The source for this difference is that a person has deliberately transgressed the Will of his creator. We are commanded to treat the body with respect and to bury it in the Earth because it was created from the Earth in order to house the soul. Note that this is only when this horrible act is done of the person's own free will (at the request of the person before he died). If it was done through malice (by others) then the ashes can be reburied in a Jewish cemetery as an act of respect towards the mais.
In the past, cremation was regarded as a deliberate attempt to deny resurrection of the dead and the coming of the mashiach, if not denial of the very existence of Hashem.
There are references that a "tinok shenishba" (ignorant through lack of education) can have the ashes reburied. However, the Ohr Sameach "Ask the Rabbi" seems to say that even nowadays, one should not sit shiva for anyone who requests cremation. Note that the answer below does not differentiate between cases.
As a result, we see from a number of sources.
according to Jewish law, one should not "sit shiva" (observe Jewish
mourning rites) for someone who was cremated voluntarily, nor is one
obliged to bury their ashes. You will not be able to properly mourn
for her, and no kaddish will be said for her. This may have an impact.
In addition, the body of a voluntarily cremated person is not liable
for resurrection; this is not so much because of the physical
impediment, but rather in line with the concept that one who doesn't
believe in resurrection will not experience it.
Cremation declares that this world is the beginning and end of Man. A
basis of Jewish faith is that this is not true. The body is held on
deposit, and together with the soul, it really belongs to G-d. G-d
decides when and where a person should die, and what should be done
with the body once it has fulfilled its "this-worldly" purpose.
Here are some of the reasons cremation is forbidden with the footnotes pointing to the Halachos involved. These help explain why someone should not sit shivah as explained in footnote 4
Why Does Jewish Law Forbid Cremation?
Jewish law ("Halachah") is unequivocal that the dead must be buried in
As a deterrent measure,2 cremated remains are not interred in a Jewish
cemetery.3 Furthermore, we are told that many of the traditional laws
of mourning are not observed after the passing of an individual whose
body was cremated.4 Kaddish, however, is recited for such individuals,
and it is certainly appropriate to give charity and do mitzvot in
memory of their souls.5
Code of Jewish Law, Yorah Deah 348:3; 362:1.
The rabbinic responsibility to institute ordinances to deter people from violating Biblical commands is referenced in Mishna, Avot 1:1;
Talmud Yevamot 21a, based on Leviticus 18:30.
Melamed L'hoil Vol 2 #114 (Responsa of Rabbi David Hoffman, 1843-1921, noted German authority on Jewish law.) Whether or not there
is an obligation to bury the ashes elsewhere, in order to prevent
further disgrace, is the subject of dispute between halachic
This is based on the principle (quoted in the Code of Jewish Law, Yoreh De'ah 345:5) that we do not mourn after individuals who have
"strayed from the ways of the community" (Responsa Minchat Elazar vol.
2 ch. 34).
Chatam Sofer Responsa (by Rabbi Moses Sofer, 1762-1839, famed rabbi of Pressburg, Slovakia), vol. 3 (Even Ha'ezer 1) ch. 69.
Note the seriousness of this:
Our Sages teach that those who deny the notion of the resurrection
will not merit to be resurrected45 within their own bodies, rather
their souls will be enclothed in different bodies when that awaited
Based on this idea, many authorities conclude that a person who opts
for cremation is subject to this consequence as well.47
(However, this applies only to such instances where the cremation was
done at the behest of the deceased; only in such instances can it be
said that the person rejected the notion of the resurrection, etc. Not
too long ago six million of our people were denied proper burial, most
of them cremated. Without a doubt these holy martyrs will be at the
forefront of those who will return during the Messianic Redemption.)
Mishna, tractate Sanhedrin 10:1.
See Igrot Kodesh by the Lubavitcher Rebbe, vol. 1 p.142-153.
See Minchat Elazar responsa cited above in footnote 3.
He then summarizes the entire discussion and gives a number of reasons why cremation is wrong. The list is too long to put here, but can be found at the linked page.