Force vs. Mass: Investigating Fundamentality

[sganesh88]

Which is "more" fundamental? force or mass? A few books i read specifies mass to be fundamental but i have difficulty in accepting it.
A line of thought that satisfies me is this:
A spring stretched to a given length is assumed to exert a particular force- x meter --> y units of force) correspondingly the force varies linearly with the stretching. (k*x meter --> k*y units of force (hooke's law))
Only now does Newton's 2nd law enter the picture. He says that for a particular body, a particular number can be given which equals the ratio of the net force acting on it(that can be independently found out by measuring the stretching of a band or spring) to it's acceleration (by pre-existing conventions on length and time) and that this number (F/a) is unique to that body and doesn't vary with the force exerted or any other parameter. This we call it as mass.
Have i gone wrong somewhere.?
If i haven't, it means force is more fundamental than mass right?
A similar discussion: https://www.physicsforums.com/showthread.php?t=201903

 

[swraman]

A mass is more fundamental. Why? Because the definition of a force uses Mass in it.

Force = mass * distance * time^-2

It doesn't matter whether the force is a weight, a spring's force, a gravitational force, or whatever but the the way which physics is taught is that a force's definition is based on mass.

 

[sganesh88]

can you tell what "a mass of 1 kg" means without ever using the word "force"?

 

[Hootenanny]

can you tell what "a mass of 1 kg" means without ever using the word "force"?

Yup: The kilogram is defined as being equal to the mass of the International Prototype Kilogram.

 

[Vanadium 50]

I suspect this conversation will go around in circles until someone finds a way to quantify "fundamentalness" (fundamentality? fundament?)

 

[schroder]

I suspect this conversation will go around in circles until someone finds a way to quantify "fundamentalness" (fundamentality? fundament?)

I tend to think that “fundamental” means to exist independently of something else. In the SI system we have length, time and mass as the fundamental units of measurement. Force, on the other hand, is a derived unit. Mass can exist independently of force, although we may use force to measure it. Force cannot exist independently of some mass which creates it or allows for it to act, as far as I know. Even light cannot exert a force unless there is some mass for it to act on. Maybe this is not the most rigorously convincing argument that can be made, but I cannot imagine a stronger argument in favor of force.

 

[HallsofIvy]

Yes, but that "fundamentalism", as Vanadium50 put it, is entirely an artifact. It would be more "natural" to use speed as a "fundamental" unit because there is a "natural" fixed speed- the speed of light. Similarly since Plank's constant, a natural constant, is in units of "action", that would be a fundamental unit. G, the gravitational constant (NOT "g"), which has units of "force times distance squared over mass squared" would also be "fundamental".

I have seen that done in some texts but it is not "convenient". The unit of distance, for example, turns out to be the diameter of an electron and the unit of time the time required for light to cross that unit distance!

 

[Gnosis]

can you tell what "a mass of 1 kg" means without ever using the word "force"?

Yes. The following defines mass:

mass = volume x density

 

[sganesh88]

Yup: The kilogram is defined as being equal to the mass of the International Prototype Kilogram.

And how will you decide whether the given mass is "equal" to the international prototype? without applying a force? You cannot. Whereas force can exist independently as you could say you're exerting y units of force, when the band or spring stretches to x meters. It depends only on the measurement of distance.

 

[sganesh88]

Yes. The following defines mass:

mass = volume x density

Where's Mac?
Infront of Ron.
Oh. good. And where's this Ron?
Well.. Behind Mac.

 

[schroder]

And how will you decide whether the given mass is "equal" to the international prototype? without applying a force? You cannot. Whereas force can exist independently as you could say you're exerting y units of force, when the band or spring stretches to x meters. It depends only on the measurement of distance.

When the spring stretches x meters, and you measure that, all you are measuring is distance! There is no force unless a mass is acted on by the spring. However, a mass can exist quite independently of force. Maybe we need to exert a force to measure it, but it's existence does not depend on our ability to measure it. A force requires a mass in order to exist. It is very logical to say the mass is more fundamental than the force.

 

[Hootenanny]

And how will you decide whether the given mass is "equal" to the international prototype? without applying a force? You cannot. Whereas force can exist independently as you could say you're exerting y units of force, when the band or spring stretches to x meters. It depends only on the measurement of distance.

