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With a pinch of handwavium, Clarabelle the witch causes an accident. She became permanently as heavy as an ordinary duck, while her body remained the same.

Her density was forever altered. She is five feet (1½ metre) tall and weighs only 4 lb (nearly 2 kg) forevermore. Aside from never again sinking in water and having to stay away from being in the same place simultaneously with a mallard, scales, and an angry mobs of peasants, what other effects does it have on her life?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – L.Dutch
    Aug 25 at 11:15
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    $\begingroup$ Corollary: What would be the effects of making a duck as heavy as an adult woman? $\endgroup$ Aug 25 at 13:23
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    $\begingroup$ @DarrelHoffman the duck would sink, end of story. $\endgroup$
    – Vesper
    Aug 25 at 13:40
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    $\begingroup$ @DarrelHoffman the duck would not have the strength to fly or walk and would sink, assuming he doesnt collapse under his own weight. Scavengers and insects will soon try to eat the body, getting chunks of increased density that will either revert to normal weight or weight them down, meaning any animal that does not have the strength/means to evacuate the food somehow will be pinned down and die. Eventually the mass is spread out enough some animals and insects can get away, weighing slightly more than supposed to. $\endgroup$
    – Demigan
    Aug 25 at 14:02
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    $\begingroup$ Does that mean her inertia also corresponds to the new weight? Most answers are assuming it does. $\endgroup$ Aug 25 at 16:16

6 Answers 6

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(1) She cannot go outside in the rain or wind without being blown away.

(1.5) She cannot work with animals or they will throw her around like a rag doll.

(2) She must be very careful when wearing clothes or lifting objects, as her light weight will affect her balance. Even holding a jar of jam at arm's length will make her topple over.

(3) She should not become pregnant, unless the baby is similarly lightweight.

(4) Perhaps her strength is affected and she cannot lift anything or wear clothes at all.

(5) Perhaps her thermal coefficient is affected and she is super vulnerable to changes in temperature.

(6) Perhaps her metabolism changes and she barely needs to eat or drink.

Note combining some of the above is disastrous. For example, if she is super weak but needs to eat normal food she cannot move after a meal. If she is super weak and bad at regulating she will freeze in the nude but collapse in clothes.

The most story potential is when she is super light, but normal strength. She wears heavy boots and pretends to be feeble. But there are some telltale signs her weight is not distributed normally.

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    $\begingroup$ I am reserving an upvote until the various combinations are depicted in a Venn diagram. $\endgroup$
    – Willk
    Aug 24 at 14:10
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    $\begingroup$ @Willk Unfortunately I do not have enough dimensions to draw all the possible combinations at once. $\endgroup$
    – Daron
    Aug 24 at 14:30
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    $\begingroup$ @Daron This is not true. Here are some Venn diagrams for 7 through 11 sets. $\endgroup$ Aug 25 at 1:25
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    $\begingroup$ @AdamChalcraft A simple Venn diagram like that always clears up any possible confusion :o $\endgroup$
    – Mr47
    Aug 25 at 8:14
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    $\begingroup$ @DKNguyen We don't know which of the rules will hold for the baby. Imagine weighing 4 lbs and carrying around an 8lb baby. Imagine you only need a thumblefull of rolled oats per day but the baby requires 1 metric babysworth of nutrients. Imagine stuff changes weight when it goes from the mother into the baby and back. The placenta should mititage some of the horror but nevertheless -- the horror D: $\endgroup$
    – Daron
    Aug 25 at 12:16
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The answer by Daron mentions a lot of drawbacks. But assuming that her body magically became lighter without becoming any weaker or more fragile, then there are also a couple advantages:

  • She can now jump very high, because her legs have less mass to move.
  • She will be able to run extremely fast. Even though she will have to greatly adjust her walking and running technique to exert less vertical and more horizontal force, which might take her some time.
  • She will be amazing at climbing. Due to the tiny amount of mass she would have to lift, she would beat the records of professional speed climbers without even breaking a sweat.
  • She can fall from any height without injuring herself, because even at terminal velocity, her body won't have a lot of kinetic energy.
  • She might even be able to fly under her own power by building some wings and flapping them with her arms.

