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You use a relative pronoun to identify somebody of something:

The girl who looks sad is my sister.

The person that you are speaking to can look around and see that there is a girl who looks sad: he then knows, from what you said, that the girl is your sister.

It doesn't work well with "feel" and doesn't work at all with "think" because neither you nor the person that you are speaking to can tell what the girl is feeling or thinking.

This is true both of the relative pronoun form and of the reduced participle form.  


Additions following edits to the question:

The girl who feels no pain is my sister

This sentence might arise if somebody talks about a girl that suffers from congenital insensitivity to pain. You could then point out that the girl that they are describing is your sister. The sentence works because your sister's medical condition is a general truth, which can be expressed using present simple the girl feels no pain. Somebody could have been told about it some time ago, and it's still true, even though they cannot directly observe what she is feeling right now.

The girl feeling no pain is my sister - your sentence
The girl [that is] feeling no pain is my sister - equivalent

This sentence doesn't work because the use of the active participle describes something that is happening right now (present continuous). We are back in the situation where you and the person that you are speaking to cannot know what the girl is feeling right now.

You use a relative pronoun to identify somebody of something:

The girl who looks sad is my sister.

The person that you are speaking to can look around and see that there is a girl who looks sad: he then knows, from what you said, that the girl is your sister.

It doesn't work well with "feel" and doesn't work at all with "think" because neither you nor the person that you are speaking to can tell what the girl is feeling or thinking.

This is true both of the relative pronoun form and of the reduced participle form.  

You use a relative pronoun to identify somebody of something:

The girl who looks sad is my sister.

The person that you are speaking to can look around and see that there is a girl who looks sad: he then knows, from what you said, that the girl is your sister.

It doesn't work well with "feel" and doesn't work at all with "think" because neither you nor the person that you are speaking to can tell what the girl is feeling or thinking.

This is true both of the relative pronoun form and of the reduced participle form.


Additions following edits to the question:

The girl who feels no pain is my sister

This sentence might arise if somebody talks about a girl that suffers from congenital insensitivity to pain. You could then point out that the girl that they are describing is your sister. The sentence works because your sister's medical condition is a general truth, which can be expressed using present simple the girl feels no pain. Somebody could have been told about it some time ago, and it's still true, even though they cannot directly observe what she is feeling right now.

The girl feeling no pain is my sister - your sentence
The girl [that is] feeling no pain is my sister - equivalent

This sentence doesn't work because the use of the active participle describes something that is happening right now (present continuous). We are back in the situation where you and the person that you are speaking to cannot know what the girl is feeling right now.

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You use a relative pronoun to identify somebody of something:

The girl who looks sad is my sister.

The person that you are speaking to can look around and see that there is a girl who looks sad: he then knows, from what you said, that the girl is your sister.

It doesn't work well with "feel" and doesn't work at all with "think" because neither you nor the person that you are speaking to can tell what the girl is feeling or thinking.

This is true both of the relative pronoun form and of the reduced participle form.