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Shapeshifters are creatures which are able to, based on will or some sort of external stimuli, change between different forms while still remaining the same individual. Sometimes they retain the same personality, sometimes the different forms entail different personalities as well. A common example from fiction, which I'll use for the purposes of this post, is werewolves, but a good answer would ideally apply to other types of shapeshifters as well.

Though exceptions both ways exist both in terms of individuals and subspecies, an adult gray wolf normally weighs around 35-40 kg. Human body weight obviously varies a lot, but taking this BMI chart, a mid-range human 175 cm tall should weigh around 70 kg; a 40 kg adult human of virtually any height would be considered anywhere between simply underweight and grossly underweight. A 70 kg gray wolf would qualify as huge in our world.

Let's ignore the skeletal shifting and such for now, and focus on the body mass. Let's also mostly ignore the rate of change of mass. (If an answer addresses these, great, but it's not required.)

A wolf changing into a human would approximately double its body mass, assuming it is a fit but not excessive weight in both forms.

When it changes back into wolf form, that same half of its body mass has to be shedded.

Where does the mass go, and where does it come from? (Depending on which side of the shift has the larger body mass.) I realize that shapeshifters don't really lend themselves to hard-science explanations, but I would prefer answers which have at least some degree of believability beyond "magic by fiat by author's decree".

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    $\begingroup$ Aren't most werewolves substantially larger than your more mundane gray wolf? $\endgroup$ – Telastyn Sep 22 '14 at 19:17
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    $\begingroup$ Even if werewolves are large compared to regular wolves (large enough for this not to be a problem), there is sometimes call for other types of shape-shifting where there is a definite mass change. (Well, I suppose I should say "apparent mass change"; we don't know that Ladyhawke isn't a super-massive, dense bird, for instance, but it's the way to bet.) $\endgroup$ – Monica Cellio Sep 22 '14 at 19:26
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    $\begingroup$ @kikjezrous [science-based] (should be used for questions that require answers based in hard science, not magic or pseudo-science.) is a little stronger than I feel is even possible for this question. $\endgroup$ – a CVn Sep 22 '14 at 20:16
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    $\begingroup$ Before voting to close this, please do join the discussion over on Worldbuilding Meta. $\endgroup$ – a CVn Sep 23 '14 at 7:46
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    $\begingroup$ Related: scifi.stackexchange.com/questions/49927/… $\endgroup$ – Revetahw Jun 18 '16 at 18:10
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If you're looking for a more general method which ditches biological systems and uses Von Neumann machines, see gethubphagocyte's (now known as trichoplax) excellent answer.

Otherwise:
First of all, we've got to establish that mass is not created nor destroyed (unless your werewolf is partially antimatter and your untransformed human has a way of handling astronomically amounts of energy) to work within physics. Additionally, I assume you wouldn't want a general change in density, since a gigantic monster that used to be a little kid wouldn't be very effective if it just started to float into the stratosphere.

No density change:

This means we're not actually gaining/losing weight (let's call it mass; since that's what I assume you really want to know), we're just getting or dropping more mass. The generally established way to do that is through the digestive system, so that's what I'd suspect is the best way to start.

Werewolves already are known to have the ability to heal upon transformation (I think, I'm not very familiar with them), which hints at a temporarily supercharged metabolism and actually gives some amount of consistency to this theory. What if upon shapeshifting, they begin to eat ferociously as the creature's body kicks into overdrive, rapidly growing/expanding new parts while absorbing others (a mechanism which is already seen in [special tragic circumstances][s]). This would also explain the way that a shapeshifter could reduce their mass, through abortion and eventually excretion, however, it would take a measure of time greater than the few minutes/second associated with shapeshifting.

You could say again, that the body starts to act very rapidly, and absorbs/sheds the unneeded parts quickly, a process which I suspect would be rather painful as well as leaving telltale refuse where it occurs.

Density change:

Now, if you didn't mind a change in density, different body parts could be destroyed and recreated in lighter forms, such as muscle turning into fat, bones hollowing, large airsacs filling space, etc. It'd lead to some interesting anatomies, and depending on the intelligence of the shapeshifter, could be deliberately used to exploit odd effects (floating/sinking, whatever). Still, there'd be limits on the range of forms which could be assumed by the shifter, since you can only distribute so much mass in so many ways while keeping a functional body.