However, if she considers a career as a superhero, then she should be aware that she is probably not going to be a very effective fighter. Her punches will not pack a lot of weight, while she herself can easily be knocked around. Also, the above abilities will be greatly diminished when she carries anything heavy, like armor or weapons. But does she even need to engage in physical combat? She is still a witch, after all. She can defeat her foes with her magic.

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    $\begingroup$ Running fast will actually be harder for the same reason that her jumping ability will be incredible: her weight will no longer be enough to keep her in contact with the ground. Every step produces both horizontal and vertical force, and a person can't take a second step if they are not in contact with the ground. $\endgroup$
    – Tom
    Aug 24 at 17:46
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    $\begingroup$ Plus she wouldn't get much traction with only a duck's worth of weight pushing her feet into the ground. She'd slip and slide and bounce all over the place, to the extent that walking at all would probably be difficult without carrying a heavy pack to provide some weight. $\endgroup$
    – N. Virgo
    Aug 24 at 21:34
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    $\begingroup$ @DKNguyen Wind-resistance will be a real problem, unless she has a nice tailwind. $\endgroup$ Aug 24 at 23:03
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    $\begingroup$ @N.Virgo Weighing less means you get less traction, but also that it takes less force to accelerate. The mass of the person completely normalizes out - mass is irrelevant for acceleration (not force) due to friction. A heavy car and a light car can accelerate at the same rate, all other things being equal, adding weight to a car does not make it less likely to skid. $\endgroup$ Aug 25 at 12:51
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    $\begingroup$ @NuclearHoagie I think the reason people think that is because of cars and snow. Heavy cars are said to "press" through the snow better. Or that is a myth in its own right born of engine weight being positioned over the driven wheels providing more traction so people think more weight = traction. But that's not the same thing because the proportion of ground pressure vs inertial mass are being changed in that scenario. whereas in this case the ratio is kept constant if you just increase the mass. $\endgroup$
    – DKNguyen
    Aug 25 at 13:41
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Fictionally, what she may wish to do

She will probably wish to acquire lead wraps around her legs, or a lead weighted belt. They could weigh anything from 10-20 kg (enough to stabilise her in light/no wind, and take very long paces/fast gait, or carry heavy stuff), to I guess 40-70 kg (enough to have a mostly normal life). She could have multiple sets.

If the weights are much higher she will overbalance. If around the ankles they move more with each step putting rotary strain on joints that is reduced if they are around the thighs or waist.

In the real world, she would have serious health problems within a short time

One serious consequence not mentioned - she won't get normal body exercise because she isn't fighting gravity. Think of astronauts needing to exercise if in space for a long time, muscle mass, cardio impact, etc. Even sleeping her body just isn't working against gravity. My guess is, she won't fare well.

Astronauts exercise to counter this, but even so, the effects cannot be mitigated enough to avoid a problem. Wikipedia has an article on the effect of a space environment on the body.

Most of these effects are linked to loss of the body's effective weight (microgravity) which is her problem....

Overview: Significant adverse effects of long-term weightlessness include muscle atrophy and deterioration of the skeleton (spaceflight osteopenia). Other significant effects include a slowing of cardiovascular system functions, decreased production of red blood cells (space anemia), balance disorders, eyesight disorders and changes in the immune system. Additional symptoms include fluid redistribution (causing the "moon-face" appearance typical in pictures of astronauts experiencing weightlessness), loss of body mass, nasal congestion, sleep disturbance, and excess flatulence

Twin studies: On 12 April 2019, NASA reported medical results, from the Astronaut Twin Study, where one astronaut twin spent a year in space on the International Space Station, while the other twin spent the year on Earth, which demonstrated several long-lasting changes, including those related to alterations in DNA and cognition, when one twin was compared with the other.

Serious medical impact on circulation: In November 2019, researchers reported that astronauts experienced serious blood flow and clot problems while on board the International Space Station, based on a six-month study of 11 healthy astronauts...

