Praise be to Allah.
Before we answer your question, we must express our appreciation for your interest in the religion of Islam and your efforts to find out the truth. You have left a false religion, Christianity, to look for the true religion, and this is a worthy attitude which indicates that you are not influenced by blind tradition and that you have freed yourself from the customs with which you were raised. Our Lord, may He be blessed and exalted, has criticized those who blindly follow falsehood, as He says (interpretation of the meaning): When it is said to them, Follow what Allah has sent down, they say, Nay! We shall follow what we found our fathers following. (Would they do that!) even though their fathers did not understand anything nor were they guided? [al-Baqarah 2:170].
Allaah described some Christian people who, when they found out about the religion of Islam and heard the Revelation that Allaah had sent to His Prophet (peace and blessings of Allaah be upon him), followed the truth and submitted themselves to Him, as Allaah says (interpretation of the meaning):
And when they (who call themselves Christians) listen to what has been sent down to the Messenger, you see their eyes overflowing with tears because of the truth they have recognized. They say, Our Lord! We believe; so write us down among the witnesses.
And why should we not believe in Allah in that which has come to us of the truth? And we wish that our Lord will admit us (in Paradise on the Day of Resurrection) along with the righteous people. [al-Maidah 5:83-84]
We must also express our appreciation of your understanding of the importance of the five daily prayers and the necessity of praying them at the right times. We would like at this point to reaffirm an important truth in the Islamic religion, which is that the One Who revealed it and prescribed its rules and chose this religion for His slaves is Allaah, may He be exalted and glorified, from Whom nothing on earth or in heaven is hidden. He is the Knower of the Unseen, He knows what was, what is and what is yet to come. He knew before He created heaven and earth that there would come a time when mankind would develop the science of medicine and that there would be doctors who carry out lengthy operations such as open heart surgery, organ transplants such as liver transplants, operations to treat cancer of the oesophagus, complicated operations to treat injuries sustained in traffic accidents, and so on. For this reason, and because Islam is suitable for all times and places, there is no conflict between Islam and scientific progress or work-related duties. Before we give a detailed answer to your question, we would like to mention the following points:
Operations of this nature are usually carried out by a team of surgeons, where assistant surgeons work alongside the main surgeons so that they can take turns when necessary.
Some operations are carried out by several doctors who play different roles assigned to them according to their specialties. It is not always the case that one doctor will do a whole lengthy procedure by himself from beginning to end. So you will see that one makes the incision, another is a heart doctor, a third is specialized in operating on blood vessels, then the first one comes back to sew up the incision at the end. In some operations, the role of the specialist does not even take up half of the entire time spent on the surgery.
The kinds of operations that take a very long time, such as ten hours or more, are very rare indeed, few and far between.
With regard to how a surgeon can do his prayers, the detailed answer is as follows:
The basic principle is that every prayer should be offered at the right time, as Allaah says (interpretation of the meaning): Verily, the prayer is enjoined on the believers at fixed hours. [al-Nisa 4:103]
If the operation is lengthy, the doctor can try to start after praying one of the prayers at the beginning of its appointed time, and try to finish before the end of the time for the following prayer, so that he offers each prayer within the allotted time.
He should try to arrange his schedule, as much as possible, in such a way that the time allotted for the surgery does not overlap the time for two prayers in a row. For example, he could start a lengthy procedure early in the morning, and continue until just before the time for Asr, so that he can pray Zuhr at the right time, and also give himself several hours to work uninterrupted. So, for example, if he begins an operation at 8.00 a.m. and finishes at 2.00 p.m., he will have six hours in which to work continuously, if he wishes.
If he can go to pray at the right time during an operation, and other members of the surgical team can do his work by taking turns, then they should do that. We wonder, if doctors need to go to the washroom during an operation, what do they do? If the surgical arrangements can take that possibility into account, and we know that some surgeons take a short rest or have a snack during the time of surgery, whilst another doctor takes over, then performing prayer is even more important than those things.
If the above is not possible, then there is nothing wrong with combining two prayers, such as joining Zuhr and Asr, and praying them at the later time, i.e., the time of Asr.
In very rare cases, when the surgery lasts for a very long time, and the time for two prayers has passed, such as when a surgeon starts before Zuhr and finishes after Maghrib, and he could not leave to do his prayers, then he should pray according to his circumstances. Indeed, he can even pray during the surgery, by starting his prayer with the words Allaahu akbar (Allaah is Most Great), reciting Quraan and tilting his head to indicate the rukoo (bowing) and sujood (prostration), as much as he can, tilting it lower for the sujood than the rukoo. This is how fighters on the front line pray when engaged in combat with the enemy during lengthy battles, or when pursuing the enemy or being pursued. He should pray according to his circumstances, and Allaah burdens not a person beyond his scope [al-Baqarah 2:286 interpretation of the meaning]. Praise be to Allaah Who does not make the religion too hard for us.
The evidence for these rulings is proven, and the sayings of the scholars regarding prayer in different circumstances is well-known and widely-disseminated in the books of Islamic fiqh (jurisprudence), which clearly indicates the flexibility of this blessed religion and its ability to deal with all the new developments in the human realm, ancient and modern. This is no wonder, for has it not been revealed by the All-Wise, Praiseworthy and All-Knowing?
Finally, we call on you to hasten to enter the religion of Islam, which guarantees happiness to the one who follows it in this world and the next, and offers answers to all problems. We are prepared to answer any questions you may have. Allaah is the Source of Strength and He is the Guide to the Straight Path.