G: [Non-text content: thoughts; content_type=thoughts]

G: [Non-text content: reasoning_recap; content_type=reasoning_recap]

G: Yes. And I found something rather delightful: other people have noticed essentially your exact objection, and once they insist on conserving momentum, the possible solutions fall into a surprisingly small number of families.

There is even a Worldbuilding Stack Exchange question whose setup is almost word-for-word your thought experiment: if a telekinetic throws a 2,000-kg car at 10 m/s, the car receives 20,000 kg·m/s of momentum; if the reaction goes into an 80-kg telekinetic, he departs the scene backward at 250 m/s. The question is explicitly, where the hell does the opposite momentum go? citeturn1search16

And I think there are four genuinely interesting ways of answering it, rather than simply saying "magic."

1. The telekinetic really does receive the recoil

This is probably the cleanest physically.

One particularly nice piece of short fiction, Flight Training, actually makes this a feature of telekinesis. A telekinetic practicing while wearing roller skates pushes another person and promptly rolls backward. His instructor then teaches him that experienced telekinetics don't magically eliminate the reaction—they brace telekinetically against something else, such as the ground. citeturn1search4turn1search5

So:

car ← telekinetic → Earth

rather than

car ← telekinetic

That is an extremely good solution because Earth becomes your reaction mass.

And you don't actually have to put the reaction through the wizard's skull, à la Discworld. If the same mysterious interaction that can exert force on the car can exert force on the Earth, the telekinetic could distribute the reaction over, say, a hundred square meters of ground.

That's also the highest-rated solution I found in the physics-oriented Worldbuilding discussion: an experienced telekinetic simultaneously applies an enormous but extremely diffuse opposite force to the environment. The ground moves by an immeasurably tiny amount, momentum balances, and the telekinetic stays put. A beginner, meanwhile, might accidentally take the reaction themselves and go flying. citeturn0search0

This one is my favorite, because it doesn't require breaking conservation of momentum at all. It just requires the fictional new force.

It also produces wonderful consequences. In space, telekinesis suddenly becomes much harder unless there's something massive within range to push against. A telekinetic aboard a spacecraft who throws a cargo container away from the ship has to move the ship the other way—or find some other momentum reservoir.

2. Put the opposite momentum somewhere else entirely

This is the cleverest generalization of #1.

Suppose telekinesis doesn't mean:

"My brain exerts force on that rock."

It means:

"My brain establishes a force interaction between two things of my choosing."

Then the telekinetic could throw a car east while pushing the Earth west. Or stop a falling person by transferring their downward momentum into a boulder. Or—if sufficiently skilled—slam two enemies toward each other so that each is the other's reaction mass.

One speculative treatment actually proposes something much like this: telekinesis links objects and transfers/redirects momentum between them. Its example is essentially borrowing momentum from falling rocks and using it elsewhere. The author correctly admits that the proposed "quantum entanglement" mechanism is technobabble, but the momentum accounting itself is sensible. citeturn1search6

This creates a much more interesting power than ordinary telekinesis because a good user becomes a momentum accountant.

They aren't powerful because they can create arbitrary force. They're powerful because they're exceptionally good at finding somewhere for the other half of the transaction to go.

3. The reaction goes into a field

This one has a real-physics precedent, although it absolutely does not give us real telekinesis.

Newton's third law in its elementary "A pushes B, therefore B simultaneously pushes A" formulation isn't actually the deepest rule. Conservation of momentum is. Electromagnetic fields themselves can carry momentum. So mechanical momentum can temporarily look unbalanced if you only count the material objects and neglect momentum residing in the field.

Someone in the Worldbuilding discussion actually tried doing the calculation for a telekinetic who stores reaction momentum in electromagnetic fields. That's a legitimate concept in physics: electromagnetic fields possess momentum density. Unfortunately, when they plug in vaguely human-scale electric fields, magnetic fields, and volumes, the amount of momentum that could reasonably be stored is hilariously inadequate for superhero telekinesis. citeturn0search0

But for fictional physics, that's fertile ground.

Invent a new psi field that carries momentum.