And again from Wikipedia, this time under health impact of microgravity (which is effectively what your witch will experience):

Space motion sickness: Despite their experiences in some of the most rigorous and demanding physical maneuvers on earth, even the most seasoned astronauts may be affected by SMS (space motion sickness), resulting in symptoms of severe nausea, projectile vomiting, fatigue, malaise (feeling sick), and headache. These symptoms may occur so abruptly and without any warning that space travelers may vomit suddenly without time to contain the emesis, resulting in strong odors and liquid within the cabin which may affect other astronauts. ....... Even when the nausea and vomiting resolve, some central nervous system symptoms may persist which may degrade the astronaut's performance.

Despite a multitude of studies searching for a solution to the problem of SMS, it remains an ongoing problem for space travel. Most non-pharmacological countermeasures such as training and other physical maneuvers have offered minimal benefit. Thornton and Bonato noted, "Pre- and inflight adaptive efforts, some of them mandatory and most of them onerous, have been, for the most part, operational failures."

Musculoskeletal impact: In addition to muscle loss, microgravity leads to increased bone resorption, decreased bone mineral density, and increased fracture risks. Bone resorption leads to increased urinary levels of calcium, which can subsequently lead to an increased risk of nephrolithiasis. In the first two weeks that the muscles are unloaded from carrying the weight of the human frame during space flight, whole muscle atrophy begins. Postural muscles contain more slow fibers, and are more prone to atrophy than non-postural muscle groups. The loss of muscle mass occurs because of imbalances in protein synthesis and breakdown. The loss of muscle mass is also accompanied by a loss of muscle strength, which was observed after only 2–5 days of spaceflight during the Soyuz-3 and Soyuz-8 missions. Decreases in the generation of contractile forces and whole muscle power have also been found

Cardiovascular impact: In a regular environment, gravity exerts a downward force, setting up a vertical hydrostatic gradient. When standing, some 'excess' fluid resides in vessels and tissues of the legs. In a micro-g environment, with the loss of a hydrostatic gradient, some fluid quickly redistributes toward the chest and upper body; sensed as 'overload' of circulating blood volume. In the micro-g environment, the newly sensed excess blood volume is adjusted by expelling excess fluid into tissues and cells (12-15% volume reduction) and red blood cells are adjusted downward to maintain a normal concentration (relative anemia). In the absence of gravity, venous blood will rush to the right atrium because the force of gravity is no longer pulling the blood down into the vessels of the legs and abdomen, resulting in increased stroke volume. These fluid shifts become more dangerous upon returning to a regular gravity environment as the body will attempt to adapt to the reintroduction of gravity. The reintroduction of gravity again will pull the fluid downward, but now there would be a deficit in both circulating fluid and red blood cells. The decrease in cardiac filling pressure and stroke volume during the orthostatic stress due to a decreased blood volume is what causes orthostatic intolerance. Orthostatic intolerance can result in temporary loss of consciousness and posture.....

Finally the Wikipedia article on bioastronautics is less detailed but adds that

Cell functioning: Of particular interest from a biological perspective are the effects of reduced gravitational force felt by inhabitants of spacecraft. Often referred to as "microgravity", the lack of sedimentation, buoyancy, or convective flows in fluids results in a more quiescent cellular and intercellular environment primarily driven by chemical gradients. Certain functions of organisms are mediated by gravity ..... (L)ong duration space flight also has physiological impacts on astronauts. Accelerated bone decalcification, similar to osteopenia and osteoporosis on Earth, is just one such condition

