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Feb
25th
2014

The Physics Of UnicornTeleportation · 6:18am Feb 25th, 2014

About the physics of magic, I have, with friends, tried to work out the physics of UnicornTeleportation:

We concluded that in free fall, the energy-requirements should scale thus:

e (energy) should scale:

e=vdm

Volume times distance times mass.

Volume is a factor because one displaces a volume of spacetime to new coordinates in spacetime. ¿Do you remember the formula for volume of a sphere?:

(2τ/3)r^3

The radius cubed is important for teleporting ponies because they do not stack well:

Princess Twilight Sparkle teleports herself. She then teleports herself and 3 friends for a total of 4 ponies. The area of the ground is 4x larger, but the total volume is 8x larger. Let us set the value of the first teleport to 1 and see how many times more energy Princess Twilight Sparkle needs for the second teleport:

v=8
m=4
d=1

e=vdm

e=8*1*4

e=32

The second teleport requires 32 times as much energy.

Pineta has generilzed this. I shall let Pineta explain:

The proportionality is a fair guess, but that doesn't balance dimensionally. So let's write it:

e = k v d m + Δe

where k is a constant to make the dimensions fit, and Δe, which can be positive or negative, accounts for the difference in energy between the initial and final state (accounting for the effects you mention: gravitational potential and kinetic energy, and anything else).

We must remember to conserve momentum, velocity, orientation, kinetic energy, and angular momentum. This means that bad things can happen if a vertical component is involved or objects move relative to 1 another:

——

Pineta

Temporarily Permanent points out that Time-Dilation occurs. I knew this, but figured that the amount would not be worth mentioning, but it is worth mentioning.

¡Examples!:

Princess Luna teleports onto the FriendshipExpress. The Friendship express travels at 100 KPH. The backwall of the carriage crashes into Princess Luna at 100 KPH.

Princess Celestia tries to teleport from Ponyville to Canterlot. She forgets to add energy for compensating against the gravitational potential because Canterlot is at an higher elevation. She emerges inside the CanterHorn.

Princess Mi Amore Cadenza is gigameter above Earth (i do not know enough about Equus for this example, so I use Earth). She teleports to the surface of Earth. The ground moves laterally at over a thousand kilometers per hour, but that is the least of her problems because she moves down at 11 kms and slams into the earth, leaving a crater.

Feel free to use these physics in your work.

Credits:

Capn_Chryssalid
For pointing out that since one moves a volume of spacetime, one must account for the displaced volume in the calculations.

Chatoyance
For finding prior work about the mathematics of teleportation.

Temporarily Permanent
For pointing out that I should mention Time-Dilation.

Pineta
For generalizing the formula.

External Links:

* Exercise In Speculation The Theory And Practice Of Teleportation —— Larry Niven (OnLineReading)
* Exercise In Speculation The Theory And Practice Of Teleportation —— Larry Niven (DownLoadLink)

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Comments ( 20 )

This blog post is Chryssalid approved.

Injecting a little physics into the world of magic can be good fun. Or... that's my view on it. "Magic is magic" is no doubt what a lot of people think (dismissively), and that is true. Just as 'scifi science is not real science.'
But I mean practically and narratively speaking, it can be a productive and entertaining addition to the story. It opens avenues for the creative use of magic. The example with the moving train here is a great one, I think. I've always been a big proponent of characters being clever and unexpected in coming up with new ways to use old tricks. But to do so, you need some internal rules for your characters to break or bend.

1872222

Your approve means a lot. About the train:

Princess Luna could teleport 100 meters laterally to where the train is. Because of conservation-laws, the floor of the train would travel under her hooves at while Princess Luna conserves her initial velocity, kinetic energy, speed and momentum. She could teleport onto the train safely but it would require as much extra energy as accelerating her to the speed of the train because she literally has to accelerate to the speed of the train.

Because we conserve momentum, velocity, kinetic energy, and angular momentum, we would have to displace mass such as air in the opposite direction of her acceleration during the teleport. Total change in velocity, kinetic energy, and momentum must equal 0.

Your effort was prodigious, and I am impressed. Want another look?

You might want to see 'The Theory And Practice Of Teleportation' by the famed science fiction writer Larry Niven. It comes from his story collection 'All The Myriad Ways', which is sadly now out of print.

I have found a link to an online PDF you can read in your browser, here:
http://www.125books.com/move-other-bk?file=w%20%20Exercise%20In%20Speculation%20The%20Theory%20And%20Practice%20Of%20Teleportation%20-%20Larry%20Niven.pdf#rss

Or download a PDF or epub of the work here:
http://www.125books.com/search-bk?s=0&kw=%20The%20Theory%20And%20Practice%20Of%20Time%20Travel%20%20%20Larry%20Niven%20pdf%20file&ser=y

Niven examines such issues as changes in caloric value with height and distance, the rotation of the earth, and more. It is quite an exhaustive examination, and one I remember fondly. You might find it interesting.

2208219

I edited my blogpost about UnicornTeleportation. I added your links and credited you.

