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thinkren
26th May 2003, 10:52 PM
The New York Times is running an interesting article on the problems (http://www.nytimes.com/2003/05/27/science/27KILO.html?pagewanted=2) with the standard definition of mass. (free registration, blah, blah...)

I found the following especially interesting:

The idea of the watt balance is to measure the electromagnetic force needed to balance a reference kilogram. As long as the gravitational field is precisely known for the location of the experiment, the mass on the scale can be related to power. (The gravitational field is a complicated calculation that needs among other things constantly updated changes in tidal forces.)

It reminded of something I was told in high school that I never fully understood. I remember my physics teacher said that gravitational mass and inertial mass just happens to be equivalent, there is no good reason for this to be the case. Einstein conveniently took this to be the cornerstone of one of the most important rule in physics, but there is no explanation of why this is. I may have remembered this wrong, so will someone please set me straight on the matter of weight (as determined by gravity) vs. mass (determined by resistance to acceleration)?

P.S. Somewhere in the depth of my memory, I also have the faintest echo of having heard some talk of attempts to actually measure any difference between the two that may possibly exist. Can anyone confirm or deny such an attempt?

fishbob
27th May 2003, 01:33 AM
gravitational mass and inertial mass just happens to be equivalent, there is no good reason for this to be the case There is a good reason for this to be the case. Our units for mass were defined in earth's gravity. Take a 1 kg brick to the moon and it will not read 1 kg on a scale, but it is still the same brick with the same 1 kg mass. Gravitational mass, refers to the force of gravity on the mass - a property of the nearest planet, while inertial mass refers to force required to accelerate the brick - a property of the brick.

Tez
27th May 2003, 05:24 AM
Originally posted by fishbob
There is a good reason for this to be the case. Our units for mass were defined in earth's gravity. Take a 1 kg brick to the moon and it will not read 1 kg on a scale, but it is still the same brick with the same 1 kg mass. Gravitational mass, refers to the force of gravity on the mass - a property of the nearest planet, while inertial mass refers to force required to accelerate the brick - a property of the brick.

This misses the point

Its an amazing fact that the "m" in the equation F=m*a and the "m" in F=GMm/r^2 are the same. The anthropocentrism fishbob mentions isn't part of the puzzle!

There is a great book by Jammer - "Concepts of Mass" I think its called - I read it a few years ago and at the end came away somewhat undecided about our use of mass in modern physics.

There have been tests - I'm not sure what the current sensitivity is, but I'd hazard at least around 10 orders of magnitude - i.e. theyre equivalent to one part in 10^10, since we can test General Rel to 1 part in 10^14, and as you say the foundation of GR is the equivalence principle...

garys_2k
27th May 2003, 11:38 AM
Einstein never did explain WHY they are equivalent, but declared that they WERE equivalent. This is one of the deepest mysteries in physics right now, the true nature of mass itself.

I've seen two schools of thought on this, the "gravity causes inertia" effect by Woodward and Mahood, and the "gravity and inertia have extrinsic causes" by Dobyns and Rueda. HERE (http://arxiv.org/PS_cache/gr-qc/pdf/0002/0002069.pdf) is a link to a paper on the latter theory.

The whole subject makes my brain itch, but perhaps once we have general relativity married to quantum mechanics the whole gravity-inertia thing will make sense.

Houngan
27th May 2003, 02:37 PM
Originally posted by fishbob
There is a good reason for this to be the case. Our units for mass were defined in earth's gravity. Take a 1 kg brick to the moon and it will not read 1 kg on a scale, but it is still the same brick with the same 1 kg mass. Gravitational mass, refers to the force of gravity on the mass - a property of the nearest planet, while inertial mass refers to force required to accelerate the brick - a property of the brick.

Whoop, whoop, whoop!!! WARNING!!!!

You gots it wrong, brotha. It will still most definitely weigh 1 kg, that's what mass is. It will, however, weigh far fewer NEWTONS that before. (a more appropriate place to use the work 'weigh', anyweigh. Er, anyway.

Mass scales weigh against other masses, that's why they're always right, regardless of gravity. Now, I'm not saying that some less-than-precise companies produce scales that read in mass units, yet rely on gravitational forces for the comparison, but a good ol' 3 rail scale will tell the truth on Saturn or on Pluto.

H.

DanishDynamite
27th May 2003, 02:46 PM
Houngan:Whoop, whoop, whoop!!! WARNING!!!!

You gots it wrong, brotha. It will still most definitely weigh 1 kg, that's what mass is. It will, however, weigh far fewer NEWTONS that before. (a more appropriate place to use the work 'weigh', anyweigh. Er, anyway.Errr....I think this was fishbob's point. The "weight" of something is related to the gravitational force. The "mass" of something isn't.

thinkren
27th May 2003, 04:00 PM
A big thank you to everyone who contributed to this thread. Especially fishbob, to whom I own an apology for mis-representing what I meant to say. Although I do acknowledge, as you pointed out, that gravity is different on different planet surfaces, for example, I meant to express the curious observation that gravity still affects matter in the same way mass is manifested as measured using inertia. Your efforts are apreciated, but Tez and garys_2k answered my question nicely (thanks guys!), although it will take me some time to follow up on the resources they provided.