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    $\begingroup$ Good point about this being effectively microgravity. However she would experience considerably more gravity than astronauts in space (effectively around 1/30th of Earth gravity), which may be enough to mitigate some of these issues. $\endgroup$
    – Esther
    Aug 25 at 13:42
  • $\begingroup$ Why wear weights when you can wear a manual Iron Man suit? $\endgroup$
    – DKNguyen
    Aug 25 at 20:11
  • $\begingroup$ She would need to wear the weights as a belt, or on her shoulders, not on her legs. If she tried to wear them on her ankles she would trip over them. Imagine YOU are wearing weights on your ankles. Now imagine you don't weigh anything, and have no mass to work against the weights. $\endgroup$ Aug 25 at 23:16
  • $\begingroup$ Losing bone and muscle density might not be much of a problem if this effect is permanent; unlike an astronaut she's not going to have to suddenly deal with 1g again after her bones/muscles weren't used to carrying weight anymore. And I would expect the effects of low gravity to be quite a different subset of the effects of microgravity. Things like gravity-based separation of fluids of different densities still work at low g, just slower, so body processes that rely on this effect may still work; whereas in micro gravity these processes stop working completely. $\endgroup$
    – Ben
    Aug 26 at 3:32
  • $\begingroup$ @fluffysheap I think we're imagining that she still has the leg muscles to move feet/legs that weigh as much as they used to. Say she was originally 60 kg; one leg would have been about 10 kg, and now weighs 1/3 of a kg. Putting 10 kg of weight back on her new leg is basically the same as she started in terms of effort required to move it (if well-distributed). But putting weight significantly greater than her new total body weight on her shoulders would be a disaster; even a small lean would move her centre of mass outside the supporting base of her feet, causing her to topple over. $\endgroup$
    – Ben
    Aug 26 at 3:45
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She'd become a world class couple figure skater.

If she retains her previous strength she'll instantly break world records all over track and field, especially in all the jumps. She'll probably be a very fast swimmer, gliding over the water. She'll be a great race car driver and cyclist. She'll be a great cross country skier (but not good at downhill).

She'll also be the best single figure skater inventing hitherto unknown jumps under the roof, etc. etc.

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  • $\begingroup$ Well, she'd be a decent figure skater in pair as well, except for the parallel jumps which would require great coordination for the witch to allocate enough spin but very few upward force to jump exactly as her partner. Otherwise, most elements performed with her will be a lot easier to make. $\endgroup$
    – Vesper
    Aug 25 at 12:35
  • $\begingroup$ @Vesper I agree -- pair (or couple) skating was my first sentence. $\endgroup$ Aug 25 at 13:14
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She won't retain this ability for long

A human body is constantly renewed, that is, atoms enter and exit the body, cells get replaced, water lost and replenished, etc. And whatever atoms that would enter that witch's bosy will still retain normal mass. Therefore, after she'd eat (which would require her to carefully calibrate her movements, because there will be less inertial mass to move when moving a spoon from the plate to the mouth), her body will start assimilating normally weighing atoms into itself, raising its inertial mass to what was before the accident. The same applies to breathing (actually this will start affecting her right away!) and drinking. The lightweight atoms will eventually be ejected from her body by normal means.

A human requires about 2 liters of water per day to maintain his water balance, also a human requires to breathe in about 11000 liters of air per day, but only about 5% of incoming oxygen is absorbed in the lungs, thus the amount of oxygen transferred into the body per day is about 11000*0.2*0.05*0.001428 = 0.15708 kg. Let's count for the witch to eat 2 kg of food per day, including water, and assume that 90% of eaten atoms actually move through intestinal barrier into the body. Thus, 1.957 kg of the body's atoms get absorbed into the witch's body each day, and in case of her not gaining body volume ("weight" for a normal human), about the same mass's worth of atoms leave her body during the day by various processes. Those atoms that leave the body will be distributed about proportionately between normal and lightweight portions of Clarabelle's body, e.g. if her body is composed of 25% normal atoms and 75% lightweight atoms at the start of a day, at the end the composition of all the atoms exited from it will contain 25% normal and 75% lightweight atoms, give or take a few. Therefore, if right after the incident Clarabelle weighed 4 lb, and continued to eat normally, after the very first day she will weigh (1.6+1.957-(1.957*1.6/53)) = 3.498 kg or about 8 3/4 lb. The next day she will lose less than 100% of lightweight atoms, thus will gain less mass than 1.9 kg, yet she will still gain mass even if not gaining weight. This process will continue at an exponential rate of e^(-x), making her weigh half the weight before the accident after 14-15 days, three quarters after a month, and after three months she would be almost indistinctive from before all this happened.