While it's true she can "teleport," Twilight's teleportation does not represent actual instantaneous displacement in spacetime. If you watch carefully, there is a pause of about a tenth of a second before she "pops", and then another pause (sometimes as long as a second) before she reappears. Now, while these values represent pauses in the real world, and not the passage of time in-universe (which is subject to subjective temporal distortion, allowing us to see high-speed events), it is still clear that the "teleport" isn't truly instantaneous as it does have a period of "lag" between disappearance and reappearance.

If we look closely at this scene, we see that Twilight "jumps" before an explosion hits her library, and is immediately caught by the blast wave when she "jumps" back in maybe 100 meters away from the treehouse, suggesting that the blast wave was faster than her. She must have jumped before the explosion, because for the "teleport" to be instantaneous Twilight would be required to "jump" almost half a second after the explosion had gone off, which I think we can agree is highly unlikely for obvious reasons. High explosive compounds have detonation velocities between 2000–10,000 meters per second (Mach 5.88–29.39), and the lapse of time between her jumping and the fireball hitting her treehouse is roughly the same as the duration between the impact and Twilight Sparkle's reappearance. Assuming Twilight "jumped" into the house to grab Owlicious and then "jumped" out of the treehouse right before the fireball hit it, that means a "jump" itself should take anywhere between 10–50 milliseconds to complete, and thus has an approximate "velocity" of roughly 2000–10,000 meters per second (Mach 5.88–29.39), probably slightly slower than the blast wave since she was thrown by the tail end of it. I'd wager that the blast wave is also on the slow side, since high-velocity blast waves have a tendency to cause a lot more widespread collateral damage than was depicted due being higher energy. So Twilight's "teleportation" is fast, but nowhere near "instantaneous".

However, I still commend you on your work. Very fascinating. Somewhat reminiscent of orbital mechanics to me, due to the complexity of accounting for the relative velocities of bodies.

2215659

The trouble with displacing spacetime (I imagine that 2 hypersphere of swap spacetime coordinates) is the time part. This gets into reference frames, worldlines, apparent synchronicity fro 1 observer and asynchronicity for other observers.Although, I avoided mathematics for the sake of the readers, I only used special relativity. I do not believe that I could work out the problem of timing without general relativity.

I suspect that the spell in S02E20 “It’s About Time”, which let Twilight Sparkle travel a week into the past is a modified TeleportationSpell.

2215838
Oh yes, I'm aware of the headaches involved with solving "spatial transference"... but as I stated in the post above, the evidence supports the claim that Twilight is actually not displacing spacetime (at least not the same manner implied by the basic interpretation of "teleportation") since there is a measurable duration between her disappearance and reappearance some distance away. In classic physics, this implies the quantity of velocity. I'll admit that there might be feasible alternate explanations involving effects like Lorentz transformations, but for now the evidence points to "teleportation" having a significantly slower-than-light velocity. I imagine that what might be happening is that the molecules comprising Twilight accelerate to hypersonic speeds and then accelerate in the opposite direction for the same value to cancel her momentum.
——How this is accomplished without invoking invariably fatal consequences like forces on the order of dozens of thousands of gees and aerodynamic heating effects on the order of thousands Kelvins... I don't know.

Anyways, I found it interesting that Twilight's time travel spell is implied to not operate as a type of quantum time travel, where she was an existence that was causally independent from the "past" version of herself and could thus "change the past" without invalidating herself. No, the episode implies that Twilight was causally determined and that her traveling to the past would not change the outcome. By my understanding, this is how some "pseudo-time machines" would operate in quantum mechanics—at least in that they would not allow changes to be made to the past in order to preserve causality.

2215908

Another thing about the TimeTravel of Twilight Sparkle and StarSwirl The Bearded is that it means that freewill does not exist:

Past Twilight Sparkle could not change the future and Future Twilight Sparkle could not change the past, despite all of their best efforts.

It was always the destiny of Rainbow Dash to perform the Sonic RainBoom and the destiny of the Mane 6 to bear the Elements of Harmony. Princess Celestia understands this when she makes Twilight Sparkle her student. She understands this when she selects Ponyville, the home of the other future ElementBearers, to host the SumerSunCelebration. She sent Twilight Sparkle to meet 4 of the 5, but understood that Pinkamena Diane Pie will find Twilight Sparkle unassisted. In MLP:FIM, everything is destine to happen.

You gave me much to think about with the problem of asynchronicity of teleportation. I have always been of the opinion that those in the teleportationbubble, for example, SunSetShimmer, perceive the teleport as instantaneous. ¿What is your opinion?

2215991

I have always been of the opinion that those in the teleportationbubble, for example, SunSetShimmer, perceive the teleport as instantaneous. ¿What is your opinion?

It's possible that they perceive the action as instantaneous—however, this presents interesting problems to the teleporting ponies. For example, if they perceive the action of "teleportation" as being instantaneous, but the action actually takes several milliseconds to complete, technically those ponies are in effect losing several milliseconds of their time on each "jump" since they do not consciously perceive of those milliseconds passing. It might not seem like much difference, but even small discrepancies will build up over time. For example, a pony who abused "teleportation" over a relatively short period of time could potentially affect their sub/unconscious perception of time, such as screwing with their circadian rhythm. That's not a particularly good example since circadian clocks are constantly entrained to the local environment by external cues like daylight, but I think you get the idea.

