What Are Tachyons?
Tachyons are theoretical faster-than-light particles with imaginary mass. A 2024 breakthrough proposed reconciling them with Special Relativity via a "Twin Space" formalism requiring both past and future boundary conditions, contrasting with standard Hilbert spaces. Critics argue the model violates quantum commutation relations, rendering it "unphysical." While tachyonic fields exist in Higgs mechanics and string theory as instabilities, observational constraints from black holes rule out heavy tachyons. Speculative models link them to dark matter. Connections bridge Aharonov's Two-State Vector Formalism and Turok's CPT-Symmetric Cosmology. A unified 2024-2026 framework (Ekert-Dragan-Turzyński) suggests quantum indeterminacy emerges from superluminal relativistic geometry, treating time-symmetric boundary conditions as fundamental.
Tachyons are theoretical particles that would always travel faster than light. Unlike normal matter, which requires infinite energy to reach light speed, tachyons would possess “imaginary mass” (involving the square root of a negative number) and would actually speed up as they lose energy — the opposite of ordinary particles .
The concept was first formalized by physicist Gerald Feinberg in 1962 as a way to explore the mathematical boundaries of Einstein’s relativity .
The 2024 Breakthrough: Tachyons Reconciled with Relativity?
A major development came in July 2024 when researchers from the University of Warsaw and University of Oxford published a paper in Physical Review D claiming that tachyons can actually be reconciled with Einstein’s special theory of relativity .
The Key Insight
The team discovered that previous problems with tachyon theory all shared one root cause: boundary conditions. They found that to properly describe tachyons, you need to specify not just the initial state of a system (the past), but also the final state (the future)
.
“To calculate the probability of a quantum process involving tachyons, it is necessary to know not only its past initial state but also its future final state” — researchers explained.
This means the future can influence the present — a radical idea that the theory itself forces upon us, not just an interpretation. The researchers also predict this creates a new type of quantum entanglement between past and future.
Immediate Pushback: “Unphysical”
However, the 2024 paper faced swift criticism. In June 2024 (even before the Warsaw/Oxford paper was fully published), physicists argued that the proposed tachyon quantum field theory isn’t actually quantum — the tachyon field commutes at all points, violating the canonical commutation relations required for quantum mechanics.
A December 2024 follow-up reinforced this critique, showing the theory fails to satisfy basic quantum requirements and that the LSZ formalism (standard for particle physics) cannot be properly applied to tachyons
Where Tachyons Do Appear (Without Faster-Than-Light Travel)
Importantly, “tachyonic fields” already exist in physics — but they don’t violate causality:
The Higgs field has imaginary mass before symmetry breaking, making it technically “tachyonic”
These fields represent instabilities, not faster-than-light particles
When they “condense” (like the Higgs field did after the Big Bang), they become normal particles with positive mass
No information travels faster than light in these systems
String theory also predicts tachyonic states, but these indicate instabilities in spacetime or D-brane systems, not physical particles.
Observational Constraints: Black Holes Rule Out Heavy Tachyons
Harvard astrophysicist Avi Loeb and colleagues published new constraints in January 2025, using the existence of long-lived black holes to limit tachyon properties.
Their logic: tachyons would escape black holes through enhanced Hawking radiation, causing rapid evaporation. Since we observe billion-year-old stellar-mass black holes:
Tachyons heavier than ~1 billion proton masses are ruled out
Future discovery of primordial black holes could push constraints down to 7–700 proton masses
Wilder Ideas: Tachyons as Dark Matter?
In March 2024, physicists proposed that tachyons might constitute dark matter — the invisible substance dominating cosmic mass. Their model showed a tachyon-filled universe could slow its expansion then reaccelerate, matching dark energy observations.
While the model fit Type Ia supernova data as well as standard cosmology, it remains speculative and untested against cosmic microwave background or large-scale structure data.
The Aharonov Connection: Two-State Vector Formalism
The 2024 tachyon paper by Bialynicki-Birula and Damski explicitly cites Aharonov, Bergmann, and Lebowitz (1964) as the foundation for their approach.
The Core Parallel
Aharonov’s two-state vector formalism describes quantum mechanics using both past and future boundary conditions:
Standard quantum mechanics: You prepare an initial state, evolve it forward, then measure
Aharonov’s approach: You specify both an initial state (pre-selection) and a final state (post-selection), then calculate probabilities between them
The tachyon researchers found their “twin space” formalism (combining states from the past and future) “bears a remarkable resemblance” to Aharonov’s work:
“The two-state vector formalism offers a useful guiding principle for understanding the twin space... ℱ contains information on pre-selected quantum states... while ℱ corresponds to post-selected states prepared in the future”*
Why This Matters
Both frameworks treat time symmetrically — the future influences the present just as much as the past. For tachyons, this isn’t philosophical; it’s mathematically forced by Lorentz invariance. The tachyon field requires knowing both “in” (past) and “out” (future) states to calculate anything.
