Why can the action potential of a neurone only go in one direction?

A stimuli starts a chain of events which eventually causes a neuron to undergo an action potential. Depending on which cell it is, chain of events and the ions involved that cause action potential are different.

In a normal skeletal muscle the action potential is caused by the influx of sodium ions, There are two sodium gates that control the influx of sodium into the cell, which depolarizes and cell and elicits an action potential. This causes the sodium gates to close. During this time an action potential cannot be initiated since the sodium gates are closed. The change in the membrane potential caused by the influx of sodium causes the potassium which is inside the cell to rush outside, therefore hyper polarizing the cell membrane and bringing the membrane potential back to its resting state.

The period when the sodium gates close to when the cell membrane is brought back to resting state membrane potential, another action potential cannot be elicited (since the sodium channels are closed and cannot be opened until the cell reaches resting state membrane potential) is called a Refractory Period.

When a neuron undergoes depolarization, it excited its nearby neurons therefore causing them to undergo depolarization. By the time the second cell depolarizes the first cell is in refractory period, because of which the first neuron cannot depolarize. However, the third neuron next to the second neuron is at a resting state and undergoes depolarization. By the time third neuron depolarizes the second neuron is in refractory period therefore second neuron cannot depolarize again (elicit an action potential). Therefore action potentials travel only in one direction.

Because the synaptic vesicles which contain neurotransmitters are only found in the knob at the end of the terminal arborization and the end of the nerve cell. So if the action potential passes in the opposite direction (towards the dendrites) it won't be able to move to the adjacent neuron due to absence of synaptic vesicles.