The Partial Test Ban Treaty (PTBT), formally known as the 1963 Treaty Banning Nuclear Weapon Tests in the Atmosphere, in Outer Space and Under Water, prohibited all test detonations of nuclear weapons except for those conducted underground.
First, let's look at what was said by the think tank gentleman:
it is worth considering conducting a demonstration (that is, not a combat) nuclear explosion. The political and psychological effect of the nuclear mushroom, which will be shown live on all television channels in the world, will hopefully return to Western politicians the only thing that prevented wars between the great powers after 1945 and that they have now largely lost, – fear of nuclear war.
A "nuclear mushroom" means an open air detonation. Not an underground one, which are more debatable.
So, why is an open air explosion an issue? Because Russia inherited the USSR's treaty obligation from 1963 banning tests and any other nuclear explosions in the atmosphere:
TREATY
banning nuclear weapon tests in the atmosphere, in outer space and under water
The Governments of the United States of America, the United Kingdom of Great Britain and Northern Ireland, and the Union of Soviet Socialist Republics, hereinafter referred to as the "Original Parties,"
...
Article I
- Each of the Parties to this Treaty undertakes to prohibit, to prevent, and not to carry out any nuclear weapon test explosion, or any other nuclear explosion, at any place under its jurisdiction or control:
(a) in the atmosphere; beyond its limits, including outer space; or under water, including territorial waters or high seas; or
(b) in any other environment if such explosion causes radioactive debris to be present outside the territorial limits of the State under whose jurisdiction or control such explosion is conducted. It is understood in this connection that the provisions of this subparagraph are without prejudice to the conclusion of a Treaty resulting in the permanent banning of all nuclear test explosions, including all such explosions underground, the conclusion of which, as the Parties have stated in the Preamble to this Treaty, they seek to achieve.
Now, bear in mind that this type of saber-rattling is hardly new with Russia since 2022. Nor fantasizing about nuke usage limited to Russia. But, yes, it is symptomatic of Putin's Russia that no one seems to bat an eye at these kinds of rants.
However, bear in mind also that actually carrying out such a demonstration could create more problems than it would solve for Russia: because NATO may choose to carry on as before and because of the potential for extreme disapproval by even nations that have been neutral wrt the "special military operation". So this type of officially-deniable (more exactly
Russian officials can distance themselves) public-consumption threats seems more likely to be done or tolerated for psychological/diplomacy reasons than with actual intent to carry through. They may also serve to make Putin appear more reasonable than "alternative Russian policymakers" by normalizing the current level of Russian aggression.
Most certainly, in today's tightly-censored Russia, those remarks are intended to happen by those in power.
To give a little bit of context to the saber-rattling, let's look at the latest coverage of what Putin had to say:
BBC June 7
Mr Karaganov is a hawkish Russian foreign policy expert. Last year he called for a pre-emptive nuclear strike. Today he suggested holding a “nuclear pistol” to the temple of the West over Ukraine.
And Mr. Karaganov is not, in fact, merely talking about a nuclear demo. No sirree.
A Difficult but Necessary Decision
Thing may also get to the point when we will have to urge our compatriots and all people of goodwill to leave their places of residence near facilities that may become targets for strikes in countries that provide direct support to the puppet regime in Kiev. The enemy must know that we are ready to deliver a preemptive strike in retaliation for all of its current and past acts of aggression in order to prevent a slide into global thermonuclear war.
But what if they (note: the West) do not back down? What if they have lost the instinct of self-preservation completely? In this case we will have to hit a bunch of targets in a number of countries in order to bring those who have lost their mind to reason.
Yup, that is what the eminently reasonable "leading public foreign policy organization" in Russia has to say these days.