Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: hamdani yusuf on 06/05/2021 23:09:51

Currently accepted gravitational theory demands that they are the same.
What's expected to happen if gravitational mass were twice of inertial mass? What if it's only a half?

Currently accepted gravitational theory demands that they are the same.
I don’t think it demands it, it’s just that experiment indicates they are the same.

I don’t think it demands it, it’s just that experiment indicates they are the same.
https://en.wikipedia.org/wiki/Mass#Inertial_vs._gravitational_mass
Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In classical mechanics, Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.
Albert Einstein developed his general theory of relativity starting with the assumption that the inertial and passive gravitational masses are the same. This is known as the equivalence principle.
https://en.wikipedia.org/wiki/Equivalence_principle
The equivalence principle was properly introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g (g = 9.81 m/s2 being a standard reference of gravitational acceleration at the Earth's surface) is equivalent to the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1g. Einstein stated it thus:
we ... assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.
— Einstein, 1907
The equivalence is assumed, which means it becomes the basis for subsequence conclusions and predictions of the theory.

The equivalence is assumed, which means it becomes the basis for subsequence conclusions and predictions of the theory.
Yes, that is what I was saying, assumed from experiment, not demanded by the result of a theory. That assumption is based on experimental results, it is an input rather than an output.
As in yourWiki quote:
Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. ...................the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.
I think we mean the same thing, I just wanted to be clear on the wording and assumptions.
If gravitational mass and inertial mass were different Galileo would have noticed in his rolling mass experiments, different masses would fall at different rates, and similarly with the pendulum having different masses, you would get different periods.

similarly with the pendulum having different masses, you would get different periods
I think most models of unequal gravitational & inertial mass would still assume that they were proportional to each other.
 Otherwise you could end up with a situation where a zero gravitational mass had a nonzero inertial mass (or viceversa)
 Or (more extreme), a positive gravitational mass had a negative inertial mass (or viceversa)
A pendulum works by the periodic interchange of gravitational potential energy (calculated from gravitational mass) & kinetic energy (calculated from inertial mass).
 The key being that the mass of the pendulum cancels out in the calculation
 so two pendulums with different masses (but same length & gravity field) have the same period.
Lets say m_{i} = k m_{g}
 m_{i} is inertial mass
 m_{g} is gravitational mass
 And k is some constant, close to 1
From the "Energy" method of calculating the period of a pendulum:
m_{g}gh = 1/2 m_{i}v^{2}
or km_{i}gh = 1/2 m_{i}v^{2}
 Where g is the acceleration due to gravity (assumed uniform)
 h is the height of the pendulum
 v is the velocity of the pendulum
Change in velocity due to a change in height is:
v=SQRT(2kgh) (note that m_{i} still cancels out)
So the period would be slightly different than if m_{i} = m_{g}...
 But the period is still independent of the mass of the pendulum.
See: https://en.wikipedia.org/wiki/Pendulum_(mathematics)#Simple_gravity_pendulum
..and expand the section on the "Energy derivation".

I think most models of unequal gravitational & inertial mass would still assume that they were proportional to each other.
 Otherwise you could end up with a situation where a zero gravitational mass had a nonzero inertial mass (or viceversa)
 Or (more extreme), a positive gravitational mass had a negative inertial mass (or viceversa)
Yes, I should have been more specific. Hamdani’s question set me thinking about what would happen if they were not always proportional, but varied with mass (passive gravitational mass that is). It might be possible if there were some differences at the atomic level eg between protons & neutrons. However, as far as I am aware all tests to check the relationship have resulted in confirmation.

Hi Hamdani (and everyone).
This discussion has already got complicated and it's not easy to pull individual quotes out of the previous posts. I hope noone will mind if I try to join the discussion now.
It seems that you (Hamdani) are making the suggestion that all current models of gravity will fall if the Equivalence Principle is violated. Is that right? (I don't agree but I should check that was what you wanted to discuss first).
Otherwise, if you just wanted to know about some differences you could observe, I think Colin2B has already described those: Galileo will roll down a slope with acceleration that depends on what he is made of etc.
I'm quite enjoying a different discussion you started about Ethics and Morality but there's about 74 pages of that  so I won't be joining that discussion until I've had a few days to read previous posts.

Yes, that is what I was saying, assumed from experiment, not demanded by the result of a theory. That assumption is based on experimental results, it is an input rather than an output.
If in the future it can be demonstrated that those types of masses are not identical, then currently accepted gravitational theory must be revised.

I'm quite enjoying a different discussion you started about Ethics and Morality but there's about 74 pages of that  so I won't be joining that discussion until I've had a few days to read previous posts.
LOL enjoy that. I occasionally have a look at that discussion, interesting but getting involved, well .......... ;D

I think most models of unequal gravitational & inertial mass would still assume that they were proportional to each other.
I agree. If they are really proportional with constant ratio, the only consequence would be the change of gravitational constant. So if gravitational mass is doubled with inertial mass stays the same, gravitational constant would be double, with all if its consequences.
On the other hand, if it depends on other factors, then those factors must be included in the formula for gravitational force and potential.
"Modified Newtonian dynamics  Wikipedia" https://en.m.wikipedia.org/wiki/Modified_Newtonian_dynamics

This discussion has already got complicated and it's not easy to pull individual quotes out of the previous posts. I hope noone will mind if I try to join the discussion now.
Do you have technical difficulties in quoting a post? Just select the sentences you want to respond to, then click action button on top of the post, and click quote selected.
You can join the discussion anytime you like. Being specific on which point you are responding to can help others to respond back.

