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After the bombing of Hiroshima, US President Harry Truman issued a speech talking about the use of an "atomic bomb". But was it possible to keep this mechanism a secret? Perhaps by pretending it was a more powerful conventional weapon, or pretending explosives were delivered in a different way?
And would that misinformation have had any effect? - would it have delayed other countries discovery and search for nuclear weapons at all? Or difference in public opinion? Or was it already too late?
No. The concept of a fission explosion had been theorized for some time. The issue was - it would cost a fortune to find out if it would actually work, given the technology of that age. In the 1920's and 1930's, radiation science was still emerging, and most people working with radiation were pursuing peaceful uses, so the idea of an uncontrolled chain reaction was more interesting theory that serious goal. A parallel theory held that plutonium could also initiate a nuclear explosion, but plutonium doesn't exist naturally... it has to be made in a reactor.
Both approaches would require 25-50 pounds of either pure U-235 or Pn. At that time, both were only known to science in quantities of a gram or less, obtained only with great difficulty. It would cost a fortune to obtain that much of either substance. Plus, they had to figure out how to keep the device safe until initiation... not simple.
And, there was the possibility that a fission bomb might just 'fizzle', as in initiating a slower chain reaction that released a lot of radiation, but not the instant and massive release of energy that the theory suggested might happen.
At that time, no nation or organization was going to devote that level of resources, greater than most nations GDP, to investigate a theory that might or might not work as theorized.
The pressing need was WW2, and the fear that Germany and Japan were also developing such a powerful weapon, plus Albert Einstein's appeal to Franklin Roosevelt in 1941. Only a person of Einstein's stature could have persuaded the US of the danger, and the need to fund the project. Only the US at that time had the resources, and was free of attacks on its economic infrastructure that it could spare that level of resources. It was estimated that when the Oak Ridge uranium enrichment facility was operating during the war, it was consuming as much as 1/7 of the total electric power in the US. Only the US had enough suitable metal to make electromagnets of that scale... since copper was needed for wartime, they used the silver in the US reserves to build the Oak Ridge calutrons that consumed so much power.
Once the theory was proven, then making a bomb became just a matter of getting the material and assembling the device. It was taking the risk to fund an unbelievably expensive project that might not work as theorized, that posed the greatest obstacle.
So while the inner workings of a nuclear bomb could be kept secret, the fact that it worked, and the devastating power it unleashed, could not.
The details communicated by Fuchs and the Rosenbergs to the Soviets cut some time off of their bomb project, but the Soviets would have achieved a nuclear bomb even without their help. Unlike the Allies in WW2, the Soviets knew it would work.
Note also that China developed a nuclear bomb in the 1960's with no assistance or purloining of secret information.
It would not have been possible for (at least) two reasons.
First, because speculation about using atomic energy in a bomb had been around for most of a decade, and people, scientists and many non-scientists as well, knew that there was a huge source of energy available there. (What was less well known was how the energy could be released and how much uranium would be needed.) It's inconceivable that had Truman announced that Hiroshima had been destroyed by a single explosion that people wouldn't have very quickly concluded that it was an atomic bomb.
Secondly, while Manhattan Project security was impressively tight -- other than the odd Soviet spy or two -- this was in wartime and everyone understood the critical importance of not letting our enemies know anything about the bomb. But once peace was restored, many of those same scientists and engineers would have felt obliged to get the basic information -- not the critical technical details, of course -- out.
I once read that after Hiroshima was bombed the Japanese government sent a scientist to investigate what type of bomb was used. I remember it being considered possible that it was an atomic bomb or a "pressure bomb". Presumably a "pressure bomb" was another hypothetical type of bomb.
In any case scientific testing should have quickly revealed that a fission bomb was used if the scientists were testing for whether a fission bomb had been used.
The idea of bombs that released atomic energy explosively had been used in science fiction since at least as early as The World Set Free by H.G. Wells in 1913. Nobody really had a theory about how to do it in real life until Uranium fission was discovered in 1938.
