Can you pray with your hands behind your back?

If it's more comfortable, I think you can.

I think that the fact that the Prophet (PBUH) was seen in different prayer positions at different times meant that he was looking for the position that was most comfortable to him at the time.

I think if we are to "pray as we saw him pray" (صلوا كما رأيتموني أصلي), we are to do the same thing he did, and that is modify our praying positions depending on our own personal needs and what is comfortable at the time, and depending on where our understanding, knowledge and awareness leads us.

Standing with your hands behind your back helps you stand tall, lengthens the spine, opens the chest and keeps your shoulders back.

It is also a sign of respect. In the military, when members are speaking to a superior,
the soldiers adopt the relaxed position Stand At Ease position, with feet shoulder width apart, hands clasped behind back but with upper body half still in position of attention (chest out, shoulders back).

People who like to view Islam as a military order would favor conformity over flexibility. They would rather see everyone doing the same thing, especially when they are praying together. But I don't see congregational prayer as a strict military setting. I think people should be allowed flexibility to suit their personal needs.

Where you put your hands while standing puts different stress points on different parts of your back. Also different sitting positions affect people differently.

Note: In the picture above, soldiers of the 130th Engineer Brigade stand at ease on Hamilton Field during the brigade's deployment ceremony June 4 at Schofield Barracks.