#because amino acids aren't that special either

[urists]

Yeah this is a great question! I would say it’s, uh, extremely unlikely for organisms with totally compatible DNA to evolve independently. Off the top of my head, there’s three main reasons for that. In order of improbability: 

The existence of a separate informational media at all

The existence of DNA as the specific informational storage, and 

The existence of compatible codons.

I’ll expand on each of these, but first:

Tl;dr: If we find something with compatible DNA to us, it’s related to us. Somehow. More detail on why below the cut.

First point of possible divergence is the existence of separate informational media at all. There’s a hypothesis on the origin of life called the RNA world hypothesis, which basically says life started with only RNA. RNA (ribonucleic acid) is a single stranded polymer of ribonucleic bases that can store information (like DNA does), but also catalyze reactions (like proteins do). It’s currently still used by your cells in several key processes, including the extraction of genetic information from DNA (called transcription) and the production of proteins (called translation); the hypothesis states that these roles are more or less left-over functionalities from when life started and RNA handled everything. 

Now given that RNA’s not as stable as DNA, the theory also postulates that the evolution of DNA was a huge step forward in survivability; DNA, with its self-checking double-helix structure, was used to store genetic information, and RNA was demoted to handling just the process of turning said information into enzymes.

That being said, there’s theoretically no reason this had to have happened. It’d be theoretically possible to have a life-form that reads information directly from its genetic storage into enzyme form, without an intermediate. If a xenobiotic life form evolved with an RNA-equivalent that was more stable, perhaps there’d never be a strong enough evolutionary pressure for the DNA equivalent to form at all - and therefore, finding an organism with the same wonky transcription-translation setup as ours would be a decent but not overwhelming point in favor of a common origin.

The next break-point is DNA as a specific choice. @headspace-hotel​ pretty much covered this in the link in their reply, so I’ll be brief: DNA’s just not that incredibly special. It’s a polymeric molecule with a sugar backbone and four bases, and while its structure is specific - i.e. cells have evolved over literal billions of years to be very attuned to and capable of discerning exactly this molecule - the choice of DNA with GTAC bases as the polymer used for storage of genetic information is just as possibly random chance as it is anything else. The exact chemical structure of DNA, and the exact bases we have? That’s not the only option for genetic information storage - it’s just the one that life on earth arrived at. Finding a life-form elsewhere that not only uses the same transcription-translation mechanism, but also stores its genetic information with the exact same chemicals? That’s more than a little unlikely, and another point in favor of a common ancestor.

And finally, we arrive at the last break point: codons! If the bases of DNA are letters, and the protein produced by a gene is a sentence, then the codons are words; they’re groupings of three bases that tell the cell which amino acid will be added to a protein next. It takes three bases to encode for one amino acid because there are only four nucleic bases but 20 genetically encoded amino acids.

If whatever life-form is found uses not only the same transcription translation mechanism, and not only the same genetic information storage molecule (i.e DNA), but also the same bases to encode for the same amino acids, I would not call it xeno-biology. That life-form shares a common ancestor with the rest of life on earth. Full stop.

After all, your cells don’t even have that! The mitochondria inside your cells use a different codon encoding schema than the rest of you! If we found a cell on another planet that had genes our bodies could functionally produce without any changes, that cell is related to us somehow. The chances of that occurring by chance are basically zero.

All of which is to say: life is complicated, and there’s a lot of points at which things could have gone slightly differently. If we ever find life on other planets, it will have a biochemistry that is at least somewhat incompatible with ours; if it doesn’t, I promise you that anyone remotely adjacent to the field of xeno-biology will immediately begin scouring the genome of every organism they can find for any hint of an overlap - and they’ll probably find one too. Independent evolution of the exact same genetics is just too improbable.

why would dna-based lifeforms on other planets imply a common ancestor with earth? could dna not evolve independently?

Okay so it could, but from what I understand it's just as well likely that the "code" for a living thing could be based on a different chemistry or have different types of base pairs or anything really. I'm not sure though, if anyone else knows anything about it I'd love to hear!