I think many foreigners know that the Emperor of Japan lives in Tokyo. However, not many know that emperors used to live in Kyoto. Until the capital of Japan moved to Tokyo in 1868, capital of Japan was Kyoto. However, between 1603 and 1868, the nominal ruler of Japan, Shoguns of Tokugawa shogunate lived in Edo, current Tokyo.
Shogun lived in Edo but the emperors lived in Kyoto since 794 and Kyoto Imperial palace was the residence of emperors from 1331 to 1869. It is interest that Tokugawa shogunate is not originally from Edo. Edo was a fishing village until Ieyasu Tokugawa, the first shogun from Tokugawa clan decided to reside. Then, until the collapse of Tokugawa shogunate, Edo overwhelmed Kyoto by population and economical importance.
Therefore when the capital moved to Tokyo from Kyoto, normal Japanese did not feel any difference. The reason is simple. The influence of emperor was limited and almost did not affect their lives. No internet, no TV and even no photo of the emperor therefore people living outside of Kyoto would not see the face of the emperor during their lives. Also people of Edo will think Shogun is stronger than the emperor and I assume many people forgot about the existence of emperors during the shogunate.
Then, there were many TV dramas and movies regarding the shogunate and its followers, but there is no drama or movie regarding emperors during the shogunate. Therefore more than 500 years, emperors lost their powers in Japan.