Additionally, you'd have to worry about some minerals which are used in some structures but not others. Calcium comes to mind, as while you could turn muscle into bone and vice versa, the fiberous muscle bits wouldn't be used, and the bones would be brittle and generally useless. The shifter could have a unique body arrangement which would keep superfluous minerals and elements stored for use later, or it would have to seek out particular foods during the transformation - quite an interesting plot device.

How?

As for the process itself, the creature could turn into an amorphous blob of undifferentiated body tissue with maybe only a brain floating in the center to direct it all. It could form a crystallizes-type structure to protect itself while transforming - getting lots of nasty microbes strewn throughout your future body is probably going to kill you before the monster hunters do, especially if your immune system doesn't expand to fit your new body.

My personal favorite is a rapid growth that leaves the shifter wracked while parts of their body start to degenerate and clot while others start to enlarge or grow, some falling off or just drying up while excess blood and fluids gush out, possibly layers of skin and body tissue falling off while the new body grows inside. Eww.

As pointed out in the comments, the brain would have to be resized/reformed as well, which would make it so that it's quite possible different forms would have different personalities and memory bases. As well, it's also probable that some memories would be lost during each transformation, so that when the shifter changes and changes back, they'd have partial permanent amnesia, made worse with each transformation. There's a high chance that between that, an insatiable drive to start eating before blacking out, and waking up in a pile of raw body parts (also monster hunters in pursuit!), quite a bit of crazy would happen.

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    $\begingroup$ I love this answer - it's firmly embedded in reality to the point of being disgusting... I now have an image in my head of a 40kg wolf crawling out of the 35kg outer layer of a human, leaving that shed "skin" behind until it comes back to eat it later before transforming back. $\endgroup$ – trichoplax Sep 22 '14 at 19:33
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    $\begingroup$ Keeping the brain intact is difficult since a human brain doesn't fit inside a wolf's skull. Insect brains undergo large changes during metamorphosis but studies have shown at least some memories can be maintained from larva to adult. Perhaps the change would be accompanied by partial amnesia where part of the human brain was lost and then rebuilt on changing back. $\endgroup$ – trichoplax Sep 22 '14 at 20:02
  • $\begingroup$ Isn't that also part of the werewolf lore? Not remembering what happened while in different forms? $\endgroup$ – neph Sep 22 '14 at 20:06
  • $\begingroup$ Yes I think so, but I was thinking that some of the human memories would also be lost, so on returning from being a wolf the human would not only have no wolf memories, but would have lost some of the memories from before the change too, due to the human brain being partially taken apart to make it fit in a wolf skull. $\endgroup$ – trichoplax Sep 22 '14 at 20:09
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    $\begingroup$ Unless a werewolf is like a wolf only from the outside and organs are located differently on the inside. You could store the brain in the chest and put something else into the head. :P Or just be a really big wolf. $\endgroup$ – user31389 Sep 23 '14 at 22:13
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To add to the magically plausible answers that githubphagocyte and kikjezrous have submitted, I offer the possibility of atmospheric exchange.

At at basic level, a body - whether human or wolf - is made up mostly of Carbon, Nitrogen, Oxygen and Hydrogen, plus some other trace elements. It is a fact that the air both these creatures need to exist is composed of Nitrogen, Oxygen, some carbon dioxide and some water, amongst other elements and compounds, containing a lot of the additional elements that is needed.

A somewhat less delightfully disgusting solution than kikjezrous' would be for the mass difference to be accounted for by exchange of the relevant elements to occur with the atmosphere and anything else the shapeshifter is in contact with, such that when a shapeshifter transforms into a larger form, mass in the form of the relevant elements is scavenged from the surrounding air (and probably also the ground), and when the shift occurs in the opposite direction, mass is released back into the air and/or falls to earth as dust or sludge.

Since a larger changed form may well be lacking in certain elements, this could explain the hunger shapeshifters are said to experience on transformation - they are looking for extra elements to compensate for the deficiencies their transformation has left them with in addition to replacing the energy required to fuel the transformation.

Too many fantasy novels seem to ignore the fact that there is stuff all around, that the characters don't just exist in the vacuum of space.