Captain_Snort
27th May 2003, 04:20 PM
I remember being taught in Primary school how the metric system fits together so logically

take a cube of water at STP that is 1 cm on either side, this is a gram, take 1000 of these, this has a mass of a kilogram, also a volume of 1 litre. 1000 of these cubes of water is a tonne and the cube will have dimensions of 1 meter x 1 meter x 1 meter.

and so on, but I suppose gravity must get in on the act and now they must be redefined.

xouper
27th May 2003, 04:41 PM
Captain_Snort: ... take a cube of water at STP that is 1 cm on either side, this is a gram, Errm, pardon my pedantic inquiry, but isn't a cubic centimeter of water one gram only at 3.8 degrees celsius, not at the "Standard Temperature"? At room temp, water has a density of .998 g/cc, no?

Houngan
27th May 2003, 06:38 PM
Originally posted by DanishDynamite
Houngan:Errr....I think this was fishbob's point. The "weight" of something is related to the gravitational force. The "mass" of something isn't.

Danish,

I was specifically clarifying this:

Take a 1 kg brick to the moon and it will not read 1 kg on a scale,

Which is wrong.

H.

chance
27th May 2003, 06:42 PM
The Opening Post reminded me of a high school physics lesson where our teacher explained that mass is the only standard left that requires a physical lump of stuff, that all other were measured against. e.g length (the meter) used to be standardised by a 1 meter length of metal kept at a constant temperature under lock and key somewhere in France. The same principle was used for other standards. Now length is measured as the number of wavelengths of something or other.

Ike
28th May 2003, 01:06 AM
I think the answer to the question of the difference in gravitational mass and inertial mass lies in the physical constant G. Newtons equation F=GmM/r^2 merely tells us that gravitational forces are proportional to the mass, or ammount of stuff in each object. G just sits there like a 'fudge factor' telling us how far off our definition of the inertial mass, m or M, is from 'gravitational mass'. it seems that if the 2 were equivilant, newtons gravitational equation should read F=mM/r^2. Interestingly, G is also the least precisely measured physical constant we have, despite the fact that it is one of the oldest.

Ike

jj
28th May 2003, 01:44 AM
Originally posted by Tez

Its an amazing fact that the "m" in the equation F=m*a and the "m" in F=GMm/r^2 are the same

Um, unless I am missing something, wouldn't the two have to be related by a constant, if the present ideas for origin of inertia are correct?

Given that, it all gets subsumed into the definition of 'G'. No big whoopie.

This is, of course, assuming that the relativistic implications of gravity are what give us inertia, much like the effect of moving charges vs. speed of light????

bjornart
28th May 2003, 03:30 AM
Yesterday I was about to post something similar to what jj just did, then I realized the point isn't that gravitational and inertial mass are the same, but that the gravitational forces and inertia are both proportional to the same property, the one we call mass.

If you imagine them not being equal you'd have:

mg = gravitational mass
mi = inertial mass

These two are not the same. They could have any relationship imaginable, but let's go for a simple one, doubling the mg will quadruple the mi.
You then have the formula:

mi = Y*mg^2

Where Y is bjornart's constant of gravity. If you want to use gravitational mass to calculate intertial forces you then have the formula.

F = Y*mg^2*a

Phew, it took me some time to realize this. :)

Tez
28th May 2003, 03:56 AM
Originally posted by jj

Um, unless I am missing something, wouldn't the two have to be related by a constant, if the present ideas for origin of inertia are correct?

Given that, it all gets subsumed into the definition of 'G'. No big whoopie.

This is, of course, assuming that the relativistic implications of gravity are what give us inertia, much like the effect of moving charges vs. speed of light????

What are our present ideas for the origin of inertia? I havent heard any... And I've certainly seen nothing convincing that would explain why they have to be related by a constant! Einstein simply said lets take it as fundamental doctrine that theyre linearly related with a constant of proprtionality 1 and see where that takes us...

Tez
28th May 2003, 04:10 AM
And if anyone's interested there are stacks more places one can go with this. Why is "active gravitational mass" (A bodies propensity to cause gravity) the same as passive gravitational mass (its propensity to respond to a graviational field).
Why are the only non-inertial masses we see gravitational? (it used to be thought that there were things like electromagnetic mass, but it never really worked out).

For \$8.76 you can get Jammers book (a 1997 reprint of the famous 1961 edition) from Amazon - will give you many many hours of things to ponder - very little mathematics, just enough to be rigorous.. For \$40 you can get his revised 2000 edition from Barnes and Noble...

jj
28th May 2003, 08:09 AM
Originally posted by bjornart
Yesterday I was about to post something similar to what jj just did, then I realized the point isn't that gravitational and inertial mass are the same, but that the gravitational forces and inertia are both proportional to the same property, the one we call mass.

Ok, I am most certainly not the one who came up with this, but consider... If gravity has a speed of propagation, and we mvoe something, the effects of its own gravity, lagging, now do what?

The point being is that to some extent, or so it's ben argued, gravity is to inertia as electrical charge is to magentic fields.

If so, that would explain very clearly why they both depend on the same idea of mass.

It's been a long time since I read this, mind you.

Houngan
28th May 2003, 12:44 PM
Gag. This is why I respect physicists.

Feynman, in one book or another, said something to the effect of, "we can measure this and that, and say that inertia is measured in such-and-such a fashion. Now however, we're asking WHY does it keep moving?"

At that point, I said to myself, "dammit, it just does. That's the way things are." Some questions are too deep for me.

H.