I'm quite enjoying a different discussion you started about Ethics and Morality but there's about 74 pages of that  so I won't be joining that discussion until I've had a few days to read previous posts.
LOL enjoy that. I occasionally have a look at that discussion, interesting but getting involved, well .......... ;D
I'm glad if the thread turns out to be entertaining :). Perhaps you could share your thoughts there, or show some counter arguments or counter examples for some assertions posted there, either by me or by other contributors. That would be interesting.

You can join the discussion anytime you like
Thank you and thanks for the advice about quoting.
If they \(gravitational and inertial mass) are really proportional with constant ratio, the only consequence would be the change of gravitational constant.
Yes. Well done. The Gravitational constant AND/OR something else just gets multiplied by a constant. I think the original laws that appeared in Newton's Principia only stated F is proportional to a change in momentum. We can choose constants and/or units to keep the formulae simple.
If in the future it can be demonstrated that those types of masses are not identical, then currently accepted gravitational theory must be revised.
It seems that you are suggesting all current theories of gravity will fall if the Equivalence Principle is violated.
I can see that you have previously linked to Wikipedia pages about General Relativity (GR) and the E.P. (Equivalence Principle). It is true that the EEP (Einstein Equivalence Principle) did provide considerable motivation for the development of GR. However, the connection between the EEP and GR is frequently overstated.
GR cannot be deduced from the EEP. It was quite possible for Einstein to have developed an alternative theory of gravity that was consistent with the EEP. For example, At least one version of the BransDicke theory of gravity is consistent with the EEP. It is also possible to imagine that GR (a barenecessities version of GR) could hold even if the EEP did not hold. You just have to a bit careful about how you define or use "mass" in your stressenergy tensor, whatever goes in there that will be our new definition and understanding of what "gravitational mass" should be.
For minor violations of the EEP, the main problem with such a GR model of gravity is just that the Newtonian limit won't quite agree with the Newtonian physics. [To give a brief idea of this, a test particle following a geodesic path as required under the GR model will have a trajectory that is influenced by the gravitational mass of the gravitating source but not affected by the passive gravitational mass or inertial mass of the test particle].
This doesn't mean that the GR model has to be instantly abandoned, instead you can choose to "put the blame" on the Newtonian physics. We already know that Newtonian physics becomes inconsistent with GR, so having a bit more evidence for this is hardly revolutionary.
In summary, if there was a violation of the EEP (or the WEP) then we would certainly want to check many results that have been obtained using GR as a theory of gravity and it could cause a rethink about how gravity should be explained. However, it's unlikely that a minor violation of the EEP will instantly topple General Relativity.
Best wishes, bye for now.

I'm quite enjoying a different discussion you started about Ethics and Morality but there's about 74 pages of that  so I won't be joining that discussion until I've had a few days to read previous posts.
LOL enjoy that. I occasionally have a look at that discussion, interesting but getting involved, well .......... ;D
I'm glad if the thread turns out to be entertaining :). Perhaps you could share your thoughts there, or show some counter arguments or counter examples for some assertions posted there, either by me or by other contributors. That would be interesting.
Oh dear. And have @alancalverd accuse me of being a philosopher? ;D

BTW, somehow this video just popped up in my YouTube recommendations. It mentions gravitational and inertial mass somewhere in the middle of the video.

Thinking about this problem, it is the same problem that was posed to Newton by his friend Dr. Bentley. Newton realised that “... if all the stars are drawn to each other by gravitation, they should collapse into a single point. One will be drawn to another; that star will grow and pull in still more and more. In time, everything must be drawn in. "According to Newton, each star in the universe ought to be attracted towards every other star. They should not remain motionless, at a constant distance from each other, but should all fall together to some central point. Newton admitted as much in a letter to Richard Bentley, a leading Cambridge philosopher of the time." (Quote from Wikipedia)
Although Newton equivocated in this particular instance by offering an explanation that God must make "constant minute corrections" to keep the Universe from collapsing, he had in effect already offered a valid explanation. When Newton stated that: “all the stars are drawn to each other”it was the explanation for why everything did not accelerate into one condensed clump of matter; it is also the explanation for ‘inertial’ gravity.
Take for instance a ball of steel weighing 50 Kg and a feather weighing just a few grams. When both objects are dropped together in an absolute (figurative) vacuum, they fall together and hit the ground simultaneously. Why? According to Newton, gravity acts according to the density of the object. What this means is that the force of gravity exerted on an object is determined solely by the density of the object and not by any other property. Therefore if the earth is pulling at an object with a force equivalent to 9.8 m/s2 then the force of gravity exerted by other objects in the universe is exactly equivalent to the force exerted by the earth on that object. So if the feather is being pulled towards the earth with a certain force, it is also being pulled away from the earth with exactly the same force, the same holds good for the steel ball. The end result is that both objects fall to earth at exactly the same rate and at exactly the same time.
Add to this explanation that while eventually, imbalances might result in the Big Crunch, given that gravity is one of the weakest forces known, it would be on a time scale that would in all probability be immeasurable.

