Allow me to approach the matter from two directions: as a physicist and as a Christian.
"Do ghosts exist?" Yes, and no.
Rest assured, what you saw on Ghostbusters and on TV have nothing to do with the actual study of eternity.
Speaking as a Christian with insight:
Before the body is conceived, the person's destiny is already firmly settled, by those who have lived on earth. The spirit inhabits the body at the moment of the parents' most intense moment: coitus. Two bodies and spirits join. They form a conduit for the third spirit to enter and inhabit the unborn person.
Many spirits find that their lives will be unacceptable to them so they leave the body before it is stillborn. It is a tragedy that happens to many families who anticipated a baby to love but the life course chosen for the person would have been too rough or would not have given the person the redemption he came to acheive.
We go through the seven stages of mortality and finally die. But, as the best plans of mice and men often go astray, so can our lives be heaved off of our expected journey, resulting in premature death or suicidal thought.
Then the Judgment. Did our actions live up to the expectations of our ancestors? Did we please God with acts of mercy? Did we show the courage we were destined to develop or did we become spineless cowards? God will not put us through mortality more than once: once is more than enough to prove our character.
Sadly, some people endure far more trauma than God intended them to suffer: the bitterest memories of a spirit are "amputated" like a limb that threatens the whole body. These "amputated" memories still persist as eternal as the rest of our spirits.
No one can see a ghost, but we can feel them, as one would discern the presence of a loved one in a nearby room. All living things have spirits: that is the dividing line between all that lives and all that does not live. Yet we will find spirits even in what we thought was never alive -- plants, for example.
As a physicist:
Note that the time differential applies to all scalar and non-scalar fields, that operate on frequencies impossible in 4-dimensional space. Hence, spirits are 0-dimensional, meaning indestructible. These persistent fields form a 0-dimentional gravitational/time/non-scalar bond that far exceeds the power of all the energy and baryonic matter in our universe.
M-theory proposes an 11-dimensional multiverse but subsequent work at Sandia and Fermilab have confirmed certain non-conforming theories that in turn justify non-scalar/non-planar fields whose resonance defies measurement or even accurate quantification.
In short, your spirit resonates with other spirits. Your spirit is that spark of Divine Creation in you that will never cease: the memories you bring from earth with you will never leave you. That spark of the Divine is a fraction of infinity, but is still infinite. If you leave this planet with memories of senseless cruelty in you, they will drive you madder and madder as eternity continues. There is no way out of that.
Similarly, your memories of kindness and decency will be everlasting solace: you kept the faith, finished your course, and did as you originally intended, which resulted in your honorable redemption.
Your body will eventually wear out and die, but YOU will not.