You didn't ask me to measure it without using the notion of a force, you merely ask me to define it.

Your claim that force is somehow 'independent' is a fallacy. Can you define for me what a force of one Newton is without referencing any other quantities?

 

[sganesh88]

When the spring stretches x meters, and you measure that, all you are measuring is distance! There is no force unless a mass is acted on by the spring. However, a mass can exist quite independently of force. Maybe we need to exert a force to measure it, but it's existence does not depend on our ability to measure it. A force requires a mass in order to exist. It is very logical to say the mass is more fundamental than the force.

Mass is a quantity. It is an attribute of a 'thing', not the 'thing' itself. So it doesn't make any sense to say that mass can exist independently. Unless you try to whack that thing with a known force, it is impossible to measure it's 'attribute' namely mass. Using the term 'mass' for 'thing' has just become a general practice.

 

[Hootenanny]

Unless you try to whack that thing with a known force, it is impossible to measure it's 'attribute' namely mass.

I know that we're in the classical physics forum here, but one can determine the mass of an electron by measuring the energy/momentum of photons emitted from electron-positron annihilation. No application of a 'known' force required.

 

[sganesh88]

You didn't ask me to measure it without using the notion of a force, you merely ask me to define it.

Your claim that force is somehow 'independent' is a fallacy. Can you define for me what a force of one Newton is without referencing any other quantities?

First of all, I'm not claiming anything. I'm just asking whether force or mass is "more" fundamental. And I've given the way i thought about this problem, concluding that force is more fundamental. If there's a fault in that line of thinking, i'd like to know about it. If force and mass are dependent on each other for their definitions, then it's downright circular.

And as to the definition of 1N, i would rather define "1 unit of force"(could be named 1 Gan :) ) as that produced when a spring of a particular material stretches through a distance of x meters under the action of that force. And it is impossible to define force without referencing "any" quantity. Note that i have not included mass in the definition. Can you define mass in such a way? This definition of force could be used to measure and compare forces with the standard 1 unit without considering the quantity of mass. Whereas to compare a given mass with the international prototype, you got to apply a force.

 

[sganesh88]

I know that we're in the classical physics forum here, but one can determine the mass of an electron by measuring the energy/momentum of photons emitted from electron-positron annihilation. No application of a 'known' force required.

oh.. that's an interesting info.

 

[Hootenanny]

First of all, I'm not claiming anything. I'm just asking whether force or mass is "more" fundamental. And I've given the way i thought about this problem, concluding that force is more fundamental.

Okay, fair enough, but you need to be willing to listen to other people's opinions.

And as to the definition of 1N, i would rather define "1 unit of force"(could be named 1 Gan :) ) as that produced when a spring of a particular material stretches through a distance of x meters under the action of that force. And it is impossible to define force without referencing "any" quantity.

Indeed, I agree that it is impossible to define force without referencing any other quantities. However, it is possible to define mass (or rather the kilogram) independently of other quantities as it currently is in the SI system.

Can you define mass in such a way?

As I said before, YES!

The kilogram is defined as being equal to the mass of the International Prototype Kilogram.

As you say, measuring mass is a different matter all together, but that is not the discussion here.

 

[schroder]

First of all, I'm not claiming anything. I'm just asking whether force or mass is "more" fundamental. And I've given the way i thought about this problem, concluding that force is more fundamental. If there's a fault in that line of thinking, i'd like to know about it. If force and mass are dependent on each other for their definitions, then it's downright circular.

And as to the definition of 1N, i would rather define "1 unit of force"(could be named 1 Gan :) ) as that produced when a spring of a particular material stretches through a distance of x meters under the action of that force. And it is impossible to define force without referencing "any" quantity. Note that i have not included mass in the definition. Can you define mass in such a way? This definition of force could be used to measure and compare forces with the standard 1 unit without considering the quantity of mass. Whereas to compare a given mass with the international prototype, you got to apply a force.

Several people have pointed out the fault in your line of reasoning. It is quite obvious that you do not want to know about it. Have a nice day!

 

[baywax]

Can you have mass without distance?

 

[Math Is Hard]

What do we actually gain in understanding of anything in nature or our natural laws if we determine that mass is more "fundamental" than force or vice versa?

