Can the Power Stone Lift Thor’s Hammer?

Jeremy Ng (ISB 11)

Jeremy Ng is a Serious Mathematician and Physicist as well as the owner of Youtube channel Square Physics, which boasts 10.6k subscribers. There, Jeremy shares his love for math and science by primarily explaining scientific phenomenon in hit sci-fi films. Visit his channel and view his most popular upload: Flash vs Dash | Ultimate Battle, which has racked up to 1.6 million views.

A little while ago, Film Theory uploaded a video about whether or not certain characters of the Marvel Cinematic Universe (MCU) were worthy of lifting Thor’s hammer— Mjolnir. After deeming Tony Stark (Iron Man), Natsha Romanoff (Black Widow), and Steve Rogers (Captain America) worthy, MatPat ended by concluding that— surprisingly— Thanos would belong to that list of champs. Sure, inter-galactic genocide might be a bit misguided based on our contemporary understanding of human rights, but MatPat justifies that Thanos fulfills Odin’s “Worthiness Criteria™️” because of his willingness to sacrifice his own well-being in pursuit of the greater good and his peace-loving nature (yeah, you’ll have to watch the actual video to get that one).

But, what if Thanos isn’t worthy of lifting Mjolnir? What if he doesn’t actually have all those altruistic qualities and is just as bad as most people think he is? Would he still be able to lift the hammer solely with the power that the Power Stone grants?

(From iPad Fiends)

As a physics fanatic and owner of a Youtube account with (mostly) green Social Blade stats, I’ll be taking on a more mathematical and scientific approach to calculate whether or not the power stone is strong enough to lift Thor’s hammer a meter above ground.

To start, let's have a look at how strong the power stone is. Since the franchise never explicitly stated its strength, we'd have to estimate it with the demonstrations we got. It turns out this is actually very simple: we can get the data needed in the scene from Avengers: Infinity War where the power stone destroys an entire moon and turns it into tiny meteors.

To get a reasonable estimate of the power stone’s strength, we can calculate the energy required to achieve this feat. We use the equation that calculates the gravitational binding energy of a planet. where G is a gravitational constant, m is the mass of the object, and r is its radius:

Rhea is a moon that orbits Saturn along with Titan. Since Thanos is actually standing on Titan in the scene, we can reasonably guess that the moon he destroys then is actually Rhea. Therefore, we will be using Rhea's mass and radius for this calculation. After plugging in the numbers, we see that the gravitational binding energy of the moon was about 2.77⨉10²⁶ joules, meaning the power stone had to exert that much energy to perform such a great feat.

Now let's take a look at Thor’s hammer. As established before, his hammer detects whether or not someone approaching it is worthy. If not, it will increase its mass such that the user cannot lift it. This is why people like Iron Man are able to hold it in space but can no longer lift Mjolnir when its on Earth-- simply because the gravitational force is too strong.

“people like Iron Man are able to hold it in space but can no longer lift Mjolnir when its on Earth...”

Because of a lack of information, we’ll just have to assume that the hammer will increase its mass indefinitely in order to prevent the person from lifting it. But, when the mass of the hammer gets too high, a black hole will eventually form, because the hammer would be too dense. This point is called the Schwarzschild density. So, if the density is the maximum mass that the hammer can weight, we can calculate whether or not the power stone can lift the hammer.

“...or just around 2.925 x 10²³ baboons”

After doing some basic calculations, we can determine the maximum mass Mjolnir can accumulate before it turns into a black hole. This mass turns out to be approximately 117sextillion 476quintillion 472quadrillion 700trillion kilograms, or just around 2.925 x 10²³ baboons. From this, we can compute that the energy required to lift this hammer on Earth would be about 1.151 septillion joules. Seeing as this is less than the 2.77⨉10²⁶ joules of energy previously exerted by the power stone, we can definitively conclude that, yes, the stone can lift the dude.