“And yet, here we are. Beyond the laws of physics. Welcome onboard.”

To begin this post, we feel it is only appropriate to share the Doctor’s own views on Physics.  Click the link.  You won’t be disappointed.

Laser Weapons:

In Doctor Who, we frequently see the race of aliens called the Daleks arrive on the scene and start yelling “Exterminate!” and shooting people with their laser-like “gunsticks”.  Basically, they shoot their victims with a blue beam which temporarily exposes the victim’s skeleton (as seen in the screenshot for the video below).  The likelihood of the skeleton actually being visible for this brief period of time is obviously very low, however such laser weapons are not impossible at all.  The technology to make them just does not exist yet. Lasers are what Michio Kaku refers to as a Class 1 Impossibility.  They are impossible today but do not violate known laws of physics, so they might become possible someday (Kaku, 2008, p. xvii).  They cannot currently exist due to the lack of an appropriate portable power source and a stable lasing material.  Currently, the only way to provide enough power to run one of these would be to use a miniature hydrogen bomb, but that runs a high risk of exploding you along with your target.  Ray guns are possible, but must be connected to a power supply via cable.  Advances in nanotechnology provide some hope that laser weapons will become possible in the future by creating tiny power packs capable of delivering massive amounts of power (Kaku, 2008, p. 41).  Moreover, once scientists are able to power these handheld lasers, they must then deal with the problems that will arise during real-world usage.  When a laser is directed through any atmosphere, “water vapour molecules, water droplets and carbon dioxide molecules [soak] up the beam, causing localised heating along the beam path which [causes] the beam to dissipate” (Kopp 2008).  This is what is known as “thermal blooming” and it just gets worse the more power you put behind the laser.  In fact, all High Energy Laser (HEL) weapons have great difficulty passing through clouds, dust or other such obstructions.

Time Travel:

To start off our discussion of parallel worlds, it seems appropriate to provide a brief explanation of time travel.  It is what Kaku calls a Class 2 Impossibility: something that hovers near the edge of our current knowledge of physics which might be possible, but only many years in the future (Kaku, 2008, p. xvii).  It is consistent with the known laws of universe and no matter how hard physicists try, they cannot seem to come up with any reason why it could not work.  (Kaku, 2008, p. 242).  It is allowable according to the general theory of relativity as long as you do not travel back in time to a period before the time machine was built.  This is why we have not seen any tourists from the future – thus answering a common gripe made by doubtful scientists (Gribbin, 2009, p. 30).  It would be impossible to travel backwards to a time before the time machine existed; you would make yourself a paradox.  This just cannot happen.  Another problem that is frequently brought up is known as the Grandmother Paradox: What if you go back in time and kill your own grandmother?  There is one simple solution to this: you can’t do this because it hasn’t happened.  You exist, therefore your grandmother must have lived long enough to have your mother and so on.  No matter what you do, you cannot change this because you yourself are incontrovertible proof that you haven’t killed your grandmother.  This brings up sticky issues of lack of free-will/pre-destination, but it does fix the problem.  Most importantly, whatever you do has to be self-consistent.  “Time travelers don’t change the past because they were always part of it” (Gott, 2001, p. 16).

Parallel Worlds:

The idea of parallel worlds used to just be a fun idea to mull over when you were bored, but in 1957, Hugh Everett proposed his “many worlds” idea and made it into not only a plausible but a highly regarded theory in quantum physics.  Everett suggested that in an experiment like the one involving Schrodinger’s cat, the wave function does not collapse when someone looks inside the box.  Instead, since both outcomes are equally likely, the entire Universe splits, or branches.  In one branch of reality, the scientist observes a dead cat and in another branch, a living cat.  In short, “any universe that can exist, does” (Kaku, 2008, p. 244).  As Gribbin (2009) explains, “The best reason for taking the Many Worlds Interpretation seriously is that nobody has ever found any other way to describe the entire Universe in quantum terms” (p. 31).  In fact, Everett’s idea is so popular that the debate now is not so much about whether these worlds can or do exist, but whether we can actually ever reach them, or if we have decohered from them to such an extent that we can never join them again.

