Short answer (the factual bottom line)

The claim that Paul McCartney died in 1966 and was secretly replaced by a look‑alike is an urban legend. There is no reliable evidence that Paul McCartney died then or was replaced. Paul McCartney has lived a public life as a recording artist and performer since the 1960s; he has given interviews, appeared in public, released records and toured for decades. As of my last update (June 2024) Paul McCartney was alive and active as a musician.

Step‑by‑step: how the story started and spread

• In late 1969 an urban legend began among students and rock fans in the United States claiming that Paul McCartney had died in a car crash in 1966 and that the remaining Beatles had covered up his death and replaced him with a look‑alike. This became known as the “Paul is dead” rumor.
• The rumor spread rapidly because people began to point to alleged "clues" hidden on album sleeves, in lyrics, and in backward‑masked audio. College radio shows and newspapers picked up the story and it went national and then international.
• Beatles members, their record company, and many journalists repeatedly denied the rumor. The rumor persisted in part because fans enjoy the puzzle of “finding clues,” and because certain ambiguous album art and studio artifacts can be read in many ways.

What believers pointed to (common "clues") and simple rebuttals

• Abbey Road cover: Paul is barefoot and out of step with the others — interpreted as a funeral procession sign. Rebuttal: album art is artistic and open to interpretation; people attribute symbolic meaning after the fact. Being barefoot is not proof of death.
• Backward‑masked phrases: People claimed phrases heard when songs are played backward say things like “Paul is dead.” Rebuttal: pareidolia (hearing meaningful words in noise) and suggestion explain most such claims; context and production notes don’t support a deliberate hidden confession.
• Misheard lyrics: A line sometimes heard as “I buried Paul” in “Strawberry Fields Forever” fueled the rumor. Rebuttal: John Lennon later addressed the snippet and the comment is ambiguous; Lennon and others explained it was not an intentional statement that Paul had died.
• References to 'Billy Shears' or the name 'William Campbell': Fans invented replacement identities. Rebuttal: these are stories and label names used in songs — not documentation or evidence of any real replacement.

Concrete facts that contradict the rumor

• Paul McCartney made numerous public appearances, studio recordings, interviews and live performances after 1966. The Beatles’ final live rooftop performance (widely documented) and many subsequent recordings and public events include Paul.
• Paul formed a post‑Beatles band (Wings), released solo records, toured worldwide, and appeared in magazines, TV shows and films. These public records and contemporaneous documentation make the idea of a secret replacement extremely implausible.
• There are legal, financial and practical records — tax records, recordings with session logs, concert credentials, contracts — that show continuity of Paul McCartney’s professional identity over decades.
• The Beatles and their record labels publicly and repeatedly denied any such death/replacement conspiracy, and Paul himself has addressed the rumor multiple times over the years (including playing with the joke, e.g. album and tour references long after the rumor began).

Why the rumor spread and why people still find it appealing

• Humans are pattern‑seeking: we find meaningful patterns in ambiguous stimuli (apophenia). Once the idea is suggested, people hunt for “clues” and confirm what they expect to find (confirmation bias).
• The late 1960s culture — with fascination about death, mystery, and rock mythology — made such a story attractive and shareable among youth and media.
• Sensationalism and the media ecosystem (college radio, newspapers, then TV) amplified the rumor quickly before fact‑checking could catch up.
• Conspiracy narratives are self‑perpetuating: every ambiguous piece of evidence gets interpreted to support the story, and denials are read as part of the cover‑up by believers.

On analyses that try to prove substitution (voice, photo, forensic claims)

Some people have tried technical analyses (voice spectral comparisons, photographic comparisons). These are not conclusive: voice and face vary with age, recording methods and performance context; photos and audio can be cherry‑picked. No peer‑reviewed forensic study has provided credible evidence of a fatal 1966 event and subsequent replacement.

Conclusion — the factually supported position

There is no credible evidence that Paul McCartney died in 1966 or that anyone replaced him. The story is an urban legend that grew from misinterpretations, misheard words, deliberate suggestion, and cultural appetite for mystery. Paul McCartney’s public life, recordings, concerts and official records provide consistent, well‑documented evidence that he continued his career after 1966.

Final note on sources and accuracy

This answer summarizes well‑documented historical and public records about the rumor and about Paul McCartney’s public career. I stated the date of my latest comprehensive knowledge (June 2024). For up‑to‑the‑minute confirmation you can check major reputable news outlets and official sources (the Beatles’ official site; interviews and news reports from BBC, The New York Times, other mainstream outlets) which have repeatedly discussed and debunked the rumor over the years.

If you want, I can provide a concise timeline of public events and appearances (with dates and citations) showing Paul McCartney’s documented activity after 1966, or a focused list of original 1969 press items and radio transcripts that show how the rumor was reported and propagated.