Using the German genius Heisenberg's flawed math, neither the Japanese nor the Germans had a chance at building a working bomb.
On the other hand, the great American mathematician Feynman's correct math led to an entirely different outcome for the U.S. than for what the Germans and Japanese achieved in their atomic projects.
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Actually it is a little more complex than that. You see I had a graduate engineering seminar taught by one of the members of the german nuclear bomb team. In that seminar he explained the German nuclear bomb program where it went right and were it went wrong and what was done internally to sabatoge it.
First, there was a cross section experiment to determine the nuclear cross section of graphite. The nobel prize winner blew the experiment and recorded the wrong results.
Now german culture steps in. Nobody in his right mind would try to replicate the experiment to check the results of somebody who won a Nobel prize. It just was not done, it would be an insult to that person.
As a result of the "wrong nuclear cross section for carbon" it was concluded that carbon would not properly moderate or slow nuetrons down enough to help support a chain reaction. As a result of this error, the german nuclear bomb program focused on using heavy water as a moderator and hence invaded Norway to get to its vast hydroelectric resources to produce heavy water. (Oops)
The US in its spirit of checking things redid the experiement and found the error and decided carbon is just so easy to get that they would use a graphite moderated core in the US bomb program, hence the graphite bricks under the stadium where the first nuclear chain reaction in the US took place.
Now back to germany, many of the scientists and their lab machinists looking at the option of completing the bomb quickly and getting sent to the eastern front to fight the Russians and decided to go slowly, very slowly. The made just enough progress so that the german military wouldn't go crazy, but not a bit more. Some of them also had some ethical qualms, but it was mostly about the survival of the lab workers and staff.
An interesting side light was when the US Army captured the nuclear research center some SOB officer came up and really pisssed the german scientists off. He then bullied them and asked where they kept their valuable equipment. The thought for a moment and told him the most valuable thing in the lab was the enriched Uranium isotopes. So he personally hauled the highly radioactive materials off with him without proper shielding. They all had a good laugh over that stupid fool who probably would pay dearly for his arrogence..
Are you certain of that?
See
http://www.physicstoday.org/pt/vol-53/iss-7/p34.html
for an account by Hans Bethe. Apparently much of the Germans' problem was too much deference to authority.
Physics Today, August 1995, had an article on Heisenberg including material from the "Farm Hall" tapes. The article includes copies of slides Heisenberg prepared for the top Nazi leadership (Goebbels, Goering, Speer, inter alia.) It is clear that Heisenberg understood the physical principles required to make a nuclear bomb. He had personally recommended against it in 1942, on the grounds that it would take too long and cost too much.
Edward Teller relates the story of trying to recruit Neils Bohr for the Manhattan Project. Bohr said that building the bomb would be impractical, you'd have to turn the whole country into a factory. Bohr returned to Denmark and was there when the Nazis invaded. Heisenberg met with him in Copenhagen, and apparently tried to convince him to accept some sort of position in Germany. Although much has been made of this meeting, there was absolutely no serious German "Manhattan District Engineering Project".
Bohr escaped to Sweden and then on to the U.S., where he joined the Manhattan Project. When Teller finally ran into him in Los Alamos, he was all set for one of those "I told you so moments". The cagey Bohr turned the tables on him and immediately confronted Teller with, "I told you, you'd have to turn the whole country into a factory!", a testimony to the enormous scope of the Manhattan Project.
Although the Germans did not seriously pursue a fusion bomb, the threat of a German atomic weapon was the impetus for the Manhattan Project. It is said that the U.S. spent more money looking for a German atom bomb than the Germans spent on nuclear research during the War. (Roosevelt lied! Intelligence was flawed!)
After the war, top German nuclear physicists were interred in relative comfort in an estate in the English countryside called Farm Hall. Their conversations were secretly being recorded to see if they revealed anything of value about a German weapons program. Heisenberg's reaction on seeing newspaper reports of Hiroshima are telling. His first reaction was that it could not be true, he asserted that somebody just made a bomb with a lot of uranium in it and made a mess and killed a lot of people. (Heisenberg, father of the "dirty bomb".) As it began to sink in over time that the Americans (and the British with a lot of help from scientists driven out of Europe by the Nazis) had done what the Germans had not done, there began to form in the minds of the German scientific community what has come to be known as the "explanation" (I forget the German word.) It was more a rationalization of their failure than a truthful explanation. According to the "explanation", the German scientist could have made a bomb, but they did not want to help the Nazis (why in this single endeavor alone is unclear) and besides they were morally superior to those Americans and their English toadies. (Sound familiar?)