[jeffreyH]

Alan's post above is one everyone should read through carefully. Make sure you understand it all.

[GoC]

Henry Cavendish established in 1797, and practically every national laboratory and astronomical observation since then has confirmed,  that G is independent of the density of the attracting body.

A BH actually proves that statement incorrect.

The difference between a black hole and regular mass is frequency is not possible in a black hole. The frequency produced in a spherical planet is reduced to the center of a planet if atomic clocks follow frequency. A correlation has been established. Time continues to tick slower to the center of a planet if we extend the observed tests.

[timey (OP)]

Alan - you seem to have fallen into the very common trap of believing that you have nothing left to learn.

Henry Cavendish established in 1797, and practically every national laboratory and astronomical observation since then has confirmed,  that G is independent of the density of the attracting body.

The program "Gravity and Me: The force that shapes us" is really very informative and entirely disagrees with you on this point.

It takes you on a journey around Britain with a set of laboratory scales and a laboratory weight and quite clearly shows one by how many Newtons that laboratory weight changes due to locational position and conditions.

The physicists are very clear that when they measure the gravity on Dartmoor, that the density of the granite at that position is having an effect on the measurement!

The program takes you to the Cavendish experiment site itself, giving explanation of this experiment.
It also takes you to a laboratory where gravity is measured every day by a highly sensitive machine where gravity is observed to differ on a daily basis, and these differences can be due to the simple fact of the extent of rain fall on that day.

Gravity mapping from space clearly shows that anomalies of gravity on Earth are present due to density differences.

https://earthobservatory.nasa.gov/Features/GRACE/page3.php

Atomic clocks are used to measure how differences in gravity effect the rate of time.
However, at present these clocks are laboratory bound and have only been able to measure the differences in the rate of time due to change in altitude and relative motion.
The reason why NIST are developing laboratory sensitive portable atomic clocks is actually with the intention of measuring locations of differing density.

You are correct that G is used for astronomical measurements, but really this is an approximation because near Earth gravity measurements differ for many reasons, and one of those reasons is the geological density of the location.

The program also discussed a mobile phone relativity app where the app records one's altitude and speed of motion during the day telling one by what rate they are ageing due to position of altitude and relative motion...
If you are going to be making comment as an authority on gravity, watching this program would be of immense benefit to you.

But you could also change x to get the same result, so the observed frequency isn't a function of M alone but of the gravitational potential -GM/x.

The experiment that I suggest is to designed to determine exactly whether the observed frequency of a (stationary to the gravity field) clock is just a function of gravity potential (position of altitude from centre of Earth), or if density of M (gravitational field) will also affect the observed frequency of the clock in any particular fashion, (i.e. increase or decrease the observed frequency).

[nilak]

Your thought experiment seems ambiguous  to me. You say the gravitational potential is the same for two points of the same position of altitude from the centre of the earth. That is an aproximation that doesn't take into account local densities. It you add them to the equation, you will find a higher gravity then higher gravitational potential in the denser location. However, the difference is so small that I don't think it you can measure any effect on clocks. But you say that in the denser region clocks will tick faster. What is the reason and what would be the magnitude of the effect?

[timey (OP)]

Your thought experiment seems ambiguous  to me.

It is your understanding of the suggested 'actual' (not thought) experiment that is ambiguous.

You say the gravitational potential is the same for two points of the same position of altitude from the centre of the earth.

This is dependant on what you mean by gravity potential...
Gravity potential energy is pe=mgh, where pe stands for potential energy, m is a body of mass in relation to Mearth, g is the strength of the g-field at h, and h 'can' be the height from the centre of the earth.
The g-field of Mearth is not the same thing as the gravity potential of the g-field Earth.
pe=mgh is not the same thing as g(r)=GMearth/r^2.

That is an aproximation that doesn't take into account local densities. It you add them to the equation, you will find a higher gravity then higher gravitational potential in the denser location.

Yes you are correct...
GMearth/r^2 is an approximation.  It does not take into account the gravity anomalies found in locations of earth that are at the same altitude from centre of earth, but of differing geological densities.
Taking into account the gravity anomalies of Earth, one will find that the 'g' of g(r)=GMearth/r^2 is differing according to the density of the location.
...And this is exactly what my suggested experiment seeks to measure.
The experiment seeks to place 2 identical atomic clocks in differing locations of the exact same altitude from centre of earth, (to equalise GR altitude time dilation), where these locations share the exact same radius of centripetal motion, (to equalise SR motion related time dilation), but are of known significant difference in geological density.

However, the difference is so small that I don't think it you can measure any effect on clocks.

