Exploring the Effects of Changing Universal Gravitational Constant

[Ulysees]

The bit about the anthropic principle is much too interesting and important to discuss it hidden in here, let's make it a thread under Quantum Physics, I think many people including myself will want to understand it.

How they came up with it, what experiments support the underlying concept of the observer giving rise to the existence of the observable and vice versa, all that sort of thing.

 

[Loren Booda]

Quantum Physics? I think the Anthropic Principle is better served by the Philosophy forum.

 

[rbj]

getting a little OT, but not too far OT.

The bit about the anthropic principle is much too interesting and important to discuss it hidden in here, let's make it a thread under Quantum Physics, I think many people including myself will want to understand it.

How they came up with it, what experiments support the underlying concept of the observer giving rise to the existence of the observable and vice versa, all that sort of thing.

Quantum Physics? I think the Anthropic Principle is better served by the Philosophy forum.

yeah, this is more about Cosmology (which all the branches of phyics inform), i would think.

i remember having some discussions about it with a purported physicist at Wikipedia (Userighlander). he added some stuff about it's origin that i thought had both interest and veracity. there were these "Dicke coincidences" that had something to do with the question that wasn't so much "how come do these fundamental constants, that have no known dependence on other parameters, happen to take on these values that allow for matter, solar systems, and planets to form" (the basic FTU question), but Dicke's question was more of "why is the universe about 10¹⁰ years old, instead of 10¹¹ years or 10⁸ years?" and the reason was that, too long and stars (incl. our sun) are going to change and burn out and not be sutitable to sustain life on our planet, too short and these "main sequence" stars would not have happened. i believe there had to be two eras of stars around here, the first bunch of stars were able to cook up elements as far as iron on the periodic chart, but they had to crap out and collapse and there needed to be super novas to cook up the heavier elements for which our planet would have needed 4 1/2 billion years ago.

this is all from memory of reading other sources. i think it reflects what real physicists were saying (and pervect or integral or zap or russ or doc can correct anything they see fit). at least I'm not trying to make anything up. i don't know the details.

anyway, it is a sort of philosophical extension to move the question from "why is the place we're hangin at as old as it is?" to "why are the knobs that manage the place we're hangin at set to the values that they are?" and the Anthropic Principle simply says that, if they were set to much different values (or, for some constants, slightly different values), we wouldn't be here to ask the question. so, it can look like a sort of "well, duh!" explanation but it does have uses (like explaining why the universe isn't a trillion years old).

but the difference is that we know that it had, at one time, been 100 million years old (but there wasn't likely any life around back then asking these questions) and we know (or at least think) that someday the universe will be a trillion years old (and there likely won't be life left around then, but who knows?). so all of these ages of the universe get to have their moment and no age is less likely than any other age, it's just that only some range of ages of the universe that is more likely to be lived in and measured and pondered. the difference is that we don't know that there ever was a universe that had a Fine-Structure Constant that was much different than (137.036)^-1. and if this is the only universe that exists, it is remarkable that these constants took on the values that they had to for matter to be like it is. it then seems we are awful lucky which is the deep question that the notion of the FTU poses.

 

[rbj]

No, it's actually very simple, imagine a computer program (like Celestia) that simulates many objects in the solar system using numerical integration so it can deal with chaotic motion - someone could go to the source code and change a line to another value:

#define G 6.67e-11

but that's a dimensionless number. if you say that everything in Celestia has internal numbers that are fixed to numbers of meters of real things and numbers of kilograms of real thing and numbers of seconds of real intervals of events, changing that dimensionless G would have to change the size of the meters, kilograms, and seconds. that's because, when you write programs to model real physical processes, you have to non-dimensionalize all of the parameters. look up nondimensionalization in Wikipedia. i know from my very own experience in signal processing that we must do that. in modeling audio signal processing, the kernel of the code has no idea that the sampling rate of the physical situation i am modeling is 44.1 kHz or 48 kHz or 96 kHz. it doesn't matter to the program - it just defines the variable parameters (the "states") of the present discrete instant of "time", in terms of the previous discrete instant of "time". all of the parameters must be dimensionless numbers.

Then objects will move differently. That's the idea of the teacher. Same equations, same units, different G. Nothing to do with length expansion or anything relativistic. This is a High School exercise remember.

So can you imagine the effect of changing that constant of the program by 10%?

no, i can't. the whole program can work the same way with G set to 1 (and if you are modeling other physical equations) with c set to 1 and with $\hbar$ set to 1. but now you would be understanding that all of your lengths and masses and elapsed times would be in terms of their Planck units. set the program with the same initial conditions (in terms of these Planck units) and let the program go, and exactly the same thing should happen. and, in fact, exactly that is happening in your modeling program but if G is 6.67 × 10^-11 because somewhere else it is being compensated with the old "multiply and divide by the same quantity trick".

U, you say "it's actually very simple," but remember that "Theories should be as simple as possible, but no simpler." (quote from Einstein.)

Planets would move faster and in more elliptic orbits closer to the sun. But change the constant by a factor of 10^22, adjust the step of integration to something much smaller for stability, and everything collides with the sun coalescing into a "black hole".

ultimately, it's because, in your non-dimensionalized model, the masses of particles in terms of the Planck Mass are getting heavier and/or the size of atoms and constituent particles in terms of the Planck Length are getting smaller and/or the rate of atomic processes (evidenced by the frequency of radiation of particular processes in atoms, such as the Cesium radiation they base the second on) has to be getting faster. those are the salient measures. and somewhere in Celestia or any modeling program, changing G actually changes one or more of those, for something to be observationally different.

just because it's a high school exercise doesn't mean that students should learn fallacies from it.

 

[Ulysees]

#define G 6.67e-11

but that's a dimensionless number.

Of course it's a dimensionless number. It's from a computer program - units are implied.

if you say that everything in Celestia has internal numbers that are fixed to numbers of meters of real things

Or kilometres of real things. Or nanometres of real things. Units are implied in a computer program, and only displayed to the user where the programmer wants to.

changing that dimensionless G would have to change the size of the meters, kilograms, and seconds.

Only if the programmer had to simulate the real world with its given strength of gravity. But this is not about the real world. The teacher's question is about an imaginary, hypothetical world:

"what if the world were different in terms of its gravity strength?"

