Answer

I’m not familiar enough with this field, so I can only give you general guidelines.
If this is some kind of practice, there is no reason to prohibit it, even if the person who came up with it was an idol worshipper. I don’t know who invented pants, but even if he was an idol worshipper, it is still permitted to wear them. Practice of any kind is not inherently forbidden.
If the practice itself has some connection to a particular idol, then it needs discussion. If it is part of that idol’s worship, then I think it depends on whether you are doing it out of a desire to worship it, or because of the benefit of the practice. Idolatry exists only if you do it as an acceptance of a deity as divine authority (see Maimonides, Laws of Idolatry 3:6), meaning that you do it because it commanded it and this is its mode of worship. If that ritual brings medical or psychological benefit, I don’t think it should be prohibited just because some people take it in idolatrous directions.

It should be remembered that the medieval authorities (Rishonim) disagree about the nature of the prohibitions of idolatry and its accessories (sorcery, “you shall be wholehearted,” and the like). Maimonides and those in his camp explain that it is a prohibition against being foolish, simply because it doesn’t work. According to them, if something works, there is no prohibition in it. According to Nachmanides and those in his camp, there is a prohibition against resorting even to things that do work if they come from the “other side” — the demonic side. The point is not that idol worshippers invented it, but that the practice itself draws on dark forces (see also Harry Potter). I don’t know how one identifies the source of a technique or what powers it uses, and I tend to think there is no such thing as dark forces anyway. Well, I’m just an ordinary Muggle.

It seems to me that nowadays meditation is treated as just a practice, so I don’t think it should be prohibited. Although it is worth checking whether it really works or whether this is just idiotic New Age nonsense. If it doesn’t, then perhaps it would be prohibited as an accessory of idolatry, according to Maimonides and his camp, who see the prohibition as being foolish and believing in things that don’t work.
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Questioner:
From an initial reading on Wikipedia, it seems that there are many scientific studies showing various benefits of meditation (stress relief, increased attention and concentration, and more). I’m asking specifically about the use of mantras like Om. According to Wikipedia, "Om" signifies "the infinite absolute," and in addition, according to Hindu belief, even before the world was created, Brahman (which is their creator god) thought; from that thought a vibration was created that sounded like "Om." In other words, Om is the first creation that Brahman created, and when the world was created, Om accompanied it. Therefore some interpret the word Om as meaning "Here I am."
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Rabbi:

First of all, is the mantra a necessary part of the practice? If you say "Here I am," will the result be different? I assume not.
But if "Om" is the infinite absolute or its first utterance with creation, in the sense of “Forever, Lord, Your word stands firm in the heavens,” then there is nothing idolatrous about it. It’s a translation of our tradition — which says the same thing — into Hindu language. What’s wrong with that? Is it forbidden to speak Hindi?
It reminds me of a movie I once saw about a trance party where people dance in ecstasy for two full days and mumble Hindu mantras with the names of Hindu gods (Shiva, etc.). I assume that most of them had no idea what those words meant.
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Questioner:

The issue is that my instructor wants me to use mantras, and I understood that the whole issue of mantras is a complicated topic.
There is a good article on the subject by Rabbi Natan Ofir:
http://www.daat.ac.il/daat/chinuch/darkey/meditatsya-2.htm
But I wasn’t able to understand the bottom line all that well — whether it is permitted to say mantras or not.

As far as I understand, the mantras are names of points in the body, although maybe those names are also used for other things. Usually people say those mantras internally.

