Let's say part of the mainstream believes that a drug X is more effective than drug Y. Another part of the mainstream believes that drug x is less effective than drug Y. A scientist appears who wants to challenge it and show that the drug X is equivalent to the drug Y, generating the same result and the same side effects, since both act exactly by the same mechanism.
I know the example seems a little forced, but it is just to provoke the classic definition that always aligns the alternative hypothesis with the research hypothesis.
In this case there should be the equality (expressed as a small interval) the alternative hypothesis and therefore the difference (outside of cited small interval) as an null hypothesis?
In statistics there are tests of equivalence as well as the more common test the Null and decide if sufficient evidence against it. The equivalence test turn this on its head and posits that effects are different as the Null and we determine if there is sufficient evidence against this Null.
I'm not clear on your drug example. If the response is a value/indicator of the effect, then an effect of 0 would indicate not effective. One would set that as the Null and evaluate the evidence against this. If the effect is sufficiently different from zero we would conclude that the no-effectiveness hypothesis is inconsistent with the data. A two-tailed test would count sufficiently negative values of effect as evidence against the Null. A one tailed test, the effect is positive and sufficiently different from zero, might be a more interesting test.
If you want to test if the effect is 0, then we'd need to flip this around and use an equivalence test where the H0 is the effect is not equal to zero, and the alternative is that H1 = the effect = 0. That would evaluate the evidence against the idea that effect was different from 0.
ChatGPT has agreed with the cited user, and gave me the following answer to the same question (Don't be upset with me. I quote this answer because it raised reflections on me):
Yes, in this case, the alternative hypothesis would be that the two drugs, X and Y, are equivalent in terms of effectiveness and side effects. The null hypothesis would be that there is a significant difference between the two drugs in terms of effectiveness or side effects. The scientist's aim would be to gather evidence that supports the alternative hypothesis and rejects the null hypothesis.
It's worth noting that the null hypothesis is often stated as the opposite of the research hypothesis in order to provide a clear statement of what the scientist is trying to disprove. However, in this case, the null hypothesis does not necessarily contradict the mainstream beliefs that you mentioned. It simply states that there is a difference between the drugs, whereas the mainstream beliefs disagree on the direction of that difference.