The greater monogenesis theory of all extant languages and cultures from a single distant historical proto-language is a matter of debate amongst linguistics, but the similarity in many low-level root words is far beyond chance.
If you mean the similarity between word roots on a world-wide scale, the answer is decisively no. Human language vocabularies are large enough that many seductive-looking similarities will necessarily exist by pure chance, and nothing more than that has ever been observed on a world-wide scale. Mark Rosenfelder has a good article dealing with this issue on his web pages.
In fact, the way human languages are known to change implies that common words inherited from a universal root language spoken many millenniums ago would not look at all the same today. It’s a common misconception that there are some “basic” words that change more slowly than others, but in reality, the way it works is that the same phoneme changes the exact same way in all words, or at most depending on some simple rules about surrounding phonemes, with very few exceptions. So that “basic” words end up diverging like all others.
One confounding factor here is that because of quirks of child development, kids around the world start babbling with more or less the same meaningless sounds first, and enthusiastic parents and relatives often interpret this as referring to them and adopt these “words” themselves. For this reason, words for parents, grandparents, older siblings, etc. in languages all around the world are often derived from babbling sounds like “ma-ma,” “ba-ba,” “na-na,” etc. but this again has nothing to do with a common ancestral language.
The restrained theory of a common root Proto-Indo-European language is near universally accepted.
It is universally accepted. The problem is understood well enough that figuring out whether a given language is IE is answerable with as high certainty as anything else in any science. (And it’s been like that ever since mid-to-late 19th century.)
All of this divergence occurred on a timescale of five to six millenia.
That’s actually doubtful. The order magnitude is in thousands of years, and it’s clearly over ~4,000 years, but anything more than that is doubtful. (I’m pointing this out specifically because there are people who propose more precise numbers based on spurious methods.)
Generally speaking, the standard and well-substantiated methods in historical linguistics are capable of proving language relatedness with practically zero chance of false positives, but at the same time provide almost no information on the timing of their divergence. Even the lower bound on the age of proto-Into-European is based on the fact that we have written sources reaching almost ~3,000 years into the past for some of the branches.
Some linguistics nitpicks:
If you mean the similarity between word roots on a world-wide scale, the answer is decisively no. Human language vocabularies are large enough that many seductive-looking similarities will necessarily exist by pure chance, and nothing more than that has ever been observed on a world-wide scale. Mark Rosenfelder has a good article dealing with this issue on his web pages.
In fact, the way human languages are known to change implies that common words inherited from a universal root language spoken many millenniums ago would not look at all the same today. It’s a common misconception that there are some “basic” words that change more slowly than others, but in reality, the way it works is that the same phoneme changes the exact same way in all words, or at most depending on some simple rules about surrounding phonemes, with very few exceptions. So that “basic” words end up diverging like all others.
One confounding factor here is that because of quirks of child development, kids around the world start babbling with more or less the same meaningless sounds first, and enthusiastic parents and relatives often interpret this as referring to them and adopt these “words” themselves. For this reason, words for parents, grandparents, older siblings, etc. in languages all around the world are often derived from babbling sounds like “ma-ma,” “ba-ba,” “na-na,” etc. but this again has nothing to do with a common ancestral language.
It is universally accepted. The problem is understood well enough that figuring out whether a given language is IE is answerable with as high certainty as anything else in any science. (And it’s been like that ever since mid-to-late 19th century.)
That’s actually doubtful. The order magnitude is in thousands of years, and it’s clearly over ~4,000 years, but anything more than that is doubtful. (I’m pointing this out specifically because there are people who propose more precise numbers based on spurious methods.)
Generally speaking, the standard and well-substantiated methods in historical linguistics are capable of proving language relatedness with practically zero chance of false positives, but at the same time provide almost no information on the timing of their divergence. Even the lower bound on the age of proto-Into-European is based on the fact that we have written sources reaching almost ~3,000 years into the past for some of the branches.