The theory of “decoherence” was first formulated in 1970 by Dieter Zeh, a German physicist.  Zeh pointed out that Schrodinger’s cat cannot be separated from the environment inside the box.  Coming into contact with even a single molecule of air inside the box radically affects the cat’s wave function.  Suddenly, that wave function splits into two distinct wave patterns that no longer interact: the one for the live cat and the one for the dead cat.  That one air molecule forces the dead!cat and live!cat wave functions to permanently separate.  This “decoherence” means that the two wave functions no longer interact because they are no longer vibrating in phase with each other (Kaku, 2005, p. 167).  If we add to this Hugh Everett’s “many worlds” interpretation, then the wave function never collapses; it just keeps splitting and splitting with each new interaction.  (Kaku, 2005, p. 168).

What is even more fascinating is the accompanying concept that all of these parallel worlds exist alongside us.  Kaku explains that “although wormholes might be necessary to reach such alternate worlds, these quantum realities exist in the very same room that we live in.  They coexist with us wherever we go” (Kaku, 2005, p. 170).   The reason we cannot see or touch these other worlds is because our wave functions have decohered from them.  All of these worlds have very different energy signatures since each is made up of trillions and trillions of atoms.  “Since the frequency of these waves is proportional to their energy (by Planck’s law), this means that the waves of each world vibrate at different frequencies and cannot interact anymore.  For all intents and purposes, the waves of these various worlds do not interact or influence each other” (Kaku, 2005, p. 170).  According to Kaku, and many other sources, communication with and especially travel to any of these parallel worlds should be impossible because we have decohered from them.

Despite the tantalizing proximity of worlds where dinosaurs still exist, “communication between the different branches of Everett’s Multi-verse…would be impossible, according to the same equations that describe the existence of such multiple realities…Except for one intriguing possibility…time travel.” (Gribbin, 2009, p. 28).  It is this possibility that makes the frequent parallel universe jumping in Doctor Who seem almost plausible.  A traveler could go back in time down one branch of history and then move forward up an entirely different branch than the one they came from.  This means that you could conceivably travel to a parallel universe, but it would be very difficult to arrive in a specific parallel universe (Gribbin, 2009, p. 30).  You would have to make all of the miniscule choices and movements that result in whichever universe you’re aiming for – many of which would be so seemingly unimportant that you would have a very hard time figuring out which tiny insignificant details were actually incredibly significant and which were not.  Moreover, it seems almost certain that if you were to time travel and then interact in any way with the environment you travelled to, you would end up moving up a different branch of reality anyway even if you had not planned to (unless you ascribe to the self-consistency theory of time travel in which you cannot really change anything because whatever you will do is whatever you have already done and vice versa).  This is a fascinating idea to be revisited in the future when a time machine exists.  Doctor Who does not address this as a possible method of travelling between parallel universes, instead the show relies on huge disturbances of the entire fabric of space/time in order to weaken what they conceptualize as the “walls” between worlds so that the characters can transfer back and forth for a limited period of time.

In the episode “Turn Left,” Donna is transported to a universe in which she turned left instead of right while driving one day and so never met the Doctor.  He takes it as a sign of how important she is (or will be) that the universe has formed a whole parallel world around her, even though, as they discuss, parallel worlds are “sealed off.”  This episode also treats parallel worlds as things that can be made and destroyed.  When they kill the creature who created the other world, that world then ceases to exist, instead of her just no longer being in it, unlike within Everett’s “many worlds” theory wherein every possible world already exists (“Turn Left”).  

In another episode, “Army of Ghosts,” Rose and the Doctor accidentally end up in the parallel world where her father is still alive and her parents are happily married but they never had a daughter.  In this episode, several of the characters even have small, wearable “transporters” that will take the wearer from one parallel world to the next as long as the breach in time remains open.  What is funny about this plot point is that the show’s writers and the character of the Doctor himself are all perfectly frank with the audience that, normally, none of this could be happening, but they go to great lengths to explain that since an alien ship has already caused a breach in time, that breach is now allowing them to subvert the laws of physics for a brief period.  Every episode where the Doctor deals with parallel worlds, especially when the plot involves contact between two such worlds, the Doctor clearly explains the impossibility of what is going on and how his actions (or those of the characters around him) are ripping the universe apart in some way or another.  When Rose gets stuck in one universe, while the Doctor is still in another, he does his best to say goodbye to her.  He explains: “There’s one tiny little gap in the universe left.  Just about to close.  And it takes a lot of power to send this projection.  I’m in orbit around a supernova.  I’m burning up a sun just to say goodbye.”  He has to appear as a projection.  He cannot come through completely to a parallel universe because the “whole thing would fracture.  Two universes would collapse” (“Doomsday”)