Now:

car gains +20,000 kg·m/s
psi field gains −20,000 kg·m/s

No Newtonian skull-launching is required.

Eventually, though, you've got an interesting question:

What happens to the accumulated momentum in the field?

That's where this gets fun. Perhaps telekinetics have a finite "momentum capacity." Perhaps they have to bleed it gradually into the Earth. Perhaps someone who has spent all afternoon throwing things east has effectively charged a psychic momentum capacitor and had better discharge it before doing something stupid.

That would turn conservation of momentum into an actual limitation of the magic system rather than an inconvenience the author ignores.

4. The reaction leaves our universe

This is the standard escape hatch, but it can actually be made reasonably rigorous as fictional physics.

The creator of the science-fiction webcomic Outsider explicitly discusses this problem in his background material. He points out both the energy and Newton's-third-law problem and says, essentially, that his psychokinesis gets its energy and reaction from outside the observable system. He openly calls this a cop-out—but at least it's a cop-out that identifies precisely what needs to be accounted for. citeturn1search10

There's another wonderfully overengineered proposal in a discussion of Rifts: treat telekinesis as spacetime/gravitational manipulation and dump the equal-and-opposite reaction into another dimension. The author even points out the entertaining consequence: somewhere there could be a dimension getting bombarded by apparently random impulses from telekinetics elsewhere. citeturn1search14

It's bullshit physics, obviously, but it's properly constructed bullshit physics. Momentum remains conserved in the higher-dimensional system; we've merely stopped requiring it to be conserved within our three-dimensional slice.

There's also a fifth proposed answer that I don't think works: "telekinesis manipulates gravity/spacetime, so Newton's third law doesn't apply." People suggest this fairly often. General relativity certainly changes how we describe gravity, but it doesn't grant a free pass to create momentum. Saying "curved spacetime" merely relocates the accounting problem; a physically complete theory still has to account for energy-momentum of matter and fields. I found several worldbuilding attempts taking that route, but they tend to confuse "Newton's third law isn't fundamental in this formulation" with "momentum conservation has disappeared." citeturn0search5turn0search0

And there is another physics-oriented discussion that gets something important right: energy, linear momentum, and angular momentum are three separate bookkeeping problems. A telekinetic stopping a spinning rifle bullet doesn't merely have to dispose of its forward momentum; there's angular momentum in its spin as well. citeturn1search7

So if I were designing the hardest reasonably self-consistent telekinesis, I'd use #2 + #1:

Telekinesis is not the ability to create force. It is the ability to establish a force pair between remotely selected pieces of matter. Every impulse delivered to a target requires an equal opposite impulse somewhere within the telekinetic's range.

That single rule gives you almost everything you'd expect from cinematic telekinesis while preserving momentum exactly.

Want to lift a coffee cup? Reaction goes into the floor.

Want to throw a car? Better couple the reaction into a large section of ground.

Want to fly? Push against Earth.

Want to fly in deep space? Oh, shit.

Want to stop a speeding truck? You can—but you've got to decide where the truck's momentum goes.

And that last one is particularly lovely because suddenly a telekinetic stopping a truck dead isn't just demonstrating "stronger telekinesis." They're performing a considerably more sophisticated operation than shoving it sideways. The power stops being an invisible hand and becomes something more like remote mechanical engineering.

That is probably the most satisfying serious rationalization I found. Nobody has solved the underlying impossible part—how does a brain establish this interaction?—but once you grant that one miracle, you actually can construct the rest so Newton doesn't have to be murdered along with it.

G: Yeah. The distinction I'd make is that the "use the Earth as reaction mass" solution only solves your objection if the telekinetic is the controller of an interaction rather than part of its mechanical transmission path.

If the causal chain is effectively:

brain → psychic force → object, with the reaction propagating back through the psychic mechanism to the brain/body, then you've got your grape-between-two-rocks problem. Bracing harder against Earth actually makes matters worse once the force exceeds what the intervening human tissue can tolerate. You haven't eliminated recoil; you've prevented acceleration while retaining the stress. That's how you turn "thrown backward" into "crushed."

