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In my book(Principles of Physics by Resnick,Halliday,Walker) , the authors write:

If $G$ - by some miracle - were suddenly increased by a factor of 10, you would be crushed to the floor by Earth's gravitation.

Now, by what miracle can $G$ be changed? Is it possible?

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    $\begingroup$ According to a particular interpretation of the Multiverse, there is another "parallel" universe where $G$ is indeed 10 times larger than the value of $G$ in our universe. No miracle at all -- indeed, there are parallel universi with every possible value of $G$. That is, if you agree with that interpretation. $\endgroup$ – K7PEH Dec 20 '14 at 5:35
  • $\begingroup$ You may want to move this to the Worldbuilding se. $\endgroup$ – JDługosz Dec 20 '14 at 5:37
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/21721/2451 and links therein. $\endgroup$ – Qmechanic Dec 20 '14 at 9:23
  • $\begingroup$ @Qmechanic: Sir, it is related but not a duplicate! My question is asking when it can change while the other one wanted the proof of the constantcy of G. $\endgroup$ – user36790 Dec 20 '14 at 10:34
  • $\begingroup$ It is a universal constant! $\endgroup$ – user213933 Apr 20 at 7:34
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I can't tell you about that miracle, but I can tell you that Resnick, Halliday, Walker didn't think hard enough about that sentence, because you wouldn't be crushed to the floor. Instead the floor would be falling towards the center of the Earth with you while the materials in the core and mantle would be quickly heating up as the planet would settle into a new equilibrium between its internal pressure and gravity. It would probably shrink its diameter by several hundred miles in the process while the heating would set enormous amounts of trapped volcanic gases free. The crust would shatter in gigantic volcanic eruptions not seen since the Hadean. If you happened to be above one of these cracks, you would probably get thrown to the height of the original stratosphere by these eruptions (the atmosphere would, of course, collapse to a much thiner layer in minutes, heating up to a red glowing gas in the process), and everywhere else you would be crushed by cubic kilometers of hot ash and lava which would be resurfacing the planet within minutes of the gravitational anomaly. And that would just be the beginning... the falling wave of material would then elastically bounce off the core and produce outgoing shock waves that would whip up the sea of lava on the surface into many mile high cascades of molten rock. Within less than an hour of the event the remains of the moon would come crushing down on this hell and add enough kinetic energy to lift an enormous plume of material back into orbit, where it would form a ring of debris far more impressive than Saturn's ring.

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    $\begingroup$ So I guess one shouldn't do that, even as an exercise for the advanced reader. $\endgroup$ – JDługosz Dec 20 '14 at 5:50
  • $\begingroup$ @jdlugosz: I think that it's good advice to textbook authors to pick their unrealistic scenarios wisely, lest they want to become the laughing stock of their peers for being unimaginative educators? $\endgroup$ – CuriousOne Dec 20 '14 at 5:53
  • $\begingroup$ Or maybe getting students to be haunted with the idea and putting more creative energy into it after class would be considered a win. I think the example of making clear what that factor affects mathematically might be good to visualize how function works. How do you illustrate the result of peturbing a factor in the math when it can't be done in the system being modeled? $\endgroup$ – JDługosz Dec 20 '14 at 11:28
  • $\begingroup$ You can be a world class theorist and write a really fun article like Robert N. Cahn in "The 18 parameters of the standard model in your everyday life" (hep.yorku.ca/menary/misc/eighteen_parameters_of_sm.pdf). If you are not on that level, I wouldn't bother, the results will be underwhelming. $\endgroup$ – CuriousOne Dec 20 '14 at 11:31
  • $\begingroup$ I guess that our orbit around the Sun would be disturbed. Of course, the Sun itself would probably be seriously affected. $\endgroup$ – badjohn Apr 20 at 8:44
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I’m surprised nobody has mentioned this yet.

There are certain extensions of general relativity in which the value of $G$ is not a constant, but a dynamical variable that can change in spacetime. This comes naturally from string theory (where the gravitational constant is determined by a mixture of the dilaton expectation value and the compactification moduli), and is an explicit assumption in alternate theories of gravitation, such as Brans-Dicke theory. Thus, if these theories were true, one could hypothetically locally change the value of the gravitational constant by exciting the value of some scalar field over a large region. This would require a great deal of energy, so I wouldn’t count on it being realistic. Furthermore, experiments have placed extreme constraints on the validity of Brans-Dicke theory (however, string theory remains at large).

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You could not just dial up the value of $G$, or select a different universe where only $G$ is different but otherwise like our own.

If you change $G$, you change everything. If you rearrange the formula to express $G$ in terms of other stuff, you see that you have to change something else to make $G$ come out how you want. Note that $c$ itself drags in other stuff, so $G$ really is intertwined like a big knot.

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The question would be easy to answer if we trace down how the values of constants in an equation are obtained. Suppose one day you find a relation between two physical quantities X and Y. You find that Y is directly proportional to X ie when you increase X, the value of Y also increases. Now you sit down and plot values of Y for different values of X by conducting experiments. For simplicity, let's assume X and Y have a linear relation. Now you take the expression Y=aX+b i (where a and b are the constants)

Now all you need to do is find values of a and b such that the graph of i coincides with the graph you plotted empirically earlier. This can be done using trial and error. When you see the graphs coincide well enough (it cannot perfectly coincide because of errors during experiments), you can safely conclude the values of a and b.

The constant G was thus found using empirical data. The data was large enough thus changing the value of G is quite difficult. You might try and get more precise values of G, but changing it to twice it's original value is actually not possible. I ignored the extreme cases, like that of a black hole or multiverses, because they are yet to be studied properly and holding experiments there is quite difficult.

U can try the above steps in Desmos Graphing Calculator (android app available on playstore).

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There is no absolutely and forever theory or truth, contemporary main stream physics in only a bunch of theories that can predict things that we observed better then other theories. GR is just a theory that predict the existing observations best. We cannot be 100% percent sure that GR(so is G which is part of GR) is valid in every corner in the universe, not sure even in every corner on earth, we only make a guess that it is highly possible that it is valid in every corner.

For the miracle you mentioned, maybe it already happened, e.g. sometimes ago at some place on earth, g is not 9.8 but 98, no body knows because we didn't make an observation at that time, even we happened to observe it, we will discard the data if it can't be further verified. Likely maybe it is happening now at some corner in universe or even earth. Maybe it will happens in some future days.

If the whole universe is just a simulation on some outer world computer which totally make sense, maybe someday the "person" in the outer world that creates the simulation program want to see what will happen if g is 98, then g becomes 98 suddenly in every corner in universe. If earth still exists at that time, we will all be doomed.

To the editors:this is more meta physics, but the question itself is meta physics. Please don't delete my answer which I wrote a lot.

@CuriousOne your answer is thoughtful but the author's point is to give reader a intuitive sense about g and don't need to deal with the details.

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