In the meantime, however... she will suffer a set of inconveniences

First, her inertial mass will make her movements too fast, making her steps too light and throwing her lightweight body towards the ceiling with each step. If she'd just stay within her house, it won't affect her for long enough to harm her health. Yet, if she'd go outside, she can end up tossed by the harsh wind, whacked and toppled over by some thrown stones or other incoming physics, and should she somehow end up in water, everyone seeing her float like a balloon would yell "WITCH!!!". However, this could be used by her to an advantage, as she will be able to climb trees up to the very top and actually run on treetops like a squirrel, thus avoiding capture and bonfire sentence. This stage won't last long if she'd eat well, about 2-3 days and the wind would stop being a threat, for example.

Second, she will have to adjust her almost-weightless body (while it is so) while holding and operating stuff like pots and buckets. For example, a 5-liter pot filled with water will be heavier than her entire body, and while pulling it out of an oven or furnace along horizontal surface won't be a difficult task, because she won't instantly get weaker, and after all she still can use her legs against that oven instead of the floor to leverage her strength, lifting it upwards will make her unstable, at least until she couldn't get her feet under the pot, or rather, under the mass center of her and the pot, which will be a little more than halfway towards the pot. I say this would be minor one, as her strength will no longer be spent on lifting her arms together with the pot, so instead of 15 kg, comprising of 10kg of arms and 5kg of pot, she will have to lift only 6, yet developing a proper pulling technique would take a while.

Third, some interesting physics would interfere with her biology while atoms replenishment will be underway. For example, if blood water will be a tenth normal and 90% lightweight, the normal tenth will tend to sink, inducing countercurrents in veins below heart level that can potentially weaken the witch's body. Thankfully, this effect even at its hardest won't inhibit blood flow (or lymph flow) at any rate of normal/lightweight atoms distribution, because lower weight of altered blood will actually help blood system to maintain blood flow. Yet, the flotation effect could invoke various problems on small scale (intracellular effects) which I am unaware of. Overall I assume that the following month Clarabelle would experience weakness, sweating, lack of appetite and possibly fever or hemorrhaging due to increased strain on immunity system which will react on some cells performing badly. This likely won't lead to her death, though.

Maybe there will be more effects, but they will likely cease after about three months, should Clara survive.

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  • $\begingroup$ It's her weight that changes, so it would be very different if her mass stayed the same. (E.g. a crude method would be to inflate her with hydrogen or helium, but we could imagine some subtler anti-gravity force field generator instead.) Most of this answer wouldn't apply then, so what would life be like if her original mass were preserved? $\endgroup$ Aug 28 at 3:10
  • $\begingroup$ @RayButterworth if weight is lost but inertial mass isn't... there would be a potential E=mc^2 break. Lift her up, drop her down, SLAM you get more energy than spent while lifting. A perpetuum mobile is a something that won't fit into science-based $\endgroup$
    – Vesper
    Aug 28 at 6:36
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    $\begingroup$ Goodyear Blimps have a weight of less than 200 pounds but a mass of 10 tons. This 100× difference doesn't involve any mass/energy conversion. $\endgroup$ Aug 28 at 12:17
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Just some fun math to wrap things up.

According to https://www.medicalnewstoday.com/articles/323446 the average, in-shape 5-ft (1.5m) person weighs 97-123 lbs (44-56 kg).

According to https://www.aqua-calc.com/calculate/weight-to-volume, a 56 kg (taking the high end for this) person, on average takes up 0.05545 m³ of volume.

Now, supposing Clarabelle weighs 2 kg, this gives her a density of

p = m / V = 2kg / 0.05545m³ ≈ 36kg/m³

For comparison,

  • normal air at sea level is 1.3kg/m³
  • water is 997kg/m³

Clarabelle is still sufficiently denser than any common gas I can find, so she's pretty safe from floating away into the sky, but not by much. She'd float on top of water, not really in it as a duck would.

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