Can I have a good explanation of what exactly is Tension? I appreciate simple answers.
Also, this is my intuition on tensors:
It is a vector that doesn't follow vector laws. Is this true? I would appreciate any
corrections to my current definition.
It is a vector that doesn't follow vector laws.
A quantity that doesn't obey vector laws cannot be considered a vector.
Tension (or compression) in general is not a force but a pair of equal and opposite forces acting at a certain point. In problems in Physics and engineering, we often consider only one of the two forces in the tension pair and call it tension or tensile force. In this way, we can consider tension as a vector.
When you go by the layperson's definition of a tensor in Physics that says, "tensor is a physical quantity which has one magnitude and multiple directions.", you may consider tension as a tensor. However, tension does not fit the mathematical matrix in order to be a mathematical tensor. This is why the layperson's definition of a tensor isn't a valid one.
I hope my explanation helps.
A tensor is not a physical quantity per se. In some cases, a tensor (rank 0 or 1) may represent a scalar or vector quantity but in a general sense, It is a mathematical tool or expression that Physicists use to express a physical state that has multiple directional properties. For example, stress itself is a scalar. But the state of stress in a bulk material is a tensor. The state of stress is not a physical quantity. It is simply a description of a number of variables that have different directional properties. To express this state mathematically, we use a device called a tensor.
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"A quantity that doesn't obey vector laws cannot be considered a vector."
Alright, let me rephrase myself. It is a quantity with a direction that doesn't obey vector laws.
Is this valid for tensors?
I think the problem here is my intuition on tensors. Is my intuition true?