In Relation to Rebirth After Death, How is Karma any Different than Supernatural gods?

To answer your question, we need to use a rational mind.

Take a look into yourself. What do you see? Something. Take a look deeper into yourself. How does everything arise in yourself? 5 senses make everything arise. Take a look even deeper into yourself. How does everything arise in yourself? Feeling and contact makes everything arise. ... Take a look the deepest possible in yourself. How does everything arise in yourself? Everything arises from desire/wanting. This is the ultimate truth why everything arises in yourself.

Take a look at the ultimate truth of everything arising in yourself. How does EVERYTHING (a thought, visual representation, sound, smell, etc.) arises from nothing in yourself? First, desire/wanting for SOMETHING arises. Then, desire/wanting creates the effort to overcome the obstacles. When the effort is big enough, the obstacles are destroyed, and SOMETHING arises. This is the ultimate truth how everything arises from nothing in yourself.

Take a look outside yourself and imagine time going backwards. What do you see? Everything going backwards in time. Take a look closer outside yourself and imagine time going more backwards. How does everything arises outside yourself? From things mixing together everything arises. Take a look even closer outside yourself and imagine time going backwards even more. How does everything arises outside yourself? From atoms, etc. ... Take a look the closest outside yourself and imagine time going backwards indefinitely. How does everything arises outside yourself? Everything arises from desire/wanting. This is the ultimate truth why everything arises outside yourself.

Take a look at the ultimate truth of everything arising outside yourself. How does EVERYTHING (a rock, plant, animal, sand, etc.) arise from nothing outside yourself? First, desire/wanting for SOMETHING arises. Then, desire/wanting creates the effort to overcome the obstacles. When the effort is big enough, the obstacles are destroyed, and SOMETHING arises. This is the ultimate truth how everything arises from nothing outside yourself.

Analyse the ultimate truth of how everything arises from nothing outside yourself. What do you see? You see centillions and centillions of desires/wanting chained one after the other, forming centillions and centillions of layers of desire/wanting. From centillions and centillions of layers of desire/wanting everything arised. From centillions and centillions of layers of desire/wanting galaxies, planets, plants, animals, etc., arised. From centillions and centillions of layers of desire/wanting you arised. You are centillions and centillions of layers of desire/wanting. Everything is centillions and centillions of layers of desire/wanting.

If you are centillions and centillions of layers of desire/wanting, you are more than your physical body. If you are more than your physical body, centillions of layers of desire/wanting will remain after your death. When centillions of layers of desire/wanting remain after your death, you remain. When you remain, you are. When you are, you become. When you become, you are born. When you are born, you desire. When you desire, you cling and crave. When you cling and crave, you suffer.

When you suffer, centillions of layers of desire/wanting are forming wanting you to suffer (remember: the ultimate truth why everything arises in yourself). When centillions of layers of desire/wanting are formed wanting you to suffer, centillions of layers of desire/wanting are forming wanting you to cling and crave. When centillions of layers of desire/wanting are formed wanting you to cling and crave, centillions of layers of desire/wanting are forming wanting you to desire. When centillions of layers of desire/wanting are formed wanting you to desire, centillions of layers of desire/wanting are forming wanting you to be born. When centillions of layers of desire/wanting are formed wanting you to be born, you will be reborn again.

The more you cling and crave, the more you suffer. The more you suffer, the more you sin. The more you sin, the angrier you are. The angrier you are, the more you are angry and the more you desire to be angry (remember: the ultimate truth why everything arises in yourself). The more you desire to be angry, the more centillions of layers of desire/wanting will be formed wanting you to be angry. The more centillions of layers of desire/wanting you to be angry are formed, the angrier you will be after death. The angrier you will be after death, the angrier being you will become after next birth. The angrier being you become after next birth, the more you will suffer. The more you suffer, the more in hell you will live.

The less you cling and crave, the less you suffer. The less you suffer, the less you sin. The less you sin, the happier you are. The happier you are, the more you are happy and the more you desire to be happy (remember: the ultimate truth why everything arises in yourself). The more you desire to be happy, the more centillions of layers of desire/wanting will be formed wanting you to be happy. The more centillions of layers of desire/wanting you to be happy are formed, the happier you will be after death. The happier you will be after death, the happier being you will become after next birth. The happier being you become after next birth, the more you will be happy. The more you are happy, the more in paradise you will live.

When you stop clinging and craving, suffering will come to end. When suffering comes to end, you come to realise: "in bliss I am". Thus, after you die, in bliss you will be reborn.

If I strike a white cue ball hard on a billard table, someone without an understanding of the transfer of momentum would say every thing that happen subsequently, happen by chance.

Someone who sees the cue ball approaching a pack of balls could ask why should we expect any thing to happen to the pack of balls, there is no reason for it.

When subsequently all the balls come to rest in a particular configuration, someone else would say God arranged it. So it is understandable when God strike the white ball rolling he meant it to send some balls into the pockets of hell an others in perpetual purgatory.