You are very wrong about this.  If a laboratory scale can detect the difference in the weight caused by the anomaly, an atomic clock will be more than able to measure the difference in rate of time this will cause.

But you say that in the denser region clocks will tick faster.

Conventional physics will tell you that the clock in the denser location will run slower.  This is why BH's are thought to be being observed as running at very slow, or stopped rates of time.
Although a clock will run faster when it is subject to greater potential energy at greater heights from the centre of gravity, my model predicts that a clock will also run faster if subject to a greater gravitational field, therefore my model predicts that in comparing the 2 clocks under the conditions of the suggested experiment, that the clock in the denser location will run faster.

What is the reason and what would be the magnitude of the effect?

The reason for this is defined by the afore suggested re-calculation of the ultraviolet catastrophe under the remit of +energy=shorter seconds and the consequence that because stars of greater temperature are greater in mass value, that time will be running faster for bigger stars than for smaller stars...

In the suggested experiment the magnitude of the effect would be dependent on the anomaly of g.

[jeffreyH]

Henry Cavendish established in 1797, and practically every national laboratory and astronomical observation since then has confirmed,  that G is independent of the density of the attracting body.

A BH actually proves that statement incorrect.

The difference between a black hole and regular mass is frequency is not possible in a black hole. The frequency produced in a spherical planet is reduced to the center of a planet if atomic clocks follow frequency. A correlation has been established. Time continues to tick slower to the center of a planet if we extend the observed tests.

That is incorrect. The gravitational potential of a black hole at radius r is the same as for any uncompressed mass of the same value. Assuming that r is outside the surface of the uncompressed mass. Therefore your view of the situation is in error.

[nilak]

Gravity potential energy is pe=mgh, where pe stands for potential energy, m is a body of mass in relation to Mearth, g is the strength of the g-field at h, and h 'can' be the height from the centre of the earth.

Ok, g is the strength of the field at h, but when you use , g is needs to be constant for any height, otherwise you need the g function of h and to integrate the function over h.
Also you can use infinite as a reference point for gravitational potential if the field is not constant.

[timey (OP)]

Your maths text has come out wonky and I can't see what equation you post, but why would this be relevant to a physical experiment?

Under the remit of a change to a greater altitude the equation pe=mgh will incorporate a decrease in value of m, a decrease in value of g, and an increase in value of h, resulting (via the equation pe=mgh) in an increased value of pe.

Under the remit of the suggested experiment and a difference in gravitational field due to density, the equation pe=mgh will incorporate h being held equal for both locations, and in the denser location, an increased value of m, and an increased value of g, resulting in the clock in the denser location (via the equation pe=mgh) having a greater value of pe.

The g of each location can be compared in each location via scale and weight, and therefore the magnitude of the difference in rate of time observed of each clock can be calculated held relative to measurement.

[nilak]

I don't know why you vary m which for calculating gravitational potential it is replaced with 1.
To calculate the gravitational potential at those two points say A and B, I think you can measure the direction and strength of the gravitational field from A and B till a certain height where the difference between them becomes small say 1000km, then extrapolate the g function till infinity. Then integrate the gravitational potential function of h, using the measured g(h).

But, this is for a hypothetical lonely planet with no rotation and no translational motion.
However, you talk about a real experiment and I don't think it is possible to determine the gravitational potential with the precision you want to test your prediction. Also I think the difference in clock rates will be much smaller than the measurement standard deviation.

[alancalverd]

Alan - you seem to have fallen into the very common trap of believing that you have nothing left to learn.

Henry Cavendish established in 1797, and practically every national laboratory and astronomical observation since then has confirmed,  that G is independent of the density of the attracting body.

The program "Gravity and Me: The force that shapes us" is really very informative and entirely disagrees with you on this point.

It takes you on a journey around Britain with a set of laboratory scales and a laboratory weight and quite clearly shows one by how many Newtons that laboratory weight changes due to locational position and conditions.

I have a lot left to learn, but I can recognise the difference between G (the universal gravitational constant) and g (the local acceleration due to gravity). I learned that at the age of 16, and I haven't met any physicists (or geologists, who use the variation in g when prospecting for oil) who didn't know it. Maskeleyne's famous 1774 estimate of the mass of the earth was based on the variation of g around Schiehallion.  If the program misled you in that respect, you should complain.

As I have pointed out many times, scientists tend to be very pernickety about language, and even about symbols, and we sometimes make the  mistake of thinking that others have as much respect for precise communication.

And by the way you can't measure g with "laboratory scales" for the very reason I mentioned. You need to use a spring balance or an electromagnetic force balance. "Scales" compare the gravitational force gm₁: gm₂ on two lumps of matter, so g cancels out. Terminology matters.   

