# If the universal gravitational constant was changed from 6.67 X 10(continued on post)

## Main Question or Discussion Point

If the universal gravitational constant was changed from 6.67 X 10^-11 to 6.67 X 10^+11 what would happen?
Hi. I am doing a physics project for grade 12 physics. Here is the question: The universal gravitational constant, G, is suddenly changed from 6.67 X 10^-11 Nm^2/kg^2 to 6.67 X 10^+11 Nm^2/kg^2. Discuss the implication of such a change.
- What changes would there be in your life? The life of your descendants?
- In what ways would life be different? What safety precautions would you have to exercise?
- Think about everyday life and how it would be changed in such an environment.
- You have all the money and resources that you need. How are you going to redesign the world to accommodate this change?

So far i have calculated that if this did occur, FG would be 1.0 X 10^22 times stronger than what it would normally be on earth. So basically everything would just be crunched into a ball. Actually everything in the universe would just get smashed together into a huge ball. If you can help try and answer some of the question above, thanks. It’s worth 12% of my mark :(.

My teacher gave me a hint and told me to calculate how long it would take for the Earth to crash into the sun and compare that to how long it would take for Pluto to do the same.

This is the way it is being marked is:

Creativity #/10
-originality
-entertainment value
-insight

Sensory Impact #/10
-neat
-quality
-time/effort

Physics Implications #/10
-references to kinetics and dynamics
-mathematical calculations
-insight

Presentation:
Multimedia
-report
-comic
-magazine
-newspaper
-text/photos
-slide show
-oral presentation
-dramatic presentation
-video
-power point
-poster
-etc...
So we can basically present it any way we want my teacher said.

Must be neat/professional/signs of time and effort/eye catching/holds attention

Physics Content:
-Reference to laws (Newton’s 3 laws)
-how changes affect our lives
-calculations to quantify the effects
-demonstrates a clear understanding of Universal Law of Gravity

So as I said, if anyone can help I would greatly appreciate it because this project is worth 12% of my mark.

## Answers and Replies

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rbj
okay, Jackster, this might be difficult to get, and i wouldn't have understood it when i was in high school (which was 34 years ago), but, it turns out that it is actually a meaningless question about what operationally changes if some dimensionful parameter or "constant" changes. when we measure a physical quantity, we do so against a like-dimensioned standard (often this is called a "unit") and that ratio of like-dimensioned quantities, a dimensionless number, is the salient quantity that we measure or simply perceive in our everyday experience. (e.g. when we measure a length of something, we are actually counting tick marks on a ruler or tape-measure. similarly, when we measure a period of time, we are counting ticks of some kinda clock.)

if you go to the relativity forum, you will see similar questions about why the speed of light, c, is what it is and the same issues regarding measurement and perception apply. whether it is G or Planck's constant h or c, all of these quantities can be set to the constant 1, if you define everything in terms of Planck Units. i would recommend to check out the Wikipedia article regarding Planck units, but recently some editors have really f$\mu$cked it up. so if you go to that article, hit the "history" tab and view a version that is a couple months old, and you will have a better read.

the thing is that Nature doesn't give a rat's ass what units we humans (or the aliens on the planet Zog) choose to use. if we choose to measure things in terms of Planck units, there is no graviational constant, no Planck's constant, no speed of light to change. they are all normalized to 1.

now, if you think that you measured a change in any of these dimensionful parameters (given some anthropocentric units like meters, kilograms, and seconds), what really changed was the number of Planck Lengths per meter or the number of Planck Times per second or the number of Planck Masses per kilogram. those numbers are dimensionless and asking why those numbers are what they are is the meaningful question. but if you measure and define everything in terms of Planck units, there simply is no G, c, or $\hbar$ to vary, they are removed from all mathematical expressions of physical law.

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jackster18,

If gravitational force were increased by 22 powers of ten, it might not affect the other fundamental forces (strong, weak, electromagnetic - still a factor of 1015 removed) directly, but it most likely would affect the size of masses and most certainly their orbits.

In addition to changes in the Planck units (like the Planck mass), cosmological parameters including the horizon radii of the universe and black holes would probably reduce 1022 times. Look out also for effects of gravity that could rely on its strength squared, maybe feeding back into such calculations.

