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I am an student in physics department and I will graduate very soon.In my past four year I have done a good work and get a nice gpa.But as I get more and more familiar with advanced content such as quantum field theory,I become very comfusing about what I learn in my high school. Because I think I don't really "understand" the knowledge in high school,even I am very familiar with how to calculate them.

For example,how does the numbers "add" and"multipy".It won't make me very confusing if the numbers are just real numbers,mathematically.But no one tell me a percise theory about how the numbers operate between too numbers with unit,since the physical quantity can be written as "R + unit”.

It sounds very reasonable that 10cm is equal to 0.1 meter.But It doesn't mean “10cm+1m”is the same as "0.1m+1m".I just mean,the addtion principle should be defined carefully.If not,maybe somthing weird will happen.But I don't remmenber my high school teacher having taught that.I just know,1kg/1 dm^3=1kg.cm^(-3).And 1kg/0.00001m^3=1*10^6kg.m^(-3)=1kg.cm^(-3).

But the point is I have totally forgotten the reason.And I think the operation between real numbers is the not same as the what we use in physics.Because in physics we are talking about numbers with unit,not pure number.

I think I really need some book about it to read.But all lecture notes in college never mention it.Even the classical mechanics course for freshman will talk about V=dr/dt,E=1/2mv^2.But it almost drive me crazy what heck is m times v^2.

Secondly,I am much confusing about the charge.Why the positive charge will have a positive value and the negetive charge will have a negtive value.We never think about it when we are measuring mass,length.As I have said before,I don't really remember what I learn in my high school.I always think since the two kind of charge is different,we use + and- to make a difference.Can't we use other symbol to show the difference?

For example,we can say positive charge is 3 C,and the negative one is 3 c*.If we accept we can use negative value to represent a negative charge.Why won't we define the mass as -4 nkg or something else.Maybe I think to much but I just can't stop myself.Please help me .

For example,how does the numbers "add" and"multipy".It won't make me very confusing if the numbers are just real numbers,mathematically.But no one tell me a percise theory about how the numbers operate between too numbers with unit,since the physical quantity can be written as "R + unit”.

It sounds very reasonable that 10cm is equal to 0.1 meter.But It doesn't mean “10cm+1m”is the same as "0.1m+1m".I just mean,the addtion principle should be defined carefully.If not,maybe somthing weird will happen.But I don't remmenber my high school teacher having taught that.I just know,1kg/1 dm^3=1kg.cm^(-3).And 1kg/0.00001m^3=1*10^6kg.m^(-3)=1kg.cm^(-3).

But the point is I have totally forgotten the reason.And I think the operation between real numbers is the not same as the what we use in physics.Because in physics we are talking about numbers with unit,not pure number.

I think I really need some book about it to read.But all lecture notes in college never mention it.Even the classical mechanics course for freshman will talk about V=dr/dt,E=1/2mv^2.But it almost drive me crazy what heck is m times v^2.

Secondly,I am much confusing about the charge.Why the positive charge will have a positive value and the negetive charge will have a negtive value.We never think about it when we are measuring mass,length.As I have said before,I don't really remember what I learn in my high school.I always think since the two kind of charge is different,we use + and- to make a difference.Can't we use other symbol to show the difference?

For example,we can say positive charge is 3 C,and the negative one is 3 c*.If we accept we can use negative value to represent a negative charge.Why won't we define the mass as -4 nkg or something else.Maybe I think to much but I just can't stop myself.Please help me .

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