[alancalverd]

Apropos Dartmoor, or more accurately Bodmin Moor, the engineers working on the A30 improvement scheme umpteen years ago asked for 1000 geological survey points along the proposed route before they would complete the design and fix a price, The first three boreholes hit granite at about 2 m depth so the accountants cancelled the geology contract and insisted on a quote for a design based on granite at 2 m. It turned out that the geologists had hit the only granite boulders in 30 miles of peat bog. Unsurprisingly, the project ran somewhat over time and budget.     

[timey (OP)]

As always your diction is entertaining and interesting, but to say so it has nothing to do with placing 2 identical clocks at locations of differing geological density, but of equal height from centre of earth and equal radius of centripetal motion.

The part of the program where they measured the precision laboratory weight with the laboratory sensitive scales revealed that the mass of this weight registered as greater or lesser on the scales as per Newtons under differing gravity potential conditions.

Edit: When they measured Dartmoor because it is closer to the equator, the geological density there compared to a previous measurement on Snowdonia was mentioned as a factor.

[alancalverd]

Not scales. Never. Scales don't "register newtons": they compare the gravitational force on two masses. Either the program was lying or you have incorrectly renamed a force balance. If the presenter said "scales" he should be taken outside and re-educated. And the precision of the test mass is irrelevant - any lump of nonmagnetic material would do.

But the point is that time depends on the local gravitational field, not the nature of the source of that field. All you have quoted is a demonstration that field depends on mass and distance, and that mass depends on density and volume, so dense rocks produce a stronger field than less dense rocks at a given distance. Nothing new there - it was known to Cavendish, which is why he used gold and lead in his experiments.

[timey (OP)]

Ok - let me re-phrase.

A lump of metal of a particular mass was placed upon apparatus.
This was used to demonstrate that the lump of metal registered different values when it was placed on the apparatus at the base of Snowdonia, at the top of Snowdonia, and on Dartmoor closer to the equator.
When they measured Dartmoor, it was remarked upon that because the geological density of Dartmoor is lesser than Snowdonia, that this would be a factor as to the value registered when the lump of metal was placed on the apparatus.

Sticking to conventional physics for this post, if clocks were placed at locations of differing geological density but at the same height from centre of earth, and at same radius of centripetal motion, then as per the remit of conventional physics, the clock in the greater gravity field should run slower.

Under the remit of conventional physics a clock in the greater gravity field will be observed to run slower.

[alancalverd]

......as predicted and proved by experiment, many times!

We know

g_y  = g_max - w²Rcos²y

where g_max is g at the poles, w is the angular velocity of the earth, R the radius of the earth, and y is the latitude.

It is surprising that a shift of only 2 degrees of latitude was distinguishable from the subterranean density effect, but the above equation is sufficiently accurate over small variations in y that it can indeed be used for locating geological anomalies like ore and oil deposits.

Fortunately, national laboratories that maintain time standards are aware of the local value of g and hence can account for the difference between, say, WWV time signals (from Colorado) and MSF (from Cumbria).

Now it seems that your hypothesis is that two clocks operating in the same value of g would run at different rates if their local geology was different. Very spooky. What mechanism do you think tells the clock whether it is sitting over sand, or over granite but under a lead roof, if g is the same in both cases?   

[timey (OP)]

Under the remit of conventional physics a clock in the greater gravity field will be observed to run slower.

......as predicted and proved by experiment, many times!

We know

g_y  = g_max - w²Rcos²y

where g_max is g at the poles, w is the angular velocity of the earth, R the radius of the earth, and y is the latitude.

It is surprising that a shift of only 2 degrees of latitude was distinguishable from the subterranean density effect, but the above equation is sufficiently accurate over small variations in y that it can indeed be used for locating geological anomalies like ore and oil deposits.

Fortunately, national laboratories that maintain time standards are aware of the local value of g and hence can account for the difference between, say, WWV time signals (from Colorado) and MSF (from Cumbria).

Now it seems that your hypothesis is that two clocks operating in the same value of g would run at different rates if their local geology was different. Very spooky. What mechanism do you think tells the clock whether it is sitting over sand, or over granite but under a lead roof, if g is the same in both cases?   

if clocks were placed at locations of differing geological density but at the same height from centre of earth, and at same radius of centripetal motion,

Then g would 'not' be the same for each clock.

A clock will be observed to run faster at a greater altitude - where as per the equation pe=mgh, the difference between the lower clock and the higher clock is that for the higher clock m has decreased in value, g has decreased in value and h has increased in value resulting in an increase in potential energy for the higher clock.