2216018

It would take quite a bit of teleportation to loose even a minute.

2216041
True, but Twilight teleports quite a lot, sometimes many times in a row.

Okay, can we make this work? An inclusive theory of teleportation would have to allow for initial and final states with different positions, velocities, orientations, and angular velocities.

e = v d m

(e=energy, v=volume, d=distance, m=mass)

The proportionality is a fair guess, but that doesn't balance dimensionally. So let's write it:

e = k v d m + Δe

where k is a constant to make the dimensions fit, and Δe, which can be positive or negative, accounts for the difference in energy between the initial and final state (accounting for the effects you mention: gravitational potential and kinetic energy, and anything else).

Next point to speculate: Where does this energy come from and go to? It seems every unicorn has an inner reserve of magical energy, but Twilight can also draw magical energy from other sources. While some energy is dissipated as heat, light and sound, is there something else? If a unicorn teleports from a high to low altitude, there could be a lot of energy to dissipate. Is there some sort of large magical reservoir to which excess energy can be dumped? (And maybe also drawn from?) If so, perhaps one can also use this to transfer linear and angular momentum.

Of course, from the audience's perspective, this interpretation is indistinguishable from another interpretation: Magic does not have to conserve energy, momentum, or any other physical property.

2651447

I always imagined that Twilight Sparkle just compensated for gravitational Potential and differences in velocity as part of the teleportation process while compensating for orientation and angular momentum by physically moving her body before the jump. After all, she already has a balance-system and motor-cortex. ¿Why not use them? I always imagined the sequence as thus:

0 Jump so as to achieve final orientation and angular momentum.
1 Teleport.
2 Land.

In the last few months, I thought about the example of Princess Mi Amore Cadenza. It seems to me that she need only input the minimum activation-energy for teleporting a gigameter straight down. The gravitational potential energy provides the rest. She can even use the gravitational potential for matching velocity with the ground, which races off to the east. The thing is to prevent emerging at 10 km/s, she while have to dump the potential energy. For conservation of momentum, she will have to accelerate her immediate surrounding so as to compensate for her momentum. Basically, for her to emerge motionless relative to the ground, she would have to send a blast of air supersonically, mostly down, but a little to the west. Basically, her emerging motionless relative to the ground would cause a big boom. At least it would not require anything more than activation-energy. She might even be able to harvest some of the energy from the difference in gravitational potential for later.

I still have not figured out the source of magical energy. ¿Do you have any hypotheses?

By the end of the weekend, I shall rewrite the blogpost for including your insights and crediting you too, just as I did for Chatoyance and Capn-Chryssalid. I see that I forgot to edit in the insight about time-dilation by Temporarily Permanent, so I shall do that too and credit him. If I have not done so me next week, then please remind me —— ¡I have a CutieMark in procrastination!

Ah, teleportation. This was fun to read, even if it's not my usual science (mechanics for the win!).
Thanks for linking me to this, it was interesting.

2683357

I am glad that you should enjoy this.

jxj

I'm more of a mechanics guy, so I could horribly off base so feel free to correct me. Recently I started looking at a quantum model for teleportation based off of electron tunneling.
Modeling a pony as a probability wave, you have a region where they are most likely to be found (where there body is) with the amplitude of the wave rapidly approaching zero as it radiates out, however it never quite zeros out.
Simply put, the probability of finding a pony where there body is isn't 100% it is 99.9 repeating %. This means that the probability of finding the pony elsewhere isn't 0%, it's 1x10^(-infinity) %. This isn't zero, even if it is infinitely close to it.
To teleport, a pony would manipulate the probabilities, making it infinitely probable that they will appear at their target and infinitely improbable that they will be where they currently are, thus they will disappear from where they are and re appear at their target.
A nice thing about this model is that it gets rid of some of the problems mentioned above. there is no distance component, it takes the same amount of energu to teleport 1 foot as it does 1 mile. It also gets rid of the special scenarios mentiones. For example, if Celestia teleported from Ponyville to Canterlot she wouldn't need to add extra energy to gain elevation since she is targeting a state with the required potential energy.
Like I said this isn't my area of expertise, so input would be nice.

2683803

This post is about UnicornTeleportation. This manipulating probability:pinkiehappy: is how PartyPonies such as Mister CheeseSandwich and Miss Pinkamena Diane Pie Teleport. :pinkiehappy: Physics amd Miss Pinkamena Diane Pie do not go together. :pinkiegasp:

jxj

2684394 so quantum mechanics doesn't exist?

2684416

It is a joke about the extremely low-probability things Miss Pinkamena Diane Pie can do. Jordan179 writes stories with Miss Pinkamena Diane Pie manipulating probability

Jordan179

jxj

2684433 ahh, sorry. I misinterpreted your comment.

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