Remember that homework belongs in another forum.

- What changes would there be in your life? The life of your descendants?
- In what ways would life be different? What safety precautions would you have to exercise?
- Think about everyday life and how it would be changed in such an environment.
- You have all the money and resources that you need. How are you going to redesign the world to accommodate this change?
Aren't these funny question to ask about a change that would utterly destroy the whole reality that we know? Similar in anticlimactic characteristic to asking someone: Suppose our entire universe were suddenly annihilated -- how would you reorder your personal priorities for the rest of the afternoon? Everything everywhere is going to be obliterated tomorrow: have you prepared yourself by stocking up on flashlight batteries and bottled drinking water? This sounds like a psychology experiment about how the phrasing of a question can alter the boundaries in which people conceive of an answer.

Hmm. Calculate your Schwarzchild radius, that of your car, your house, Sol, etc. with each value.

rbj
jackster18,

If gravitational force were increased by 22 powers of ten, it might not affect the other fundamental forces (strong, weak, electromagnetic - still a factor of 1015 removed) directly, but it most likely would affect the size of masses and most certainly their orbits.

In addition to changes in the Planck units (like the Planck mass), cosmological parameters including the horizon radii of the universe and black holes would probably reduce 1022 times. Look out also for effects of gravity that could rely on its strength squared, maybe feeding back into such calculations.

Remember that homework belongs in another forum.
Hmm. Calculate your Schwarzchild radius, that of your car, your house, Sol, etc. with each value.
okay guys, the issue is what would happen if G changed its value with no reference to a change in any of the 26 or so dimensionless fundamental universal constants. there's a reason that neither G nor c nor $\hbar$ are on that list of 26. if all of the dimensionless constants remained constant, you could not know if there was a change in one of these dimensionful constants in and of itself. if, say, the ratio of the Bohr radius (about the size of atoms) to the Planck Length remains constant, if the ratio of the elementary charge to the Planck Charge, if the ratio of the period of Cesium radiation (that they base the second on) to the Planck Time were constant, if the ratio of the particle masses to the Planck Mass remained constant, if none of those change, a change in G is meaningless. everything else would adjust in such a way so that when we measure G, it would, in terms of "new" meter sticks, kilogram standards, and cesium clocks, come out to be the same, from our ability to measure it.

okay, if you say "a change in G means that one (or more) of those ratios changed", then i would say that the root issue is that that dimensionless ratio (or ratios) changed. it's the dimensionless parameters that are the salient parameters. the Wikipedia Planck units article at least used to quote from a book by John Barrow about the Constants of Nature. i'll try to find it and quote it here.

rbj
that quote from Barrow is regarding the same question except it's c that's changing. but the same principle regarding dimensionful vs. dimensionless varying "constant" applies.

[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck mass mP] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged.
John Barrow, 2002, The Constants of Nature

What matters is that the change in G is relative (in the sense of measurement units, not necessarily velocity or acceleration dependence) to the observer. Therefore, whatever is an object to this observer would embody the change in G. Dimensionless fundamental "constants" are no more fundamental or constant than the established G with respect to the observer.

rbj
What matters is that the change in G is relative (in the sense of measurement units.
okay, so today you measure the length of some thing to be 10.01 cm in length using some ruler and tomorrow you measure the same thing (with the same ruler) to be 10.03 cm. do you know that it was that thing that changed or if it was your ruler that changed? or maybe a little of both? all you really know is that ratio of lengths changed. that is fundamentally all you know.

Therefore, whatever is an object to this observer would embody the change in G.
dunno what that means.

Dimensionless fundamental "constants" are no more fundamental or constant than the established G with respect to the observer.
that, i completely disagree with. and i think that physicists like Barrow, Baez, and Duff would also disagree with it.

To be observed as true constants, dimensionless fundamental constants require simultaneity for demarcation and comparison of at least two spacetime points. Objectivity requires the thing and the ruler likely nonsimultaneous (nonidentical), i. e., compared between at least two (probably four) events. For measurement, the ruler requires 2 points in space, the thing 2 points in space, and the lapse of time 2 points each for ruler and thing.

