I thought one day that newton found that the gravitational acceleration is 9.81m/s^2 down and used that as a constant before he discovered or claimed Fg= GMm/r^2. As far as I know G is a constant today too. would it be correct to say that as long as there are constants we lack in the knowledge of that particular area of study?
Sometimes, not always. You are right that where there's a constant, there's a question: "Why does it have that value?", and deeper understanding might answer that question. But at least some constants cannot be explained that way, or we'd face an infinite regression of questions. The problem of calculating the value of every constant from an understanding of some deeper underlying physics is somewhat similar to defining words; every dictionary must contain either circular definitions or undefined words.
Wow! well put! thats a very good analogy. But what is it that makes up the constant such as G or the plank constant h? Is it still a constant upto date?
At the end of an unending string of questions, sometimes there are things that just Are. Constants are things that just are. Heck, even the equations themselves are reflections of how the universe is. There doesn't necessarily need to be more to know.
across the earth's surface the gravitational field is far from constant. It varies quite a bit and the variations are easily measureable. Now I wonder if you could discover why that is so ? As a hint, the answer will be found in geology and gravity anomalies Dave
Not really, especially in this case. In fact, I'd think if there were no constant in this law, it would be more strange.
Here's a second hint in case Dave wasn't being specific enough: http://en.wikipedia.org/wiki/Gravity_of_Earth#Variation_in_gravity_and_apparent_gravity
There appear to be two kinds of 'constant'. Pi, e and the like would be numerically the same, wherever there are Scientists and Mathematicians in the Universe. Other 'constants' are dependent upon the units used - such as G,g,ε_{0}. I wouldn't say the Pi demonstrates a lack of knowledge.
There are two types of physical constants: 1) You can modify our unit system to get G=1. This is possible with all constants which have units. They are not fundamental and do not demonstrate a lack of knowledge. They are convenient if you do not want to measure a length in nanoseconds instead of meter or a mass in 10^{8} planck masses instead of kg. 2) You can construct constants which do not have units, where the fine-structure constant is the most prominent one. They are the same in every unit system - you cannot get rid of them. Currently, there is no way to calculate/predict those values, they are purely measurement results. In the current model of particle physics, there are 25 of those constants (26 with cosmology).
But isn't G more than just a number to get the units to come out the way we want them? It represents the same proportionality regardless of what value we give it by changing the unit system. And don't we lack knowledge about the hows and whys of the proportionality that it represents?
No, it really is a proportionality constant. Someone on these forums called G "what we get for wanting to do physics with everyday units of measurement" and I liked that. The other kind of constant, as mfb said, is a different type of beast altogether. Although I wouldn't say it betrays a lack of knowledge necessarily.
I know it's a proportionality constant. That's my point. What is it a proportionality of? And what do the units have to do with that proportionality? I guese what I'm trying to say is; what does the unit system have to do with the actual physical quantity of the proportion being what it is. I think the answer would have to be: nothing.
Its a proportionality because we want to use an arbitrary mass measurement: 'kilogram', an arbitrary length measurement: 'meter', and an arbitrary time measurement: 'second'. If you change any of these the value of G will change. Furthermore, if you take less-arbitrary measurements (like using planck units), G can go to 1, a.k.a. disappear. G, like other dimensional constants like h (planck's constant) have particular values because we choose to represent them in units that are 'everyday' in nature. Edit: A good example of this is c, the speed of light. It's a large number that crops up all the time in algebraic-level special relativity that makes the equations incredible annoying to evaluate. However if you change your units (which usually are represented in meters) to something more befitting c (like light-seconds or light-years), c becomes 1 and suddenly your equations are easy to handle. It's only because it's easier for us to visualize objects in meters than in lightyears that c can be an annoying number.
So does this mean that by changing the units you're making the proportionality that G represents disappear? Or is the proportionality the same as it was before? Sorry, got to go. I'll check this thread tomorrow night.
Sort of. Lets take the example of planck's constant h because it's easier to explain. If you don't know, h is the proportionality between the Energy of a photon of light and the frequency of that light: $$E=hf$$ h is given by a really small number (like 6.6 x 10^-34) but in specific units (I think joule-seconds in this case). Meaning that if you wanted to know how many joules a photon with a frequency given in inverse seconds (hertz) has, you would use that number. If you wanted the energy in electron volts instead, you would use a different number for h, because you are changing the units that you are using and the previous value of h was only valid for the specific units you were using before. You could find dimensions with ratio 1:1, meaning E=f in those specific units of measurement. This makes the calculation a lot simpler, but may mean you'll get a value of energy with units that have no connection to the practical world. Going back to G, the 'proportionality' is really a proportionality of units only. So if you change the units of course you will change the proportionality. To summarize, these dimensional constants are important because they let us consistently use units of measurement that we are comfortable with, but the numbers themselves don't tell us anything about the science itself.
Ah, I think I see what the problem is. I did a little studying on natural units this evening and I can see where you're coming from on this. However, I'm still not on the bandwagon with this yet. I need to do a little more studying. I just don't have much time right now. This quote from Paul S. Wesson concerning G = c = 1 pretty much reflects my feelings at the moment: "Mathematically it is an acceptable trick which saves labour. Physically it represents a loss of information and can lead to confusion." Thanks for the help Vorde.
No problem at all. Just to comment on the 'loss of information part', that's absolutely true. Just because one can fix ##E=f## for the case (h=1) or ##E=m## for the case (c=c^2=1) does not mean that ##E=f## is true by itself. It can lead to confusion quite easily, and that's why natural units are never bothered with at lower levels, especially when students aren't comfortable with dimensional analysis.