The Turok Connection: CPT-Symmetric Cosmology
Neil Turok hasn’t worked directly on tachyons, but his “mirror universe” hypothesis (developed with Latham Boyle) shares the same time-symmetric, boundary-condition philosophy:
The Mirror Universe Model (2018–present)
Turok proposes our universe has a CPT-symmetric partner on the other side of the Big Bang:
Our universe: Time flows forward, matter dominates
Mirror universe: Time flows backward (from our perspective), antimatter dominates
“Picturing the big bang as a mirror neatly explains many features of the universe which might otherwise appear to conflict with the most basic laws of physics” — Turok
Where They Diverge
Critical difference: Turok’s model is classical/geometric — a spacetime solution. The tachyon formalism is quantum mechanical, requiring actual future measurements to calculate present probabilities.
Turok has also critiqued Hawking’s no-boundary proposal (which shares some time-symmetric flavor) as “deeply ambiguous” and “a disaster” quantum mechanically
. This suggests he might view the tachyon formalism’s quantum consistency claims with similar skepticism.
The Standard: Hilbert Spaces
What it is: The mathematical “room” where normal quantum mechanics lives.
Key feature: One boundary — you only need to know the past (initial state) to predict the future.
Past (known) → [Evolution happens here] → Future (unknown, calculated)
↑
State |ψ⟩
|
Hilbert space ℋ
Math: One state vector |ψ⟩ evolving forward in time under the Schrödinger equation.
Problem with tachyons: If you try to put tachyons in a normal Hilbert space, Lorentz invariance breaks — the math becomes inconsistent when you switch reference frames
The New Framework: Twin Space (ℱ ⊗ ℱ*)
What it is: Two “rooms” glued together — one for the past, one for the future.
Key feature: Two boundaries — you must specify both initial state AND final state.
Past (known) ←→ [Tachyon lives here] ←→ Future (known)
↑ ↑
State |ψ⟩ State |φ⟩
| |
Space ℱ Space ℱ*
\___________ glued together ___________/
Twin space ℱ ⊗ ℱ*
Math: You calculate probabilities between pre-selected (past) and post-selected (future) states. The tachyon field connects both boundaries simultaneously.
Why this works: Lorentz transformations mix space and time. For faster-than-light particles, “before” and “after” become relative — some observers see the particle arrive before it departs. The twin space handles this by treating both time directions equally.
I’ll explain the tachyon quantum field framework and its posterior developments (boundary-condition formalisms) in direct comparison to Hilbert spaces, keeping this extremely simple and visual as you prefer.
The Standard: Hilbert Spaces
What it is: The mathematical “room” where normal quantum mechanics lives.
Key feature: One boundary — you only need to know the past (initial state) to predict the future.
Visual:
Past (known) → [Evolution happens here] → Future (unknown, calculated)
↑
State |ψ⟩
|
Hilbert space ℋMath: One state vector |ψ⟩ evolving forward in time under the Schrödinger equation.
Problem with tachyons: If you try to put tachyons in a normal Hilbert space, Lorentz invariance breaks — the math becomes inconsistent when you switch reference frames .
The New Framework: Twin Space (ℱ ⊗ ℱ*)
What it is: Two “rooms” glued together — one for the past, one for the future.
Key feature: Two boundaries — you must specify both initial state AND final state.
Visual:
Past (known) ←→ [Tachyon lives here] ←→ Future (known)
↑ ↑
State |ψ⟩ State |φ⟩
| |
Space ℱ Space ℱ*
\___________ glued together ___________/
Twin space ℱ ⊗ ℱ*Math: You calculate probabilities between pre-selected (past) and post-selected (future) states. The tachyon field connects both boundaries simultaneously.
Why this works: Lorentz transformations mix space and time. For faster-than-light particles, “before” and “after” become relative — some observers see the particle arrive before it departs. The twin space handles this by treating both time directions equally.
The Critical Difference
Table
AspectHilbert Space (Normal)Twin Space (Tachyons)Information neededOnly pastPast + FutureTime directionOne-waySymmetricCausalityFixedRetrocausal (future affects present)Particle speed< light speed> light speedMassReal (positive)ImaginaryEnergy relationE² = p² + m²E² = p² - m² (flipped sign)
Posterior Developments: Three Boundary-Condition Frameworks
These all extend beyond standard Hilbert spaces by adding future constraints:
1. Aharonov’s Two-State Vector Formalism (1964)
Same structure: Pre-selected state ⟨ψ| (past) + post-selected state |φ⟩ (future)
Used for: Weak measurements, quantum paradoxes
Difference: Applied to normal particles, not specifically tachyons
Math: “Weak value” ⟨ψ|A|φ⟩/⟨ψ|φ⟩ — measurable effects from both boundaries
2. Tachyon QFT (Bialynicki-Birula & Damski, 2024)
Same structure: ℱ (past states) ⊗ ℱ* (future states)
Used for: Lorentz-invariant faster-than-light fields
New feature: Entanglement between past and future — the boundary conditions themselves become quantum-correlated
3. Turok-Boyle CPT-Symmetric Cosmology (2018+)
Same philosophy: Time-symmetric boundary conditions
Applied to: The entire universe, not particles
Structure: Our universe (forward time) + mirror universe (backward time) across Big Bang
Difference: Classical geometry, not quantum field theory
Visual Comparison: All Three Frameworks
HILBERT SPACE (Standard QM)
━━━━━━━━━━━━━━━━━━━━━━━━━━━
Past ──→ [Particle] ──→ Future
(known) evolves (unknown)
TWIN SPACE (Tachyons)
━━━━━━━━━━━━━━━━━━━━━━━━━━━
Past ←──→ [Tachyon] ←──→ Future
(known) connects (known)
both ways
TWO-STATE (Aharonov)
━━━━━━━━━━━━━━━━━━━━━━━━━━━
Past ──→ [Weak measurement] ←── Future
(known) ↑ (known)
│
Both influence
the present
CPT COSMOLOGY (Turok)
━━━━━━━━━━━━━━━━━━━━━━━━━━━
Mirror ──→ [Big Bang] ←──→ Us
Universe (boundary) Universe
(time ↓) (time ↑)
Why This Matters
Hilbert space assumes time has a direction — cause → effect.
