Questions to deniers of traditional view on Rebirth 1.

If there's no rebirth, what happens after death of a non-arahant? Does a new life ensue dependent on the one which has just ended?

2.

Rebirth is tightly connected with kamma.

a) Do you observe ripening of all results of wholesome and unwholesome actions in the current life?

b) If you don't, what's in your opinion the fate of those kammas which haven't produced result in the current life?

3.

Current existence is traditionally thought of as being a manifestation of kamma amassed in previous existences.

If there's no rebirth, current life hasn't been preceded by any other existence which would contribute its kamma to it.

How do you then explain differences between people and their experiences, which in MN 135 in particular are explained through kamma?

4.

From experience (one salient example is fate of many Nazi war criminals) it's known that retribution for deeds both evil and good often doesn't occur in the current life (yet the law of kamma somehow needs to operate), it's also unlikely that aranantship will be achieved in the current existence. 

Without afterlife and no arahantship in sight, what then should be  incentive to do good and deterrent against doing evil?

5.

If a person doesn't attain nibbana in the current life, isn't there any hope for them?

Thank you for your time
1.
  If there's no rebirth, what happens after death of a non-arahant? Does a new life ensue dependent on the one which has just ended?


Life continues all the time. New lives inherit some characteristics from previous lives. Information is rarely lost completely. Influences carry on. They are not necessarily linear 1:1, but due to grasping some people may identify with a previous life. 


  2.
  Rebirth is tightly connected with kamma.
  a) Do you observe ripening of all results of wholesome and unwholesome actions in the current life?


Nope. Some are latent until a following life or lives. The question is, whose life? 


  b) If you don't, what's in your opinion the fate of those kammas which haven't produced result in the current life?


N/A


  3.
  Current existence is traditionally thought of as being a manifestation of kamma amassed in previous existences.


Not correct. This is an eternalistic view. There are influences from the past sure, but the experience of current existence is primarily an interpretation we make in the here and now. 


  If there's no rebirth, current life hasn't been preceded by any other existence which would contribute its kamma to it.


Previous lives did contribute. Not necessarily your lives. 


  How do you then explain differences between people and their experiences, which in MN 135 in particular are explained through kamma?


N/A


  4.
  If a person doesn't attain Nibbana in the current life, isn't there any hope for them?


For them? Sure there's hope for them. But not for the dead John Smith, right?

To summarize, there are past and future lives, OUR lives. There's karmic influence that carries on. There's identification with a living organism in this life, or with a story from a past life. There's hope for and fear of a future life, due to craving.

There's no entity or identity that carries on from life to life, only disjointed influences. In fact, even in this life it is the same, the assemblage of disjointed influences into a bundle is a magic trick performed by the grasping mind.