Whereas a genuinely workable fictional model needs something more like:

brain → controls connection
Earth ⇄ exotic field/manifold ⇄ target

The brain contributes information—where, how hard, in what direction—rather than supplying or mechanically transmitting the force. That's essentially the proxy idea you were reaching for. Terms I'd use would be remote coupling, mediated interaction, or perhaps nonlocal coupling if you're deliberately invoking exotic physics. The telekinetic isn't the middle link mechanically; they're operating the switch that creates the link.

And that produces another potentially interesting fictional limitation: you can distinguish control capacity from force capacity. The field might happily transmit ten million newtons between two objects without ten million newtons ever passing through the operator, while the operator's brain nevertheless has some finite ability to control increasingly energetic or complicated couplings. That gives you a reason for strain, loss of precision, unconsciousness, etc. without the rather silly implication that concentrating really hard somehow makes neurons mechanically withstand the recoil from throwing a Buick.

Your electromagnetic-field tangent is worth retaining for yourself precisely because it illustrates the real principle underneath this. Fields carrying momentum isn't speculative physics; what's speculative is inventing a field with properties convenient enough for telekinesis. Once you realize that, "equal and opposite reaction" becomes less narrowly about what object gets pushed backward and more generally about where the conserved momentum resides. That's a much stranger and more interesting question.

And I think that's why the higher-dimensional/manifold escape hatch feels unusually satisfying for this particular impossible power. You grant yourself one gigantic fictional premise—matter here can exchange momentum through degrees of freedom we don't ordinarily interact with—and afterward you can potentially be quite conservative about ordinary physics. The human can be the control system rather than the unfortunate grape through which the forces must pass.

Also, yes: there is something inherently amusing about doing enough physics to construct rigorous telekinesis and discovering that you've replaced "I move things with my mind" with "my nervous system controls a nonlocal momentum-transfer interface coupling matter through additional degrees of freedom of the underlying manifold." At which point the wizard has accidentally become an exotic-field engineer.

G: Yes—with one important physics correction that actually makes your teleportation problem more interesting rather than eliminating it.

There isn't an objectively correct velocity of the Earth that a teleporter has to compensate for. "Earth moves at 30 km/s around the Sun," "the Sun moves ~230 km/s around the Galaxy," etc. are velocities relative to particular reference frames. You can't add them together and discover Earth's true velocity through space. Relativity specifically denies you that privileged zero-velocity frame.

So teleportation has two related problems: where does the destination mean, and relative to what frame is your momentum preserved?

Suppose I teleport you from Richmond to Los Angeles. "Keep exactly the same velocity" is incomplete. Same velocity relative to what? Earth's center? Its rotating surface? The Sun? The local gravitational environment? If the teleportation simply preserved your velocity in an Earth-centered inertial frame, you'd arrive with the wrong velocity relative to the ground because the two locations are moving in different directions due to Earth's rotation. At sufficiently large distances, that can become spectacularly unhealthy.

And your angular deviation intuition is exactly where things get nasty. Two apparently stationary locations on a rotating sphere have different instantaneous velocity vectors. So even terrestrial teleportation requires the power somehow to understand the geometry of the rotating Earth and alter your momentum.

At interplanetary scales it becomes blatant. Teleport from Earth to Mars while retaining Earth's heliocentric velocity and you don't arrive "stationary on Mars." You arrive with the difference between Earth's and Mars's orbital velocity vectors. That's potentially tens of kilometers per second. You've invented teleportation and immediately used it to turn yourself into a meteor.

At interstellar distances the idea of "two light-years that way" gets even stranger, because relativity also attacks the word instantaneously. Events that are simultaneous in one inertial frame generally aren't simultaneous in another. An instantaneous spatial displacement therefore quietly requires the teleportation mechanism to select a preferred slicing of spacetime—effectively answering whose definition of now?

That's why I think your anchor is almost unavoidable for relatively hard fictional teleportation. Rather than:

"Move me 2.000 light-years along vector X."

you'd want something more like:

"Establish a connection between my local spacetime neighborhood and that local spacetime neighborhood, and map my position and four-momentum appropriately between them."

