This can be described as oscillating or wavering between different options or opinions without a clear direction or decision being made.
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The word for walking back and forth is "pacing."
A pendulum swinging, a see-saw moving up and down, and a rocking chair swaying back and forth are examples of things that go back and forth.
A pendulum swings back and forth rapidly due to gravity and inertia.
The particles in a solid move back and forth in place.
"Oscillate" means to move back and forth in a regular rhythm.