The teacher might be nice and reward you for the display of off-topic peripheral knowledge, but his question you didn't understand.

the whole program can work the same way with G set to 1

The program would only work the same way if at the same time you changed both G and some other program constant. Eg change all masses by the same factor. But you're not allowed to change anything else: the teacher only asks you to change the gravity strength G.

 

[rbj]

Of course it's a dimensionless number.

but the real G is not. if you're SI, it's 6.67428 × 10^-11 N m² kg^-2 (or, in terms of the base units 6.67428 × 10^-11 m³ kg^-1 s^-2)

It's from a computer program - units are implied.

but their association with the units used to measure real physical quantities cannot be arbitrarily coupled. the "meters" and "seconds" in your simulation are not necessarily the meters of the reality you are simulating. only if G = 6.67428 × 10^-11 m³ kg^-1 s^-2 and c = 299792458 m s^-1 and $\hbar$ = 1.054571628 × 10^-11 kg m² s^-1 will the "meters" and "seconds" and "kilograms" in your simulation represent the real thing in reality. If the simulation is using numbers to represent lengths in meters, time in seconds, and mass in kg, then they can only be associated with the meters, seconds, and kg out here with G, c, and $\hbar$ set to the above values. otherwise the "meters" aren't real meters, they're some measure of length, but what your simulation says is a meter doesn't have anything to do with a meter. unless, of course, the number of Planck Lengths per meter, a dimensionless quantity, has changed (and/or something similar to the second and/or something similar to the kilogram). and that is what is operationally meaningful.

what you don't realize U (and apparently don't wish to realize), is that just increasing G in your simulator probably ended up changing 3 different knobs that are important. it probably made your meter stick (in the simulator) shorter and/or made the masses of all of the particles that make up matter heavier and/or also speed up processes in atoms (which speeds up the processes of things like clocks that are made out of atoms).

Or kilometres of real things. Or nanometres of real things. Units are implied in a computer program, and only displayed to the user where the programmer wants to.

no. they are not of real things. they are scaled. your program will call them "meters" if such display is turned on, but they are shorter or longer than the meters (in reality) that you're associating them with.

Only if the programmer had to simulate the real world with its given strength of gravity.

the whole point is that you cannot meaningfully represent "the strength of gravity" with G. (unless you choose a complete set of natural units, perhaps atomic units, that don't normalize nor define G.) that may seem unintuitive to the high school physics student, but that's the case. the same is true for the Coulomb force constant. do you say that $1/4 \pi \epsilon_0$ is what determines the strength of E&M?Ulysees, please read the paper(s) and web pages cited in this thread (but for Planck Units, go back to early March in the history since it's getting screwed up so bad in Wikipedia). read them to the extent that you can reverberate back the concepts and points made therein. maybe buy a copy of John Barrow's book: The Constants of Nature and read at least to page 50. then come back here and make your case with a few equations, because otherwise you're just pissing in the wind.

But you're not allowed to change anything else: the teacher only asks you to change the gravity strength G.

precisely. (at least if you remove the words "gravitational strength" since that meaning is ill defined. but G is well defined.)

and that's why there is no operational meaning to the concept of changing only G. if you're not allowed to change anything else, if you're not allowed to change, say, the (dimensionless) ratio of particle masses to the Planck mass, no one (who is subject to the laws of physics) can know the difference if only G is changed. God (or "Q" on Star Trek or some other omnipotent being that can do such and notice the difference because they, themselves, are not subject to the laws of nature) changes G, and afterward we mortals (who are subject to the laws of nature) set out to measure it with our meter sticks, atomic clocks, and kilogram standards, and with those measuring standards (that are subject to the laws of nature), we find out that it is still appears to us as somewhere around 6.674 × 10^-11 m³ kg^-1 s^-2 . that's the whole point that you need to figure out U.

 

[Ulysees]

It's a shame you don't give a toss about helping that High School student with his teacher's legitimate thought experiment promoting creativity and abstract thought. The teacher is promoting the opposite of what some people here are doing, who like Mr Data endlessly recite sections from books in their "database" unable to think creatively, and often missing the point.

But what is unforgivable is you have continued to flood the thread in an attempt to obfuscate your original misreading of the question with a lot of mostly irrelevant remarks - the teacher was asking for a violation of the laws of physics, in one parameter only. And to only use Newton's laws. That is a legitimate exercise, and the equations accurate as long as speeds are non-relativistic (well below the speed of light).

jackster18, I am sure you are smart enough to give the teacher what he wants, and ignore the flood here. I ensure you, the teacher's underlying models are sound (Newton's laws). And you can use them correctly to calculate what he asks. Unless a final speed works out to be close to the speed of light or over, which it may well do, you can mention this at the end for some extra marks.

 

[rbj]

It's a shame you don't give a toss about helping that High School student with his teacher's legitimate thought experiment promoting creativity and abstract thought. The teacher is promoting the opposite of what some people here are doing, who like Mr Data endlessly recite sections from books in their "database" unable to think creatively, and often missing the point.

But what is unforgivable is you have continued to flood the thread in an attempt to obfuscate your original misreading of the question with a lot of mostly irrelevant remarks - the teacher was asking for a violation of the laws of physics, in one parameter only. And to only use Newton's laws. That is a legitimate exercise, and the equations accurate as long as speeds are non-relativistic (well below the speed of light).

well, since you don't believe me, and since from your usage ("give a toss", "maths") , you sound British. i don't know precisely where it is located, but you might want to consider rolling over to Imperial College and talking to the physics chair, Michael Duff.

physics, indeed all of science, moreover all of learned knowledge, is a continuing revelation of this commodity called "truth". some things we thought were true in times past (like pre-copernicus), we don't think are true today. we've either made discoveries that preclude the older "truth", or we simply thought better of it. (Einstein probably knew about, but never as far as i know, made any reference to the Michaelson-Morley experiment. he just had a better way to think about relative and absolute motion.) it's likely at one time, nearly all physicists thought that the speed of light, as an absolute physical quantity, was a fundamental parameter of the universe. that, if c were somehow changed to 100 km/hour, our experience of reality would be altered. books get written about that like Mr. Tompkins get written with such a view, but now are considered by these leading physicists to be an anacronysm or obsolete. like pre-copernicus astronomy.