The universe doesn't collapse quickly to a singularity because the elements aren't simply drawn to a single point.
If we take a simplistic Big Bang model of a huge mass exploding into random chunks, bits of various sizes will pass in the vicinity of other bits and be drawn towards their mutual barycenter. Any two lumps of matter whose initial motion vectors are not directly opposed, will approach with some angular momentum around the barycenter, and thus may end up in a stable orbit as their angular momentum is conserved.
However once all the matter has coalesced into rotating galaxies, the question of mutual coalscence of the galaxies arises. But as far as we know, the galaxies are actually dispersing because there is nothing to stop the general "outward" motion arising from the primordial explosion.
Meanwhile the question of why inertial and gravitational mass are identical, remains unanswered.

A gravitating source is mainly made of protons, neutrons and electrons. There will be neutrinos flying around but let's ignore them. The subject of this force does not feel the acceleration due to free fall. It is also made up of protons, neutrons and electrons.
Each particle has exactly the same force applied to it at the same time. I will ignore the almost imperceptible tidal forces. This means that the acceleration is undetectable. An accelerometer won't measure it.
This is the underlying principle for the equivalence. The constituents of the source and subject of the force are identical.

if all the stars are drawn to each other by gravitation, they should collapse into a single point
As I understand it, at the time, astronomers thought there was just one, unchanging galaxy.
But the rotation of the galaxy would prevent all the stars from collapsing in on each other, just like the rotation revolution of the planets around the Sun prevents the Solar System from collapsing into the Sun.
Is the rotation of the galaxy the answer to Bentley's paradox? (Wikipedia doesn't say...)
See: https://en.wikipedia.org/wiki/Bentley%27s_paradox
This article points out a parallel between Bentley's paradox, and Einstein's static universe:
https://www.aps.org/publications/apsnews/200507/history.cfm
 While rotation can prevent collapse at the scale of a planetary system, or a galaxy, I suspect that it becomes more difficult at the scale of a galaxy cluster
 And it would not be effective at the scale of the universe...
 However, as alancalverd pointed out, the (accelerating) expansion of the universe does overcome the gravitational attraction
Edit: Correction from Hamdani Yusef

The accelerating expansion of the universe also shows that the universe is being prevented from collapsing back to the same state as before the big bang. If the universe were eternal, with no big bang initiation, there would be nothing to start the expansion in the first place. Big bang deniers trip over their own d**ks trying to get around this.

As I understand it, at the time, astronomers thought there was just one, unchanging galaxy.
Astronomers still believed that well into the sixties. The fact that matter; settles into rotating masses like galaxies, solar system and stars, was essential to the shape the Universe eventually took. It also seems to support the view I put forward that the Big Crunch when/if it does come would take place on a time scale practically incomprehensible to us.
Interestingly: If a steel ball with a mass of 50 kg is attracted towards the earth and away from the earth with equal force, the net force exerted on it would be zero and the same would hold good with the feather that weighs just 2 gms. So what is left? One thing that could be considered is comparative masses. Since the mass of the earth is significantly larger than either of the objects, what is left is, the acceleration due to the mass of the earth = 9.8 m/s2 so that both objects fall to earth under the same acceleration.
This would mean that although both objects fall to the earth with an acceleration denoting they had mass, it is not their mass that is the motivating force but the mass of the earth that exerts a force. This might also explain why the space station, which could be considered to be an object in free fall around the earth, does not experience gravity; or rather does not experience gravity as calculated by its distance from earth.

According to Newton, gravity acts according to the density of the object. What this means is that the force of gravity exerted on an object is determined solely by the density of the object and not by any other property.
I think you will find that Newton said “gravity acts according to the mass of the object”
This is also the case for inertial acceleration.

This would mean that although both objects fall to the earth with an acceleration denoting they had mass, it is not their mass that is the motivating force but the mass of the earth that exerts a force.
The masses of all the objects are important. They all exert a gravitational attraction on each other. They is why the nbody problem is so difficult. Do you actually pause to think before you press the keys or does it all just come flowing out in a rush?

A gravitating source is mainly made of protons, neutrons and electrons.
True at small scales such as a solar system. At galactic scales, the gravity source is composed primarily of things other than these protons and neutrons.
There will be neutrinos flying around but let's ignore them.
Neutrinos move too fast to contribute to a gravity source. They pretty much all move at far greater speeds than the escape velocity of the system which creates it, so they don't contribute significantly to its gravity, and yes, can be essentially ignored.
Your point in the post holds true despite the actual composition of the mass in a gravity source.
if all the stars are drawn to each other by gravitation, they should collapse into a single point
As I understand it, at the time, astronomers thought there was just one, unchanging galaxy.
Apparently nonrotating as well, or it simply isn't true, as evidenced by the Earth not falling into the sun and other orbital stabilities that you point out.
Still, the Bentley thing doesn't work even for nonrotating systems. Take 3 point masses, initially at rest in a 345 triangle configuration. They will not meet at nor are even attracted to their mutual barycenter, and will in fact eject one of the three from the system leaving the other two in a stable orbit. Small targets do not easily fall onto one another.
Is the rotation of the galaxy the answer to Bentley's paradox? (Wikipedia doesn't say...)
The universe as a whole doesn't rotate, but the Bentley paradox assumes a bounded collection of mass (the nonrotating galaxy at the time), not the unbounded universe as a whole which has no center to which all the matter might be attracted more than another.
It kind of applies to galactic superclusters which have very little angular momentum to mass ratio, and thus are very much collapsing to a point just like Bentley suggests. Yes, it would be a paradox in a static universe, but it's not a paradox since it is not a stable (static) system and the gathering to a point is happening. We're all being sucked into the Virgo cluster which is itself being pulled into the Great Attractor, and that into the Shapley attractor which is where it all ends. All the other gravity wells are far away enough that expansion will never allow them to combine with the Shapley attractor. Everything will indeed get sucked into something. It just takes a lot of time.
This process is not the same as my 345 example because the objects involved are not point masses and thus they lose kinetic energy to heat as they interact physically. The motions of the galaxies around these gravity wells is not an orbital relationship despite having angular momentum in relation to any of them.