The result is that dimensionless parameters may be constant or not, but to a participating observer, most likely not (vanishingly simultaneous). One does not know whether the laboratory standard (ruler) is perfectly objective in comparison to the quantum mechanics of measurement. Also, when we observe the value of either a dimensional or dimensionless parameter, we are comparing it to an internalized standard of the same dimension - a third improbability of inconstancy.

Thanks everyone for trying to help, i do appreciate it, but I have no clue what anyone is talking about. Im only in grade 12, i think i know less then 5% of what you guys are saying. If possible please put it in lame mans terms :/ .

Also some of the words everyone is using makes my mind spin. I guess my vocabulary is low :(.

The Newtonian constant G affects the strength of gravitational attraction. It determines the orbit of planets, the weight and acceleration of massive objects, (at least in part) the birth and death of the universe, and the bending of spacetime - most prominently near black holes. If you increase the value of G by 1022, it will increase all of these forces likewise.

rbj
Thanks everyone for trying to help, i do appreciate it, but I have no clue what anyone is talking about. Im only in grade 12, i think i know less then 5% of what you guys are saying. If possible please put it in lame mans terms :/ .
Also some of the words everyone is using makes my mind spin. I guess my vocabulary is low :(.
i'm trying not to use big words or anything like that. i just want you to consider the thought: what if you today measured some thing, say the height of your favorite beer mug, to be 15 cm tall, and tomorrow you took the very same ruler and measured the very same beer mug and found it to be 16 cm tall. what changed? was it the beer mug or was it the ruler (or maybe a little of both)? whatever it was, the net thing you did is measure a dimensionless quantity by counting the tick marks on the ruler. that is the way it is with any physical experiment, any physical measurement. we only measure dimensionless values. we only perceive the mass or size or time of stuff in relative terms. if some dimensionless constant changes (like the ratio of proton mass to electron mass, which is about 1836 something) then we know the difference. if it's just a single dimensionful quantity that is alleged to have changed, we would not know the difference. nothing would be different, including what we think the value of that dimensionful quantity is.

The Newtonian constant G affects the strength of gravitational attraction. It determines the orbit of planets, the weight and acceleration of massive objects, (at least in part) the birth and death of the universe, and the bending of spacetime - most prominently near black holes. If you increase the value of G by 1022, it will increase all of these forces likewise.
Loren, the newtonian constant, G, is something that we measure with our meter sticks, clocks, and kilogram standards. it does not represent a parameter of the universe that Nature defines or even knows about. like the speed of propagation of the fundamental interactions (E&M, gravity, nuclear forces), what we denote as c, nature does not define a particular quantitative value for it, except that it is real, positive, and finite. that's it. Nature does not decree it to be 6 x 10-11 anything. that value is a construct purely of human origin that had its birth when Cavendish constructed the first experiment to measure this gravitational interaction using meters, kilograms, and seconds (maybe he used English units, i dunno).

you should take a good look at the Wikipedia articles on Planck Units and Fundamental Physical Constants. but look at a version of Planck Units before March 2008 like this one, because some new editors have screwed the article up, and i am no longer trying to defend it from BS. please read the section entitled Planck units and the invariant scaling of nature (where i got that Barrow quote). the example there was about the meaning of a changing c, but it could be the meaning of a changing G and the principle would be the same. if any single dimensionful constant changed, yet all of the dimensionless constants (all of the dimensionless ratios of like-dimensioned physical quantity) remained the same, no mortal would notice any difference. if G suddenly increased by a factor of 1022, then the Planck length would be (from God's POV, not ours) 1011 times longer. but since the axiom is that the dimensionless constants remain the same, so would the meter be 1011 longer, we would 1011 times taller and fatter (from "God's POV" or whatever observer who is unaffected by physical law) but we wouldn't know the difference. the size of and distance between planets would increase (from "God's POV") by the same factor. but relative to us and our meter sticks, they would appear to be just the same size as before. the Planck Mass would be reduced by factor of 10-11 and so would the masses of atoms, people, planets, and the big steel balls in the Cavendish experiment. clocks would tick slower by the same factor, including the period of Cesium radiation we use as a time standard. but so would our minds and our sense of time. when we run the Cavendish experiment to again measure G, it would, from our mortal perspective, come out to be the same number as it had before.