the teacher doesn't know it (yet), but was not merely asking about violation of the law of physics. the teacher is asking a sort of meaningless question. it's like looking at a bathtub full of water and asking "what would happen if water were added?" (thinking that the answer is it would measurably overflow.) but when water is added, the tub (and observer and all of the observer's meter sticks) gets bigger and the tub is still full. when water is removed, the tub gets smaller (along with the observer and all of the instruments one would use to measure the volume). the observer cannot tell the difference. and if there is no way for any mortal to know the difference, eventually the question becomes meaningless.

dimensionful parameters, like G, c, and $\hbar$, are only human constructs. they are not properties of the system associated with them (in this case, the universe). currently, they believe there are about 26 dimensionless parameters that are used in the totality of known physical law. one is the cosmological constant (in terms of the Planck Time) and the remaining 25 come from the Standard Model. the masses of the particles (leptons and quarks) relative to the Planck Mass is as close as you're going to get to a "Strength of Gravity" parameter. if those masses changed (relative to the Planck Mass), something would be different. they may (likely will, IMO) discover new interactions with their own coupling constants that they can only measure and not explain yet with the existing physics. then the number, 26, will increase. they may also discover and verify theories where some of the 26 are derived from other numbers. then the number of fundamental constants will decrease. but the point is that G is not on that list.

obviously, Ulysees, you haven't grasped this point. that's okay.

you say that it's unforgivable that i continue to stand by it, even with regard to jackster, the high school student with an assignment for his physics class. i say what's unforgivable, is for him to have to choose between getting the grade and reporting the accurate physics due to the teacher's ignorance (that's okay, there is plenty of that going around) and arrogance (student may be no more enlightened than teacher under penalty of grade). i had to do similar crap in high school, too, but the issue was about history, sociolgy, economics, and policy. (like writing a paper explaining why capitalism is decidedly better than socialism. or why the U.S. had little choice but to drop the bomb on Hiroshima and Nagasaki. why police act in the best interests of society. why we live in the freest and bestest and happiest of societies and are the envy of nations. why we stand and say the pledge-allegience or sing the national anthem. all that politically correct stuff. when we were little kids, they taught us that George Washington chopped down the cherry tree.)

political orthodoxy is to be expected in a public school, just as you would expect to learn to do the rosary and learn the catechism if you attended a Roman Catholic school. parents who are more enlightened then have to try to help their kids unlearn such brainwashing that cannot be avoided. i just resent (even more) having to do that with science or math (another example: around the turn of the previous century, the state of Indiana nearly passed a law declaring $\pi$ to be 22/7).

 

[ks_physicist]

There is nothing wrong with the question the teacher asked, at the level the teacher asked it. The teacher is not asking students to develop a research proposal for a doctoral thesis, but to think about how G is used and what gravity affects.

Perhaps paired questions would make the intent more clear, such as "Calculate the force of attraction between you and the Earth using the known value of G, and re-calculate it with a value of G equal to 6x10^11."

I can tell you with absolute certainty that I occasionally have to say things to my 9th grade Freshmen that make me feel a little queasy because I'm saying something I know to be "wrong", but I know that I have to present them with the simple version now or they'll be hopelessly lost. When I have them do projectile motion problems, I do not have them factor in the difference in gravitational force due to the altitudes, yet I know that to be "wrong". I teach them kinematics equations, even though they can calculate velocities in excess of c given a constant acceleration and a long enough period of time.

I can imagine the frustration I would see in my students' faces if I spent a class period talking about Planck lengths and dimensionless constants. They're not ready to understand the problem in that depth; it isn't even something that came up as a topic (that I recall) in undergraduate physics. I suspect that you would get the same sort of answer/comment from this student's teacher. (Perhaps the students should invite the teacher to the discussion...)

 

[rbj]

"Calculate the force of attraction between you and the Earth using the known value of G, and re-calculate it with a value of G equal to 6x10^11."

nothing wrong with that. (it's an exercise in math.)

I can imagine the frustration I would see in my students' faces if I spent a class period talking about Planck lengths and dimensionless constants. They're not ready to understand the problem in that depth...

i agree with that and, if you look, i had such a caveat in my first post on this thread.

but, my concern is regarding teaching fallacies to kids (because the truth is a bit more difficult to understand) as fact. that's why Science or NY Times science reporters don't know what questions to ask a physicist who, like the cold-fusion guys, is taking his Variable Speed of Light theory directly to the public media rather than to test it first in the peer-reviewed context. it gets a lot of attention and some excitement, but propagates fallacies. it was precisely such an event that pissed off Michael Duff and prompted him to write that one paper i cited.

 

[jackster18]

good god this is turning into a war

 

[jackster18]

oringinally posted by Ulysees
"But what is unforgivable is you have continued to flood the thread in an attempt to obfuscate your original misreading of the question with a lot of mostly irrelevant remarks - the teacher was asking for a violation of the laws of physics, in one parameter only. And to only use Newton's laws. That is a legitimate exercise, and the equations accurate as long as speeds are non-relativistic (well below the speed of light).

jackster18, I am sure you are smart enough to give the teacher what he wants, and ignore the flood here. I ensure you, the teacher's underlying models are sound (Newton's laws). And you can use them correctly to calculate what he asks. Unless a final speed works out to be close to the speed of light or over, which it may well do, you can mention this at the end for some extra marks."

I don't want to take sides here, but Uly is right rbj...iv been waiting for someone like this to just give me simple answers...its just grade 12, we assume a lot of dumb things when doing calculations..like assume no air resistance...etc. And yea i started skipping what you guys were talking about in your posts because it start to turn into a war of "no I am right, no I am right"...blah blah...lol...Anyways...my group got 29/30, which is 97 % :)...and yea rbj i know its not true physics, like i just said we assume a LOT, and i mean a LOT of stuff...its horrible i know, i guess i will learn REAL physics when i go to university. Heres one of our calculations:

Calculating the time it takes for Earth to reach the Sun with the new universal gravitational constant.