According to Newton, gravity acts according to the density of the object. What this means is that the force of gravity exerted on an object is determined solely by the density of the object and not by any other property.
I think you will find that Newton said “gravity acts according to the mass of the object”
This is also the case for inertial acceleration.
IIRC Newton actually considered density to be the primal factor, mass being the product of density and volume. This is rigorous as density is the general property of a material (iron) and mass is merely the property of a particular lump of said material (cannonball).

The accelerating expansion of the universe also shows that the universe is being prevented from collapsing back to the same state as before the big bang.
Not according to Newton's first principle!
A body continues in a state of rest or uniform motion unless a force acts on it.
If the lumps of matter are being dispersed from a point origin, the distance between them increases with time so the gravitational force between them decreases. Nothing is needed to prevent collapse because nothing is inhibiting expansion.

The accelerating expansion of the universe also shows that the universe is being prevented from collapsing back to the same state as before the big bang.
Not according to Newton's first principle!
A body continues in a state of rest or uniform motion unless a force acts on it.
If the lumps of matter are being dispersed from a point origin, the distance between them increases with time so the gravitational force between them decreases. Nothing is needed to prevent collapse because nothing is inhibiting expansion.
The acceleration IS the thing preventing collapse. The gravitational force decreasing does not lead to an accelerating expansion. It would tend toward inertial motion over time. While this would mean the universe would still expand it could also mean an ultimate reversal into a collapsing state. Hence the prevention.

IIRC Newton actually considered density to be the primal factor, ........... mass is merely the property of a particular lump of said material (cannonball).
Interesting, I missed that.
Yet at the end of the day the volume doesn’t really play a part if gravity acts as if from a point source, unless the test mass is close to a large surface in which case the volume (distribution of mass) has to be considered.

The acceleration
What acceleration? Once the primordial body has exploded, there is no further force acting on the shrapnel. That's the problem with CGI in space fiction movies: exploding spacecraft don't boil and billow like cumulus clouds, they just expand radially and very quickly.

So I guess you all prefer Chemistry and Biology?
It's not possible to do much with this thread apart from have some fun.
Have you considered this:
Newton used the idea of density instead of mass in his ideas about gravity because there was some confusion about the fact that a hotair ballon seems to fall upwards in earths gravitational field? Maybe he was just searching for a negative gravitational charge that could be repelled instead of attracted.
I just thought I might as well throw that idea in here. It's fun. It's most certainly NOT serious.

If they \(gravitational and inertial mass) are really proportional with constant ratio, the only consequence would be the change of gravitational constant.
Yes. Well done. The Gravitational constant AND/OR something else just gets multiplied by a constant. ................ We can choose constants and/or units to keep the formulae simple.
Aye, there’s the rub.
We can certainly use different formulae and constants, but what of Hamdani’s original question “What's expected to happen if gravitational mass were twice of inertial mass? What if it's only a half?”
Certainly projectile trajectories would be different. A ball thrown from the top of a building would travel a different distance compared to the distance fallen, this implies that orbits would also have a different radius. Changes to Kepler’s laws?
The rate at which a pendulum will swing should change with a new ratio of inertial to passive grav mass.
There would be a different equatorial bulge due to difference between centrifugal and gravitational force.
A plumb bob at a certain latitude would have a slightly different vertical offset, again due to difference between centrifugal and gravitational force.
A mechanical governor would expand to a different circumference, again due to difference between centrifugal and gravitational force.
There must be a lot more, but if that ratio had always been there we wouldn’t think it odd and might be speculating what it would be like if they were equal!
What would we do with the relationship
.
E ≈ m_{0}c^{2}+½m_{0}v^{2}
Is the energy dependant on whether mass is passive grav or inertial? in the second term it would change if motive was inertial or gravitational. Would we have m_{0} as the sum of inertial & gravitational?
Strangely, I always expected that the fact they are the same might be explained by some energy conservation law or, like PoundRebka shift, that without it you could build a perpetual motion machine.
Have you considered this:
Newton used the idea of density instead of mass in his ideas about gravity because there was some confusion about the fact that a hotair ballon seems to fall upwards in earths gravitational field? Maybe he was just searching for a negative gravitational charge that could be repelled instead of attracted.
I just thought I might as well throw that idea in here. It's fun. It's most certainly NOT serious.
Well, it might be serious if he was originally trying to include hot air balloons, but then realised this was a flotation thing!

