This Buddhist doctrine of rebirth should be distinguished from the theory of reincarnation which implies the transmigration of a soul and its invariable material rebirth. Buddhism denies the existence of an unchanging or eternal soul created by a God or emanating from a Divine Essence (Paramatma).

If the immortal soul, which is supposed to be the essence of man, is eternal, there cannot be either a rise or a fall. Besides one cannot understand why "different souls are so variously constituted at the outset."

To prove the existence of endless felicity in an eternal heaven and unending torments in an eternal hell, an immortal soul is absolutely necessary. Otherwise, what is it that is punished in hell or rewarded in heaven?

"It should be said," writes Bertrand Russell, "that the old distinction between soul and body has evaporated quite as much because 'matter' has lost its solidity as mind has lost its spirituality. Psychology is just beginning to be scientific. In the present state of psychology belief in immortality can at any rate claim no support from science."

       Buddhists do agree with Russell when he says "there is obviously some reason in which I am the same person as I was yesterday, and, to take an even more obvious example if I simultaneously see a man and hear him speaking, there is some sense in which the 'I' that sees is the same as the 'I' that hears."

Till recently scientists believed in an indivisible and indestructible atom. "For sufficient reasons physicists have reduced this atom to a series of events. For equally good reasons psychologists find that mind has not the identity of a single continuing thing but is a series of occurrences bound together by certain intimate relations. The question of immortality, therefore, has become the question whether these intimate relations exist between occurrences connected with a living body and other occurrence which take place after that body is dead."

As C.E.M. Joad says in "The Meaning of Life," matter has since disintegrated under our very eyes. It is no longer solid; it is no longer enduring; it is no longer determined by compulsive causal laws; and more important than all, it is no longer known.

The so-called atoms, it seems, are both "divisible and destructible." The electrons and protons that compose atoms "can meet and annihilate one another while their persistence, such as it is, is rather that of a wave lacking fixed boundaries, and in process of continual change both as regards shape and position than that of a thing."[11]

Bishop Berkeley who showed that this so-called atom is a metaphysical fiction held that there exists a spiritual substance called the soul.

Hume, for instance, looked into consciousness and perceived that there was nothing except fleeting mental states and concluded that the supposed "permanent ego" is non-existent.

"There are some philosophers," he says, "who imagine we are every moment conscious of what we call 'ourself,' that we feel its existence and its continuance in existence and so we are certain, both of its perfect identity and simplicity. For my part, when I enter most intimately into what I call 'myself' I always stumble on some particular perception or other -- of heat or cold, light or shade, love or hatred, pain or pleasure. I never catch myself... and never can observe anything but the perception... nor do I conceive what is further requisite to make me a perfect non-entity."

Bergson says, "All consciousness is time existence; and a conscious state is not a state that endures without changing. It is a change without ceasing, when change ceases it ceases; it is itself nothing but change."

Dealing with this question of soul Prof. James says -- "The soul-theory is a complete superfluity, so far as accounting for the actually verified facts of conscious experience goes. So far no one can be compelled to subscribe to it for definite scientific reasons." In concluding his interesting chapter on the soul he says: "And in this book the provisional solution which we have reached must be the final word: the thoughts themselves are the thinkers."

Watson, a distinguished psychologist, states: "No one has ever touched a soul or has seen one in a test tube or has in any way come into relationship with it as he has with the other objects of his daily experience. Nevertheless to doubt its existence is to become a heretic and once might possibly even had led to the loss of one's head. Even today a man holding a public position dare not question it."

The Buddha anticipated these facts some 2500 years ago.

According to Buddhism mind is nothing but a complex compound of fleeting mental states. One unit of consciousness consists of three phases -- arising or genesis (uppada) static or development (thiti), and cessation or dissolution (bhanga). Immediately after the cessation stage of a thought moment there occurs the genesis stage of the subsequent thought-moment.
Each momentary consciousness of this ever-changing life-process, on passing away, transmits its whole energy, all the indelibly recorded impressions to its successor. Every fresh consciousness consists of the potentialities of its predecessors together with something more. There is therefore, a continuous flow of consciousness like a stream without any interruption. The subsequent thought moment is neither absolutely the same as its predecessor -- since that which goes to make it up is not identical -- nor entirely another -- being the same continuity of kamma energy. Here there is no identical being but there is an identity in process.
Every moment there is birth, every moment there is death. The arising of one thought-moment means the passing away of another thought-moment and vice versa. In the course of one life-time there is momentary rebirth without a soul.

It must not be understood that a consciousness is chopped up in bits and joined together like a train or a chain. But, on the contrary, "it persistently flows on like a river receiving from the tributary streams of sense constant accretions to its flood, and ever dispensing to the world without the thought-stuff it has gathered by the way."[12] It has birth for its source and death for its mouth. The rapidity of the flow is such that hardly is there any standard whereby it can be measured even approximately. However, it pleases the commentators to say that the time duration of one thought-moment is even less than one-billionth part of the time occupied by a flash of lightning.
Here we find a juxtaposition of such fleeting mental states of consciousness opposed to a superposition of such states as some appear to believe. No state once gone ever recurs nor is identical with what goes before. But we worldlings, veiled by the web of illusion, mistake this apparent continuity to be something eternal and go to the extent of introducing an unchanging soul, an atta, the supposed doer and receptacle of all actions to this ever-changing consciousness.