So at least the show is giving a tip of the hat to the laws of physics when it says that everyone gets stuck in whichever parallel universe they were in when the breach closed.  Though, of course, this does not hold true in the next two seasons when the characters bleed through from one universe to the other anytime the plot needs spicing up.  One memorable example of this was when Rose kept popping up in the normal universe to help with things and deliver cryptic messages even though she should have been stuck in the parallel universe.  At the end of this plot line, the Doctor once again states that passage between the worlds should be impossible and it will soon be so again because the anomaly for that episode (the Reality Bomb) just stopped affecting space/time.  

He has just enough time to, once again, say goodbye to Rose forever before saying “We’ve gotta go.  This reality’s sealing itself off.  Forever” (“Journey’s End”).

In sum, though Doctor Who has many fantastical gadgets and adventures that seem completely impossible, many of them do have some basis in reality and are at least plausible in terms of quantum physics.  Though jumping between parallel worlds is nowhere near as doable as he makes it look, parallel worlds at least can (and probably do) exist.  Though handheld laser weapons that expose your skeleton upon impact do not exist, such weapons could very well exist in only a few years, due to the advances of nanotechnology and their impact on the feasibility of portable power sources.

Black Holes and the Possible Impossible Planet

There are several different types of black holes, but for the purposes of this project, we focused on a non-charged, non-rotating black hole, also called a Scharzschild black hole. There was nothing in “The Impossible Planet” to indicate that the black hole in question was not a Schwarzschild black hole. The essential predicament in the episode is that the Doctor and Rose land themselves on a small planet orbiting around a black hole, and Satan just happens to live there. The Doctor describes the planet as “impossible” and says that in order to counteract the gravity of the black hole, “you’d need a power source with an inverted self-extrapolating reflex of 6 to the power of 6 every 6 seconds” (Jones & Strong, 2006). That sounds really cool, but it’s completely wrong and not even a real thing. The truth is that if they were within the black hole’s event horizon, no amount of force would keep them from being crushed, and if they were not within the event horizon, they are in no immediate danger of being crushed.

A black hole has two important parts: a singularity and an event horizon. The singularity is the single point in the center at which anything that arrives there is crushed out of existence. The event horizon is the point of no return; once an object is within the event horizon, there is a 100% chance that it will reach the singularity. Outside of the event horizon, a black hole acts just as any other object of its mass would; it has gravity, so things can orbit around it, or fall in if they get too close. The question at hand is, how close is too close? When discussing an object around a black hole, there are three possible locations for the object to be. Location 1 is within the event horizon, completely doomed. Location 2 is outside of the event horizon, but not far enough away to be in orbit; in this situation, the object is doomed with a larger time frame, as it will eventually drift within the event horizon. Location 3 is in orbit around the black hole. The remainder of this discussion will focus on location 3, and where exactly it can be found.

Constants

For calculation purposes, the Impossible Planet will be assumed to have the mass and radius of Pluto. (Why? The planet appears very small in the episode, so the smallest planet-like object seemed like a good fit.) Parameters are converted to “geometric units” (1second=2.998X1010cm, 1gram=0.7425X10-28cm).

The planet is also assumed to be orbiting at a velocity of 77,484 m/s, which is the orbit velocity of Mercury. (Why? Mercury is the closest planet to the sun, and the Impossible Planet seemed relatively close to the black hole, so their orbit speeds may be similar.)

Angular Momentum = L = mass x velocity x radius

m = 1.31X1022 kg = 9.73X10-4cm

v = 77,484 m/s = 7,748,400 cm/s

r = 1,137 km = 113,700,000 cm

L = 8.57X1011 cm

Angular momentum is a large factor in the calculation of circular orbit radius.

Circular orbit radius = L (L ± (L2 – 12M2) / 2M               where M is the mass of the black hole.