if we measure any changing in G (conceivably a change in measurement is conceptually possible), the net quantities measured (that we determine G from, in terms of our meters and kilograms and seconds) are all dimensionless numbers. it is those dimensionless numbers that are salient. G is just a human construct. an artifact of the units we arbitrarily established to measure things and Nature doesn't give a rat's ass what units we use to measure things.

edit: here is a reference to that article by Michael Duff: Comment on time-variation of fundamental constants where he takes on specifically claims of a varying c, but applies the same reasoning to G.

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I understand what your traying to say. That you could measure in any units you wanted. Like my name is Jack. I could say...1 m = 2.35 Jack's. But your trying to say that if G did change everything else would change along with it?

What Im trying to say is that if just G itself changed, along with nothing else changeing what would happen, if you were even able to watch it happen.

And yes, i understand what you mean about the ruler, that you dont really know what changed...so like, if G did change ur saying that we wouldnt really know if G changed. It may have been something else that changed, or something else changed along with G chaninging at the same time? And this is because if G changed, other things would change along with it...as in us getting fatter you said, so really we would see no change at all. I think i get what you mean.

I will try and find that article your talking about.

On the link you had set up i found this by clicking (V1) at the bottom:

The possible time variation of dimensionless fundamental constants of nature, such as the fine structure constant alpha, is a legitimate subject of physical enquiry. By contrast, the time variation of dimensional constants, such as h-bar, c, G, e, k..., which are merely human constructs whose number and values differ from one choice of units to the next, has no operational meaning. To illustrate this, we refute a recent claim that black holes can discriminate between two contending theories of varying alpha, one with varying c and the other with varying e.

But how do i get the rest of the article?

What my teacher is basically asking for is what would happen if the force of gravity is increased. Meaning if just the force of gravtiy increased and everything else stayed the same.

Dale
Mentor
rbj's point is maybe a little advanced for high-school level physics, but perhaps it might help to learn a little about http://en.wikipedia.org/wiki/Planck_units" [Broken]. In Planck Units all of the fundamental constants like G, c, and h are set to 1. Although the resulting units would be a little difficult to use in everyday situations they represent a more fundamental system of units than SI.

Usually when textbooks talk about G they talk about how small it is. They compare it with the Coulomb constant which is relatively large and talk about gravity being a weak force. However, in Planck units the question is a little different. In Planck units gravity and electrostatic attraction are the same "strength", and what is different is that the mass of a proton is much smaller than its charge.

So, instead of asking "why is gravity so weak and what would happen if it were stronger?" you could ask "why are the masses of elementary particles so small and what would happen if they were greater?" The answer will be what your teacher is actually looking for, but with more insight into the nature of unit systems and universal constants.

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Thank you rbj and DaleSpam for persevering and elucidating why units like those of the Planck system can be arbitrarily fixed, most commonly to 1. I still entertain whether the observer, through the relativity or uncertainty of its measurements, can disturb the objectivity of such a system. Just a thought.

rbj
But how do i get the rest of the article?
hit the PDF link in the upper right.

Dale, you're right about the level of this, and i tried to warn Jackster about that. I just didn't want him doing this paper for HS and saying stuff like that Mr. Tompkins story.

jackster, to be clear, if just G changed to another real, finite, and positive value and none of the dimensionless fundamental constants that Baez listed changed, you and every other mortal (who, along with your tools and instruments, must be subject to the same physical laws that have G in them) can not know the difference. if the number of Planck Lengths per meter remain constant, and the number of Planck Times per second remain constant, and the number of Planck Masses per kilogram remain constant, then when we set about to measure G again, we'll measure it to be the very same value.

now, if we somehow measure it to be a different value, and we notice it and say to each other "G appears to have changed its value to [whatever]", then what happened is either one, two, or all three of these things changed: the number of Planck Lengths per meter changed, or the number of Planck Times per second has changed, or the number of Planck Masses per kilogram has changed. being ratios of like-dimensioned stuff, those are dimensionless numbers and if they change, it's salient and we'll know it.

