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The words 新しい{あたらしい} and 新た{あらた}に sound very similar to me, but I wonder
whether they are really related. If so the root must have undergone metathesis
(switching the order of sounds). Are they actually etymologically related?

Note: I saw [this
question](https://japanese.stackexchange.com/questions/4769/when-would-you-
use-%E6%96%B0%E3%81%82%E3%82%89%E3%81%9F%E3%81%AA-
and-%E6%96%B0%E3%81%82%E3%81%9F%E3%82%89%E3%81%97%E3%81%84) but I'm asking
about etymology rather than usage. (Though there does happen to be some
relevant information in the answer there.)
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2016-08-10T13:08:41.820
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etymology history adjectives
Are 新しい and 新たに etymologically related?
One theory is indeed that 新しい derives from あらたし via metathesis as あらたし in the
beginning of the Heian period became あたらし and then あたらしい.

[語源由来辞典](http://gogen-allguide.com/a/atarashii.html) lists another theory:
あらたし (meaning "new") was confused with the already existing あたらし meaning 惜しい.
あたらし was used with the meaning "new" and the other meaning of 惜しい fell largely
out of use.

In any case, 新しい and 新た are etymologically related.
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2016-08-10T13:50:25.293
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For _new_ , there are several old words that we can find, poking around in
Shogakukan's 国語大辞典:

  * 新{あら}た  
From [Old Japanese](https://en.wikipedia.org/wiki/Old_Japanese), appearing in
the [万{まん}葉{よう}集{しゅう} poetry
compilation](https://en.wikipedia.org/wiki/Man%27y%C5%8Dsh%C5%AB), dating to
roughly 759.  
Derived from 生{あ}る _"to come into being"_ (same stem as for 現{あらわ}れる _"to
become manifest, to appear"_ ) + た as a suffixing element indicating state,
probably related to the た still used in modern Japanese to indicate completion
and past tense.  
Probably cognate with 荒{あら} _"rough"_.

  * 新{あらた}し  
Appears in the [Early Middle
Japanese](https://en.wikipedia.org/wiki/Early_Middle_Japanese) of the [Heian
period](https://en.wikipedia.org/wiki/Heian_period).  
Derived from older 新{あら}た + adjectivizing suffix し.

  * 新{あたら}し  
Appears in the [Early Middle
Japanese](https://en.wikipedia.org/wiki/Early_Middle_Japanese) of the [Heian
period](https://en.wikipedia.org/wiki/Heian_period).  
Shogakukan explains that Middle Japanese saw both _aratashi_ and _atarashi_
used to mean _"new"_. As Earthliŋ notes, this was probably a shift in
pronunciation from _aratashi_ , with the metathesis (reversal of the _ra_ and
_ta_ sounds) influenced by Old Japanese-derived adjective 惜{あたら} or 可惜{あたら}
and its derived forms 惜{あたら}し or 可惜{あたら}し, itself cognate with 値{あたい} _"value,
worth"_ and 当{あ}たる / 当{あ}てる, from ancient root form _atu_. Over time, 惜{あたら}し
_"wonderful, valuable, precious"_ fell out of use, and _atarashi_ became the
standard reading for the _"new_ " sense instead.
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