Consider the simplest case of a body falling under gravity.
We say that F = mg = ma as if m and g were godgiven fundamental constants, but they aren't. If m_{g} ≠ m_{i} we would just measure a different value for g.
Fact is that there is no fundamental unit of mass. Until recently it was defined as the ratio of the gravitational force on an object to that of an arbitrary lump of platinum, and its modern redefinition, whilst giving us a more reproducible measurement, still harks back to the arbitrary number we associated with the ISK.
And "big G" doesn't throw any more light on the subject. F = Gm_{g}M_{g}/r^{2} would just give us a different value for G because all our measurements of F depend on F = m_{i}a.
I'm leaning towards the notion that m_{g} might not necessarily equal m_{i}, but that the ratio is both fixed and immeasurable. Can anyone think of an experiment that actually measures the ratio without presuming the answer?

I'm leaning towards the notion that mg might not necessarily equal mi, but that the ratio is both fixed and immeasurable. Can anyone think of an experiment that actually measures the ratio without presuming the answer?
The experiments and various successors comes to mind.
I don't think the exact numerical value for the ratio of is all that important, just that it is a fixed constant ratio. Setting the ratio to 1 is more a matter of choosing the right units.
Physicists set c =1 ; h = 1 and even 2 = 1 if they want to. Their only concern is the general behaviour of a system. The units don't change the fundamental behaviours. Are you suggesting that we should care if the calculation is actually right? This isn't the technology section, you aren't talking to Engineers here.

Are you suggesting that we should care if the calculation is actually right?
As an aviator and an engineer, I always care if the calcs are correct. As do my customers and investors.
Anyway, I looked up Eotvos' experiment on Wikipedia and right at the end of the introduction it says
It is sufficient for the inertial mass to be proportional to the gravitational mass. Any multiplicative constant will be absorbed in the definition of the unit of force
which is exactly what this stupid engineer said earlier.

Lots of interesting stuff in here.
https://www.britannica.com/science/gravityphysics/Gravitationalfieldsandthetheoryofgeneralrelativity#ref210883

I always care if the calcs are correct
I've read it a few times and said it to myself but I just don't get it....You seem to be using that phrase as if it's a good thing. :)

If you want to survive your flight or make a profit from your project, it is very important that the prior calculations be correct, and based as far as possible on known physics.

I'm leaning towards the notion that m_{g} might not necessarily equal m_{i}, but that the ratio is both fixed and immeasurable. Can anyone think of an experiment that actually measures the ratio without presuming the answer?
I suppose that depends on how we measure inertial mass.
The mass we usually measure is grav mass using say the force on a spring scale. If we use the same force to accelerate the mass horizontally we should get the same value of mass.
If we use a falling weight/pulley to accelerate a mass on a dynamics trolley then, eliminating friction, and weighing the trolley (gravitational mass) we can calculate the inertial mass from the force applied and the motion of the trolley. The 2 mass values should be the same.
Have I missed something here?

if gravitational mass different from inertial mass it would be a great disaster here

if gravitational mass different from inertial mass it would be a great disaster here
german shepherd puppies
Let me guess what you are selling  or trying to ;D

If we use a falling weight/pulley to accelerate a mass on a dynamics trolley then, eliminating friction, and weighing the trolley (gravitational mass) we can calculate the inertial mass from the force applied and the motion of the trolley. The 2 mass values should be the same.
Have I missed something here?
It was a very near miss ("force" becomes a bit tautologous as we define force from F = ma) but the idea is sound.
Start by dropping a mass m, and measure g. (For student demonstrations you may assume g = 9.81 ms^{2})
Now arrange a trolley with mass m pulled by a falling mass of 2 m. If m_{i} = m_{g} than the system should accelerate at 2g/3. (students may assume weightless strings and frictionless pulleys, as usual)
That's the easy bit. For $64,000, explain why m_{i} = m_{g} !

It was a very near miss ("force" becomes a bit tautologous as we define force from F = ma) but the idea is sound.
Yes, I did hesitate thinking more of circular arguments and definitions. Not easy with many of these fundamental properties.
I’m sure it can be shown with a pendulum period vs length, but you have to make small angle approximations and leave m_{i}/m_{g} in there.
There ought to be a way using centrifugal force of a lateral mass to lift a vertical mass. One fictitious force lifts another?
That's the easy bit. For $64,000, explain why m_{i} = m_{g} !
What do you mean? I left you the easy bit :)

just like the rotation of the planets in the Solar System prevented the Solar System from collapsing into the Sun.
The correct term is revolution of planets, instead of rotation.

Lots of interesting stuff in here.
https://www.britannica.com/science/gravityphysics/Gravitationalfieldsandthetheoryofgeneralrelativity#ref210883
Here is a statement found in the article.
The Eötvös experiments therefore show that the ratio of gravitational and inertial mass is the same for different substances.
It seems that the experiments had somehow excluded the effects of other kind of forces such as electric and magnetic forces, which is not easy for high precision measurement. You need to block cosmic rays, for instance.
If the result shows that the ratio is different for different substances, we can still claim the mass equality by introducing a new type of force, which is not considered as gravity.

Physicists set ... 2 = 1 if they want to
Maybe  but they don't do it without qualification. For example:
 2 pints = 1 quart (ie the units have to be the same)
 sin(2π) = sin(1π) (ie you have to state the function that is being applied)
 2 = 1 in modulo 1 (ie you have to identify the number system or algebraic symmetry operating in the system)

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.