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RBJ, when I have time I am going to read the references you mention in more depth.

Still, in this case, it is clear that the teacher wants to know what would happen if when you calculated the gravitational force using F=Gmm/r^2, you used a different numerical value of G.

rbj
RBJ, when I have time I am going to read the references you mention in more depth.

Still, in this case, it is clear that the teacher wants to know what would happen if when you calculated the gravitational force using F=GMm/r^2, you used a different numerical value of G.
well, if the M and m and r are the same, then F will come out different.

but if the question is what if G changes and only G changes, then my response is that all by itself, it's an "operationally meaningless" question. such a difference is "observationally indistiguishable". (quotes from Duff and Barrow.)

or another way to say it is if we measure everything in terms of Planck Units (and we are allowed to do that, Nature doesn't care what units we use), there simply is no G to vary, no c to vary, no h to vary.

Originally Posted by RBJ
"but if the question is what if G changes and only G changes, then my response is that all by itself, it's an "operationally meaningless" question. such a difference is "observationally indistiguishable". (quotes from Duff and Barrow.)"

This is what the teacher wants. And to my teacher it is operationally meaningful...i guess.

originally posted by RBJ
"or another way to say it is if we measure everything in terms of Planck Units (and we are allowed to do that, Nature doesn't care what units we use), there simply is no G to vary, no c to vary, no h to vary."

This plank units thing was also posted by other people as well. Yes i do appreciate everyone trying to help but my teacher does not want anything to do with Plank Units. We dont learn that in grade 12 and i asked him about it and he said not to put stuff like that in it.
__________________

rbj
well, i can't help you about your teacher. your teacher has company with some physicists who have proposed the possibility of such dimensionful universal "constants" changing. but, from what i can tell from here at PF, at the sci.physics.research newsgroup, from blogs and webpages of various active leading physicists and from their publications, the constants of Nature that are salient are only the dimensionless constants. probably the two most commonly referred to are the Fine-structure constant and the Proton/electron mass ratio.

whether they are called "planck units" or "foos and fargs", you should be able to tell your teacher and your class (if you're presenting this) that you can always choose units that can make G be whatever finite and positive value you want (so why not one).

here is a little more of this. for every measurement system, there are Base Units and there are Derived Units. most often the base units include the units of length, time, and mass. ("length", "time", and "mass" are dimensions of physical quantity, no matter what units one might use to measure such. you can add, subtract, compare and equate physical quantities only if they have the same dimension. it is not meaningful to add one meter to one kilogram. but with appropriate conversion factors you can meaningfully add 1 meter to 1 inch.)

now in the SI system of units, these base units (meter, kilogram, second) were determined completely independently and anthropocentrically. that's history. then we came up with derived units for quantities like velocity (meters per second), acceleration (meters per second per second), force, and energy. now let's take a look at the last two:

we know that Force is proportional to the rate of change of momentum or, if the mass is constant, proportional to mass times acceleration. we would write this as:

$$F \propto m a$$

or

$$F = K \ m a$$

where K is our constant of proportionality. now, i could define a unit of force i'll call a Farg. and i'll define a Farg so that 1 Farg of force will accelerate 2 kilograms by 1 m/s2. without units in the equation that would look like

$$F = \frac{1}{2} \ m a$$

m=2, a=1, and we would be left with F=1. that constant of proportionality is not just 1/2, it is "1/2 Farg-second2 per kilogram-meter". now you and/or your teacher might suggest that is just stupid. why choose a unit of force so that you have to remember that conversion factor in the equation for Newton's 2nd law? so, instead, smarter people than me choose a unit of force that they called a "Newton" such that 1 Newton of force will accelerate 1 kilogram by 1 m/s2. now then you would still have

$$F = K \ m a$$

but now K would be a conversion factor that is "1 Newton-second2 per kilogram-meter". if you considered force to be dimensionally a completely different quantity than mass times acceleration, you would need that conversion factor in there just to convert quantities of dimension "mass times acceleration" into a quantity of dimension "force". but if instead we say that "force is precisely the same quantity as mass times acceleration", then we don't need that K at all. we can say

$$F \ = \ m a$$

and understand that a Newton is not just proportional to a kilogram-meter per second2, that it is a kilogram-meter per second2. that's what a Newton means. it was deliberately defined to be none other than a kilogram-meter per second2 so that we can say F=ma and completely get rid of the constant of proportionality. This is what is meant by the unit of force, the "Newton", is a "derived unit", not a base unit.

