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1

Ever noticed the difference between negative temperature and positive temperature? You can feel the difference!


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Since you are at the university now, you could register to take the classes offered by the university in the seven fields you listed. Each class will have it's own recommendations for textbooks. There are no magical textbooks. What really helps is to have a good teacher (hopefully the professor/instructor in class) who can explain the difficult points along ...


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This answer started as a comment to orion's excellent answer. I'd like to expand on it. There are two different classes of measurement being addressed here: Geometric measurements and physical phenomenon measurements. I'll address them separately. The geometric measurements such as $A = πr^2$ have rational exponents because the relationship between ...


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The answer to your question is three-fold. First, a number of integer exponents come from the definition of "being to the power of something" itself. Second, fundamental physical laws are (at least effectively) regular and local which does not allow for non-integer exponents. And third, the non-irrationality of exponents is not true in non-linear dynamics, ...


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Using a similar argument as @Jason, we should first concentrate on the nature of the observables we use and also on geometry and conservation laws. Surely we use time, space, mass as references precisely because the laws of physics relate these quantities in a simple way. This is precisely for this reason that we have been able to discover relations at ...


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I would in fact put the question on another level: Why do most formulas in mathematics&science have rational exponents? The thing is – in a way all exponents are rational: the power operation is first only defined for integers (by iterated multiplication). When we then rearrange the equations, rationals arise naturally as roots. But you can never ...


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There is a non-subjective and quite mathematical approach to this question. First, we have the simple linear proportionalities that aren't really physical laws but just definitions of physical quantities. Why are different sensible measurable quantities usually in linear or power-law proportions will be further clarified later. An example is $F=ma$ (just ...


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The math we use to describe the behavior of the world around us has two types of quantities: values and units. "3.4" is a value. "Meter" is a unit. There are extra rules that value-unit pairs have to follow in order for the results to have any physical meaning: Two value-unit pairs must have the same type of unit if they are added or subtracted, i.e., ...


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You ask a very interesting question. The other answers here point at some fine examples and reasonable explanations. However, I think they only touch on the largest cause for your observation: the human factor. Assumption Most formulas in physics have integer exponents. No other answer really challenges this hypothesis. To have an irrefutable proof of ...


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Let's ignore the uninteresting cases where fractional exponents arise from bad definitions of relevant physical quantities. In general, the simplicity of expressions governing many phenomena has to do with existence of unique length/time scales. In general situations, where there are multiple length scales or when there are no length scales, you often find ...


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The reason for this is not just 'simplicity', as others have pointed out. It is also due to the way these expressions come into existence. Usually, we have a simple, linear relation, obtained intuitively or due to definitions; i.e., $$v=a*t$$ The velocity traveled is acceleration $v$ multiplied by time $t$. Now, if we we want to get the distance traveled ...



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