The force of gravity is the only force acting upon the Earth and is therefore the net force. The acceleration towards the Sun can then be calculated. As the Earth gets closer to the Sun (Δd decreases), the force of gravity will increase and so will the acceleration. Assume that the average acceleration of the entire trip, as constant acceleration, accurately represents the changing acceleration of what is actually happening. Also assume that the radius of the Earth and the Sun remain what they currently are (they have not collapsed into themselves with the increased gravity) and use the average distance of the Earth from the Sun. Calculating average acceleration, which will be the average of when Earth is at its current position and when it reaches the surface of the Sun:

Current position:
mE = 5.98x1024 kg
msun = 1.99x1030 kg
Δd = 1.50x1011 m
G = 6.67x1011 N•m2/kg2
Fg = ?

Fg = G * mE * msun / Δd2
Fg = 6.67x1011 N•m2/kg2 * 5.98x1024 kg * 1.99x1030 kg / (1.50x1011 m)2
Fg = 3.53x1044 N

At surface of Sun (where distance between centres is radius of Sun + radius of Earth):
mE = 5.98x1024 kg
msun = 1.99x1030 kg
Δd = 6.38x106 m + 6.96x108 m = 7.0238x108 m
G = 6.67x1011 N•m2/kg2
Fg = ?

Fg = G * mE * msun / Δd2
Fg = 6.67x1011 N•m2/kg2 * 5.98x1024 kg * 1.99x1030 kg / (7.0238x108 m)2
Fg = 1.61x1049 N

Average acceleration:
FNet = (Fg1 + Fg2) / 2
FNet = (3.53x1044 N + 1.61x1049 N) / 2
FNet = 8.05x1048 N

FNet = ma
a = FNet / mE
a = 8.05x1048 N / 5.98x1024 kg
a = 1.35x1024 m/s2



Assuming constant acceleration, the time the Earth takes to reach the Sun from its current position can now be calculated. Also assume that there is only one component to the Earth’s motion, which is towards the Sun, ignoring any of the orbital velocity it had at the beginning (making the initial velocity toward the Sun = 0):
a = 1.35x1024 m/s2
Δd = 1.50x1011 m
v1 = 0
Δt = ?

Δd = v1Δt + ½aΔt2
Δt = sqrt(2Δd / a)
Δt = sqrt(2(1.50x1011 m) / 1.35x1024 m/s2)
Δt = 4.71x10-7 s

Therefore it will take the Earth 4.71x10-7 s to reach the Sun.


And yes i know you see its not real physics but this is what we do in grade 12...its probubly really simple to the people that have been trying to help me here.

But anyways, here's what we wrote:

If the gravitational field were to change from 6.67x10-11 to 6.67x1011, the force of gravity would increase 1.0x1022 times its normal strength. If this occurred all planets and nearby objects (asteroids, comets, etc.) would be pulled towards each other due to the enormous gravitational field between them. Other stars and planets in our solar system would also be pulled towards each other. All of this mass would then be pulled into the black hole at the centre of our galaxy, the Milky Way. Each galaxy in the solar system would do the same thing and eventually the black holes would be pulled towards each other until there was one massive black hole with all of the mass of everything in the universe.

Due to the astronomical increase in the force of gravity, people’s lifestyles would change drastically, not only to survive, but also to continue living a long life. People would have to adapt to a new lifestyle and learn how to cope with a new kind of environment.

If this change did occur we would not be able to adapt in time because we would already be dead. Even if we knew this change was going to take place, we might have some hope of being able to adapt, and possibly find a way to reverse the change. If scientists knew this change was going to occur, they would need to create some sort of invention that would reverse the effects of gravity. If we made no changes all living organisms would die and all nonliving structures such as buildings would collapse in a fraction of a second. Humans would not be able to withstand the enormous force that would immediately crush them. There would be no future generations because all human life would have expired the instant G changed.

One possibility of reversing the effects of gravity would be to build some sort of transparent bubble-like enclosure that could either surround the entire Earth or every object on earth, and stop the change of the gravitational constant. These bubbles would act as a device that could either increase or decrease the gravity of the object. These bubbles could be used in many practical applications.

There would be many safety precautions that we would need to follow in order to keep ourselves alive.

One practical application to take advantage of this ability to change the amount of gravity would be in generating power. An example to generate more power would be in hydroelectric dams. When the water falls over a cliff, it could go through a section where gravity would be increased. When the gravity is increased it would make the water travel at a higher velocity which would increase its kinetic energy which would then generate enormous amounts of electrical energy when passing through the turbine at the bottom of the cliff. This would also mean that the water would only need to fall from short distances in order to create large amounts of energy. This means we could build smaller hydroelectric plants. This could also be applied to wind energy.

The bubbles, which could increase and decrease the force of gravity, could be used in health applications. Many people who are confined to beds or wheelchairs have an increased risk of pressure sores. With nursing help, people who are bed-bound are turned, repositioned and provided with skincare on a regular daily basis. Decreasing gravity would alleviate many pressure sores that these people would otherwise be at risk from.

In addition, these bubbles could be used to do research on humans in zero gravity. These effects could be studied on Earth rather than going out into space. The time and cost needed to study the effects of zero gravity in space would be eliminated.

In jets, there are G forces when the plane turns. If the pilots make too sharp of a turn, then blood rushes down from their head causing them to become unconscious. If there were no G forces there would be no limitations to the maneuvers that pilots could make when flying a plane and they would always remain conscious.

Increasing the force of gravity would be a unique and sure-fire security system to stop theft of valuable objects. If you increased the force of gravity on a valuable item, the thief would not be able to take it because it would be too heavy. There would have to be some type of system to ensure that no one would be able to change the force of gravity on the item of value.

A lower level of gravity would allow for easier transportation of goods and personal travel. For example, trucks need gas to move the mass of the objects inside the truck. Because there would be less gravity, it would take less energy to move the cargo in the truck, which would decrease fuel consumption. This would also decrease the amount of contact between the road and the tires. Roads would last longer and require less maintenance.

Disregarding the anti-gravity bubbles, the current laws of physics may or may not still apply when the universal gravitational constant changes. Since it is most likely that the universe would collapse upon itself into a singularity, similar to the conditions at the time of the big bang, it is difficult to predict how the universe would interact with itself. Scientists believe that the laws of physics that govern the universe today do not work in such extreme conditions. Some theories suggest that all of the forces in the universe combine into one force, so Newton’s gravitational constant and his equation of universal gravitation would probably not work.

and here's another calculation we put in, we did about 10 or something. I am not sure if this is the same one i put above but anyways:

Calculating the time it takes for Earth to reach the Sun with the new universal gravitational constant.

