Operation: Toys and Bacon

Today's invited guest is Jon Haarr.  Jon writes one of my favorite blogs, Toys and Bacon.  Seriously, can there be a better combination than toys and bacon?  I think not!  But I digress.

Jon writes,

...I realized there's something about the Transformers that always made me think. It's how they deal with weight, density and size changes when they transform. Soundwave is a transforming robot. In order to function as a spy for the evil Decepticons, he transforms into a good old fashioned cassette player, perfectly able to blend in among actual cassette players. The kicker is of course that in his natural mode - as a robot - he's huge....

My questions are: What kind of energy would go into these transformations? Let's say that Soundwave does in fact weigh the same in robot mode as he did when he was disguised as a cassette player. What would Soundwave's structural integrity be in robot mode, and how would it affect his daily work as an evil, giant, murdering machine? And then, let us play with the idea that Soundwave is made of traditional metal and that he maintains the weight from his natural, robot mode. How would that affect his disguise mode, and what would happen if that cassette player stood on someone's shelf?

Note the  change in size between here...

...and here.

This is something that's bothered me about Transformers ever since I got Optimus Prime and Megatron toys for Christmas as a kid.  In robot form, they're roughly the same size and would seem to be a fair match for each other in a fight.  However, problems arise when they transform into disguised mode, after which Optimus becomes a "toy-sized" truck, whereas Megatron transforms into a life-sized handgun.  Hasbro's never been a stickler for length scales,¹ but this is a bit much.  Even as a fairly stupid seven-year-old, I could tell by Toy Land standards Megatron was hideously deformed, and it was all I could do to convince the other toys not to mention it in front of him because he was probably pretty sensitive about it.

Where was I going with this?  Ah, yes!  Soundwave.  Let's consider three cases:

1. Soundwave Maintains His Robot Weight.  At first glance, this might seem like a fair assumption.  After all, he's a robot first and foremost, so it makes sense that he'd keep his robot weight when disguised.  However, as Jon pointed out to me, "It's obvious that he's not that heavy in his 'disguise', because we see people pick him up." Just how heavy would he be?  In the cartoons, he looks like he's at least as tall as a two-story building.  Conservatively, this would put his height around 20 feet.  Assuming he's made of iron with a density of 7.9 g/cm³ and a thickness and width of 4.0 feet and 5.0 feet, respectively, he would weight roughly 100 tons.  Even if you had the entire Ukrainian weightlifting team at your disposal, you still couldn't pick him up, so you can kiss those IKEA shelves goodbye.  To be fair, this isn't nearly the densest material known to man,²  but he's still going to have a hard time convincing anyone that he's just a plain ol' cassette player.  This brings us to option #2....

Soundwave...one bad robot you don't wanna mess with.

2. Soundwave Maintains His Cassette Player Weight.  Perhaps Shockwave is small-boned—er—alloyed.  Just how dense would he be if this were the case?  If I assume a cassette player has a mass of 2.0 pounds and use the dimensions above, then in robot form Shockwave would have a density of 80 grams per cubic meter.  That's incredibly light.  You might think that a light breeze would be enough to knock him over, but it's even worse that that.  If he maintained his cassette player weight, he'd be less than half the density of helium, so you'd have to tie a string around him to make sure he doesn't go floating off into the stratosphere.  The only way Soundwave is on remotely good scientific ground is if the Transformers discovered some novel unknown physics on Cybertron, which brings us to option #3...

 
But who said  he's just  an evil killing machine?

3. Soundwave Maintains a Constant Density While Transforming.  Although this is what the cartoons seem to suggest, the change in size would represent a clear violation of mass conservation.

Or would it?  I've dealt with the problem of spontaneous weight gain previously in The Hulk Revisited.  In that problem, I hypothesized that Marvel's Hulk gains weight by adsorbing air molecules with the result that he would suck out the equivalent of all the air in a 1500 square foot apartment upon transfiguring, instantaneously killing everyone (friend and foe alike) in said apartment with the resulting vacuum.  However, Jon's question is unique in that he specifically mentions energy.  One could imagine that Soundwave, during his transformation from 1980's cassette player to soulless killing machine, converts some excess energy to mass.  From above, we know roughly 100 tons of mass is unaccounted for during the transformation.  Perhaps Soundwave converts this mass to some new form of energy via Einstein's mass-energy equivalence equation E = mc².  Here, c = 3.0×10⁸ m/s is the speed of light.  Using this equation, we find that the excess mass is equivalent to about 8.2×10²¹ J of energy.  That's about 80 times the energy that the entire United States uses in a year!  I suppose it's possible an evil villain like Shockwave has this much extra energy lying around, but if he does, I imagine he'd find a more terrifying use for it than turning himself into an object whose most destructive power consists of playing Chris de Burgh's "Lady in Red" at moderately high volumes.

Thanks for a great question, Jon.


[1] See my earlier critique of G.I. Joe's U.S.S. Flagg aircraft carrier.
[2] A teaspoon of a neutron star weighs about as much as all of humanity.

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions.   Follow him on Twitter at @aarontsantos.