Why weakness in left arm is often associated with heart problems?

I sometimes read that weakness in left arm is often associated with heart problems. But I have not seen any explanation. Here I venture one. See if it makes sense.

Most health problems are related to issues with circulation systems. Weakness in left arm is probably caused by some blood clots. If the blood clots from arms flow toward the heart, most likely they will melt for chest area is warmer than arms. However, left arm is closer to the heart than the right arm. Blood clots from left arm have less time to warm up than blood clots from the right arm. If unmelted blood clots reach the heart, they could cause heart problems. Therefore weakness in left arm is often associated with heart problems. 

Hope this explanation is not too far fetched.