 

[Cyrus]

OP, google "Buckingham Pi Theorem".

Then you will have the answer to your question.

Using the word "more" fundamental is absolute nonsense. Fundamental means, MOST BASIC FORM NECESSARY. How can something be more fundamental??

AWK...what pointless dribble in this thread. Don't try and do physics with philosophy. Results are garbage.

 

[Pythagorean]

Can you have mass without distance?

Probably not, since the mass of an object pertains to it's density (matter per distance cubed) and it's volume (distance cubed)

 

[baywax]

Probably not, since the mass of an object pertains to it's density (matter per distance cubed) and it's volume (distance cubed)

Thanks Pythagorean.

So this could indicate that space is the fundamental element to all physics equations until we get into quantum studies. Or does space play a part there as well?

 

[Pythagorean]

Thanks Pythagorean.

So this could indicate that space is the fundamental element to all physics equations until we get into quantum studies. Or does space play a part there as well?

It's a philosophical question obviously, so there's probably a lot of unfalsifiable answers depending on how you define fundamental, and what you decide it's fundamental to. Some people think space and time are the fundamental units of the universe, I just think they're the fundamental units of human understanding.

Yes, there's space in qm. Probability functions in qm describe the likeliness a particle will be within a certain place, so you can use that along with the properties of identical particles to find out average distances certain particles will have from each other based on their most probable positions (or their average position technically, which is not always the same thing).

 

[Dale]

In the standard model, the ratio of the mass of each fundamental particle to the Planck mass is a http://math.ucr.edu/home/baez/constants.html" which cannot be derived from any other part of the theory and can only be determined by experiment. Therefore, mass is fundamental in the standard model of physics.

 

[baywax]

It's a philosophical question obviously, so there's probably a lot of unfalsifiable answers depending on how you define fundamental, and what you decide it's fundamental to. Some people think space and time are the fundamental units of the universe, I just think they're the fundamental units of human understanding.

Yes, there's space in qm. Probability functions in qm describe the likeliness a particle will be within a certain place, so you can use that along with the properties of identical particles to find out average distances certain particles will have from each other based on their most probable positions (or their average position technically, which is not always the same thing).

That's great to know. At some point people were talking about no time existing in qm yet if there are positions there must be time, even if we're talking about simultaneous occurrences. Am I pretty well off the topic yet?

 

[Pythagorean]

In the standard model, the ratio of the mass of each fundamental particle to the Planck mass is a http://math.ucr.edu/home/baez/constants.html" which cannot be derived from any other part of the theory and can only be determined by experiment. Therefore, mass is fundamental in the standard model of physics.

I wonder, is this a consequence of gravity not being observable on the quantum level (I may be confusing quantum for standard model)? If it were, could we probably reduce the unit of mass to ratios of their motion (space/time) like the argument goes classically if we could describe gravity with the standard model?

Or perhaps if you want to get theoretical, to the wavelength and frequency of gravity's photon equivalent (giving you information about the "mass" of the source)?

 

[sganesh88]

@Cyrus
"Using the word "more" fundamental is absolute nonsense. Fundamental means, MOST BASIC FORM NECESSARY. How can something be more fundamental?? "
As schroder defined previously, if some quantity A can exist independently of the other quantity B, it is "more" fundamental. Speed as a quantity cannot exist without Distance and Time. We're talking about the fundamental nature of the quantities and not their units. Just like ampere being the fundamental unit and not coulomb.
An interesting read regarding this: http://amasci.com/emotor/fund.txt ( Cyrus, the title of the page, interestingly, and to you, annoyingly is "WHICH IS MORE "FUNDAMENTAL,"
ELECTRIC CURRENT OR CHARGE?" ;-) )
@Hootenanny
"The kilogram is defined as being equal to the mass of the International Prototype Kilogram. As you say, measuring mass is a different matter all together, but that is not the discussion here. "
Good. So you say this is the definition of mass of 1 kg but does not correspond to measurement. But when you bring in the word "equal" aren't you bringing in the measurement of quantities as well?

 

[Hootenanny]

@Hootenanny
"The kilogram is defined as being equal to the mass of the International Prototype Kilogram. As you say, measuring mass is a different matter all together, but that is not the discussion here. "
Good. So you say this is the definition of mass of 1 kg but does not correspond to measurement. But when you bring in the word "equal" aren't you bringing in the measurement of quantities as well?