Hi all,
So Jeffery
While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.
If what you state is correct, how do my bathroom scales work ?

Hi all,
So Jeffery
While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.
If what you state is correct, how do my bathroom scales work ?
Your bathroom scales work by preventing gravity from moving an object. The tension in a spring will do it. The tension propagates through the spring until it overcomes gravity. Gravity does not propagate through objects, otherwise you would be able to measure your acceleration during free fall.
Look at the slinky drop video in slow motion and see the tension acting against gravity. It is not gravity propagating through the slinky but the release of tension.
This is why the two Fs in the equation about are not the same. Also why I believe you will never be able to properly measure a difference between m_{i} and m_{g}.

Hi all,
So Jeffery I believe your last post contradicts your previous post.
Hi all,
So Jeffery
While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.
If what you state is correct, how do my bathroom scales work ?
Your bathroom scales work by preventing gravity from moving an object. The tension in a spring will do it. The tension propagates through the spring until it overcomes gravity. Gravity does not propagate through objects, otherwise you would be able to measure your acceleration during free fall.
Look at the slinky drop video in slow motion and see the tension acting against gravity. It is not gravity propagating through the slinky but the release of tension.
This is why the two Fs in the equation about are not the same. Also why I believe you will never be able to properly measure a difference between m_{i} and m_{g}.
As a spring scale follows Hooke’s Law
https://en.m.wikipedia.org/wiki/Hooke's_law
Which measures Force 🤔

Gravity does not propagate through objects,
So my head is weightless if I stand up?
One of the odd things about gravity is that it does indeed propagate through objects, and rather than being attenuated as happens with other forces, it is enhanced.

Static fields do not propagate.
https://en.m.wikipedia.org/wiki/Speed_of_gravity
The speed of physical changes in a gravitational or electromagnetic field should not be confused with "changes" in the behavior of static fields that are due to pure observereffects. These changes in direction of a static field are, because of relativistic considerations, the same for an observer when a distant charge is moving, as when an observer (instead) decides to move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate, also does not cause the direction of its field to change, but requires that it continue to "point" in the direction of the charge, at all distances from the charge.
The consequence of this is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.
In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.

Hi all,
So Jeffery I believe your last post contradicts your previous post.
Hi all,
So Jeffery
While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.
If what you state is correct, how do my bathroom scales work ?
Your bathroom scales work by preventing gravity from moving an object. The tension in a spring will do it. The tension propagates through the spring until it overcomes gravity. Gravity does not propagate through objects, otherwise you would be able to measure your acceleration during free fall.
Look at the slinky drop video in slow motion and see the tension acting against gravity. It is not gravity propagating through the slinky but the release of tension.
This is why the two Fs in the equation about are not the same. Also why I believe you will never be able to properly measure a difference between m_{i} and m_{g}.
As a spring scale follows Hooke’s Law
https://en.m.wikipedia.org/wiki/Hooke's_law
Which measures Force 🤔
And the force propagates through the spring. Gravity does that only indirectly. It pulls the weight which changes the stress on the spring. If you were put in place of the weight you would feel the acceleration as the stress on the spring slowed you down. You would not feel this acceleration in free fall. It's force Jim, but not as we know it.

To quote your Wikipedia reference
In classical theories of gravitation, the changes in a gravitational field propagate.....[at].... the speed of light .
Now a gravitational field is only associated with a mass. So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c, and if we introduce another lump of material between a gravitational source and a detector, the change in net gravitational field at the detector will propagate at c.
The anomalous property of gravity is that we can't interpose anything that will reduce the detected field at a distant point.

Hi all,
mmm Jeffery I think you surpass yourself you manage to contradict yourself in one statement:
And the force propagates through the spring. Gravity does that only indirectly. It pulls the weight which changes the stress on the spring. If you were put in place of the weight you would feel the acceleration as the stress on the spring slowed you down. You would not feel this acceleration in free fall. It's force Jim, but not as we know it.
Do you know what weight is ? ;) :)

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.
How do we feel forces?
What should be added to make the second equation balanced?

Hi all.
So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c,
and also,
The speed of physical changes in a gravitational or electromagnetic field
Seems like we're talking about the "speed of gravity". This could be a whole new thread for discussion on its own.
It's complicated and depends on whether you're using Newtonian gravity or General Relativity. I'm not an expert on this but I would advise caution and extreme skepticism about the Wikipedia articles that have previously been cited.
For example, creating mass/energy ex nihilo isn't something that can be tested in reality. It can't even be considered on a theoretical level using Einstein's Field Equations from GR. There's less that would stop you considering the possibility with Newtonian gravity (ignoring the violation of some conservation of energy) but it is generally agreed that Newtonian gravity assumes instantaneous action at a distance. So if you add (or remove) a mass then instantly the whole universe knows about it, the transmission of that new gravitational force occurred at inifinte speed.
There were several attempts to impose a finite "speed of gravity" in Newtonian physics but this results in unstable orbits for massive bodies in our solar system unless the speed is incrediably high (far above the speed of light).