"The so-called being is like a flash of lightning that is resolved into a succession of sparks that follow upon one another with such rapidity that the human retina cannot perceive them separately, nor can the uninstructed conceive of such succession of separate sparks."[13] As the wheel of a cart rests on the ground at one point, so does the being live only for one thought-moment. It is always in the present, and is ever slipping into the irrevocable past. What we shall become is determined by this present thought-moment.

If there is no soul, what is it that is reborn, one might ask.
Well, there is nothing to be reborn.

When life ceases the kammic energy re-materializes itself in another form. As Bhikkhu Silacara says: "Unseen it passes whithersoever the conditions appropriate to its visible manifestation are present. Here showing itself as a tiny gnat or worm, there making its presence known in the dazzling magnificence of a Deva or an Archangel's existence. When one mode of its manifestation ceases it merely passes on, and where suitable circumstances offer, reveals itself afresh in another name or form."

Birth is the arising of the psycho-physical phenomena. Death is merely the temporary end of a temporary phenomenon.

Just as the arising of a physical state is conditioned by a preceding state as its cause, so the appearance of psycho-physical phenomena is conditioned by cause anterior to its birth. As the process of one life-span is possible without a permanent entity passing from one thought-moment to another, so a series of life-processes is possible without an immortal soul to transmigrate from one existence to another.

Buddhism does not totally deny the existence of a personality in an empirical sense. It only attempts to show that it does not exist in an ultimate sense. The Buddhist philosophical term for an individual is santana, i.e., a flux or a continuity. It includes the mental and physical elements as well. The kammic force of each individual binds the elements together. This uninterrupted flux or continuity of psycho-physical phenomenon, which is conditioned by kamma, and not limited only to the present life, but having its source in the beginningless past and its continuation in the future — is the Buddhist substitute for the permanent ego or the immortal soul of other religions.

  The wise man makes his own heaven while the foolish man creates his own hell here and hereafter. 

The Buddhist concept of heaven and hell is entirely different from that in other religions. Buddhists do not accept that these places are eternal. It is unreasonable to condemn a man to eternal hell for his human weakness but quite reasonable to give him every chance to develop himself. From the Buddhist point of view, those who go to hell can work themselves upward by making use of the merit that they had acquired previously. There are no locks on the gates of hell. Hell is a temporary place and there is no reason for those beings to suffer there forever.

The Buddha's Teaching shows us that there are heavens and hells not only beyond this world, but in this very world itself. Thus the Buddhist conception of heaven and hell is very reasonable. For instance, the Buddha once said, 'When the average ignorant person makes an assertion to the effect that there is a Hell (patala) under the ocean he is making a statement which is false and without basis. The word 'Hell' is a term for painful sensations. 'The idea of one particular ready-made place or a place created by god as heaven and hell is not acceptable to the Buddhist concept.
The fire of hell in this world is hotter than that of the hell in the world-beyond. There is no fire equal to anger, lust or greed and ignorance. According to the Buddha, we are burning from eleven kinds of physical pain and mental agony: lust, hatred, illusion sickness, decay, death, worry, lamentation, pain(physical and mental), melancholy and grief. People can burn the entire world with some of these fires of mental discord. From a Buddhist point of view, the easiest way to define hell and heaven is that where ever there is more suffering, either in this world or any other plane, that place is a hell to those who suffer. 
And where there is more pleasure or happiness, either in this world or any other worldly existence, that place is a heaven to those who enjoy their worldly life in that particular place. However, as the human realm is a mixture of both pain and happiness, human beings experience both pain and happiness and will be able to realize the real nature of life. But in many other planes of existence inhabitants have less chance for this realization. In certain places there is more suffering than pleasure while in some other places there is more pleasure than suffering. 

Buddhists believe that after death rebirth can take place in any one of a number of possible existences. This future existence is conditioned by the last thought-moment a person experiences at the point of death. This last thought which determines the next existence results from the past actions of a man either in this life or before that. Hence, if the predominant thought reflects meritorious action, then he will find his future existence in a happy state. But that state is temporary and when it is exhausted a new life must begin all over again, determined by another dominating 'kammic' energy. This repetitious process goes on endlessly unless one arrives at 'Right View' and makes a firm resolve to follow the Noble Path which produces the ultimate happiness of Nibbana.
 
Heaven is a temporary place where those who have done good deeds experience more sensual pleasures for a longer period. Hell is another temporary place where those evil doers experience more physical and mental suffering. It is not justifiable to believe that such places are permanent. There is no god behind the scene of heaven and hell. Each and every person experiences according to his good and bad kamma. Buddhist never try to introduce Buddhism by frightening people through hell-fire or enticing people by pointing to paradise. Their main idea is character building and mental training. Buddhists can practise their religion without aiming at heaven or without developing fear of hell.