The ‘gravitational constant’ is measured via the Cavendish apparatus shown right. Some metal balls are mounted on a torsion balance and attempts to measure the attractive force between them are made. Calculations are performed and the result is the value of the Newtonian gravitational constant.
Many questions arise:
- What is really being measured here?
- What is being calculated?
- Why is it not constant over time?
- What do gravity and mass have to do with this?
- Why do even simple equations seem confusing and self-referential?
- What is mass anyhow?
Problems in general
The notion of gravity is usually thought of as connected to one or more of:
- Objects falling to Earth
- Objects having ‘weight’
- Planets orbiting stars etc.
These are all thought of as involving the same phenomenon (gravity) but they are all different processes with potentially different causes and it is wrong to lump them all together prior to actual proof that they all have the same root cause.
Note that the Cavendish experiment involves none of these mechanisms:
- Nothing falls to Earth
- The weight of the balls is irrelevant
- Nothing orbits in free-fall
Moreover, the experiment takes place within the gravitational field of the Earth and relies upon it for correct functioning but the nature of the field itself is not thought relevant to the results. The apparatus is sometimes shielded from magnetic fields via a Faraday cage, but the Earth’s gravity cannot be blocked out.
The gravitational attraction between the weights is very small compared with the Earth’s attraction, and this in turn actually varies at different places on the planet.
This is bad technique. Imagine you want to place two ping pong balls on the surface of a still pond to see if they are attracted by surface tension. You don’t have a still pond and so you try using a slow flowing stream and just subtract off the speed of the flow to compensate. Effects from the water flow in and around the balls simply outweighs the effect you are trying to measure.
More problems arise from the theoretical model used to make the calculations.
What is ‘mass’?
Newtonian physics actually defines three types of mass which all have their action via different mechanisms but are all assumed to have the same numerical value:
- Inertial mass:
- Active gravitational mass:
- Passive gravitational mass:
We can add a fourth type of mass for ‘clarity’:
- Weight mass:
The weight mass is generally treated as being synonymous with the passive gravitational mass but:
- All objects fall to the Earth with the same acceleration which means that the passive gravitational mass is effectively unmeasurable: Gravity debunked
- An object placed upon scales is not accelerating towards the planet and so the passive gravitational mass may not be said to be involved
- If there is no acceleration then the inertial mass cannot be said to be involved. Therefore, we need a new type of mass
All these masses are treated as if they are the same thing and are invariably referred to as ‘mass’. This linguistic trick allows continual switching between the masses without the need for justification and without the reader noticing what is happening.
Until the masses are proven to be equivalent, this is a dishonest practice.
Mass as an ‘intrinsic property’ of matter
Mass is often described as ‘an intrinsic property of matter’. This is highly deceptive.
This description lends weight to the idea of mass (4 types) as somehow ‘invariant’ or maybe ‘constant’. This in turn makes the idea of a gravitational constant seem more likely.
The assertion is that both ‘mass’ and big G are fundamental properties of Nature, that their values are constant and that, as a consequence, there is something there to be measured. The big problem is that the measurement of these quantities varies in both time and space.
This suggests to the unbiased mind that the underlying quantities are varying, but the scientists will have none of it and insist that the problem is with the measurement techniques. The language used implicitly suggests that there is something invariant to be measured and that if any measurement is contrary to this then it is the measurement that is at fault.
This is not science. We require that theory emerges from measurement and that verification of the theory proceed from further measurements. What we have, however is that a theory has been proposed and that measurements do not agree and so they are explained away by measurement ‘error’.
Measurements are not errors, they are the foundations of science.
A fundamental constant of Nature?
An AI engine tells me:
The universal gravitational constant ((G)) does not vary; its value is a fundamental constant of nature. However, the measurements of (G) show significant variation, a result of experimental uncertainty and the immense difficulty in accurately measuring the constant due to gravity’s weakness.
No. Absolutely not true.
All we have is measurements. A theory is not automatically ‘true’ by itself but relies upon measurements.
The assertion is that something called a ‘Fundamental Constant of Nature’ exists but is somehow unmeasurable! If we can’t measure it then how do we know that it exists in any sense at all? If attempts to measure it give different results then how can we say that it is a constant? Where is the evidence for this?
Big G is not a fundamental of nature and is not even a fundamental of the measurement system as it cannot be measured directly and must be calculated from other ‘measurables’. It may be regarded as a fundamental of Newtonian theory, but if this is at odds with Reality then what is the point of the theory?
The idea that there is ‘something out there to be measured‘ lends a strong bias to scientific thought, but this really is an illusion. The reality is that all we have is a set of measurements and everything else is merely an interpretation of those measurements.
The gravitational constant varies over time
Why do measurements of the gravitational constant vary so much? – Lisa Zyga
https://phys.org/news/2015-04-gravitational-constant-vary.html
Now scientists have found that the measured G values oscillate over time like a sine wave with a period of 5.9 years. It’s not G itself that is varying by this much, they propose, but more likely something else is affecting the measurements.