So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c,
...... it is generally agreed that Newtonian gravity assumes instantaneous action at a distance. So if you add (or remove) a mass then instantly the whole universe knows about it, the transmission of that new gravitational force occurred at inifinte speed.
It is generally agreed that Newton was wrong. The assumption in GR is that information does not travel faster than light and a number of papers that explain why Wiki is correct.
You might want to follow the link in this post https://www.thenakedscientists.com/forum/index.php?topic=82133.msg636147#msg636147

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation.
I feel a 185 lb force on my feet when I stand, which is due to F=mg so I have to disagree.

For example, creating mass/energy ex nihilo isn't something that can be tested in reality.
My colleagues do it every day, converting the mass of an electronpositron pair into the energy of two photons. My clients do it on a larger scale, called nuclear power generation. Admittedly most of the useful applications are the other way around, annihilating mass rather than creating it, but the fact remains, and we now have sufficient evidence from the detection of gravity waves that gravity propagates at c.

You might want to follow the link in this post
Thanks for the suggestion, I will check it out.
My colleagues do it every day, converting the mass of an electronpositron pair into the energy of two photons.
I was thinking someone would say something like that. Energy and mass are both used in the stressenergy tensor for GR. It's fine to convert one to the other. The problem is only when you create one from nothing (or remove one and leave nothing). It might seem that I have been quite unkind to you, Alancalverd, but that was not my intention.
I mentioned that I am not an expert concerning the speed of gravity and I'm not, I'm certainly not. I only started learning about General Relativity a couple of years ago by reading a book to pass the time. Not having any lecturing staff to talk to, I made a post in another forum asking what would happen after an instantaneous removal of the sun and how long it would take before the earth's orbit was altered (i.e. "what is the speed of propagation for gravity"). There were some very unkind replies at first and then I seem to recall I was taken outside and slapped for an hour (ok, maybe my memory is a little distorted but I do know it felt like I was being slapped). The fact that such ideas are frequently used as examples to show the difference in transmission speed for Newtonian gravity vs. GR was not considered an excuse for my ignorance. I was told that only popular media and trashy science videos ever discuss such an absurd thing and it was never done in any peer reviewed literature. One of the more note worthy replies I received was something like "No one but no one should ever suggest the stressenergy tensor can be that discontinuous and still be allowed to live". The thread was closed down immediately and if there had been an "idiot of the week" board then my picture would have been pinned to it.
I can assure you, Alancalverd, that I get things wrong quite often.

I'm quite impervious to insult, ES  years of jousting with a mad chemist can toughen the hide!
There is no such thing as Newtonian gravity or Einsteinian gravity, just gravity. Masses attract each other, and we have two usefully predictive mathematical models (thanks to Newton and Einstein) of that attraction.
The time delay between the disappearance of the sun and a change in the earth's orbit makes intuitive sense until I consider the example of a stone orbiting on the end of a string. If I jerk the string, it's obvious that the impulse travels along the string at the speed of sound and jerks the stone a few milliseconds later. But if I let go of the string it is somehow counterintuitive that the stone will continue to orbit for a few milliseconds before flying off at a tangent. Deeper thought of course tells me that the reason the speed of sound is finite is because the string has density and elasticity, and can thus continue to exert a force on the stone after I have released it. So in the case of gravitation I'm looking for the gravitational analog of the permittivity and permeability of a vacuum, which determine c for electromagnetic radiation. But it would be a false analog because whilst materials reduce c or absorb e.m. radiation, interposing material between two masses always increases the gravitational force on both.
The more I think about gravity, the less I understand it. But I take comfort from the fact that I'm not alone!

I'm quite impervious to insult, ES  years of jousting with a mad chemist can toughen the hide!
Do you mean "years of being loudly wrong"?

Ipsi dixit.Quod erat demonstrandum. Sic semper.

Matter tells spacetime how to bend and spacetime tells matter how to propagate through the gravitational field. So where is the propagation of gravity? Gravitational radiation propagates, the field is static.
About the scenario where the sun suddenly disappears. See here https://image.gsfc.nasa.gov/poetry/venus/q89.html
If gravity propagates then each planet will continue orbiting for different periods of time. Also Pluto, for instance, will be attracted to where the sun was 5.5 hours ago. Not ideal for consistent orbits. The propagation will centre on where the sun was 5.5 hours ago and not where it is simultaneously.
We believe that entangled particles can be in consistently different states at vast distances and yet the gravitational field needing no time to update is horrifying. It is like spooky action at every distance.

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation.
I feel a 185 lb force on my feet when I stand, which is due to F=mg so I have to disagree.
No, you feel the force because you are not in free fall. The ground is preventing gravity from moving you through the gravitational field. Therefore, the continuous action of gravity now does feel like a force and compresses your body, causing a detectable stress. Now an accelerometer will work, for the same reasons.

When in free fall, an object can be thought of as being in an approximate inertial frame. This frame is being dragged by gravity towards the source of the field. If this dragging is prevented by the electromagnetic forces holding the ground together, then the object can be thought to be in an accelerating frame. With respect to the dragged inertial frame.

you feel the force because you are not in free fall.
I agree and that force can be calculated by F=mg.

you feel the force because you are not in free fall.
I agree and that force can be calculated by F=mg.
But that describes the force of something acting against gravity. You calculate g, which is the acceleration of an inertial frame in free fall. When the frame is no longer falling the force is due to the prevention of free fall. It is a subtle but important distinction. The force is not a direct consequence of the action of gravity.

