# Logical Error of Cavendish Experiment

• Mammo
In summary, the Eötvös experiment found that there was no difference in the gravitational force exerted on different substances. Cavendish made an error in assuming that the Earth's composition was uniform, and using this assumption to calculate the Earth's mass.
Mammo
Following Newton's new law of universal gravitation an experiment was devised to measure the faint gravitational attraction between two lead balls Wikipedia Cavendish experiment. This was a way of 'weighing the world'. The mass of the Sun could then be calculated from the value of the mass of the Earth. The mass of any star could then be measured by comparing it to the mass of the Sun. But there was an initial logical assumption made; that the nature of the matter comprising the entirety of the Earth is the same as that of the lead balls. This is not necessarily the case. The concept of entropy was unknown in the past. It is possible that the matter at the center of the Earth has a lower entropy compared to surface baryonic matter, for example. This would imply that the calculated density of Earth, 5.5 times that of water, is an overestimate. The mass of the Sun could therefore be an overestimate etc. Is it possible that there simply isn't a Missing Mass Problem after all? Wikipedia Dark Matter.

I am not sure where you are going with this. Is this a homework assignment?

Mammo said:
It is possible that the matter at the center of the Earth has a lower entropy compared to surface baryonic matter, for example. This would imply that the calculated density of Earth, 5.5 times that of water, is an overestimate.

How does that follow? I don't see the connection.

There have been a number of experiments ("Eötvös experiments") comparing the gravitational force on different substances. As far as I know, all of them found no difference, sometimes with very high precision. Of course, we haven't compared all possible pairs of substances.

Gravitational attraction depends on mass, not entropy. Why do you think Cavendish made an error?

Let's take Cavendish's bent on things. He wanted NOT to determine G, rather he wanted an estimate on the mass of the Earth.
If you were in Cavendish's time, then you may not know Gauss's theorems yet (since Gauss came later). What you could do, is assume that the Earth is a uniform sphere. Since the entire Earth attracts anything beyond it integrated envelope (the surface) with an inverse square force, we can estimate the mass of the Earth by comparing the force exerted on a test mass by a known mass. The ratio brings you close. Knowing the size of the Earth gives you an estimate on density.

Remember, although Cavendish probably knew that the Earth's composition was not uniform, this experiment is okay since it assumes a uniform density (he had to). Now that we have Gauss's law, we can okay this assertion.

I think what you are implying is that some matter may possesses gravity that does not roll off like the inverse square. IF this were the case and exotic matter is at the core, than we have not seen it. Furthermore, you can check for yourself to see what would happen if you added higher order terms to a static inverse square force.

Have fun, hope this helps.

Mr.Amin said:
I think what you are implying is that some matter may possesses gravity that does not roll off like the inverse square. IF this were the case and exotic matter is at the core, than we have not seen it. Furthermore, you can check for yourself to see what would happen if you added higher order terms to a static inverse square force.
This is more like it. This is what I'm talking about. Newton's law of universal gravitation is essentially an assumption which works very well on planetary scales. But there is another possible solution. The fundamental particle is not necessarily a point object which radiates gravity uniformly. A string shape of the fundamental particle would give an asymmetric gravitational field. The order of the particles is then a factor which determines an object's gravity field an how it reacts within the gravity field of another object. Entropy is an essential part of chemistry. I don't understand why so many people have a problem with considering this possibility when applied to matter.

The assertion of Newton's law of universal gravitation has led to the assumption that there isn't exotic matter at the center of the Earth. It would have been an easy mistake to make, considering that all objects of different weights were found to accelerate at the same rate in freefall.

Perhaps the forthcoming LHC results will lend credibility to this simple idea.

Would you care to then explain why the most accurate measurements of gravity at the micron scale out of, say the U. of Washington, still verify the validity of Newtonian gravity?

It appears that if we go by purely empirical data alone, that there's more support for Newtonian gravity than your scenario, which has no empirical evidence at all.

Zz.

