The biblical connection to this point is a matter of description. The biblical concept of time is that time is linear, not cyclic. Genesis 1:1 uses a word reshith (beginning) that indicates nothing had preceded it. 2 Peter 3:10 tells us that at the end of time, "the elements shall be dissolved in fervent heat." In Revelation, God says, "I am the Alpha and the Omega, the beginning and the end." Passages like 1 Corinthians 2:7, John 1:1, and numerous others tell us that time is a created thing that will ultimately end. From a scientific standpoint, it is interesting to think about the conditions that would be present without the passage of time. One of the more obvious parts of Einstein's work is what is known as the principle of equivalence. This principle, among other things, says that time and space are not different things--they are just different ways of describing the same thing. If I ask you how far is it from Chicago to my home in South Bend, you might say 100 miles or you might say two hours. Both descriptions are correct; they are just different ways of measuring the same thing. What would happen if time were to stop and you and I were able to continue to do the things we are doing now? If I were driving my car across the country and left Los Angeles when the clock in my car said 5:00, it would still say 5:00 when I got to Denver. It would still say 5:00 when I got to Chicago. The same thing would be true when I arrived in New York. If time is not passing, you are omni-present--present in all places at the same time.
Because God does not experience the passage of time, He has all of eternity for whatever He chooses to do. When we enter eternity, the same thing will be true of us. No longer will we be restricted by the shackles of the clock and all the limitations that involves. In addition to that, all of the negative things that time brings upon us will be a thing of the past as well. Death will not exist because death is dependent upon the passage of time. If I could stop time somehow, I would cease to age. It is time that leads to death. Physical pain will not exist if time stops because it is dependent on nerves and electrical responses.
I have a son who has a type of muscular dystrophy. One of the tests they have done is a test to measure the progression of the disease's effects. They put a shock into my son's foot and measure the time it takes for the pain sensation to register in his brain on an electroencephalogram. By comparing this time to the time in the past, they can get a measure of the progression of the problem. If time stopped, would the pain sensation ever get to his brain? No--not physical pain. For physical pain, there must be time.
All of this is described in Revelation 21:4 when the writer says, "And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away." This description is a description of what it will be like to be in heaven--a timeless condition in which none of the negative effects of time can affect us.
Someone might ask why we ever had to be created as physical beings to begin with. Why could our souls not have simply existed in heaven as spiritual beings? The answer to that lies in what we have just discussed. In a timeless state, there are many things that cannot exist. We have already mentioned death and pain, but there are many other things as well. If there is no death, there is no grief over the loss of a loved one. Boredom cannot exist unless time is present for the boredom to be produced. Loneliness cannot exist because we can go all places at once and be with all people at once. The reader can probably think of literally hundreds of things that cannot exist if there is no time. How can beings in heaven have knowledge of these things? The only way they can have that kind of knowledge is to have lived in the physical world. Without the knowledge of the physical, beings in the spiritual would be incomplete.
Even love is dependent upon having been in the physical world. To build a loving relationship with another human or with God, time is necessary. Patience, faithfulness, compassion, and other characteristics of love are rooted in time-related experiences. A self-sacrificial love cannot be an instantaneous thing. Nurtured and flavored by experiences, love can grow. Abraham is the classic example, but there are many. When Jesus wept at Lazarus' death, it was obviously not over the loss of his friend because he had told his disciples that Lazarus would be raised. Jesus saw the negative experiences of living in the physical world and in being human. The whole concept of God becoming flesh involves the timeless entering the time-dependent. The message of Hebrews 4:15 ("For we do not have a high priest who is unable to sympathize with our weaknesses, but we have one who has been tempted in every way, just as we are--yet was without sin.") is especially relevant in the context of all the negatives that time brings. In heaven, we will not have to endure death, pain, boredom, loneliness, etc., but because we have known these things in the physical world, we will be complete beings. Perhaps the concept of "judging angels" mentioned in 1 Corinthians 6:3 involves this because we have been where they have not and our love and service to God is unique and complete because of that.