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We have all heard of the gravity formula $F = G \frac{m_1 m_2}{r^2}\ $, establishing a relation between the mass of an object and the gravity force it is affected by. Welp, turns out Newton was wrong! The real equation is $F = G \frac{x_1 x_2}{r^2}\ $; and $x = m$ for every substance known to man - except for this newly discovered substance, phlebotinum. For phlebotinum, $x = ym$, and $y$ is a very big number. What that means is that a teaspoon of phlebotinum, with a mass of a few grams, has enough gravity to meaningfully interact with its environment - destructively so.

I want to narrow down the value of $y$ for the weaponisation of this substance. However, an implication I did not realise upon first asking this question is that the planet is a source of gravity too; therefore if phlebotinum has the equivalent gravity of a mountain, it would also be as hard to pick up as a mountain.

So I'll have to make $y$ a bit lower. That leaves me with the question: can you still weaponise a substance that is affected by gravity more intensely than usual? With the goal finding a value of $y$ so that the effects of extreme short-range gravity can be utilised properly, without making the phlebotinum impossible to handle.

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    $\begingroup$ How would the planet, on which the city is build, would affect the hail of phlebotinum balls? One could image that said "ton" would never get off the ground. Other ones would say that maybe sending them one by one is possible but the acceleration of said ball from 2000 metres would be more devastating that the gravity force of it. $\endgroup$
    – SZCZERZO KŁY
    Dec 14, 2020 at 10:00
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    $\begingroup$ @KeizerHarm Certainly, since the phlebotinum (p) violated the equivalence principle, it nullifies general relativity (The stree-energy tensor and Einstein tensor no longer share the same relations through curvature since the p-mass is "bending" space more than its mass would allow). This alone breaks a fundamental pillar of physics, but its a little deeper than that. See my answer here (worldbuilding.stackexchange.com/questions/191777/…) where I discuss mass's relationship to momentum and energy. (1/2) $\endgroup$
    – user110866
    Dec 16, 2020 at 9:12
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    $\begingroup$ This means that special relativity must be corrected, and so must the relativistic dispersion relationship because at this point we have to decide between inertial mass-energy and gravitational mass-energy since this distinction now determines the dispersion relationship in a gravitational field vs. any other field. This means that the mass-energy conservation is broken and this implies a breaking of time translation symmetry! Clearly this is a problem so relativity and the dispersion relationship would have to be rescued but how? This would require reformulating physics. (2/3) $\endgroup$
    – user110866
    Dec 16, 2020 at 9:35
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    $\begingroup$ Even with the given prompt, the problem is compounded by the notation that for a kilo of p-mass to exercise a gravitation newton of force on a kilo of regular matter at a meter, "y" would need to be on the order of 10000000000! Note that the acceleration of p-mass on Earth would be 9.81 m/s^2 multiplied by y! If y is only a factor of 1000, its gravitational acceleration would still be 9810 m/s^2, while its effects on surrounding matter would not be noticeable (~ 0.000000001 N at a meter on a kilo of regular matter)! (3/3) $\endgroup$
    – user110866
    Dec 16, 2020 at 9:44
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    $\begingroup$ @user110866 Thank you kindly for helping me down Mount Dunning-Kruger :) You are completely right, and I would be wise to do further research at how physical equations arrived the way they are before I begin modifying them for alternate realities. Nevertheless, I asked for a reality check and I say you have given me a thorough one, broadening my understanding of the physics involved, so I would love for you to make that a proper answer so that I may upvote and accept it. $\endgroup$
    – KeizerHarm
    Dec 16, 2020 at 9:49

2 Answers 2

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[Adopted from an original series of comments]

In general its never a good idea to start with a modified physics equation and work forward unless you really have deep understanding of physics (and even then!). Its usually best to start with the effect (a short-range gravitational-like attraction between mass) and work forward from there to avoid breaking physics. In analogy, this sounds a bit like asking the appropriate amount of money banks should add to everyone's bank account so the whole world would be rich...both economics and physics are complicated and very mathematically intense; changing one fundamental thing to produce a certain desired effect has the tendency to change everything in strange and unusual ways.

PcMan raised the issues of decoupling gravitational mass and inertial mass. To elaborate, since the phlebotinum (p) violated the equivalence principle, it nullifies general relativity. The stress-energy tensor and Einstein tensor no longer share the same relations through curvature since the p-mass is "bending" space more than its mass would allow. This alone breaks a fundamental pillar of physics, but its a little deeper than that. See my answer here where I discuss mass's relationship to momentum and energy.

This means that special relativity must be corrected, and so must the relativistic dispersion relationship because at this point we have to decide between inertial mass-energy and gravitational mass-energy since this distinction now determines the dispersion relationship in a gravitational field vs. any other field. This means that the mass-energy conservation is broken and this implies a breaking of time translation symmetry! Clearly this is a problem (spontaneous breaking of ground state symmetries leads to a whole slew of issues), so relativity and the dispersion relationship would have to be rescued, but how? This would require reformulating physics!

Even with the given prompt, the problem is compounded by the notation that the acceleration of p-mass on Earth would be 9.81 m/s$^2$ multiplied by the y-factor! For example, y is only a factor of 1000, the p-matter's gravitational acceleration would be 9810 m/s$^2$, while its effects on surrounding matter would not be noticeable (~ 0.000000001 N at a meter on a kilo of regular matter)! Lets suppose y is 10, the material would still be launched towards Earth's surface with an acceleration of about 91 m/s$^2$! However, a gram of p-mass would only exert a gravitational pull of 6.67$\cdot$10$^{-11}$ N on another gram of matter at a distance of a millimeter. Weaponizing this substance would essentially boil down to dropping it with explosive results. Constructing a container that could stand such pressures could be a challenge. Even more dangerous is that our gravity/inertia masses are decoupled for which we have no intuitive knowledge, for example, its easy to role a ball of it across a table but it falls with explosive force if pushed over the edge!

In conclusion, simple changes to fundamental equations rarely leads anything desirable, but usually brings lots of undesirable side-effects.

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    $\begingroup$ Once again thank you for enlightening me. Clearly this is not an avenue I will be pursuing in my quest for something physically interesting that doesn't break the laws of physics. I may instead explore adding a wholly different field, not tangled with the rest of physics; and still a field that gives every object some potential energy much like magnetism and gravity does; so as not to disrupt conservation of energy but still allow for exotic matter that behaves weirdly. But that I think will be a story for a different question, and this time I will do more research on the beforehand :) $\endgroup$
    – KeizerHarm
    Dec 16, 2020 at 10:55
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Invalid question: false and contradictory assumptions.

The real equation is F=Gx1x2r2 ; and x=m for every substance known to man - except for this newly discovered substance, phlebotinum. For phlebotinum, x=ym, and y is a very big number. What that means is that a teaspoon of phlebotinum, weighing a few grams, has enough gravity to meaningfully interact with its environment - destructively so.

Incorrect derivative.

Your tweaking of the equations uncouples INERTIAL mass from the Gravitational mass, but does NOT break symmetry of gravitational mass. This means your phlebotium would STILL WEIGH an immense amount.

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  • $\begingroup$ Did you forget to read the final paragraph of the question? $\endgroup$
    – KeizerHarm
    Dec 14, 2020 at 18:46
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    $\begingroup$ This is a valid answer, this is what we call frame challenge and we expect people to do it :) $\endgroup$
    – The Square-Cube Law
    Dec 16, 2020 at 12:42

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