I think we should stop the thread here. The comment I made started with a capital "IF." This implies that you would go an compute the force roll off using
1/r^2 + beta/r^3 + gamma/r^4 etc... (It's easy with pad and pen. Start with the taking derivatives.)
Such deviation would be measurable over years of experiments. But we don't see them on a large number of scales. Therefore, the model of Cavendish's experiment and the models of gravity do not need extra factors. In lesser words, Cavendish's experiment was fine.

And keep in mind entropy affects energy distribution. Mass can be thought of as the localization of energy.

Mammo said:
The assertion of Newton's law of universal gravitation has led to the assumption that there isn't exotic matter at the center of the Earth. It would have been an easy mistake to make, considering that all objects of different weights were found to accelerate at the same rate in freefall.
Science operates on positive evidence, not negative evidence. Currently, there is no evidence that there isn't an invisible purple dragon in my garage, but that does not make it ok to assume that there is an invisible purple dragon in my garage. The same goes for this "exotic matter" in the center of the earth. We need a reason to believe it exists: an absence of evidence (some might quibble with that anyway...) that it doesn't doesn't qualify.

russ_watters said:
Science operates on positive evidence, not negative evidence. Currently, there is no evidence that there isn't an invisible purple dragon in my garage, but that does not make it ok to assume that there is an invisible purple dragon in my garage. The same goes for this "exotic matter" in the center of the earth. We need a reason to believe it exists: an absence of evidence (some might quibble with that anyway...) that it doesn't doesn't qualify.
There is positive evidence that Newton's law of universal gravitation doesn't fit with the world of quantum mechanics. If this wasn't the case then I wouldn't be suggesting the idea of exotic matter. It is a very subtle concept which needs a great deal of contemplation. If there was exotic matter at the center of the Earth, it wouldn't be easily detectable. The shape of the Earth's tidal Earth bulge would be slightly 'shield shaped', having an added central acceleration. There is some scientific work in this area which is of course very controversial. See 'gravity shielding' experiments Wikipedia Gravitational Shielding

There are serious considerations by some members of the scientific community for the need of a fundamental review of gravitational theory. This paper for example: General Theory of Relativity: Will it survive the next decade?

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Mammo said:
There is positive evidence that Newton's law of universal gravitation doesn't fit with the world of quantum mechanics. If this wasn't the case then I wouldn't be suggesting the idea of exotic matter. It is a very subtle concept which needs a great deal of contemplation. If there was exotic matter at the center of the Earth, it wouldn't be easily detectable. The shape of the Earth's tidal Earth bulge would be slightly 'shield shaped', having an added central acceleration. There is some scientific work in this area which is of course very controversial. See 'gravity shielding' experiments Wikipedia Gravitational Shielding

There are serious considerations by some members of the scientific community for the need of a fundamental review of gravitational theory. This paper for example: General Theory of Relativity: Will it survive the next decade?

You say there's positive evidence, but cited NONE. Your link about "gravity shielding experiments" refers to Wikipedia in which the first sentence said "...hypothetical process of shielding an object from the influence of a gravitational field..." This is NOT evidence! There are none! The Podkletnov effect, which is the closest thing one might claim to be a gravitational shield, has been discredited and has not been duplicated independently.

Furthermore, gravitational shielding has nothing to do with "error" in Newtonian laws! It just means that there are ways to generate "negative" gravity.

Again, and this is the last time I will ask this, please provide peer-reviewed citations to back up what I asked earlier, keeping in mind the https://www.physicsforums.com/showthread.php?t=5374" that you agreed to upon joining this forum.

Zz.

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I believe I am being reasonable. The 2006 paper General Theory of Relativity: Will it survive the next decade? states:

The significance that general relativity (GR) plays for our understanding of nature, makes the theory a focus of series of experimental efforts performed with ever increasing accuracy. However, even after more than ninety years since general relativity was born, Einstein’s theory has survived every test. Such longevity does not mean that it is absolutely correct, but serves to motivate more precise tests to determine the level of accuracy at which it is violated. This motivates various precision tests of gravity both in laboratories and in space; as a result, we have witnessed an impressive progress in this area over the last two decades. However, there are a number of reasons to question the validity of this theory, both theoretical and experimental.