What do you think about this?
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Rabbi:
The article is very superficial (it is a survey, so it does not claim to enter the topic). There is not even a hint there as to what the halakhic problem with mantras is, so you won’t find a halakhic solution there. Maybe one should check the sources he refers to (Rabbi Ovadia, Rabbi Halevi), and I’ll try to take a look.
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Questioner:
By the way, I forgot to mention that methods like meditation have benefits for stress relief that have been proven in scientific studies.
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Rabbi:
I see that the sources from Rabbi Ovadia are mainly oral reports. There is a responsum in Aseh Lekha Rav, vol. 2, siman 47 (I have it at home in the Otzar HaHokhmah database, and I can check it when I’m there).
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I’ve now looked, and I’m sending you Rabbi H. D. Halevi’s relevant responsum.
He does indeed go into detail about the technique, but he does not provide an orderly halakhic analysis. He is also discussing transcendental meditation, and I don’t know if that is what you are talking about.
In general, I’m skeptical of his conclusion that the matter is forbidden (and certainly of the assumption that we have everything within our own tradition and don’t need to resort to anything else).
The practice itself, if it works, really doesn’t seem to me to depend on where it came from. It’s a medical technique, so why should its source matter?! As for the mantras, there is indeed a prohibition against mentioning the names of idols, but I understand that one can choose other words instead (similar ones?). Moreover, if it works, then apparently it isn’t because of those names specifically (because idolatry has no real substance). So either way, the use is not in the category of idolatry.
In any case, if you really have to use those specific words, and if they really are names of idols (I’m not sure that in your case they are), then there is room to discuss whether it is permitted or forbidden.
At least in such a case, maybe it would be better to try dealing with stress first in the conventional way, and only if that doesn’t work to move on and see what the meditation world has to offer.
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Questioner:
Regarding the prohibition of “it shall not be heard from your mouth,” I’ve often heard rabbis mention Jesus by name. Is Jesus considered idolatry for purposes of this prohibition?
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Rabbi:
A big question. It is commonly thought that Catholic Jesus — yes (because of the Trinity, though that too is debatable — whether this is idolatry and whether Jesus is in fact the name of an idol), but Protestant Jesus is not. Therefore, in itself, I don’t think there is a prohibition here.
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Questioner:
Is there a prohibition against saying expressions like: “the sun god” or “the sea god,” or is the whole prohibition only regarding a specific name?
And in addition, is the prohibition only on verbally saying the name of idolatry? Or is there also a prohibition on writing it or saying it internally?
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Rabbi:
I don’t think there is a prohibition here. And if one says it in the context of studying history and the like, then certainly there is no prohibition. As I said, even if it were the only practice that was effective, I don’t think there would be any prohibition in it, as long as you don’t believe in it.

In conditions where there is a prohibition, I assume writing is also prohibited, since we hold that writing is like speech. Saying it internally is not speech, and I don’t think that is prohibited.
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Questioner:
According to that, it comes out that it is permitted to use mantras, because you are only required to say them internally and not out loud — isn’t that so?
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Rabbi:
You don’t say them aloud? Then it seems to me that yes. Isn’t there a possibility of using a similar word?
Are the words names of idols?
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Questioner:
According to their methods, they claim that certain specific words should be used. But still, it seems to me that it would be preferable to avoid even saying them internally, because maybe at some point it will accidentally come out aloud.
Although I don’t think the mantras refer to names of idolatry. Rather, as far as I understand, the mantras are the representative sounds of certain points in the body (called chakras), but just to be on the safe side, it is probably better to avoid it.

If you want, there is an expanded explanation on Wikipedia about one of the central mantras (which perhaps one should not even write by name, based on what came up here):
https://he.wikipedia.org/wiki/%D7%90%D7%95%D7%9D_(%D7%9E%D7%A0%D7%98%D7%A8%D7%94)
By the way, earlier when you said that writing is like speech, did you mean even typing on a computer? Or only writing in the physical world?
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Rabbi:
This refers to writing that is not for an academic, cultural, or historical purpose. Otherwise, it seems to me permitted. With writing on a computer there is more room to be lenient, because it is writing that does not endure.
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Questioner:
I saw that it is written in the Shulchan Arukh, Yoreh De’ah 147:1: “It is forbidden to mention it by name, whether for a need or not for a need.” Doesn’t what you wrote about an academic, cultural, or historical purpose fall under the heading of “for a need,” and therefore be prohibited?
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Rabbi:
In my opinion, no. The fact is that everyone does this. When people study Christianity or one form of idol worship or another, do they not mention its name? Even the Talmud speaks about someone who defecates to Peor. Apparently “mentioning” means making meaningful use of it.
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Questioner:
Have a good week, Rabbi,
Following up on this answer, I came across סעיף 4 of that same section, which says:
It is permitted to mention the name of idol worship that is written in the Torah, such as “Bel bows down, Nebo stoops” (Isaiah 46:2), “who set a table for Gad” (Isaiah 65:11).
That is probably the reason the Talmud speaks about someone who defecates to Peor (since it was mentioned in the Torah). But regarding the name of idol worship that is not mentioned in the Torah, perhaps it is forbidden to mention it even for an academic purpose — could that be?