Someone else who have encountered both these views, will say that the view that the transfer of momentum from one ball to the rests that it come into contact are no different from the view of god. The function of the transfer of momentum is no different from the function carried out by a personal god.

And the transfer of momentum is still a supernatural agency, and so on...

What can you say to that?

They are views that arise without an understanding of transfer of momentum or kamma. This is just an analogy! Please don't take me to task on this analogy.

Some times when we don't SEE for ourself (Paccattam Veditabbo Vinnuhi) an underlying truth. Every view is possible!

So when we "see for ourself"(Paccattam Veditabbo Vinnuhi) the workings of kamma then certain views are impossible, others are not plausible and we arrive to right views.

The only convincing evidence is to see our own past lives and if we are unable to do that, the other alternative is to have some faith in the saying of someone like the Buddha. If we can't do both, as in having no ability and no faith and no practice, we remain as we are full of delusion/confusion as to what are the right views. Practice leads to knowing for ourselves and also results in more confidence in the dhamma.

It starts with practice and ends in knowing (vijja or bodhi).

How is karma any different more believable than supernatural gods passing judgement when we are talking about rebirth after the point of death - rebirth being inextricably linked to karma?

The implication here is that death somehow negates the causal nature of mind states that is observed in the present moment; along with our ability to hold grudges from one life to the next, the continuation of physical changes effected by mental states, etc.

Karma is more believable than God, because karma is seen to work in this life on many levels - mental changes due to karma, changes to one's physical surrounding due to karma, changes in relationships due to karma, etc. The claim that this all ceases at the moment of death is just a claim. It makes sense from within a physicalist framework, but not from an experiential framework like Buddhism.

I mean no disrespect by this, but gravity is observable whereas being born as a human and then a dog after you die because of unskillful karma is not.

Sure it is... the dog observes that it has been born a dog. How else could it be observed? The mind cannot be observed through physical means, so it's a fault of our instruments, not of the process itself. Certainly not reason to conclude "therefore God".

Why is rebirth in human realm classified as higher when some humans suffer more than some animals and have less of an intellectual ability to reason than dogs or crows?

Classification is a human construct; there is no part of nature that says "humans are better". Generally, it's considered to be more difficult to be born as a human, due to the complexity and sophistication of the organism (opposable thumbs apparently mean a lot; complex brain functions, etc.). It takes specific mind states to be born as specific individuals, e.g. humans with Down syndrome, etc., but they still have much in favour of them over dogs (longer life span, opposable thumbs, a place in human society, etc.)

How are you sure this transition to lower rebirth exists, as in the hell realms which sound like really bad places that physically exist, aside from anecdotal evidence that cannot be observed through experience?

I have no reason to doubt that hell exists; it doesn't seem any less plausible than the fact that this realm exists. It seems reasonable that one's environment changes based on one's state of mind, since that is observable in this life, and it is reasonable to conclude that causality also plays a part in one's continuation after death. I am not sure that hell exists, but it seems reasonable to believe realms of that sort do.

Why does no one support rebirth with any solid evidence, but claim it as a result of karma where karma is portrayed as a natural law?

There have been many attempts to support rebirth with solid evidence, some quite convincing. E.g. the articles on this page:

http://www.medicine.virginia.edu/clinical/departments/psychiatry/sections/cspp/dops/publications-page

There is also the superior form of investigation that is meditation; through simple but dedicated practice, one can for oneself regain memories of past lives, according to Buddhist teachings.

22. So a bhikkhu who is a beginner and wants to recollect in this way should go into solitary retreat on return from his alms round after his meal. Then he should attain the four jhānas in succession and emerge from the fourth jhāna as basis for direct-knowledge. He should then advert to his most recent act of sitting down [for this purpose], next, to the preparation of the seat, to the entry into the lodging, to the putting away of the bowl and [outer] robe, to the time of eating, to the time of returning from the village, to the time of wandering for alms in the village, to the time of entering the village, to the time of setting out from the monastery, to the time of paying homage at the shrine terrace and the Enlightenment-tree terrace, to the time of washing the bowl, to the time of picking up the bowl, to the things done from the time of picking up the bowl back to the mouth washing, to the things done in the early morning, to the things done in the middle watch, in the first watch. In this way he should advert to all the things done during the whole night and day in reverse order.

23. While this much, however, is evident even to his normal consciousness, it is especially evident to his preliminary-work consciousness. But if anything there is not evident, he should again attain the basic jhāna, emerge and advert. By so doing it becomes as evident as when a lamp is lit. And so, in reverse order too, he should advert to the things done on the second day back, and on the third, fourth and fifth day, and in the ten days, and in the fortnight, and as far back as a year.

24. When by these means he adverts to ten years, twenty years, and so on as far back as his own rebirth-linking in this existence, he should advert to the mentality-materiality occurring at the moment of death in the preceding existence; for a wise bhikkhu is able at the first attempt to remove the rebirth-linking and make the mentality-materiality at the death moment his object.

-- Vism XII.22-4 (Nyanamoli, trans)