Twin space frameworks ask: What if time is just another dimension, like space? In space, you need boundary conditions on both sides of a region to solve physics problems. The new frameworks treat time the same way.
The controversy: Critics argue the tachyon version fails to be truly quantum — the field operators commute everywhere, violating the uncertainty principle that makes quantum mechanics work.
So while the math is consistent with relativity, it may not describe real quantum particles.
Unified Framework (2024–2026)
The recent work effectively unifies these previous strands:
From Aharonov: It takes the Time-Symmetric view (past + future boundary conditions).
From Turzyński/Turok: It applies this to Cosmology and Field Theory (inflation, dark matter, vacuum stability).
From Ekert/Dragan: It provides the Relativistic Geometry (1+31+3 signature flip) that explains why nature behaves this way.
Summary of the Relation:
The Ekert-Dragan-Turzyński framework can be viewed as “Aharonov’s Time-Symmetric Quantum Mechanics derived from Special Relativity.” It gives a geometric home to Aharonov’s post-selected states (they live in the superluminal 1+31+3 sector) and uses Turzyński’s field-theory tools to make it cosmologically viable (as seen in the 2025–2026 projections).
Conceptual Bridges
A. Time-Symmetry as Fundamental
Turok: The universe is exactly symmetric under combined Charge-Parity-Time reversal; the “anti-universe” before the Bang is not a separate entity but the CPT image of ours.
Ekert-Dragan: Superluminal observers experience time dimensions where our “future” is part of their “space,” making boundary conditions from both temporal directions physically relevant—echoing Aharonov’s two-state vectors, but derived geometrically.
B. Emergence of Quantum Behavior
Turok: CPT symmetry selects a unique quantum vacuum state on the extended spacetime, explaining the arrow of time and baryon asymmetry without new physics.
Ekert-Dragan: Quantum indeterminacy emerges when subluminal observers describe physics that is deterministic in the superluminal 1+31+3 sector
science.
C. Economy of Assumptions
Both frameworks explicitly reject adding inflation, extra dimensions, or new forces beyond the Standard Model where possible. Turok states: “nature has worked out a simpler way of being consistent than theorists had anticipated”
Dragan and Ekert similarly seek to derive quantum axioms from extended relativity alone.
3. Potential Synthesis: Where the Frameworks Could Converge
The most intriguing connection lies in the geometric interpretation of symmetry:
The “Mirror” as a Signature Flip: Turok’s CPT mirror across the singularity (t→−tt→−t) is mathematically analogous to the Ekert-Dragan signature flip across the light barrier (3+1→1+33+1→1+3). Both involve a discrete transformation that exchanges temporal and spatial roles.
Tachyonic Degrees of Freedom as Mediators: In the Ekert-Dragan formalism, superluminal observers perceive fields that appear as quantum wavefunctions to us. If such tachyonic fields existed in the early universe, they could naturally mediate the CPT-symmetric matching condition at the Big Bang that Turok’s model requires.
Cosmological Application of Superluminal Relativity: The 2025–2026 papers you referenced (e.g., Tachyonic Gravitational Dark Matter Production after Inflation, Jan 2026) explicitly apply the superluminal framework to early-universe cosmology. This creates a direct bridge: Turok’s CPT-symmetric background could provide the stage on which Dragan-Ekert tachyonic fields generate dark matter and structure.
Summary: A Complementary Pair
You can view these frameworks as complementary lenses:
Turok asks: “What global symmetry of the entire spacetime explains cosmological observations without inflation?” → Answer: CPT symmetry across the Bang.
Ekert-Dragan ask: “What local symmetry of observer transformations explains quantum behavior without new axioms?” → Answer: Lorentz covariance extended to v>cv>c.
The synthesis you are probing would be: If the CPT-symmetric universe contains superluminal degrees of freedom (as permitted by Ekert-Dragan), then the “mirror” at the Big Bang could be understood as a cosmological-scale signature flip, with tachyonic fields providing the dynamical link between pre- and post-bang epochs.
This is precisely the direction of the 2025–2026 work you mentioned. If you have a specific paper or preprint in mind that makes this connection explicit, please share the title or arXiv ID, and I will retrieve the precise formulation. Otherwise, the relation above represents the current theoretical frontier where these two programs intersect.
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