Projects to research building fission bombs started in the USA, the UK, France, Germany, Italy, the USSR and Japan during the World War Two era, though only the USA had sufficient resources for success during the war.
If the USA had maintained secrecy about what happened at Hiroshima and Nagasaki, the Japanese government quite probably would have revealed, before the surrender was signed or US troops began the occupation of Japan, that each city was devastated by a single bomb, if only to justify surrender to its military and people. The Japanese government might even have announced that the bombs were fission bombs.
Once knowledge of city blasting bombs was out, it would take governments that had projects to build fission bombs a short time to realize that the city blasting bombs were probably fission bombs, and therefore that fission bombs were probably possible and buildable.
Even if somehow the idea of the atomic bomb was unknown there were giveaway clues: The deadly fallout from an atomic bomb is comprised of two types of isotopes: The medium-weight isotopes that come from fission and the generally lighter ones that come from neutron capture.
Most of these isotopes simply do not occur naturally in detectable quantities. Thus that is a very strong indication that the power source was fission of uranium or some transuranic. Furthermore, a good portion of the fuel isn't used, it's also going to be present in the fallout. That will tell you what the element was the bomb was based on.
Thus simply examining the target tells you that it was a bomb based on splitting uranium or plutonium. A bit more work will be needed to figure out what isotope was used, but they'll find it.
Hence there's no way to keep it secret. The only things to keep secret are how you produce the fuel and the design of the bomb itself. (Nothing about the remains will tell you it was set off by imploding a sphere of plutonium, nor how to design that implosion system.)
No, the basic concept of the nuclear weapons was widely known throughout the scientific community at the time.
Few days after bombing the Nagasaki the US released the Smyth report (on 12 August 1945) containing all information on Manhattan project that is or can be publicly available.
If you check the Smyth report contents you can see to what details it goes. Many of this data was publicly known even before World War II. And most of this data was known to all the belligerents in the World War II. They could even give the Smyth report to Germany or Japan and they wouldn't be able to make their A-bomb before the war ended.
It was criticized at the time that it was the blueprint of the atomic bomb especially when USSR had developed their's A-bomb sooner than expected. But many key facts were omitted - the most important are:
Methods and processes used to produce highly enriched uranium and weapons-grade plutonium
The internal design specifics of the bomb
Methods of initiation of a nuclear explosion.
But it must be noted that the key secret before the bomb was used was just the fact that it actually could be created so high secrecy of the Manhattan project was very well grounded. Although the basic concepts of nuclear weapons were widely known, what was was unknown at the time was if the exact engineering solutions were possible with the technologies of the time.
As a side note, the USSR got the key secret information on developing the A-bomb through spies - most notably Klaus Fuchs
As noted, the idea of nuclear fission was well understood (at least theoretically) since the 1930's, and indeed the idea of an "atomic bomb" had been around even earlier (H.G. Wells postulated what we would likely call a "dirty bomb" today in "The World Set Free").
There were actually 3 major secrets to the atomic bomb, but even then they were penetrable if you were willing to expend the resources necessary to do the experimental work.
Secret number 1: How do you extract and purify the fissile material for the bomb? This is a question which delves more into the realm of heavy engineering, and since the answer wasn't clear, the "Manhattan Project" went to the great expense of trying out every method to discover which one worked best. If the American and British nuclear programs were not infiltrated by spies, this would likely have set the USSR and everyone else back by a decade, since no other nation could afford to try out so many methods in parallel.
