Does English "day" really come from PIE *dʰegʷʰ- (“to burn”)?

Question

day

From Middle English day, from Old English dæġ (“day”), from Proto-West Germanic *dag, from Proto-Germanic *dagaz (“day”), from Proto-Indo-European *dʰogʷʰ-o-s, from *dʰegʷʰ- (“to burn”).

Cognate with Saterland Frisian Dai (“day”), West Frisian dei (“day”), Dutch dag (“day”), German Low German Dag (“day”), Alemannic German Däi (“day”), German Tag (“day”), Swedish, Norwegian and Danish dag (“day”), Icelandic dagur (“day”). Cognate also with Albanian djeg (“to burn”), Lithuanian degti (“to burn”), Tocharian A tsäk-, Russian жечь (žečʹ, “to burn”) from *degti, дёготь (djógotʹ, “tar, pitch”), Sanskrit दाह (dāhá, “heat”), दहति (dáhati, “to burn”), Latin foveō (“to warm, keep warm, incubate”).

Latin diēs is a false cognate; it derives from Proto-Indo-European *dyew- (“to shine”).

Proto-Indo-European phonology

Coronals/dentals[edit]

The standard reconstruction identified three coronal/dental stops: */t/, */d/, */dʰ/. They are symbolically grouped with the cover symbol T. In so-called "thorn clusters" of the form TK in all branches except Anatolian and Tocharian a metathesis occurred, resulting in dorsal-coronal clusters of non-obvious phonetic makeup. **Metathetized and unmetathetized forms survive in different ablaut grades of the root *dʰégʷʰ "burn" (whence also English day) in Sanskrit, dáhati "is being burnt" < dʰégʷʰ-e- and kṣā́yat "burns" < dʰgʷʰ-éh₁-. See the section on PIE phonological rules, below, for more discussion and examples.

I doubt this etymology just because I can't find any reference of this kind of saying that *PIE dʰegʰ- "day" and *dʰegʷʰ- "burn" are cognates.

PS: the reconstructions are based on here, in footnote 8 on page 2 of which the author even deny this connection and E. day comes from *PIE dʰegʰ- "to repeat itself (over and over again); cycle".

Answer 1

In PIE we have

dheĝhr day (root dheĝh- "cycle")

dhoğhos burning (root dheğh- "to burn")

dius sky, daylight (root dei̯- "sky")

All three are not related or their relation is unknown. Traditionally English "day" is considered to derive from the PIE root for "burn", although the author whom you link in the question points out that it is more likely to derive from PIE root meaning "cycle" which already was used for "day" and "yesterday" (dhĝhi̯es) in PIE, and which also gave for example, Russian "den'" "day" which indicates that the PIE word for day had an r/n stem (-r suffix in Nominative and -n in other cases), and as such, very archaic.

An ironic consequence of this hypothesis if we accept it would be that the both parts of the English word "yesterday" originate from the same root: the yester- part is from dhĝhi̯es "yesterday" while the second part is from dheĝhr "day". The corresponding PIE form would be dhĝhi̯esterom dheĝhr (according the rules, the first word due to large consonant cluster would be pronounced starting with ĝh- already in PIE). It is unknown whether such form was used already in PIE or originated later, but it does not seem impossible especially given that dhĝhi̯es is adverb rather than a noun. For instance, in Russian you can say "вчера" "yesterday(adv.)" and "вчерашний день" "yesterday(adj.) day".