*See source Walker, J. (2008) for better formatted equations.*

The equation comes from the differentiation of the equation for gravitational effective-potential. The radius equation represents the maximum and minimum of the effective-potential; a circular orbit is only possible at these two points. The orbit at the minimum effective-potential is more stable, and can compensate for small displacements; this orbit has the larger radius. The orbit at the maximum effective-potential is less stable, and cannot compensate for small displacements (i.e. disturbances will send the planet hurtling into the black hole); this orbit has the smaller radius. The Impossible Planet appears to have an orbit of the second type, as the crew lives in fear of being sucked in. It is also important to note that no orbit can exist if L2 < 12M2, as the radius equation would yield two imaginary numbers.

Experimental Calculations

We will now present three scenarios, each dependent on black hole size, and determine the feasibility of the Impossible Planet.

Scenario 1: The black hole is the size of the sun (1 solar mass, radius = 3 km).

M = 1 solar mass = 1.989X1030 kg = 147,683.25 cm

Is L2 < 12M2? No it is not, so an orbit can exist.

L2 = 7.34X1023 12M2 = 2.62X1011

Cir. Orbit radius = [(8.57X1011)(8.57X1011 ± ((8.57X1011)2 – 12(147683.25)2))] / (2 X 147683.25)

= 4.35X105 cm, 4.97X1018 cm

unstable orbit: r = 4.35 km

stable orbit: r = 4.97X1013 km

Scenario 2: The black hole has a mass of 10 solar masses (r = 30 km).

M = 10 solar masses = 1.989X1031 kg = 1,476,832.5 cm

Is L2 < 12M2? No it is not, so an orbit can exist.

L2 = 7.34X1023 12M2 = 2.62X1013

Cir. Orbit radius = [(8.57X1011)(8.57X1011 ± ((8.57X1011)2 – 12(1476832.5)2))] / (2 X 1476832.5)

= 4.43X106 cm, 4.97X1017 cm

unstable orbit: r = 44.3 km

stable orbit: r = 4.97X1012 km

Scenario 3: The black hole has the mass of the largest star (2100 solar masses, r = 6300 km).

M = 2100 solar masses = 4.18X1033 kg = 310,134,825 cm

Is L2 < 12M2? No it is not, so an orbit can exist.

L2 = 7.34X1023 12M2 = 1.15X1018

Cir. Orbit radius = [(8.57X1011)(8.57X1011 ± ((8.57X1011)2 – 12(310134825)2))] / (2 X 310134825)

= 9.30X108 cm, 2.37X1015 cm

unstable orbit: r = 9.30X103 km

stable orbit: r = 2.37X1010 km

Conclusions

In this instance, rather than making impossible technology look possible, the creators of Doctor Who have made something possible look impossible. There is no mathematical reason why the “Impossible Planet” could not exist, as long as it is far enough away from the event horizon. According to NASA, “Outside of the horizon, the gravitational field surrounding a black hole is no different from the field surrounding any other object of the same mass. A black hole is not better than any other object at ‘sucking in’ distant objects” (Lochner, Gibb, & Newman, 2004). This is contrary to the general perception that black holes suck in anything and everything in sight. In fact, it will only suck things in once they are already within the event horizon. If an object gets too close to the event horizon, it will naturally drift in the same way that an object would fall to earth if it got too close. Any object in space with a large mass will pull other objects towards it. The only difference with black holes is what happens after things get sucked in. If an object gets trapped in Earth’s gravity, it will simply fall to the ground, and the damage that results will depend upon the size of the object. If an object gets trapped in the gravity of a black hole, it will eventually be crushed out of existence.

The possibility of fall from orbit is not implausible. If the planet were in an unstable orbit, with a short radius, the orbit could be disrupted. The planet does appear to be very close to the black hole, so a scenario similar to scenario 1 is most likely (i.e. an orbit radius of only a few kilometers). The explanation given in the episode for the planet’s orbit is that Satan is trapped in a pit at the center of the planet, creating massive amounts of energy. The presence of the Prince of Darkness would not cause the planet to fall into orbit. However, the disruption caused by his expulsion from his magic cage may be enough to knock the planet out of its precarious orbit. Someone will just need to find a demon-inhabited planet next to a black hole – and then make it out alive – in order to fully test this theory.

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