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  • $\begingroup$ There's an anime called s-CRY-ed which has great examples of "Alter users" turning the environment into their particular manifestations of power. The first 30 seconds of this video demonstrate it pretty well. Of course, that's a highly fantastical version of what you're talking about, but the core principle is the same. Conversely, changing from a larger creature to a smaller one could easily produce an explosion as all the extra mass goes somewhere. $\endgroup$ – Bobson Sep 23 '14 at 21:42
  • $\begingroup$ I've seen it done well, like the Jane Yellowrock series by Faith Hunter. So the shifter would be borrowing mass in the form of stone (if all you need is mass) or wood or even dead meat (if you need specific elements or compounds). Of course, shifting back means getting rid of all the extra mass, too - fun. $\endgroup$ – Megha Jun 17 '16 at 4:27
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If you're looking for a biological explanation of an actual human transforming into an actual wolf, see kikjezrous's excellent answer.

Slightly more realism can be gained if you are prepared to sacrifice the fact that the two animals are real biological animals. If you can build a story around something that can look like a human, and look like a wolf, then you could have a creature made up of a multitude of tiny creatures working together to form the shape of the animal to be approximated. These could be tiny robots, or even some kind of insect colony evolved or bioengineered to simulate other animals.

With either of these approaches, not all of the animals involved in simulating a large animal need be involved in the making of a smaller animal. If they are small enough to go unnoticed or even small enough to be completely invisible then half of them can simply wait nearby while the other half of the colony forms the smaller creature. This would allow for any range of sizes and masses, limited by the total mass of the colony. Anything smaller than that could be approximated and for creatures smaller than half the colony, more than one of them could be modelled at the same time. This would allow for a human breaking into two parts each of which becomes a wolf, each of which could also split into a flock of birds or a swarm of locusts if necessary.

Although this seems more flexible than the biological approach, and you might get away with portraying it that way in a story, this still isn't a true scientific approach as the same limitations apply to nanotech as do to biology. The smaller you make the component creatures the slower they will move and the shorter the distance they will be able to cover without running low on energy (even if they are tiny robots).

You can solve the mass problem with either the biological approach or the nanotech approach, but in either case that doesn't solve the speed of change problem. The biological approach probably involves a human going into a cocoon for a few months while the tissues are reconstituted into a wolf. The nanotech approach probably involves the human evaporating into dust and a wolf slowly crystalising over the course of at least hours and probably days, and even then only with a good source of power (moonlight probably wouldn't be up to it...).

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  • $\begingroup$ Great answer! I didn't even think of the robotic/swarm side of things. $\endgroup$ – neph Sep 22 '14 at 20:02
  • $\begingroup$ @kikjezrous I tried thinking of a biological approach first but couldn't come up with anything... $\endgroup$ – trichoplax Sep 22 '14 at 20:05
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I've seen two solutions that aren't strictly scientific (because no shapeshift that extreme is), but at least don't violate mass conservation:

  1. Eating. If you can transform your own tissue, you probably can also transform tissue you have in you, by any means. For example in your stomach. Fresh mammal like rabbits, or cows, or even rats, would work best - require least alterations.

  2. Direct absorption. If magic field transform things, but does not require them to be too similar, your fox would just dig into a hole in the ground, and leave human-shaped recess in it.

  3. I said two, right? But closest to what you want and still scientific is what some fish, frogs and octopuses do. Puff up. It does not change their mass, does not make them stronger, but make them appear larger. And just by the way, best real life shapeshifter we know is mimic octopus. But other octopuses are pretty good, too. Here is an example of puff up and skin alterations in real life.

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    $\begingroup$ This answer was posted on another question and merged hither. $\endgroup$ – Monica Cellio Oct 30 '16 at 23:22
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Has anybody thought the mass to change is already inside the body. Perhaps werewolves and other shapeshifters like them store special cells similar to stem cells that when shapeshifting, possibly through a complex metabolic process, quickly morph into the appropriate tissue thus making them more cellularly dense. This also means they probably weigh more than a human of the same size. As for the craving for human flesh, I don't know. Maybe human flesh is like drugs to them or something