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Mammo said:
I believe I am being reasonable. The 2006 paper [
url=http://arxiv.org/abs/gr-qc/0602016]General Theory of Relativity: Will it survive the next decade?[/url] states:

You seem to not know the difference between theoretical predictions or expectations, versus PHYSICAL OR EMPIRICAL EVIDENCE. There are no experimental evidence so far to indicate the failure of the current gravitational description. None!

There has been a lot of searches for such a violation, especially in terms of extra dimensions. I can cite for you a series of them. I know quite a bit about them. But there hasn't been one single experimental verification yet! So how come you think you can claim of a "logical error" in any of them when the physical evidence isn't there? If all we care about is to accept something as valid is some theoretical hypothesis, why do you think we spend billions of dollars to build the LHC when the Higgs is "logically" predicted to exist?

Zz.

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ZapperZ said:
You seem to not know the difference between theoretical predictions or expectations, versus PHYSICAL OR EMPIRICAL EVIDENCE. There are no experimental evidence so far to indicate the failure of the current gravitational description. None!

There has been a lot of searches for such a violation, especially in terms of extra dimensions. I can cite for you a series of them. I know quite a bit about them. But there hasn't been one single experimental verification yet! So how come you think you can claim of a "logical error" in any of them when the physical evidence isn't there? If all we care about is to accept something as valid is some theoretical hypothesis, why do you think we spend billions of dollars to build the LHC when the Higgs is "logically" predicted to exist?

Zz.
I agree with what you are saying; there is no direct evidence to suggest that GR is wrong. There is scientific investigation into this idea though. It isn't a taboo subject anymore.

Note that one of the authors of the given paper works for NASA JPL Slava G. Turyshev

Mammo said:
I agree with what you are saying; there is no direct evidence to suggest that GR is wrong. There is scientific investigation into this idea though. It isn't a taboo subject anymore.

Note that one of the authors of the given paper works for NASA JPL Slava G. Turyshev

Where the authors work has no relevance to this thread. And no one is saying this is a taboo subject, that is also irrelevant to this thread. In physics, nothing is taboo.. Our main job IS to study things that are not known, and to push the boundary of the validity of our knowledge. That's why most of us, including me, get employed! But you somehow are putting the cart before the horse by a series of misunderstanding, and proclaiming that something is logically incorrect and thus, proven to be wrong simply by a series of unverified theoretical predictions.

You should re-examine the process you use to draw up your conclusions.

While you are at it, read one of the latest tests on Newtonian gravity up to the 10 micro scale[1]. You may want to dial back a bit of the certainty you wrote in Msg. #6.

Zz.

[1] A.A. Geraci et al. Phys. Rev. Lett. v.78, p.022002 (2008).

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I agree that the thread title may be considered controversial or even misleading. I am still of the persuasion that there is an implicit assumption that the whole Earth is made of matter which is gravitationally equivalent to 'everyday' matter.

Mammo said:
I agree that the thread title may be considered controversial or even misleading. I am still of the persuasion that there is an implicit assumption that the whole Earth is made of matter which is gravitationally equivalent to 'everyday' matter.

I have no idea what that means, and since you have no valid support to make such a decision, there's no way either I or even you can distinguish that with our current models. In other words, what in the world gave you the idea of such a thing, when you have no valid evidence to support it. How did "cavendish experiment", which has been shown to be VERY valid up to the micro scale, lead to you coming up with what's in the center of our earth, especially now when it has been shown that your starting premise (i.e. Cavendish expt. being wrong) has been shown to be false?

Zz.

I'm not saying that the Cavendish experiment is wrong. It's that Newton's law of universal gravitation isn't necessarily correct i.e. 'that all objects attract one another equally, relative to their mass'.

