Let's be specific about what "scientifically proven" means here, because the details matter. I'm not talking about blurry photographs and cold spots. I mean peer-reviewed, replicated, published in Nature proven. Double-blind experiments with consistent results. A measurable energy signature that appears after biological death and persists indefinitely. Consciousness survives. It's detectable. It's communicative. The dead are still here, and we can prove it.
Every assumption you have about life, death, law, property, religion, and the concept of being alone in your own home just evaporated.
The science
The proof, in this scenario, comes from physicists at CERN who detect an anomalous energy pattern that correlates with recently deceased individuals. The signature is unique to each person, persists at or near the location of death (or, in some cases, locations of strong emotional attachment), and responds to direct questions with measurable fluctuations. It's not electromagnetic radiation in any known band. It's something new. The paper is 47 pages long, has 200 authors, and uses the word "ghost" exactly zero times. They call it "post-mortem consciousness persistence." The tabloids call it what it is.
Replication takes six months. Labs in Tokyo, Boston, and Munich confirm the findings independently. The energy patterns are real. They carry information. They respond to stimuli. They are, by any reasonable definition, the continued consciousness of dead people.
The world does not take this calmly.
Religion recalculates
Every major religion has a position on what happens after death. Christianity has heaven and hell. Islam has Jannah and Jahannam. Hinduism has reincarnation. Buddhism has rebirth into various realms. None of them predicted "you hang around your old kitchen looking irritated."

The theological scramble would be extraordinary. Some denominations would adapt (they've done it before; the Catholic Church accepted evolution, eventually). Others would reject the science outright. A significant faction would argue that the detected entities aren't souls at all but residual energy, demonic imitations, or a test of faith. Proving that consciousness persists after death doesn't automatically validate any particular religion's model of the afterlife. It might, in fact, contradict all of them.
If the dead just linger here, then there's no heaven. No punishment. No reward. No judgement. You live, you die, you haunt. The moral framework that underpins most religious ethics (behave well because consequences await) loses its mechanism. Some people would find this liberating. Others would find it unbearable.
Murder trials gain a witness
The legal implications are immediate and chaotic. If the deceased can communicate, even through fluctuations in an energy detector, then a murder victim can identify their killer. Testimony from the dead. It sounds like a joke, but the legal system would have to grapple with it.
The first question is admissibility. Can a ghost testify? In English law, a witness must swear an oath and be subject to cross-examination. The ghost can't hold a Bible, can't take an oath in any traditional sense, and cross-examination of a post-mortem consciousness persistence pattern is, at minimum, procedurally unusual. But the evidence rules have been adapted before. Hearsay exceptions, expert witness testimony, victim impact statements from deceased persons read by family members. There's precedent for bending the rules when the information is sufficiently relevant.
The second question is reliability. Human memory is unreliable in living people. Is ghost memory better or worse? If the consciousness persists in a degraded state (confused, fragmented, emotionally fixated) then ghost testimony might be no more accurate than eyewitness testimony, which is already the least reliable form of evidence in criminal proceedings.
Defence barristers would have a field day. "My learned friend's witness is deceased, has no verifiable cognitive baseline, cannot be sworn, and is communicating through a machine that translates energy fluctuations into yes/no responses. The prosecution's case rests, quite literally, on a ouija board with a PhD."
Property law collapses
If ghosts exist and they tend to linger at locations they're emotionally attached to, then every old house potentially has sitting tenants who never signed a lease and can't be evicted because they're dead.

Right now in England, roughly 600,000 homes are sold per year. How many of those contain the lingering consciousness of a previous owner? Do they have rights? If consciousness persists and is legally recognisable, there's a genuine argument that the deceased owner never fully vacated. Their body left. They didn't.
Estate agents would need to disclose hauntings the way they currently disclose subsidence or Japanese knotweed. "The property benefits from a south-facing garden, gas central heating, and the post-mortem presence of Mrs Dorothy Ashworth (d. 1987) who occupies the upstairs bathroom and objects to renovations." Haunted houses stop being charming and become a conveyancing nightmare.
Property values would bifurcate. Ghost-free homes command a premium. Ghost-occupied homes sell at a discount, unless the ghost is someone famous, in which case the opposite applies. "Former residence of Charles Dickens. Current residence of Charles Dickens."
Privacy for the dead
If the dead are still present and aware, they're observing us. Your deceased grandmother is watching you live your life in her old house. All of it. Every argument with your partner, every embarrassing thing you do when you think you're alone, every late-night decision you'd rather not explain to a dead relative.
The privacy implications work both ways. Do ghosts have a right to privacy? Can researchers study a ghost without its consent? Can the media interview a famous person's ghost? If Winston Churchill is still hanging around the Cabinet War Rooms, does the BBC have the right to point an energy detector at him and broadcast his responses? Churchill might enjoy it. Other ghosts might not.
The GDPR implications alone would keep lawyers employed for decades. Post-mortem consciousness persistence data is surely personal data. The data subject is technically deceased but demonstrably still a subject. Does the right to erasure apply? Can a ghost request that its energy signature be left undetected? The Information Commissioner's Office would need a new department.
The grief question
This might be the biggest change, and the hardest to predict. Grief, as we experience it, is the process of accepting that someone is gone. They're not in the next room. They're not coming back. You'll never hear their voice again. The finality is what makes it hurt, and the finality is also what, eventually, allows you to recover.
Remove the finality and grief doesn't end. It transforms into something stranger. Your mother died but she's still in the house. You can detect her presence. You can ask her yes-or-no questions through a machine. She's there but she's not there. Not in any way you can hug, or have dinner with, or argue with properly. She's a reading on an instrument.
Some people would find comfort in that. Many would find it torturous. The bereaved wouldn't be able to move on because the person hasn't moved on. Every house becomes a hospice that never closes. Every death is a transition to a diminished presence rather than an absence. Funerals become awkward. You're mourning someone who is, by all measurable accounts, standing right next to you at the wake, probably annoyed about the sandwiches.