The beginning of the asr prayer time is actually the time of merit for Asr prayer which starts when the specific time for Dhuhr prayer ends.
There are three time periods allocated to every one of the five daily prayers that are as follows:
1- The specific period: the period in which no other prayer can be performed.
2- The common period: the period in which you can perform Dhuhr and Asr or Maghrib and Isha prayers. It must be noted that their order must be observed (at noon, the Dhuhr prayer must be done before Asr, and at night, the Maghrib prayer must be done before Isha).
3- The time of merit: The period which praying in has more thawab or reward.
Taking what was said regarding the asr prayer and the period of performing it into consideration, one must say that generally speaking, the period of Dhuhr and Asr prayer is from Dhuhr till Maghrib. The duration required to perform a Dhuhr prayer after the Dhuhr time begins is the specific time of Dhuhr prayer meaning that performing asr prayer in this period is not accepted. Also, the duration required to perform an Asr prayer just before sunset is the specific period of Asr prayer. The period between the two specific periods explained is the common period for Dhuhr and Asr prayers and in other words, performing these two prayers in this period is allowed, although the Dhuhr prayer must be performed first.
The time of merit for Asr prayer starts when the specific period of Dhuhr prayer ends and continues until the shadow of the indicator (shakhes) increases by twice the size of the indicator. Therefore, what is meant when it is said “the beginning of Asr prayer time”, is the beginning of the time of merit for the Asr prayer.
 If one realizes that he/she is performing Asr prayer before Dhuhr prayer, he/she must change his/her intention to Dhuhr prayer and finish the prayer and then perform the Asr prayer and it very good for him/her to perform the Asr prayer once again (but it isn't necessary). Tawdihul-Masael (Imam Khomeini’s annotation), vol. 1, pg. 405.
Therefore if one delays his Dhuhr prayer until the specific period of Asr prayer, the Dhuhr prayer wil be qadha, and he must perform the Asr prayer in that period, and compensate for his Dhuhr prayer later. .(توضیح المسائل، امام خمینی، مسئله 731)
 Tahrirul-Wasilah, vol. 1, kitabul-salah, muqaddamatul-salah, al-muqaddamal-ula, issues 6,7 and 8, pg. 112; Imam Khomeini, Tawdihul-Masael, issue 731.
 Although at first Imam Khomeini says that the time of merit for the Asr prayer is when the shadow of the indicator reaches 4/7th of its length, but later in the issue he says that it doesn’t seem far to say that the beginning of its time begins after the specific time of the Dhuhr prayer. (Tahrirul-Wasilah, vol. 1, pg. 112, issue 6).
Any kind of a pole-like object that is vertically put on a horizontal ground is called a shakhes/indicator. A good example would be a stick that is put into the ground vertically.
The shakhes is used to tell when the sun begins its decline, which is also the sign of the Dhuhr prayer time. If a straight stick or the like are put into the ground, as Dhuhr time draws near, the shadow of the stick will recess, until it totally perishes. The shadow then begins to grow again on another side of the stick. This indicates the beginning of the sun’s decline and the beginning of the Dhuhr prayer. It has also been said that the time of merit for the Dhuhr prayer is from the beginning of the sun’s decline, until when the shadow of the shakhes reaches the length of the shakhes. For instance, if the shakhes is 10 cm long, when its shadow reaches 10 cm, that is the end of the time of merit for the Dhuhr prayer.
(Tahrirul-Wasilah, vol.1, kitabul-salah, muqaddamatul-salah, al-muqaddamal-ula, issue 6; Urwatul-Wuthqa (with Imam Khomeini’s annotations), pp. 272-273; Mohammad Hosein Fallahzadeh, Amuzesh Feqh, pp. 125 and 126).