The Imrei Emes (Likutim, Pesachim 68) says we become like malachim on Shavuos. He proves this from the halachah (Pesachim 68:) that Shavuos should be 'לה וחצי לכם חצי, half for enjoying good meals and half for Hashem [engaged in Torah and tefillah]. The question is, how does a human being know how to divide a day precisely in half? It states (Shemos 24:6) הדם חצי משה ויקח, "Moshe took half of the blood," and Rashi asks, "Who divided it [exactly in half]? A malach came and divided it." Because humans cannot divide things precisely in half, only a malach can. So, on Shavuos, how do we divide the day in half? How can they keep the Chazal 'לה וחצי לכם חצי, "half for enjoying good meals and half for Hashem" accurately? The Imrei Emes answers that on Shavuos, we become like malachim, and malachim can divide with precision.
One year after Shavuos, Rav Shach zt'l asked Reb Menachem Ziemba zt'l hy'd, "What did the rebbe (the Imrei Emes) say?" and Reb Menachem Ziemba told him this vort (written above) that he heard from the Imrei Emes.
Rav Shach replied that we can express it this way: After we spend half of Shavuos with 'לה חצי, we become like malachim, and then we will know how to divide the day in half.
Shavuos morning, at Shacharis, someone fell asleep because he was tired after an entire night studying Torah. When he woke up, Reb Chaim Brim asked him, "Did you ever see a chasan sleeping under the chuppah?"
The Megaleh Amukos teaches: "It states in Shaar HaKavanos in the name of the Arizal that throughout the year, whenever one is awake all night long studying Torah, it will redeem him from כרת. If he deserved to die, chalilah, studying Torah all night long, will annul that decree. This is said about any night of the year. Certainly, when one is awake on Shavuos night, he attains forgiveness for many severe aveiros."
The Noam Elimelech (Mishpatim גדי תבשל לא ה"ד) writes, "On Shavuos, we have a leniency to eat meat after milk, without waiting the standard shiur (time period). This is because Shavuos is the day we received the Torah, and we show that we are like the malachim [who don't wait between milk and meat]." We don't know which leniency the Noam Elimelech is referring to. The meforshim are puzzled by it because, as it appears from halachah, Shavuos is the same as the rest of the year regarding milk and meat. Some say that the Noam Elimelech refers to those who wait twenty-four hours between milk and meat (see Chulin 105.), and on Shavuos, even those machmirim won't wait so long. Although we don't know for certain the halachic issue that the Noam Elimelech is referring to, we receive his message that on Shavuos we are like malachim.
