Why is it called a particle accelerator when it's possible for the particle to go both ways: forwards and backwards? Don't they measure the difference in the d

Why is it called a particle accelerator when it's possible for the particle to go both ways: forwards and backwards? Don't they measure the difference in the direction of the particle as determined by its virtual cloud? more energy emitted from the cloud = forward and vice-versa. Loved the explanation and accompanying illustrations.