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    $\begingroup$ Mass can neither be created nor destroyed (barring magic or some misunderstanding of physics). Cells that absorb matter/energy from another part of the body are not changing the mass of the body, only redistributing it. $\endgroup$ – Frostfyre Oct 4 '16 at 3:39
  • $\begingroup$ @Frostfyre You're confusing the mass with the size. If you've got sufficient magic, you can change Hydrogen, Oxygen, Carbon, Nitrogen, or Water (1 g/cm3) into, say, Osmium (22.59 g/cm3), Uranium, Lead, or Gold (mmm, sweet profit in killing werewolves), 22 to 1 expansion ought to take care of the size discrepancy problem. But your wolf weighs a lot, and probably makes very deep tracks, doesn't swim well, etc, etc. $\endgroup$ – anonymouse Oct 24 '16 at 10:36
  • $\begingroup$ Since I waited too long to edit: Tyler's (not so well-written answer) seems to imply 70kg wolf, that looks like 40kg (ie: not abnormally large) if made of typical muscle/bone/flesh (but is not, it is made of 'special cells'). $\endgroup$ – anonymouse Oct 24 '16 at 10:42
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So long as you are happy with the creature drinking lots of water to fill up bladder like structures and then releasing it on transforming back. If suitably placed these could change the body shape too.

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I found 3 perfect ideas to explain the mass of a shapeshifter:

Ouroboros - Hemlock Grove

This method is better to explain mass loss but can be used in both ways.

When the user decide to transform into a smaller being he left behind his transformation a mass of fresh flesh (remants of their last body) that he can eat later to turn back to his normal body.

This video shows the transformation in the serie.

Steam condensation - Shingeki no kyojin (Attack on Titan) and this

Well, in the serie isn't explained how transformation happen but fans have made a lot of theories.

This method is better to explain mass increase but if you want you can do the opossite effect.

When the user decide to transform it release an energy blast, fans believe that this persons absorbs the molecules of the air to make their bodies.

  • This explain why after the transformation their bodies are so heat, chemical reactions usually produce heat.
  • This transformation doesn't need nutrients to work, only air (maybe earth?) and energy to make "the transmutation".
    • Because they would need a lot of food to get the energy they could use solar light. In the serie titans need light to move or regenerate, in dark they "sleep".

Virtual matter and teletransportation - Ajin

I don't remember if it is also a fan theory or not.
In Ajin there are some persons who can't be killed, if you kill them (e.g: split in two) after a few seconds one of the 2 part would regen in almost 10 seconds while the other would desintegrate (teletransportation? maybe...). This doesn't break matter conservation law (but yes momentum law, or I think...), but you want to make matter so this won't work for you.
Well, Ajins (inmortal persons) has more abilities, they are able to summon an IBM (Invisible Black Matter), don't ask about invisible because it isn't important here, also you can change black matter to standard matter in your mind.

They can make a creature of virtual matter. Virtual matter isn't like normal matter, is normal matter WITH one exception: virtual matter was made out of nowhere -breaking law of conservation and other laws- so virtual matter need to be desintegrated in really short time to "don't break these laws".
Think that the universe is a human, if you break a law, it punish you (I am not sure but I think a black hole would be spawned of nowhere if you break a physic law).
Humans are living beens, and like animals can make mistakes, if you make something wrong your boss/teacher/parents would punish you but not instantly, maybe they take a few seconds or minutes to realice of your mistake. The universe is the same but it doesn't need seconds or minutes, it take yoctosecond (10−24s). By some [insert magical or sci-fi reason here] they are able to delay this and they can make virtual matter for some hours (e.g: in Ajin IBM can be used by 5 minutes).

  • You don't need nutrients.
  • You don't need solar light.
  • Maybe you have only this two disadvantages:
    • You can't stay to much time transformed.
    • You need some coldown time.
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  • $\begingroup$ BTW, you don't need <br/> or anybother html tags here! Use the markup code! Separate paragraphs with an empty line. Use forced breaks within a paragraph (two spaces at end of line) rarely. $\endgroup$ – JDługosz Jun 20 '17 at 17:45
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Getting unpleasantly into the domain of handwaving magic, but in a firm-science world where lycanthropy is a thing, having them contain a portable hole, bag of holding, or other portal-type thing within them for mass exchange is not unfeasible.

In Lovecraftian terms, you could have every cell fo their being contain a tiny portal to the planes of horrors.

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