That's also what they did to define a unit of energy, the Joule. energy (or "work") is not just proportional to force times distance, we will define it to be the same as force times distance. from that we get that a Joule is a Newton-meter or a kilogram-meter2 per second2. Again, the unit of energy here in SI, is a derived unit, not a base unit.

Now, here is where your teacher has to pay attention: we defined the meter, kilogram, and second completely arbitrarily (or anthropocentrically). that is we, from the POV of Nature, pulled these unit definitions from out of our butt. but they are there; we have a unit of length, a unit of mass, and a unit of time. Then using those units (that we pulled out of our butts) we set out to measure some physical phenomena, some which appears to us to be universal, particularly the speed of light c, the gravitational constant G, and Planck's constant $\hbar$. Given those base units we started with, those 3 quantities are measured to be numbers. We can write them down. But that is because those unit definitions were fixed, predetermined with no prior consideration of the speed of light c, the gravitational constant G, and Planck's constant $\hbar$.

But suppose, instead, we think like we were thinking above in how we defined the derived unit of force and unit of energy. What if we held off and said, "Let's not define our units of length, mass, and time just quite yet. Let's play around with their definitions" - we have 3 degrees of freedom to fiddle with, until we get definitions of length, mass, and time so that in the physical equations that use c, G, and $\hbar$, those numbers come out to be 1 in terms of these units. Are we not allowed to do that? Would nature care? Does Nature give a rat's ass what units we use to measure stuff?

If we do that "there simply is no G to vary, no c to vary, no h to vary" but there is somethings that could change that we (or Nature) would care about. The meter is about as tall as we are (within an order of magnitude). If the number of Planck Lengths (that's the unit of length we just defined above) per meter changed, then sometime substantive changed. Life would be different. It's "observationally distinguishable" or "operationally meaningful". But the number of Planck Lengths per meter is a dimensionless number. If your meter stick is a "good" meter stick, it should not be losing or gaining atoms. If the number of Planck Lengths per meter (stick) changed, that means the number of Planck Lengths in the size of an atom (somewhere around what is called the Bohr radius) has changed.

So that is one place where such a meaningful question could be posed to the physicists: "What would happen if the number of Planck Lengths per Bohr radius changed? How would life be different?" You could do the same with time: "What would happen if the number of Planck Times changed in a period of Cesium radiation (that they base the second on)? How would that change things?" And you can ask such about mass: "What would happen if the amount mass of atomic particles (in terms of the Planck Mass) has changed measurably? How would that change things?" Asking those questions are meaningful because they are asking about dimensionless numbers that would be the same no matter what system of units are used. If we thought that we measured a change in G or c, it's really because one or more of those dimensionless ratios changed, and that is the salient question to think about.

If this cannot be at least mentioned in your assignment, if your teacher won't allow that, then he/she is being ignorant and you should send him/her over here and we'll straighten him/her out.

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Dale
Mentor
This plank units thing was also posted by other people as well. Yes i do appreciate everyone trying to help but my teacher does not want anything to do with Plank Units. We dont learn that in grade 12 and i asked him about it and he said not to put stuff like that in it.
That is pretty sad. That kind of thing really discourages intellectual curiosity. My recommendation is not to fight it. If he specifically said to not do it rigorously then there is nothing left for you but to prepare a boring analysis.

I would focus on the http://en.wikipedia.org/wiki/Schwarzschild_radius" [Broken] in my paper. Basically, with such a huge change in G you should find that the earth turns into a black hole. So much for decendants. It would have been a much more interesting paper if he had changed it by a factor of 2 instead of ~10^22.

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