The force of gravity is the only force acting upon the Earth and is therefore the net force. The acceleration towards the Sun can then be calculated. As the Earth gets closer to the Sun (Δd decreases), the force of gravity will increase and so will the acceleration. Assume that the average acceleration of the entire trip, as constant acceleration, accurately represents the changing acceleration of what is actually happening. Also assume that the radius of the Earth and the Sun remain what they currently are (they have not collapsed into themselves with the increased gravity) and use the average distance of the Earth from the Sun. Calculating average acceleration, which will be the average of when Earth is at its current position and when it reaches the surface of the Sun:

Current position:
mE = 5.98x1024 kg
msun = 1.99x1030 kg
Δd = 1.50x1011 m
G = 6.67x1011 N•m2/kg2
Fg = ?

Fg = G * mE * msun / Δd2
Fg = 6.67x1011 N•m2/kg2 * 5.98x1024 kg * 1.99x1030 kg / (1.50x1011 m)2
Fg = 3.53x1044 N

At surface of Sun (where distance between centres is radius of Sun + radius of Earth):
mE = 5.98x1024 kg
msun = 1.99x1030 kg
Δd = 6.38x106 m + 6.96x108 m = 7.0238x108 m
G = 6.67x1011 N•m2/kg2
Fg = ?

Fg = G * mE * msun / Δd2
Fg = 6.67x1011 N•m2/kg2 * 5.98x1024 kg * 1.99x1030 kg / (7.0238x108 m)2
Fg = 1.61x1049 N

Average acceleration:
FNet = (Fg1 + Fg2) / 2
FNet = (3.53x1044 N + 1.61x1049 N) / 2
FNet = 8.05x1048 N

FNet = ma
a = FNet / mE
a = 8.05x1048 N / 5.98x1024 kg
a = 1.35x1024 m/s2



Assuming constant acceleration, the time the Earth takes to reach the Sun from its current position can now be calculated. Also assume that there is only one component to the Earth’s motion, which is towards the Sun, ignoring any of the orbital velocity it had at the beginning (making the initial velocity toward the Sun = 0):
a = 1.35x1024 m/s2
Δd = 1.50x1011 m
v1 = 0
Δt = ?

Δd = v1Δt + ½aΔt2
Δt = sqrt(2Δd / a)
Δt = sqrt(2(1.50x1011 m) / 1.35x1024 m/s2)
Δt = 4.71x10-7 s

Therefore it will take the Earth 4.71x10-7 s to reach the Sun.

Calculating the speed the Earth is traveling when it reaches the Sun.

v1 = 0
Δd = 1.50x1011 m
a = 1.35x1024 m/s2
v2 = ?

v22 = v12 + 2aΔd
v2 = sqrt(2(1.35x1024 m/s2)(1.50x1011 m))
v2 = 3.36x1017 m/s

Therefore, the Earth will be traveling 3.36x1017 m/s when it reaches the Sun.

Calculating the time it takes for Pluto to reach the Sun with the new universal gravitational constant.

Same assumptions as with Earth, calculate average acceleration:

Current position:
mPluto = 1.31x1022 kg
msun = 1.99x1030 kg
Δd = 5.89x1012 m
G = 6.67x1011 N•m2/kg2
Fg = ?

Fg = G * mE * msun / Δd2
Fg = 6.67x1011 N•m2/kg2 * 1.31x1022 kg * 1.99x1030 kg / (5.89x1012 m)2
Fg = 5.01x1038 N

At surface of Sun (where distance between centres is radius of Sun + radius of Pluto):
mPluto = 1.31x1022 kg
msun = 1.99x1030 kg
Δd = 1.18x106 m + 6.96x108 m = 6.9718x108 m
G = 6.67x1011 N•m2/kg2
Fg = ?

Fg = G * mE * msun / Δd2
Fg = 6.67x1011 N•m2/kg2 * 1.31x1022 kg * 1.99x1030 kg / (6.9718x108 m)2
Fg = 3.58x1046 N

Average acceleration:
FNet = (Fg1 + Fg2) / 2
FNet = (5.01x1038 N + 3.58x1046 N) / 2
FNet = 1.79x1046 N

FNet = ma
a = FNet / mPluto
a = 1.79x1046 N / 1.31x1022 kg
a = 1.37x1024 m/s2

Assuming constant acceleration, the time Pluto takes to reach the Sun from its current position can now be calculated. Also assume that there is only one component to Pluto’s motion, which is towards the Sun, ignoring any of the orbital velocity it had at the beginning (making the initial velocity toward the Sun = 0):
a = 1.37x1024 m/s2
Δd = 5.89x1012 m
v1 = 0
Δt = ?

Δd = v1Δt + ½aΔt2
Δt = sqrt(2Δd / a)
Δt = sqrt(2(5.89x1012 m) / 1.37x1024 m/s2)
Δt = 2.93x10-6 s

Therefore it will take Pluto 2.93x10-6 s to reach the Sun.

Calculating the speed the Pluto is traveling when it reaches the Sun.

v1 = 0
Δd = 5.89x1012 m
a = 1.37x1024 m/s2
v2 = ?

v22 = v12 + 2aΔd
v2 = sqrt(2(1.37x1024 m/s2)(5.89x1012 m))
v2 = 4.02x1018 m/s

Therefore, Pluto will be traveling 4.02x1018 m/s when it reaches the Sun.

Calculating the acceleration due to gravity on Earth.

Again, assume the radius of the Earth remains constant. Also, the object’s mass does not affect its acceleration due to gravity. Calculate acceleration due to gravity on Earth with new universal gravitational constant:

G = 6.67x1011 N•m2/kg2
mE = 5.98x1024 kg
∆d = 6.38106 m
g = ?

Fg = G * m1 * mE / ∆d2
M * g = G * m1 * mE / ∆d2
g = G * mE / ∆d2
g = 6.67x1011 N•m2/kg2 * 5.98x1024 kg / (6.38x106 m)2
g = 9.80x1022 m/s2


Calculating how much more energy can be generated by waterfalls.

Assume that the gravitational potential energy of the water at the top of the waterfall equals its kinetic energy at the bottom (no energy is lost). Also assume that the force of gravity (and acceleration due to gravity) does not change as the water gets closer to Earth. For this calculation use 1.0kg of water falling from a waterfall 100m tall. For normal conditions:

g = 9.8 m/s2
m = 1.0 kg
h = 100m
Eg = ?