I looked in Beit Yosef, and there it says:

Beit Yosef, Yoreh De’ah 147
One who vows or swears in the name of idolatry is flogged. In the chapter Four Death Penalties (Sanhedrin 60a) we learned: one who vows in its name and one who fulfills in its name violates a negative commandment — meaning the prohibition of “And the names of other gods you shall not mention; it shall not be heard from your mouth” (Exodus 23:13). And as for what Rabbeinu wrote, that one is flogged for this, so too Maimonides wrote in chapter 5 of the Laws of Idolatry (10–11), and in my commentary to Sefer HaMadda (Kesef Mishneh there) I wrote his reason:
And it is forbidden even to mention it by name for nothing, without need. There (63b): as it is stated, “And the names of other gods you shall not mention” — that a person should not say to his fellow, “Wait for me beside such-and-such an idol.” And the Rosh wrote (sec. 3): at first glance it implies that specifically in such a case it is forbidden to mention idolatry for a need; however, it appears that in every case it is forbidden, since the verse is written generally. And the fact that it used “wait for me” is not exact, but rather it used the common case, since it is not the usual way to mention it at all without need, and it teaches us that even for a need it is forbidden. End quote. And our master wrote that it is forbidden to mention it even without need, and all the more so for a need. But his language is not precise, because since that was his intention, he should have written in this way: “It is forbidden to mention it by name even gratuitously, without need.” Also, although for the Rosh it is obvious that for a need is more prohibited than not for a need, that is because the baraita says, “Wait for me beside such-and-such an idol,” and one might have thought that this was specific; but for one who does not know the baraita, it is not obvious that for a need is more prohibited than not for a need. If so, this is how our master should have written: “It is forbidden to mention it by name gratuitously, whether for a need or not for a need.”

I have a thought that perhaps the Beit Yosef and the Rosh, when they use the word “need,” actually mean “need for use,” and not an academic need. What do you think?
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Rabbi:
That reasoning sounds plausible. Bottom line, people are not particular about this nowadays.

Continuing this discussion:
There is a basic yoga exercise called Sun Salutation. Here is a short description I found online on the site yoga.co.il:
“The practice of Sun Salutation developed with the purpose of honoring the sun — as a kind of bowing gesture before the sun, and also in order to connect the inner sun to the cosmic sun. Traditionally, Sun Salutation is practiced in the morning facing east, with a feeling of surrender and appreciation toward the sun. And in the evening facing west, with a feeling of parting from the external sun and focusing on the inner sun.”

The exercise consists of a series of stretches and movements. The question is whether it would be permitted to perform this exercise without intending to honor the sun, but only for physical activity. And if not, would it be possible to practice it by introducing a slight change, like changing the order of the stretches and movements?

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Rabbi:
I don’t understand. Why not honor the sun? It does us a lot of good. What is the problem with someone wanting to show gratitude to it? Even Moses our teacher showed gratitude to the Nile and to the dust, and left it to Aaron to strike them.
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Oren:

Maybe the concern here is that this is one of its modes of worship?

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Rabbi:
I don’t think that this is its mode of worship. If it’s about appreciation, then this is not idolatry in which it is being worshipped. And even if it were its mode of worship, here the intention is the opposite if it is being done for the sake of exercise. If it is just appreciation for the sake of appreciation, then there is no exercise here, and it is just an act without intent, and if that is its mode of worship there would be room to prohibit it.