Mammo said:
I'm not saying that the Cavendish experiment is wrong. It's that Newton's law of universal gravitation isn't necessarily correct i.e. 'that all objects attract one another equally, relative to their mass'.

But the Cavendish experiment WAS testing Newtonian gravitation! All the more sophisticated tests done by the Adelberger group[1] at U. of Washington is a more glorified Cavendish experiment!

So what you're saying here is self-contradicting.

Zz.

[1] E G Adelberger et al. Ann. Rev. Nucl. Part. Phys. 53 77 (2003).

Mammo said:
I agree with what you are saying; there is no direct evidence to suggest that GR is wrong. There is scientific investigation into this idea though. It isn't a taboo subject anymore.

What made you think it ever was?

I find it hard to believe that you read the paper of Bertolami et al. The very first page discusses the fact that the community "witnessed an impressive progress in this area [tests of GR] over the last two decades." That means that it has been being tested for the last two decades - hardly taboo.

Figure 1 - the very first one - covers tests over the last 30 years. References in the paper discuss measurements from the 90's, the 80's, the 70's, the 60's and the 50's. When exactly was this period where tests of GR were taboo again?

Furthermore, the very ideas you are pushing here - deviations from inverse square and deviations from uniform free fall are discussed in the paper, and the extremely stringent limits on these effects are shown. ZapperZ mentioned Adelberger's work - he is referenced a half dozen times in the Bertolami. How can you then be ignorant of what he has done? I don't understand this at all!

As far as the specific claim you are raising about Cavendish, how can you reconcile that with Figure 2, which shows the strength of possible new forces? (or, equivalently, deviations from Newtonian gravity) It shows the second best measured range is roughly earth-sized, and we know that there are no deviations from Newton in that range 100x better than we know G itself.

I don't know how anyone who read that paper could write what you write - your own reference disputes what you are saying.

I think there's a confusion here between testing *Newtonian gravity* in its scope of validity on one hand (Cavendish type of experiments), and then at the whole other end of the spectrum, necessary speculation about an ultimate challenge to *Einsteinian gravity* (also called GR) because we all know that it has a problem with quantum theory (or that quantum theory has a problem with Einsteinian gravity) in very extreme conditions.

The fact that people are speculating about an eventual "finite scope" of GR says nothing at all about any validity or not of another application, well within the domain of applicability, of Newtonian gravity.

It is a bit as if one were questioning whether, say, an accurate measurement of the dielectric constant of the vacuum (epsilon-0) which enters in the Maxwell equations were "based upon a logical error" because we know that at some point, electrodynamics needs to be treated quantum-mechanically (photons and all that). True, maybe at the 12th decimal or so, for the given setup, one needs to think of eventual small corrections. But that doesn't invalidate the essence of the experiment.

Mammo said:
I am still of the persuasion that there is an implicit assumption that the whole Earth is made of matter which is gravitationally equivalent to 'everyday' matter.
Of course that's the assumption! It's the default assumption that you have to make if you don't have a reason to believe anything else. You really have a problem with how logic works!

Here is the email reply from Bertolami himself:

Re: Logical Error of Cavendish Experiment‏

Dear Alan, Thank you very much for your mail and for the kind comment about our work. However, I do understand your point. The Cavendish experiment concerns the gravity pull of Earth irrespective of what it is made of. It also allows for the determination of Newton's constant, and through Kepler's law and astronomical observation, sun's mass. From there one can infer the mass of the planets.The mass of the stars of a given class (spectral type) is inferred from their luminosity and comparison with the typical mass to light ratio of that class. There is no dark matter or missing mass problem of relevance at this level. Dark matter presence is deduced through the rotation curve of galaxies, the dynamics of clusters of galaxies and, of course, through gravitational lensing, given that the observed effects cannot be explained (by a large factor of about 10-15) by the observed luminous mass. Hope these remarks are of some help. Best wishes, Orfeu Bertolami.

It sounds like Bertolami isn't supporting any of your ideas you've proposed in this thread.