Also:
Once a surprising 5.9-year periodicity is taken into account, most laboratory measurements of G are consistent
Or: “Once the variations are adjusted for, the value appears constant”. Well, yes, I guess so .. but why the variation in the first place?
Gravitational strength varies across the globe
Inertial effects
Scientists have started to think that variations in gravity may somehow be connected to ‘inertia’.
It’s not G itself that is varying by this much, they propose, but more likely something else is affecting the measurements.
As a clue to what this “something else” is, the scientists note that the 5.9-year oscillatory period of the measured G values correlates almost perfectly with the 5.9-year oscillatory period of Earth’s rotation rate, as determined by recent Length of Day (LOD) measurements. Although the scientists do not claim to know what causes the G/LOD correlation, they cautiously suggest that the “least unlikely” explanation may involve circulating currents in the Earth’s core. The changing currents may modify Earth’s rotational inertia, affecting LOD, and be accompanied by density variations, affecting G. – Zyga
Characterization and implications of intra-decadal variations in length of day – Holme, de Viron
https://www.nature.com/articles/nature12282
As the data shows, the length of each day varies slightly, with some days slightly longer and some days slightly shorter than others. The LOD variation is a measure of the speed of Earth’s rotation, and the scientists in the current study found that its periodic oscillation aligns almost exactly with the G oscillations. – Holme et al.
The equation for big G
The value of the gravitational constant is calculated by a version of the Cavendish experiment which consists of metal spheres on rotating frames. As the spheres become closer to each other a small force of attraction is detected between them and the gravitational constant is calculated from the resulting force.
The formula for the force between two masses is given as:
Where:
We can rearrange to get G in terms of Force and mass:
Note that the type of mass to be used is never specified, thereby ‘forcing’ on us the unproven assertion that they are all interchangeable.
The ‘Inertial Field Theory’
The post: Gravity as an inertial field describes gravity as an ‘inertial field’ with an accelerative component.
Within this framework, mass is not absolute and not an innate property of matter, but a result of interaction between matter and the inertial field. One consequence of this is that if there is a change in the nature of the inertial field then there will be a change in mass and consequently a change in the calculated value for G.
This way of looking at things makes it clear that the different types of mass arise not from different ‘properties’ of matter but from the different forms of interaction with the inertial field:
- Passive gravitational mass: This is unmeasurable and therefore does not exist for practical purposes. Downward acceleration is caused by the acceleration of an inertial field and is independent of anything called ‘mass’.
- Active gravitational mass: This is an oversimplified representation of the total inertial field associated with an object. It has an attractive (accelerative) component but also a static inertial component.
- Inertial mass: This is the result of an object’s interaction with the ambient inertial field and arises from attempts to accelerate an object relative to the field. This perceived mass will change if the inertial field changes. In all laboratory experiments on Earth, the ambient inertial field is the Earth’s gravitational field. This means that if the Earth’s gravitational field were to change in a particular way, then the measured inertial mass of all objects at the Earth’s surface will also change.
- Weight mass: Weight arises from attempts to move an object upwards, against the downward acceleration of the inertial field. The measured weight is a combination of the magnitude of the downward acceleration of the field and the inertial resistance to any attempt to move objects against such acceleration. For a fixed object, the measured weight will vary according to either changes in the downward acceleration or changes in the inertial resistance of the field.
Note that according to the Newtonian formulation, ‘weight’ and ‘inertia’ are different phenomena, but in the context of an inertial field, they are actually identical once the acceleration has been factored out.
To see this, imagine trying to establish the weight of something in a freely falling lift. The object is weightless until an ‘upward’ acceleration is applied to the scales whereupon the ‘weight’ of the object is immediately apparent. But this ‘weight’ is now synonymous with what might be called ‘inertial resistance’. In other words, the inertial mass is identical to the weight mass.
The equivalence principle
“The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature.” – Wikipedia
It is necessary in Newtonian theory to make this hypothesis. The two types of masses are both said to be innate properties of matter and there is no way of measuring the gravitational mass. Once this hypothesis is made, the rest of the theory can proceed.
With the Inertial Field Theory we can say that there is no need for a passive gravitational mass but we can say that the behaviour of a weight on a spring is identical to that of a weight undergoing acceleration against the inertial field. This is an equivalence that arises as a direct theoretical consequence and needs no additional hypothesis. To rephrase, here the principle derives from the theory and not the theory from the principle.
“... in a gravitational field the acceleration of a test particle is independent of its properties, including its rest mass.” – Wikipedia
The illusion of mass arises from the interaction between matter and an inertial field. There is no such measurable quantity as ‘rest mass’, which is why it plays no part in acceleration. Moreover, if the field itself can be said to be ‘accelerating’, then the test particle is, ipso facto, at rest with respect to the field.
“… in a uniform gravitational field all objects, regardless of their composition, fall with precisely the same acceleration.” – Wikipedia
If the field is visualised as accelerating then all objects maintain their position with respect to the field.
Obtaining the measurements for Big G
The equations for calculating the gravitational constant are not complicated, but they are confusing, largely because they are highly ambiguous with regards to the type of mass to be calculated.
The equation for big G is:
But which masses are we to use?