Eg = mgh
Eg = (1.0 kg)(9.8m/s2)(100m)
Eg = 980 J

Under normal conditions, one kilogram of water has 980J of energy at the top of a 100m high waterfall.


With the new gravitational constant and the new acceleration due to gravity (calculated above), calculate the energy that 1.0kg of water has at the top of a 100m waterfall:
g = 9.80x1022 m/s2
m = 1.0 kg
h = 100m
Eg = ?


Eg = mgh
Eg = (1.0 kg)( 9.80x1022 m/s2)(100m)
Eg = 9.80x1024 J

Under the new conditions, one kilogram of water has 9.80x1024 J of energy at the top of a 100m high waterfall.

Calculate how much more energy the water has under these new conditions:
9.80x1024 J / 980 J
=1.0x1022

Therefore the water has 1.0x1022 times more energy at the top of the waterfall.
Since no energy was lost as the water fell, its kinetic energy at the bottom of the waterfall equals its Eg at the top. Therefore 1.0x1022 times more electrical energy can be generated by a turbine at the bottom of the waterfall, assuming the turbine is 100% efficient.

As you can see we assume a lot lol i hope this whole psot shows up.

 

[Ulysees]

i guess i will learn REAL physics when i go to university

Actually you will only learn more widely applicable mental models of physical things, but the absolute truth you will not learn: just like in the year 1900 there was no such thing as relativity taught in universities, likewise today there is no such thing as the physics of 2100 taught in universities. Does that mean all physics is wrong and there is no REAL physics? No, it means you have to remember the context of a problem, eg Newton is great for the motion of the planets, special relativity is better for fast moving things, quantum physics is useful for very small things, future physics is great for something as yet unknown, and so on. So you're in the context of Newton's equations, you use them, you bend them as suggested. At university you could do the same with more involved laws. Teachers at university are just as entitled as your High School teacher to ask hypothetical questions bending the laws of their respective physics, as an exercise promoting original thinking.

 

[jackster18]

We also took some cool vids of of youtube about space, black holes and stuff and the teacher liked it, also we made a newreport video saying what was going to happen. Heres the websites if you want to see the videos

im only able to post urls after 15 posts :( that's no good.

 

[rbj]

Actually you will only learn more widely applicable mental models of physical things, but the absolute truth you will not learn: just like in the year 1900 there was no such thing as relativity taught in universities,

no, but the Newtonian physics taught then is just as applicable today, for the domain where it was applied (speeds much slower than c and masses much larger than those of atomic particles).

likewise today there is no such thing as the physics of 2100 taught in universities.

i think they'll be teaching something about quantum mechanics and relativity in 2100, just as they are teaching some of the physics of 1700 in 2008.

At university you could do the same with more involved laws. Teachers at university are just as entitled as your High School teacher to ask hypothetical questions bending the laws of their respective physics, as an exercise promoting original thinking.

And, whether jackster approves or understand or not. It is not an issue of "bending the laws" or violating the laws of physics to see what happens. It is the operational meaninglessness of the question that you don't get and your ignorance (and that of the teacher) has been transmitted to jackster (which either he'll have to unlearn someday or he'll screw up like the science reporters of NY Times and he'll be caught with his pants down).

It is "bending the laws" to ask "what would happen if the mass ratio of protons to electrons changed significantly?" That is a meaningful question and since that ratio can't change, as far as I know, saying that it does represents a violation of physical law. But it's a violation that actually means something.

Asking "what would happen if the mass of the proton changed as well as all other particles in the same way?" That (as explicitly pointed out by Barrow) is a meaningless question. If you say that you created a model that demonstrates qualitatively how life would be different, the fact is your model or your interpretation of it is flawed. And this is what you did, if you say that you changed G, and nothing but G, and you came up with a model that shows that some lengths have gotten smaller while others have gotten longer, then I can say with complete confidence that, because there was a meaningful discriminatory difference (the ratio of those lengths changed), there must have been a meaningful cause (a ratio of like-dimensioned parameters changed). That means you changed something other than just G whether you realize or admit it or not.

jackster, you and your teacher and Ulysees may continue on in your bliss. I have done my best to try to hold the line on this encroachment of fallacy. other than maybe DaleSpam or some other regular, i haven't had any help, but have you noticed that the PF mentors didn't come down on me for propagating garbage?

 

[Ulysees]

While I don't normally reply to dishonest garrulousness that pretends not to understand things that are obvious to everybody else, I'll make one last exception.

There are academics doing research today who notice many unexpected astronomical observations (like how fast a galaxy is rotating), and match this unexpected data by modifying the law of gravity in the long distance. Effectively G becomes a function of distance r. The observational data is then matched perfectly. Others match the data by imagining the ghostly influence of invisible matter - as in "The Invisible Man", this ghostly presence is imagined to exert forces and mess up the observations without anyone ever seeing it.

Either way, "invisible man" or "variable G(r)", someone had to bend the existing laws. That's how progress is made. No one knows the absolute truth of physical things, anyone who pretends to do so is driven by financial or psychological issues.





If they didn't have the faculty to make the thought experiment

pretending not to , I'll make an exception

 

[Ulysees]

Ignore this, I forgot to delete it:

If they didn't have the faculty to make the thought experiment

pretending not to , I'll make an exception

 

[Harmony]

I apologize for interrupting the ongoing debate, but this thread looks intriguing to me.

From my limited comprehension of Physics, if we merely change the numerical value of gravitational constant, there will be no observable change, since the other units will change correspondingly too. That means, you can assign any number to G but get no observable change.

But what if we change the teacher's question? What if the teacher said: " What if the Planck Unit change in such a way that the gravitational force becomes larger?"
In that case, would what Ulysees and Jackster18 proposed earlier (planet size, black holes, etc.) valid?

 

[rbj]

While I don't normally reply to dishonest garrulousness that pretends not to understand things that are obvious to everybody else, I'll make one last exception.

whoo! i better go to etiquette school. is Miss Manners still around? (i honestly don't know, since i don't read a newspaper anymore.)