I agree and that force can be calculated by F=mg.
Agree, but under GR, the force is applied by the ground, preventing inertial motion. g is 9.8 m/sec² which is an amount of acceleration, so your formula is really just F=ma where a is a the constant acceleration applied by anything being pushed by the properly accelerating ground.
In Newtonian mechanics, the ground is stationary and applies enough force to counter the object sitting on it. The gravity of Earth applies an acceleration a=GM/r² (and g = GM/r² at a very specific r) which when multiplied by the mass m of the object results in a force of F=GMm/r², which must meet an equal and opposite counterforce from the ground in order to remain stationary.

Hi all,
So we seem to be deviating a little from the OP, but there are definitely areas where Newton gravity and Einstein gravity disagree, and it would seem this discussion is coming up against those areas.
So one question that arises out of the last couple of posts is;
How does GR explain the acceleration that occurs during free fall without a force being a factor and how this reconciles with Newtons three laws of motion ?

So one question that arises out of the last couple of posts is;
How does GR explain the acceleration that occurs during free fall without a force being a factor and how this reconciles with Newtons three laws of motion ?
A short answer: In GR there isn't any acceleration during free fall and that's why no force is required to act. Inertial frames are not defined in the same way as for Newtonian mechanics. In GR the inertial frames are actually in free fall. So, for any object that is in free fall it has 0 acceleration in a local inertial frame and hence 0 force was required.
How does GR reconcile with Newton's 3 laws?
1. The 1st law (an object remains at rest or in state of uniform......) is replaced with "an object moves along a geodesic".
2. the 2nd law F=ma is usually upgraded to a 4dimensional version using 4vectors (because GR works better with tensors). As indicated above, the definition of an inertial frame is altered, which means that the F and a involved could be different to Newtonian expectations.
3. The 3rd law (about Equal and Opposite forces)  that can stay (but see above  inertial frames are different so forces aren't always what you expected from Newtonian mechanics).
4. I know Newton didn't have a 4th law but there are some things that were tacitly assumed in Newtonian mechanics but need to be redefined or upgraded. For example, ideas of geometry are upgraded to allow for nonEuclidean metrics.
Yes, but how does it "reconcile" in the sense of agreeing with Newtonian physics?
Newtonian physics can be recovered as the limiting case under a weak and static gravitational field and low speeds.
Late editing: I've had most of the night to think over this. It's difficult to point at the "one thing" that causes Newtonian physics to consider gravity as a force while GR does not, it's not really one thing it's many things. However, the singe most important thing is probably where you try to reestablish the original form of Newton's first law. Instead of being happy to accept that objects will move along geodesics (through spacetime) in the absence of any force, it is the insistence that they move in straight lines (through space) unless acted on by a force.

Just to muddy the waters, if gravity was acting on a single elementary particle then you could argue that F = mg would act as a force. Since it is not a composite object.

Just to muddy the waters, if gravity was acting on a single elementary particle then you could argue that F = mg would act as a force. Since it is not a composite object.
Was that a general reply to previous replies?
It seems like you are suggesting that every elementary particle needs testing (which could be difficult if you were considering quarks and just wanted to isolate one on its own). Even if you did test each fundamental particle, are you going test all combinations of those elemantary particles next (which could take a while) or try to invoke some argument about linear superposition of gravitational potential or something?
Proposing that the gravitational pull on a composite particle (e.g. a Carbon atom) is calculated just as a linear sum of the gravitational effects on its components may seem simple but it isn't: What are you going to do about "binding energy"? An atom of carbon has less mass than the sum of its parts, if gravity did pull on the carbon atom just like the sum of pulls on its components then the atom should accelerate slightly faster than g.

Just to muddy the waters, if gravity was acting on a single elementary particle then you could argue that F = mg would act as a force. Since it is not a composite object.
Was that a general reply to previous replies?
It seems like you are suggesting that every elementary particle needs testing (which could be difficult if you were considering quarks and just wanted to isolate one on its own).
Well obviously not. Since it is absurd.
Even if you did test each fundamental particle, are you going test all combinations of those elemantary particles next (which could take a while) or try to invoke some argument about linear superposition of gravitational potential or something?
Why on earth would I do that?
Proposing that the gravitational pull on a composite particle (e.g. a Carbon atom) is calculated just as a linear sum of the gravitational effects on its components may seem simple but it isn't: What are you going to do about "binding energy"? An atom of carbon has less mass than the sum of its parts, if gravity did pull on the carbon atom just like the sum of pulls on its components then the atom should accelerate slightly faster than g.
How do you come to that conclusion when gravity is not properly understood.? Unless you have solved the outstanding issues. Have you? Hang on, I'll just get some popcorn.

Just to muddy the waters, if gravity was acting on a single elementary particle then you could argue that F = mg would act as a force. Since it is not a composite object.
I think I'm a bit lost on who was replying with what, to whom and what it implied, sorry. Not to worry, it happens often and I usually find my way home. :)

Just to muddy the waters, if gravity was acting on a single elementary particle then you could argue that F = mg would act as a force. Since it is not a composite object.
I think I'm a bit lost on who was replying with what, to whom and what it implied, sorry. Not to worry, it happens often and I usually find my way home. :)
I was just making an observation. It didn't relate to any one specific post.

This is also of relevance to this thread. https://en.m.wikipedia.org/wiki/Paradox_of_radiation_of_charged_particles_in_a_gravitational_field