Gravity?

[arunma]

Ok, my head is spinning like crazy. All I know is that k>G. About the units, I really don't understand that thing you are saying about the units.

Well, it may help to ask yourself if the statement k>G makes logical sense. Essentially you are saying that 8.99x10^9N m²/C² > 6.67x10^-11 N m²/kg², which (when dividing through by redundant units) is equvalent to:

9.5x10^10 kg > 8.34 C

It clearly would not make sense to say that x kilograms is "greater" than y coulombs. Numbers with different units can't be compared. And this is why it doesn't make strict sense to say that k is "bigger" than G.

I still don't see how can k=G. Even if you change (kg to J or C to A or whatever) k should still be bigger.

On the contrary, there's no rule which requires k to be numerically larger than G. Again, the numerical values can't be compared if the units are different. Let's say, for example, that we wanted to compare the length of a football field to the mass of the earth. One might say that ~300 meters is less than 5.97 x 10^24 kilogram weight of the earth. But if I gave the mass of the earth in solar masses, then it would only weight about 10^-6 solar masses, in which case the football field would be "more." Thus you can see that comparing quantities of different dimension doesn't have any physical meaning.

Now, about the 1, isn't that just a mathematical tool used to make the calculation easier? You can even put X instead of one, no?
I remember my physics teacher told us that physicist do use 1 for the constants. But that is it, it is juts a way of writing it.

It is used primarily to simplify calculuations. But in fact there's a theorem which actually assures the existence of the system of "natural units." Besides that, the equations still have to make physical sense. For example, in Big Bang thermodynamics, we sometimes talk of a particle decoupling when the temperature of the universe is equal to its mass. In natural units, both temperature and mass are expressed as energies, and this makes sense, because mass is equivalent to energy, and temperature is a sort of kinetic energy. The intelligent scientist will see "temperature = mass," and know that Boltzmann's constant must be added to the left side, and the speed of light squared to the right side. But the equation wouldn't make sense if, say, temperature were equal to the square of mass. Consistency of units is most important in science.

Well, I hope this helps.

 

[MrLogic]

Oh, now I see it. I was only paying attention to the numbers. That's Einstein Theory of relativity. It all depends on the frame of reference.

Ok then, so why is Electromagnetism stronger than gravity? since I don't know.

 

[arunma]

Oh, now I see it. I was only paying attention to the numbers. That's Einstein Theory of relativity. It all depends on the frame of reference.

Well...no, this doesn't actually have anything to do with frame of reference or relativity. I'm sorry if I've confused you, I only brought up an example from relativity because that is one setting in which it's convenient to set various physical constants equal to 1. But you're right that the actual numbers are unimportant without considering the units.

Ok then, so why is Electromagnetism stronger than gravity? since I don't know.

Electromagnetism is stronger than gravity because the fundamental charge carriers are so light. IOW, protons and electrons have a lot of charge, but not very much mass. If these charge carriers were more massive, then gravity would be as powerful as electromagnetism on smaller scales.

Of course this brings up another question: why are the fundamental charge carriers so light? Modern particle physics supposes that there might be hidden dimensions in the universe in which gravity is much larger than it is in ours. I think Dr. Lisa Randall's book "Warped Passages" (written for a general audience) covers this in some depth, but since I haven't read it, I couldn't say for sure.