There are academics doing research today who notice many unexpected astronomical observations (like how fast a galaxy is rotating), and match this unexpected data by modifying the law of gravity in the long distance. Effectively G becomes a function of distance r. The observational data is then matched perfectly. Others match the data by imagining the ghostly influence of invisible matter - as in "The Invisible Man", this ghostly presence is imagined to exert forces and mess up the observations without anyone ever seeing it.

Either way, "invisible man" or "variable G(r)", someone had to bend the existing laws.

r is the distance from what? using cartesian coordinates, in a scenario with multiple bodies all contributing to the gravitational field, are you saying that at some fixed point (x₀, y₀, z₀), is the G there not some specific value? or does it change when the bodies around it that are contributing the the field, when those bodies move around? if r means the distance to each body, then it's a change from the inverse-square law. so that's bending the physical law (changing the GMm/r² to something else) , but it's not a changing G. it's a different issue.

if the existing law prevailed but was "bent" by changing G (say, w.r.t. time, but you could ask the same question as if G was different in the galaxy Andromeda from our G), if all dimensionless ratios of like-dimensioned quantity remained the same, no one will know the difference. if some dimensionless ratio (that we normally believe to be constant) has changed (which causes a bona fide different world that would be perceived as different by us and our measuring instruments), it's the dimensionless constant that's salient. that's the only thing that i have said from the beginning and it's the only thing I've not moved away from.

that was the original question of the thread. " If the universal gravitational constant was changed from 6.67 ...". if G was changed from what we think it is from measurement using our meter sticks, atomic clocks, and kilogram standards, if nothing else was changed (this was explicity specified by both you and by jackster), then the fact is that no mortal with instruments that cannot somehow step out of the context where they are subject to the laws of physics will know the difference. If your simulation program indicates an operational difference (i.e. a resulting simulation that isn't just like the normal one, with the current G, but with scaled time or length or mass), e.g. a result where some lengths get longer and other lengths get shorter (that's a real difference), then the parameter(s) whose change was causing that is more fundamentally a dimensionless parameter. likely it is the masses of all of the particles, relative to the Planck Mass. i.e. if you said that this law:

$$F = G \frac{m_1 m_2}{r^2}$$

was changed to

$$F = (aG) \frac{m_1 m_2}{r^2}$$

where (aG) is the new G, i would say, think of it in terms of Planck Units, that the more fundamental representation is

$$F = G \frac{(\sqrt{a}m_1) (\sqrt{a}m_2)}{r^2}$$

and it's the masses that increased or decreased. Note that it's the same G, but we're postulating that all masses are getting scaled by the square root of whatever you're scaling G in your simulation program. But if G remains constant, even if we change it, then those masses changed w.r.t. a unit mass that is defined in a system of units where G is fixed to a constant value. That is true for both Planck Units and Stoney Units. Assuming that all of the celestial bodies are made up of the same molecules with the same atom having the same sub-atomic particles, if we chose Planck Units to measure things, what happened is that the masses of all of these particles relative to the Planck Mass got scaled by $\sqrt{a}$. e.g. for the electron:

$$\frac{m_e}{m_P} \rightarrow \sqrt{a}\frac{m_e}{m_P}$$

or

$$\frac{m_e}{m_P} \rightarrow \sqrt{a} \frac{m_e}{\sqrt{\hbar c/G}}$$

See how that is the same as

$$\frac{m_e}{m_P} \rightarrow \frac{m_e}{\sqrt{\hbar c/(aG)}}$$ ?

If you chose to measure things in, say, Atomic Units (here the unit mass is defined to be the mass of the electron and G is not normalized), then you would say G changed. But Nature doesn't give a rat's ass which system of units we use. If you keep in mind that when we are using a system of units to measure things, just like measuring a length of something with a ruler and counting tick marks (a dimensionless number), we are measuring that quantity against the unit definitions resulting in dimensionless numbers. When your measurement of G appears to change, it is the value of G relative to the unit value of the kind of quantity, the dimension, that G also posseses. In SI, G = 6.67428 × 10^-11 m³ kg^-1 s^-2. In Atomic Units G is 2.4005 × 10^-43 L_A³ m_A^-1 t_A^-2 (where L_A, m_A, and t_A are the units length, mass, and time in Atomic Units; and if i didn't screw up the calculation). but there are expressions for those Atomic Units and then G comes out to be (making the substitutions)

$$G = 2.4005 \times 10^{-43}\left( \frac{\hbar^2 (4 \pi \epsilon_0)}{m_e e^2} \right)^3\left( m_e \right)^{-1}\left(\frac{\hbar^3 (4 \pi \epsilon_0)^2}{m_e e^4} \right)^{-2}$$

or

$$G = 2.4005 \times 10^{-43} \left( \frac{\hbar^2 (4 \pi \epsilon_0)}{m_e e^2} \right)^3 \left( \frac{1}{m_e} \right) \left( \frac{m_e e^4}{\hbar^3 (4 \pi \epsilon_0)^2} \right)^{2}$$

or

$$G = 2.4005 \times 10^{-43} \frac{e^2}{m_e^2 (4 \pi \epsilon_0)}$$

or

$$G = 2.4005 \times 10^{-43} \frac{e^2}{(4 \pi \epsilon_0) \hbar c} \frac{\hbar c}{m_e^2}$$

or

$$G = 2.4005 \times 10^{-43} \alpha \frac{\hbar c}{m_e^2}$$ ( $\alpha$ is the Fine-structure constant, a very important dimensionless and fundamental constant and it's about 137.035999^-1)

or

$$G = 2.4005 \times 10^{-43} \alpha \frac{(m_P^2 G) }{m_e^2}$$

or finally

$$\frac{m_e}{m_P} = \sqrt{2.4005 \times 10^{-43}} \sqrt{\alpha}$$

Expressing in Atomic Units what G is, is precisely the same as saying what the ratio is of the mass of electron to Planck Mass is (with this factor of $\sqrt{\alpha}$ tossed in. Now if you change that 2.4005 × 10^-43 value, you have done exactly the same as changing the mass of the electron to Planck Mass ratio. Or you changed the Fine-structure constant. Or a little of either. But the point is, no matter which way you look at it, no matter how you define your system of units, when you think you've observed a change in a dimensionful constant like G, what really changed, what fundamentally changed, the important thing that changed, the quantity that really matters, is in the last analysis, a dimensionless parameter which can be, or usually is, a ratio of like-dimensioned quantities.