For the 2 clocks of the suggested experiment - placed at locations of equal radius of centripetal motion, (to equalise SR effects) and at equal altitude, but at locations of differing geological density *and therefore at locations of differing g* - the clock in the denser location (compared to the clock in the less dense location) will have an increased m, and an increased g, where h remains the same for both clocks.

Will the clock that is subject to the greater g have a higher value of pe than the clock that is subject to the lesser g?

[alancalverd]

For the 2 clocks of the suggested experiment - placed at locations of equal radius of centripetal motion, (to equalise SR effects) and at equal altitude, but at locations of differing geological density *and therefore at locations of differing g* - the clock in the denser location (compared to the clock in the less dense location) will have an increased m,

NO NO NO NO NO!

The whole point of the television experiment you quoted, and the entire lives of Galileo, Cavendish, Maskeleyne, Hoyt, Newton, Eotovos, Kater and umpteen others was that the mass of a body does not change with location. Mass and weight are different, which is why we use kilograms for one and newtons for the other. . Scales compare masses;  gravimeters, spring balances and suchlike measure weight. Weight = mg.

This is really the most elementary stuff. If you don't understand it, you are wasting your life discussing relativisitic quantum mechanics because you won't understand that either.

All you have said so far is that a clock in a stronger gravitational field will appear to run slow. Everybody agrees with that, because it has been demonstrated.

[timey (OP)]

Excuse my lacking in knowledge of elementary mathematics.

So m stays the same in the equation which really does simplify the matter so...

The clock that is raised in altitude compared to the lower clock will be subject to a decrease in g and an increase in h, where the equation pe=mgh results in a greater value of pe for the higher clock.

On the basis that the above statement is true, is it?

2 identical clocks placed in locations of the same radius of centripetal motion (to equalise SR effects), and at the same altitude from centre of earth so that h is equal for both, but placed in locations of significant differing geological density - the clock in the denser location compared to the clock in the less dense location will have an increased g, where the equation pe=mgh will result in a greater value of pe for the clock in the denser location.

The clock in the greater gravity field will have more potential energy than the clock in the lesser gravity field.

Agreed?

[nilak]

The gravitational acceleration g can vary across the globe [1,2] within approx. 120mGal which is .
I understand that the chart represents the deviation from standard smooth value. For example at the equator it would be a deviation from 9.78 m/s^2
Therefore we can have at one place a1=9.80006 and at another 9.79994.
If we want to see the time dilation due to gravity at a1 and a2 we can use

If we make the notation k as a dilation factor to mean T=T0 • k
For a1 we get k1=1.000 000 000 694 715
and for a2, k2=1.000 000 000 694 707
That is 8 seconds difference in
That mean we need to be able to measure a time rate difference of 1 second over approx. 4 milion years.
Atomic clocks lose only 1 sec over 15 billion years, therefore I think you are right, we can measure the necessary time rate difference between the two locations.

https://astarmathsandphysics.com/a-level-physics-notes/173-forces-and-motion/2811-variation-of-the-acceleration-due-to-gravity-over-the-surface-of-the-earth.html [1]

https://en.m.wikipedia.org/wiki/Gravity_of_Earth [2]

[timey (OP)]

Nilak - the difference between what is observed of a clock in the g-field concerning a comparison of an elevation of just one metre has already been measured.

The only factor that is negating such an experiment that I suggest is that so far laboratory precision atomic clocks are not portable and have so far only tested the parameters of altitude and relative motion within the lab.

Here is some great discussion on this chat site, where despite the fact that some of the posters, (who are all working in the area of some type of scientific research because that is part of the prerequisite necessary to be a member of this site), are making mistakes concerning potential energy being a contributor to mass value, and other such gaffs, people seem not to be problematic about expressing the understanding that conventional physics has not got all the answers and don't seem to have a problem in exploring the fact.

If I were able to join this site (which I'm not as I cannot prove that my job incorporates research), I would add to the discussion that a cesium atomic clock will be observed to have a higher frequency of electron transitions on top of the mountain as compared to the valley, and that in most areas of physics, a higher frequency is accompanied with a higher energy.

The conversation is interesting to me in that here we can see people who are professional or semi professionals, who have jobs at universities, who are making mistakes despite their obvious status of 'university education', all engaging in the premiss of an exploratory conversation without a hint of any derision being attributed to the OP, or to the mistakes made by some of the replies.  Or perhaps the mistakes I spot went unoticed by people replying because they were concentrating on the premiss of the question rather than searching for any means possible to be obtuse to the content and deride the OP, or any of the replies.

https://www.researchgate.net/post/Where_does_mgh_potential_energy_reside_exactly