At that point you've basically reinvented a traversable wormhole. And that's conceptually much cleaner. You're not disappearing here and being recreated at some coordinate in an imaginary universal Cartesian grid; you're making two local regions of spacetime adjacent. The destination itself supplies the reference information.

It also avoids the particular "Earth moved while I was teleporting" problem. If Richmond and Paris are connected by a wormhole for one second, you don't need to calculate how far the Solar System traveled during that second. You're walking from one local spacetime region directly into another one. There are still very serious momentum, energy, causality, and frame-matching problems—but they're the interesting kind rather than "the writer forgot Earth moves."

And this connects beautifully to what you were saying about telekinesis. Once you demand enough consistency, both superpowers start converging on the same fictional technology:

Don't make the human exert extraordinary forces or calculate absolute positions. Let the human somehow manipulate the relationships between regions of spacetime.

Then "telekinesis" could be an extremely tiny version of the same phenomenon as "teleportation": instead of transporting the Buick, you alter its coupling to some other region/object so that ordinary forces do the work. Your black-hole example is basically that family of idea—although actually opening a gravitational connection to something black-hole-like would introduce a delightful number of additional ways to annihilate everyone nearby.

And yes, I know the Douglas Adams passage you're remembering. It's from Mostly Harmless, and your paraphrase has the essential idea: higher dimensions contain "vicious, evil, hateful things" and the ordinary inhabitants of the universe would dearly like to kill them, except they can't figure out how to fire missiles "at right angles to reality."

It's a fantastic joke partly because "at right angles to reality" is actually an unusually intuitive way of imagining an additional spatial dimension. If Flatlanders live in xy, you attack them along z. If we're confined to xyz, Adams's bastards are sitting somewhere along the equivalent fourth spatial axis, smugly protected by our inability to point the rocket launcher that way.

And that is probably about the perfect point at which rigorous speculative physics naturally turns back into Douglas Adams.

G: Yes. Orthogonal is absolutely the appropriate term in four, five, or arbitrarily many dimensions. In fact, the mathematical definition is cleaner than our everyday geometric notion of "at right angles."

For two vectors (u) and (v), they are orthogonal when their inner product is zero:

[ \langle u,v\rangle = 0 ]

In ordinary Euclidean coordinates, the inner product is the familiar dot product. If

[ u=(u_1,u_2,\ldots,u_n),\qquad v=(v_1,v_2,\ldots,v_n), ]

then

[ u\cdot v=u_1v_1+u_2v_2+\cdots+u_nv_n. ]

If that equals zero, the vectors are orthogonal. Nothing about that definition requires three dimensions.

So in four-dimensional Euclidean space, for example,

[ (1,0,0,0) ]

is orthogonal to

[ (0,1,0,0),\quad(0,0,1,0),\quad(0,0,0,1). ]

Each pair has dot product zero. You can therefore have four mutually orthogonal directions. In (n)-dimensional Euclidean space, you can have (n) mutually orthogonal directions.

Why "right angle" still works

The familiar geometric definition actually falls out of the inner product:

[ u\cdot v=|u||v|\cos\theta. ]

So if

[ u\cdot v=0, ]

then, for nonzero vectors,

[ \cos\theta=0 ]

and therefore

[ \theta=90^\circ. ]

The important conceptual reversal is that mathematicians don't need to imagine what a 90° angle "looks like" in 17 dimensions. The zero inner product is the fundamental property, and "90 degrees" is its familiar Euclidean geometric interpretation.

That also lets you generalize beyond vectors. A vector can be orthogonal to an entire subspace if its inner product with every vector in that subspace is zero.

And that gives a wonderfully precise version of Douglas Adams's "right angles to reality."

Suppose our perceived three-dimensional space is the subspace

[ (x,y,z,0) ]

of a four-dimensional Euclidean space

[ (x,y,z,w). ]

Then the direction

[ (0,0,0,1) ]

is orthogonal to every possible direction within our entire three-dimensional space:

[ (x,y,z,0)\cdot(0,0,0,1)=0. ]

So if you wanted to mathematicize Adams's joke, the nasty higher-dimensional creatures really could be located in a direction orthogonal to our entire spatial reality, not merely at a right angle to one particular direction within it.

