In Christianity, is heaven something we will comprehend with the consciousness we have now? Will we be the same consciousness, brain and memories of this world, or is it just the energy of our soul going back to its source – nothing that we will actually experience in terms of earthly experience?
Romans 14:12 So then, each of us will give an account of ourselves to God
I am under the impression that yes we will have memories of our lives (because without such memories how could we give account?). We would not be able to give an account if we did not have consciousness.
I think that this Scripture gives us a clear answer:
Revelation 6:9-11 When he opened the fifth seal, I saw under the altar the souls of those who had been slain because of the word of God and the testimony they had maintained. They called out in a loud voice, “How long, Sovereign Lord, holy and true, until you judge the inhabitants of the earth and avenge our blood?” Then each of them was given a white robe, and they were told to wait a little longer, until the full number of their fellow servants, their brothers and sisters, were killed just as they had been.
Not only did they have the ability to ask a question, they also remembered the way that they were killed and that they deserved justice. They also felt longing, which also supports that there is conscious experience in Heaven.
"Earthly" (Physical) Experience:
Please also keep in mind that when Revelation describes heaven there are references to many physical things. I don't believe such language would be used if we were just going to be spiritual beings returning to our source. Please read Revelation 21 & Revelation 22:1-5
I am sure that there are more evidences of this, but I am yet to search them out. I am convinced that Heaven will is not just some holding tank for souls, but rather a beautiful restoration of all creation.