincent to live his life in the absence of his father.
Upon waking up, Norman discovers that he had lain dormant for three thousand years. Realizing the success of his time travelling system, Norman explores the futuristic world briefly, and then returns to suspended animation, planning to wake again after another 5,000 years. He repeats this several times, giving the reader a brief view of various social results.[1]
5000 AD. Humanity staggers to save itself amid the world's littered, stagnant wreckage after what has become known as the great Age of Waste. There is a political rivalry between the younger generation opposing the older generation's proposed waste of resources that they (the younger generation) assert that they are entitled to.
10,000 AD. The world is dominated by the Brain – the immovable in purpose super computer that knows all, sees all, and feels nothing. Thanks to its cradle-to-grave supervision, human life is easy and comfortable, but what will happen when The Brain realizes people are superfluous?
15,000 AD. People can now program their choice of dreams and sleep their lives away. Winters awakes to find the sleeping outnumber the living. He cannot stop the implosion of civilization by himself.
20,000 AD. After an abused Age of Freedom came an Age of License. Genetic experiment heralded the terrifying Age of Anarchy. Each Individual had his own mobile "City" that provided for all his needs, resulting in a society where people had no need for each other and were incapable of cooperating, resulting in nearly all interpersonal encounters being small wars.
25,000 AD. Scientists discover the secret sought through the centuries – immortality. But is Mankind ready for it? Immortality is frightfully boring without a purpose. Humanity scatters to the far corners of the cosmos seeking knowledge and experience, leading to a quest toward "the meaning of it all."
Lead-lined chamber to protect against cosmic rays:
Can you guess now the nature of my experiment? For three years I worked on my idea, Herkimer of Johns Hopkins helped me with the drug I Shall use and Mortimer of Harvard worked out my ray-screen requirements. But neither one knew what my purpose might be in the investigations. Radiation cannot penetrate six feet of lead buried far beneath the ground. During the past year I have constructed, with Carstairs' help, just such a shielded chamber on my estate. Tonight 1 shall descend into it and Carstairs shall fill in the earth over the tunnel entrance and plant sod over the earth so that it can never be found.
Down bed compressed during his long sleep:
When he again opened his eyes he was weak but otherwise normal. The stone cabinet now yielded concentrated meat lozenges from a metal box and he partook very sparingly from the second bottle of liquid. Then he swung his legs down from the eiderdown couch, now tight-compressed from its original five feet to a bare two feet of depth by his age-long weight, and crossed the chamber to the clock.
The future people remark on his appendix:
"He has an appendix — there can be no doubt of it! This is the most amazing thing I have ever imagined! The stranger you see before you claims to have survived from the ancient days — from the age of waste! And he has an appendix, young comrades! I must talk to the biologists all over the country — the istorians as well! The whole world will be interested. Take him along with you and see that he is provided with walling for the night."
The people of the far future are immortal and go on centuries-long interstellar journeys; they copy the protagonist's idea and hibernate to avoid boredom:
A week of sight-seeing (for Ponceon had never visited Mars) and then the journey was resumed. Day after day slipped by—Ponceon and Pondero finding their chief interest in Winters' earnest struggle to acquire a hundred centuries of learning in one gulp. But after a month had gone by the routine of the ship settled into a dull rut and after a year Winters came to really know something of modern science. There were (they calculated) two hundred years more to be passed before their goal was even approached. So it came about that they all three took a leaf from Winters' personal experience and erected a leadlined chamber In the center of their sphere. They constructed a clock based on light intensities that would awake them whenever they approached a star even remotely.
