Furthermore, it's conceivable that there were multiple origins of life early on, but the others didn't "make it." Perhaps, for whatever reason, they were less efficient at metabolism or reproduction than life-as-we-know-it, so they weren't able to get a foothold.
'Possible' is a tricky word in origins biology.
For Archae and Bacteria to have *no ancestor in common* would imply a profound level of convergence, a frequentist statistical probability approaching zero.
At a certain point in development we have to start asking 'what does an ancestor actually look like', and we have to enter into a discussion of abiogenesis or some other theoretical origin point. We can't pinpoint specifics in the pre-cellular ancestors, and what that would actually look like depends on which perspective you take on likely biological origins.
However, whatever we presume for the sake of discussion to be the pre-cellular ancestor of bacteria/archae, we know that it has a very limited number of forms and features. If those forms and features share so much in common (bound by membrane, pre-RNA features of replication, etc) we have to reconsider what the statement of 'two distinct ancestors' would look like even from a theoretical perspective, *could* they be sufficiently distinct while still sharing sufficient features to produce unicellular life as similar in form and function as archae/bacteria, or are we really just looking at two slightly different versions of the same replicating system? As with a lot of questions in origins biology, the discussion is mostly philosophical and not very practical.
All current life on earth came from a common ancestor. We know this because, among many other lines of evidence, we all have the same dna code (with some minor variation). For example the DNA codon 'TCT' codes for a Serine base. There are 64 different codons and they consistently code for the same amino acid bases across the kingdoms. The odds that two separate origins of life would come up with the same code is astronomically low. However if is possible, even likely, that life arose multiple times, but the other lines died out leaving all the life known today descending from a single ancestor.
Likely, in fact.
And some of the earliest forms of life may have intermingled because they were so similar (if they weren't much more than just self-replicating RNA polymers, for example). However, at some point one form of life became advanced enough to outcompete all the others by a significant margin, and that became the "last universal common ancestor" (or LUCA) for all current life on Earth. It's possible that abiogenesis type events continue to occur on Earth today but aren't able to get a foothold on a planet with abundant life already.
As far as we can tell all life on Earth has a common ancestor, however. We can be pretty certain of this due to the similarities in the core DNA -> RNA -> protein genetic coding pipeline. There is great similarity in the fundamental molecular machinery of all life. They share the same 3-nucleotide codon length, the translation table between codons -> amino acids is remarkably similar across species, the ribosomes, t-rnas, etc. which facilitate translation of RNA to amino acid sequences is also remarkably similar. There are far too many similarities in those core mechanisms to be due to either chance or convergent evolution, which points to a common evolutionary lineage between all life on Earth.
The evidence for a universal common ancestor of all current life on Earth is pretty convincing, but that doesn't rule out that there was also multiple origins. The common ancestor is not the same as the origin, it lived much, much later. Some theories of the origin of life suggest that different metabolisms or cellular components originated separately and would have been considered living and evolving on their own, but were adopted over time into a single, more flexible or efficient mosaic organism that was our common ancestor.
I saw a show once. Said that life not only happened, but has happened multiple times. Things in the past happened that killed literally everything: asteroids cracked the crust, worldwide volcanic eruptions, etc. Life happened after and between each one.
So could it have happened in multiple locations way back when it first became possible after the latest cataclysm? Given that life seems to occur as soon as environmental conditions allow, it's very possible, if not highly likely. The fact that everything alive now shares a common ancestor just means that those other organisms met our forebears...and lost.
that carbon is the base of life on earth could be due to environmental factors like temperature. if the temperature were different - like it is on other planets - it is possible that some other element would be the base of life.