He sounded open-minded enough to appreciate my point. It's a very subtle concept.

Mammo said:
He sounded open-minded enough to appreciate my point. It's a very subtle concept.

He was just being polite. In essence, he's saying something similar to what you had received in this thread.

Zz.

Open-mindedness is not a virtue when one wants to simultaneously claim to be a scientist but also to ignore the data.

You claimed that at one time tests of GR were taboo. I pointed out that these tests have been performed for decades, and asked you when this time was. You did not answer.

You speculated that there was some sort of deviation from inverse square, and some sort of non-universality of free fall, and some sort of exotic matter. None of these have been seen. The paper you pointed us to doesn't support this - it shows these effects are so small that our uncertainty on the value of G is 100x larger.

1) GR was never "taboo." Just like any other theory (or model) it must be tested. Otherwise it is as good as math homework.

2) I already made a note as to Cavendish's intent. The by-product was the constant G. Dozens and dozens of experiments measuring G have been conducted by national standards groups and university groups around the world. I say dozens because there are a number of ways to measure G. Oddly enough they all agree fairly well, except for the German standards group. They only measured G to three sig.figs. because their apparatus was leaking.

Mammo, you can continue arguing about
a) entropy induced mass change:
Recall mass is not influenced by thermodynamics with the caveat that there is no mass-energy conversion and that your Gaussian sphere still covers the point in question

b) logic errors with Cavendish's experiment:
this has already been beaten to the ground

c) changes in gravity due to what you read in physics texts:
Keep in mind people have told you that Newtonian models work well for slow moving reference frames; GR for frames that suffer massive distortions.

Nevertheless, G is still the same for all matter and energy densities. No evidence has indicated that G should be different, this includes dark matter surveys. Even anti-matter corresponds to G.

So unless a breakthrough in physics happens (maybe it will be you) arguing things like logic errors in a thoroughly hashed experiment and truth behind gravitational shielding are superfluous.

## 1. What is the Logical Error of Cavendish Experiment?

The Logical Error of Cavendish Experiment refers to the incorrect interpretation of the results of the Cavendish Experiment, which was conducted by Henry Cavendish in 1798 to measure the gravitational constant. The experiment involved using a torsion balance to determine the gravitational force between two masses. However, Cavendish's interpretation of the results was flawed, leading to an incorrect value for the gravitational constant.

## 2. What caused the Logical Error of Cavendish Experiment?

The Logical Error of Cavendish Experiment was caused by the assumption that the gravitational force between the two masses was directly proportional to the distance between them. This assumption was based on Newton's law of universal gravitation, which states that the force between two masses is inversely proportional to the square of the distance between them. However, Cavendish failed to take into account the effects of air resistance and other external factors, leading to an incorrect interpretation of the results.

## 3. How was the Logical Error of Cavendish Experiment discovered?

The Logical Error of Cavendish Experiment was discovered by scientists who replicated the experiment and obtained different results. In the late 19th century, Lord Rayleigh and William Thomson (Lord Kelvin) independently conducted the experiment and found a significantly different value for the gravitational constant. This led to a re-examination of Cavendish's original experiment and the discovery of the logical error.

## 4. How did the Logical Error of Cavendish Experiment impact the scientific community?

The Logical Error of Cavendish Experiment had a significant impact on the scientific community as it highlighted the importance of careful experimental design and data analysis. It also served as a cautionary tale about the dangers of making assumptions and overlooking potential sources of error in scientific experiments. The error also led to a reassessment of the methods used to determine fundamental physical constants.

## 5. Has the Logical Error of Cavendish Experiment been corrected?

Yes, the Logical Error of Cavendish Experiment has been corrected. After the discovery of the error, scientists were able to replicate the experiment with more accurate methods and obtain a more precise value for the gravitational constant. The current accepted value for the gravitational constant is 6.67430(15) x 10^-11 m^3/kg*s^2, which is significantly different from Cavendish's original value of 6.754 x 10^-11 m^3/kg*s^2.

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