Passive gravitational mass: This is unmeasurable, irrelevant and non-existent for practical purposes.
Active gravitational mass: This can be calculated from the results of a Cavendish Experiment but only once we have ascertained the value for G! To see this, try using two identical masses and rearranging the above equation to get:
So to calculate the value of G we need to calculate a gravitational mass but in order to get a value for this we need to already know Big G!
This is clear nonsense, but texts on the subject just ignore it. They will just say that we need a value for mass and proceed to calculate it some other way. The Equivalence Principle is invoked in order to use a different fundamental quantity as the ‘m’ in the equation for the gravitational constant.
Mass as weight: An object is weighed on Earth and the value is divided by the measured gravitational acceleration at that location on Earth and this is used as a definition of ‘mass’. The acceleration varies over the globe and this method in any case introduces a new variable into the calculations. We are trying to measure the attractive force between two masses: why bring the Earth’s gravity into the equation?
Inertial mass: The inertial mass can be calculated without knowledge of G or the Earth’s gravitational acceleration. An attempt is made to move the mass by applying a known force and the acceleration is measured as a result. The mass is then calculated from Newton’s F=ma as:
Calculating Big G
Congratulations on getting this far. The point is to write down a formula for G using only those quantities that have been explicitly measured. Text books and science websites will use ‘m’ for mass all over the place to give the impression that the calculations have something to do with ‘mass’ but as we have seen above, this quantity is never directly measurable.
Substituting for mass in the definition of Big G we get:
Where:
So what did we actually measure?
We pulled some weights around with springs and then put them in a Cavendish torsion balance. We the applied a magic formula to calculate a value G which we then declared to be fundamental and constant and something to do with gravity.
All experiments were performed close to the surface of the Earth and so within the variable gravitational (inertial) field of the planet.
The actual ‘measurables’ of the system were:
- Acceleration, i.e. distance and time
- Force, i.e. the deformation of a mechanical spring or torsion of a wire
Everything else is conjecture.
If everything is calculated from the measurables, then these measurables may be said to be the fundamentals of the theoretical system and other quantities such as mass or gravitational constants are best described as ‘derived quantities’ of the theory. If the theory changes then so do the values of the derived variables, but not the measurements themselves. The measurements are immutable, not the derived values.
So what did we prove?
Goodness knows!
We most certainly did not prove that the value of G is constant, as experiments showed that it varied according to a 5.9 year cycle.
Statements along the lines of “The constant is still constant but we need to measure it better” are just wishful thinking. Where is the proof of constancy to be found if not in the measurements?
The calculated value of G is some sort of summary of the state of the inertial field at the Earth’s surface and how it affects the movement of objects. It probably has little to do with any innate property of matter.
The idea that this calculated and variable value represents some fundamental constant of nature is surely misplaced,
Why does the constant vary?
It varies because some of the inputs to the equation vary. Either the force between the spheres in the Cavendish apparatus changed (easily verifiable surely?) or the inertial masses of the spheres have changed.
The most likely explanation seems the latter. Inertia, according to the Inertial Field Theory (IFT), is partly a function of the inertial component of the gravitational field and it is this that appears to change on a 5.9 year cycle. In Newtonian theory, inertia is (as with almost everything else), an innate property of matter and therefore cannot change, but inertia, in the IFT is down to interaction between the weight and the Earths gravitational field.
The gravitational field of the Earth is an extension of the matter which comprises the Earth (Gravity as an inertial field) and hence rotates with it. It follows therefore that variations in day length should be associated with variations in inertia and hence also with a variable gravitational constant.
The variations in the rotational speed of our planet arise from naturel variations in the enclosing vortex structure and probably defy any attempts at theoretical prediction. Just observe a vortex in a river and note that it is fundamentally stable but with slight perturbations in speed and position as it absorbs energy from the surrounding flow. The Earths gravitational field is very likely similar to this. Perturbations may seem cyclic and at a 5.9 year cycle but this may very well change in even the near future.
Criticisms of the Cavendish experiment
Criticisms have already been made but it cannot do any harm to collect them together as a summary of the situation.
The Cavendish apparatus is intended to measure the strength of gravitational attraction between two metal spheres. The effect is expected to be small relative to the effects from the Earth’s gravitational field, but all experiments are performed within this field with the hope that the experimental results are somehow unaffected by the ambient conditions. The ambient conditions are known to be variable.
In addition to this the whole of Newtonian theory adopts a confused attitude to inertia, gravity and mass. Inertia and gravitational attraction are said to be two different phenomena and to both derive from their own innate property of matter, i.e. that of ‘mass’. The two masses are held to be different properties to start with and to achieve their effects by presumably different, although unspecified, mechanisms. However, they are also assumed to have the same numerical value as each other and are inevitably treated as if they were precisely the same thing.
The problem, though, is that these ideas when taken as a whole are not supported by experimental results. We should get consistent and constant measurements if mass is an intrinsic property of matter, but we don’t.
The experiment tries to measure a weak gravitational effect within a larger and more variable gravitational field. It plays mix ‘n’ match with different types of mass with no theoretical justification and it gets the wrong answer.