[hamdani yusuf (OP)]

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?

[Colin2B]

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.

[hamdani yusuf (OP)]

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.

[Colin2B]

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.

[evan_au]

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 non-zero inertial mass (or vice-versa)
- Or (more extreme), a  positive gravitational mass had a negative inertial mass (or vice-versa)

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_ggh = 1/2 m_iv²
or km_igh = 1/2 m_iv²
- 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".

[Colin2B]

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 non-zero inertial mass (or vice-versa)
- Or (more extreme), a  positive gravitational mass had a negative inertial mass (or vice-versa)

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.

[Eternal Student]

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 no-one 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.

[hamdani yusuf (OP)]

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.

[Colin2B]

  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 .......... 

[hamdani yusuf (OP)]

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

[hamdani yusuf (OP)]

This discussion has already got complicated and it's not easy to pull individual quotes out of the previous posts.  I hope no-one 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.

[hamdani yusuf (OP)]

  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 .......... 

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.

[Eternal Student]

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 Brans-Dicke theory of gravity is consistent with the EEP.  It is also possible to imagine that GR (a bare-necessities 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 stress-energy 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 re-think 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.

[Colin2B]

  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 .......... 

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? 

[hamdani yusuf (OP)]

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

[McQueen]

    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.

[alancalverd]

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.

[jeffreyH]

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.

[evan_au]

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

[jeffreyH]

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.