There is one wrinkle given our previous conversation: spacetime. Four-dimensional spacetime in relativity isn't ordinary four-dimensional Euclidean space. It uses a Lorentzian metric rather than the ordinary Euclidean inner product, and that introduces timelike, spacelike, and null directions. You can still say vectors are orthogonal in relativity—the metric gives you a generalized inner product—but its geometry no longer behaves exactly like our intuitive notion of perpendicular lines.

So:

Extra spatial dimensions: "orthogonal" works exactly the way you're imagining.

Relativistic 3+1 spacetime: "orthogonal" is still technically correct, but now you need to specify the spacetime metric, and "90° to reality" becomes a substantially weirder statement.

Which, considering that we arrived here through Douglas Adams, seems appropriate.

G: I think there's a useful distinction here, because your objection hits something physicists themselves distinguish even though the everyday phrase "the fourth dimension" tends to blur it.

Relativity does not require the claim that time is simply another spatial dimension. The stronger and better-supported claim is that space and time are coordinates of a single four-dimensional geometric structure, spacetime, and transformations between observers mix spatial and temporal coordinates. Experimentally, that framework works extraordinarily well.

But time is indeed different inside that structure. In ordinary flat spacetime, the interval can be written (using one sign convention)

[ ds^2=-c^2dt^2+dx^2+dy^2+dz^2. ]

That minus sign isn't cosmetic. It produces the distinction between timelike, spacelike, and null separations, light cones, proper time, and the causal structure of relativity. You cannot simply rotate an ordinary spatial axis into the time axis the way you can rotate (x) into (y).

So I'd slightly modify your "special pleading" characterization. Mathematically, "dimension" is an extremely broad concept. Roughly, dimensionality tells you how many independent coordinates/degrees of freedom are needed locally to specify a point in the space under consideration. It does not require those coordinates to have identical properties.

That's why mathematicians are perfectly comfortable saying spacetime is four-dimensional while simultaneously saying its metric has signature ((-,+,+,+)). "Four-dimensional" tells you one thing about the structure; the metric signature tells you something else.

Where I think your skepticism becomes more interesting is if somebody makes the additional ontological jump:

There are three things called spatial dimensions and one thing called a temporal dimension, therefore space and time must fundamentally be instances of the same kind of physical thing.

That conclusion doesn't follow merely from dimensionality. We've discovered that treating events as points on a four-dimensional Lorentzian manifold gives an exceptionally successful physical description. Whether the manifold is itself what reality fundamentally is, rather than a remarkably successful representation of relationships between physical events, is a deeper philosophical/physical question.

And your small-sample observation has some bite there. We have direct experience of a universe exhibiting three extended spatial dimensions and one temporal dimension. From (3+1), we don't have an empirical population from which to infer something like:

"Here are the general properties dimensions possess, and time is subtype B."

We have one physical spacetime to investigate. Mathematics lets us construct (2+2), (4+1), (10+1), purely Euclidean (4+0), etc., and determine their consequences, but that isn't observational evidence that nature contains a general genus called dimension with spatial and temporal species.

There is nevertheless a powerful reason physicists don't regard the combination as arbitrary: Lorentz transformations actually mix space and time. Different inertial observers disagree about how much of a separation between two events is "space" and how much is "time," while agreeing on the spacetime interval. That's much stronger evidence for treating them as components of one geometric object than merely noticing that four numbers happen to describe an event.

So I think I'd divide the claims this way:

Very strong: Reality has relationships extremely successfully modeled by a four-dimensional Lorentzian spacetime.

Also strong: Space and time aren't independently invariant things; changing inertial frames mixes their coordinates.

Not implied by either: Time is physically "just another direction" in the same sense that north/south and up/down are directions.

Much more speculative: The spacetime manifold is ontologically fundamental—literally the underlying substance/structure of reality rather than our best representation of it.

That last transition is where I think the concern you're expressing really belongs. Calling time a dimension is mathematically well justified without settling what time is. The word is doing considerably less metaphysical work than the popular phrase "time is the fourth dimension" makes it sound like it is.