That, Ulysees and jackster, is the lesson. And I'm done presenting it in every which way, because, frankly, I'm running out of steam and if you don't get it, you just don't get it.

 

[Mike442]

The universe would collapse inward upon itself since the inward forces of gravity would no longer be balanced by the outward forces being driven by dark energy. Einstein addressed this problem by introducing the cosmological constant into his equation of general relativity to keep the universe in balance.

 

[EternityMech]

escape velocity would radically increase

 

[RidgeRunner67]

I wished I had seen this question sooner. I never developed a comfort level for G as a constant when first introduced to it nearly 30 years ago. RBJ references G as a holding constant (consistent with most in the physics community) when applying <a> as a function of the square root of mass (presumably equally applied), but I struggle with this assumption.

It is well known that when in the attempts to ratify the Grand Unified Theory (GLT) and Unified Field Theory (UFT) that it is gravity that cannot reconcile with the other forces (strong, weak, EMF).

Excerpt from University of Tennessee, Knoxville astronomy/cosomolgy site (http://csep10.phys.utk.edu/astr162/lect/cosmology/forces.html):

"Theories that postulate the unification of the strong, weak, and electromagnetic forces are called Grand Unified Theories (often known by the acronym GUTs). Theories that add gravity to the mix and try to unify all four fundamental forces into a single force are called Superunified Theories...

Grand Unified and Superunified Theories remain theoretical speculations that are as yet unproven, but there is strong experimental evidence for the unification of the electromagnetic and weak interactions in the Standard Electroweak Theory. Furthermore, although GUTs are not proven experimentally, there is strong circumstantial evidence to suggest that a theory at least like a Grand Unified Theory is required to make sense of the Universe."

It is also well known that The Universal Law of Gravitation (ULG) breaks down when explaining the behavior of black holes. A simple logic statement could place into question this law:
- Black holes exist in our universe.
- The ULG cannot explain the behavior of mass near a black hole.
- Ergo, the ULG cannot be considered a truly universal equation.

Although largely practical for earth, our solar system, and even surrounding areas of the galaxy (perhaps equidistant to a black hole purported to be located at the center of our galaxy), G is practical in perhaps a relatively narrow context but not yet proven for the entire universe as we know it.

We also know that in Einstein's General Theory of Relativity (GTR) that length and time do not become significantly distorted until approaching the speed of light. Is it possible that for those who claim that the universe as we know it could not exist without any other constant other than G has overlooked an analogous possibility, thereby rendering G as an oversimplification of the actual behavior of gravity?

I wish I had the physics skills and experience to prove it, but if I was a professional physicist, I would begin with the mass of a black hole (using the above postulate, the center of the galaxy), and the distance from which it exists from the source location (say earth). I realized these are the same concepts applied in the ULG itself, but extending the same principle to G leads to two possibilities:

1. That the ULG is intact in formula, but incomplete in application. When applied, I could appreciate RBJ's interpretation that it is possibly mass that is underestimated in quantity in a black hole, and a factor of the square root of <a> needs to be applied to justify an adjustment for mass.
Consider this scenario of conventional wisdom: a particle with mass gets trapped in the gravitational field of a black hole and begins to accelerate towards the event horizon. As it gets closer, it will acquire mass therefore requiring additional energy to continue the acceleration.

Where does this mass come from? How does mass get "created"? Does this not violate another one of Newton's principles that mass cannot be created or destroyed? Even in the application of Special Relativity, mass can be converted to energy and vice versa, but in the above example, how do BOTH get created at the same time? Now if G increases (to be clear, I speak of G NOT as a constant, but as the purpose of what G arguably could represent), this negates the need to explain how a single particle must gain mass AND energy at the same time as it approaches the event horizon.

2. The other possibility is that the purpose of G in the ULG is oversimplified as a constant, and while practical for situations in context to our local area of the galaxy, can we really argue that G is truly representative as a universal constant if the equation cannot explain all gravity-based behavior in the universe? Would G be better represented by a formula similar to the GUT which takes into account the behavior of the relationship of matter and energy under extreme but possible circumstances (e.g. >0.99c)? Or conversely, does the fundamental equation of the ULG need to be more broadly defined to include these situations, which by definition would automatically change at a minimum the constant itself?

This is why I love the physics teacher's original question: what if G was 6.67 x 10^+11 Nm^2/kg^2 and Earth was smushed into the size of a golf ball? Doesn't that start to sound consistent with the scenario of what would happen to the Earth if it was hurled into a black hole? One could argue the mass of a black hole could easily be 1 x 10^22 greater than the mass of the sun, thereby rendering the ULG intact--granted so, but it doesn't take into account the possibility of gravitational radiation or space-time warping that occurs in extremes near the event horizon. Interestingly enough, G is used in the GUT, but the initial verification of the theory was a solar eclipse--I'm not aware if the GUT has ever been (or even could be) tested on the effects of gravity near a black hole, but it would be an interesting exercise indeed.

Issac Newton introduced the ULG in Philosophiæ Naturalis Principia Mathematica in July 1687, which is largely the foundation for the defense of gravity's behavior in modern-day defense to the limitations of GUT. I don't recall Issac Newton having the ability to apply this theory to astronomical phenomena such as quasar, supernova, and black holes, and time/space dilation. Some of this behavior is picked up in Special Relativity, which is considered to be consistent with Coulomb's Law and Maxwell's Theory, which tend to be more gravitomagnetic in nature, but they still assume G as a constant (and possible crutch). These equations, as far as I'm aware do not fully reconcile with GTR with regard to explaining the behavior of gravity, nor the explanation for G.

(from PF) Feynman once commented that gravity may be a pseudo force - it is always proportional to mass just as is inertia - if we were in a centrifuge we would not be aware of why we are forced against the wall of the container - but its really an inertial thing - an apparent or pseudo force that is always propertional to mass. Feynman concluded - perhaps gravity is due to the fact that we do not have a Newtonian reference frame.

I hope a physicist reads this reply, can find enough use in it to begin questioning the validity of G, exploring whether G or the ULG itself is oversimplified, and if so, to what extent does this change the view of the ability to better integrate gravity into the GUT and UFT? Or at least to help explain how my logic is flawed.

Would be most interested in any response to this view...