We are going round and round in circles here.

Once again: NO! One can perfectly well define a quantity without reference to any measurements. For example, we can define pi as the ratio of the circumference of a circle to it's diameter. But that doesn't mean we have to measure the diameter or circumference of a circle to deduce the value of pi!

On a related point, there has been much discussion regarding changing the definition of the kilogram to use a combination of physical constants. However, you should note that this has nothing to do with the "fundementalness" of mass.

 

[TheStatutoryApe]

However, a mass can exist quite independently of force. Maybe we need to exert a force to measure it, but it's existence does not depend on our ability to measure it. A force requires a mass in order to exist. It is very logical to say the mass is more fundamental than the force.

Is it not possible to measure the mass of an object by the gravitational force it itself exerts? Isn't gravitational force a "fundamental" element of mass?

Can you have mass without distance?

Probably not, since the mass of an object pertains to it's density (matter per distance cubed) and it's volume (distance cubed)

Does a singularity have mass? And if so does it have spatial measurments independant of the range of the influence of its force (that is other than its curve, cone, or event horizon)?




I'm fairly illiterate when it comes to the finer points of physics. Which is why I am asking these questions. I do not know the answers though I have obviously guessed at some.

 

[sganesh88]

We are going round and round in circles here.

Once again: NO! One can perfectly well define a quantity without reference to any measurements. For example, we can define pi as the ratio of the circumference of a circle to it's diameter. But that doesn't mean we have to measure the diameter or circumference of a circle to deduce the value of pi!.

But pi is a universal constant. Mass varies with the objects. If suppose mass of every object in the universe is the same, then you can give this explanation. Ok let's 'play' history. I'm given a bunch of stones of different sizes; instruments to measure distance and time accurately; and i know the second law in the less general form F=ma. I know nothing about pre-existing conventions on mass or the International Prototype kept at Paris. Now If i assign the mass of a particular stone as 1 mass unit, how can i assign the masses for others with the help of the second law. can you explain?

 

[Hootenanny]

But pi is a universal constant. Mass varies with the objects. If suppose mass of every object in the universe is the same, then you can give this explanation.

So is the kilogram! 1.5kg means 1.5 times 1 kilogram! Just like 1.5 pi means 1.5 times pi!

Ok let's 'play' history. I'm given a bunch of stones of different sizes; instruments to measure distance and time accurately; and i know the second law in the less general form F=ma. I know nothing about pre-existing conventions on mass or the International Prototype kept at Paris. Now If i assign the mass of a particular stone as 1 mass unit, how can i assign the masses for others with the help of the second law. can you explain?

Again, there is a difference between a definition and a measurement, we are discussing the definition of mass, not how to measure it!

Since you refuse to acknowledge this, I'm withdrawing from this discussion.

 

[Dale]

I wonder, is this a consequence of gravity not being observable on the quantum level (I may be confusing quantum for standard model)? If it were, could we probably reduce the unit of mass to ratios of their motion (space/time) like the argument goes classically if we could describe gravity with the standard model?

Or perhaps if you want to get theoretical, to the wavelength and frequency of gravity's photon equivalent (giving you information about the "mass" of the source)?

Well, the answer to this question requires quite a bit of guessing, but I would say "yes".

People look at the standard model and on the one hand it is great because it has made so many accurate predictions, but on the other hand it has something like http://math.ucr.edu/home/baez/constants.html" (22 are masses) and it doesn't work well with GR nor otherwise explain gravity. There is considerable hope that a Theory of Everything will have fewer fundamental parameters.

If masses turn out to not be parameters of the Theory of Everything then mass would no longer be fundamental and would instead be derivable from other fundamental properties.

 

[nuby]

I would say they are both equally fundamental.

But as far as quantities go, I would say mass is more fundamental.

mass = volume * density

force = volume * density * acceleration*edit*

Actually, what else exists in the world besides (+/-) mass , time, and distance , and combinations of these units?

 

[Pythagorean]

Actually, what else exists in the world besides (+/-) mass , time, and distance , and combinations of these units?

well, if you include mass, shouldn't you include charge?