Secret number 2: How much fissile material is needed? Finding the critical mass of enriched Uranium or Plutonium was really the key to making an atomic bomb or nuclear reactor work. Since there was no stockpile of enriched Uranium and Plutonium isn't a naturally occurring element, this complicated matters considerably. In fact, the actual nature of Plutonium could only be guessed at until sufficient quantities could be extracted from reactors. This actually provides an entry into:
Secret number 3: The layout of the bomb. While in general terms we can now describe how uranium "gun" bombs and Plutonium implosion bombs work, the actual mechanics are still closely guarded secrets. To use a simple example, many readers here can describe how steam, internal combustion or Diesel engines work, but how many of us could actually build one?
Nuclear weapons have other factors beyond what simple mechanical devices have to contend with. Consider, for example the "Thin Man" nuclear weapon. A relatively straightforward "gun" type bomb using Plutonium as the fissile material, the design could not be made to work since the Plutonium would spontaneously fission before the two parts of the mechanism could be brought together (even at 900m/s). This is because nuclear reactions are ridiculously fast compared to mechanical and chemical reactions.
If you really want an "alt history" where the mechanism for nuclear weapons remains secret, have a history where there are no Soviet spies in the nuclear program, and the US successfully implies that the working nuclear devices are all derivatives of the "Thin Man" (Dummy bomb casings shaped in the distinctive long, thin cylinders of ultra high speed gun bombs are prominently displayed, for example).
Since everyone knows that nuclear reactions are possible, and can eventually discover how to create and separate Plutonium, they will still be going on a wild goose chase trying to determine how the Americans are making their bombs work while Russian, French, Chinese and other bombs do not....
But was it possible to keep this mechanism a secret? Perhaps by pretending it was a more powerful conventional weapon, or pretending explosives were delivered in a different way?
Yet another NO answer.
Everyone has been talking about the spy problem that the Manhattan project had (the fact Stalin knew about the United States' nuclear bomb capabilities before Truman, the Vice President, is often used to discuss just how much power the Vice President did not have.). But what has not been discussed is why Stalin knew to look in the first place. After all, the US was very careful to control all documentation they were producing that even mentioned the word "atom". There are even stories of the FBI paying DC Comics (then named National Comics) a visit because one issue of Superman had some very in depth discussion of nuclear sciences for the the time, especially because the scientists making the bomb had seen the issue and they knew it was right... but it was classified that they knew what was said was right. Turns out the writer had read existing public literature and made his own logical jumps... which either meant National/DC had a very talented man writing kids comics, or the conclusion wasn't that out of the realm of possibilities given public information (this does occasionally happen with military fiction writers. Tom Clancy was frequently visited asking how he new that much detail about the classified tech he was discussing... and his response was, "I was just guessing, but thanks for letting me know I was right.").
Well, the whole effort of keeping all that stuff secret actually tipped Stalin off. Every modern country in the world was racing for a nuclear bomb and was producing papers on nuclear science and techniques BUT the United States. From Stalin's perspective, the U.S. had no one in the entire country who was interested in the bomb... despite having some of the famous physicists that fled Germany taking refuge in the country. Stalin found that a nation that was so invested in military innovation to not have a noticiable gap such as the lack of scientific output on nuclear sciences was rather odd. Especially since it was the one war time nation that had no major battles near the homefront and academic hubs. To Stalin, he (correctly) figured that the U.S. should be the leader in this field at this time. And since Stalin was paranoid of just about everyone and everything (except, for some odd reason, Hitler's military build up near the Russian boarders), he figured that the US must be tightly controlling nuclear science research from seeing public light and sent in his spies to find out what they were doing.
Basically, had Einstein and the others been allowed to publish fake papers with ideas that were wrong or they had tried and had failed, they might have slipped under Stalin's paranoia and given us a little more time with sole dominance of the Nuclear Arsenal.
In addition to the other answers:
It was not possible to hide the fact that the bombing of Hiroshima used a new type of weapon. One bomber accomplished something that would have required hundreds of aircraft dropping conventional explosives. Hiding that would have required getting rid of all witnesses, and that wasn't practical.
Also, the strange medical symptoms of many survivors (burns, vomiting) would point in the direction of a radiation weapon.
