LAB Physics - file 05
The Time Travel Particles – Tachyons
If time travel were possible?
A mathematical theory suggests particles called Tachyons. If Tachyons exist…?
● Tachyons would always travel faster than light (v > c).
● Tachyons would actually travel backward in time.
● Tachyons would require infinite energy to slow down to the speed of light (c).
However, unfortunately, most physicists believe Tachyons do NOT actually exist because it would break the law of causality. In physics, a cause must come before the effect.
Tachyons are extraordinary, hypothetical particles that always travel faster than the speed of light (v > c). The concept itself does NOT strictly violate relativity, but has NOT been experimentally proven, either. Tachyons possess imaginary mass and can NOT slow down to light speed or below. If Tachyons exist, they would move backward in time.
Tachyon’s Extraordinary Speed and Energy
Surprisingly, unlike ordinary matter, adding energy to a Tachyon slows it down, while removing energy speeds it up.
Due to the theoretical nature, Tachyons exist ONLY above the speed of light ( v > c ), with their slowest speed limit being the speed of light ( c ). And Tachyon’s maximum speed is infinite with zero energy.
An ordinary matter usually speeds up as it gains energy. This is intuitive. But Tachyon’s energy-speed relationship is opposite. It accelerates as they lose energy.
Accordingly, to slow a Tachyon down to the speed of light ( c ) requires infinite energy. This infinite boundary engenders a barrier to proving Tachyons in reality.
If Tachyons exist, they would be effectively invisible to human eyes or conventional sensors. Because Tachyons travel faster than light, they move ahead of the photons that would allow them to be visible. Tachyons could potentially emanate a faint Cherenkov radiation flash as a luminous shockwave, rather than appearing as a visible object.
Negative Energy? – Reinterpretation Principle (RIP)
Since Tachyon's energy can be arbitrarily negative, in mathematical theory, Tachyons could move backward in time.
Tachyons are mathematically consistent with the equations of Special Relativity, but fall into conflicts with relativistic causal structure. Because Tachyon's energy can appear negative in certain inertial frames of reference, it violates conventional concepts of causality.
It's a matter of sign reversal. A Tachyon with negative energy moving backward in time can be reinterpreted as a positive-energy antiparticle moving forward in time.
According to the Reinterpretation Principle (RIP, or switching procedure) in theoretical physics, a Tachyon with negative energy traveling backward in time can be inversely reinterpreted as a positive-energy antitachyon traveling forward in time. It's absolutely the same phenomenon that is inverted in the view of the interpretation.
Because Tachyons travel faster than the speed of light ( v > c ), there are inertial frames of reference in which a Tachyon appears to be absorbed before it is emitted, or to have negative energy. This phenomenon violates causality in physics.
The Reinterpretation Principle (RIP) states that an observer can NOT distinguish between the emission of a negative-energy Tachyon traveling backward in time and the absorption of a positive-energy Antitachyon traveling forward in time. It's absolutely a negative and positive sides of the same phenomenon.
This is similar to the Feynman-Stückelberg interpretation of antimatter in quantum field theory. In this interpretation, a negative-energy particle traveling backward in time is equivalent to a positive-energy antiparticle traveling forward in time.
If the reinterpretation of Tachyons holds, a signal can NOT be sent toward the past to cause a time paradox. Because a received antiparticle travelling forward in time is mathematically and physically equivalent to a particle emitted into the future by the observer. In this way, the causality can be preserved with the Antitachyon.
Instability – Tachyonic Field
In quantum field theory, a Tachyon refers NOT to a particle, but to an instability called the Tachyonic field, where a system's energy tends to drop toward a lower state.
The Tachyon is NOT considered a physical, traveling faster-than-light particle. Instead, it describes an unstable field configuration that decays before any such particle can exist. The Tachyonic field represents an instability. It acts as a field with imaginary mass.
The imaginary mass is defined as having a negative mass-squared ( m2 < 0 ). If the rest mass (m) is an imaginary number (a multiple of i = √-1 ), squaring it results in a negative real number.
It signals that the Tachyonic field is at an unstable maximum of its potential energy, causing it to spontaneously decay into a stable minimum via a process called Tachyon condensation.
A Tachyonic field indicates that the chosen vacuum state is unstable. The field rolls down from its unstable state ( φ = 0 ) to a stable minimum, where the Tachyonic nature disappears.
For most fields, φ = 0 means the empty state of the lowest energy, as the vacuum. If the field stays at zero, it shows that NO particles exist. It’s the point of equilibrium where the field is at rest. If we add energy into the field, φ starts to vibrate or oscillate around zero, which we interpret physically as the presence of a particle.
In most field theories, physics looks the same whether φ is positive or negative. φ = 0 is the special point of perfect symmetry. Nevertheless, in a Tachyonic field, such as the Higgs field, φ = 0 means instability, like an unstable state of the ball on the top of a steep hill.
Symmetry Breaking – Higgs Field
The Higgs field is an invisible energy field permeating the entire Universe, and vital to the Standard Model of particle physics, as it explains why atoms can form.
The Higgs field gives mass to elementary particles as they interact with it, rather than being related to gravity. Without the Higgs field, fundamental particles would NOT have mass and would travel at the speed of light.
Particles that strongly interact with the Higgs field acquire more mass, which prevents them from traveling at the speed of light ( c ) in a vacuum. The interaction gives particles rest mass, requiring them to travel slower than the speed of light ( c ) per Special Relativity.
On the other hand, the primary particles that do NOT interact with the Higgs field are photons and gluons. Because they do NOT couple with the Higgs field, they remain massless and travel at the speed of light ( c ). The Higgs field specifically gives rest mass to particles that interact with it, primarily fermions and the W and Z bosons.
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| Mexican hat potential |
As we can see in the image above, the Higgs field can be visualized by such a unique 3D surface plot called the Mexican hat potential. In the Mexican hat potential, a central metastable peak with unstable high-energy drops to a circular, stable, lowest-energy valley.
If you imagine a marble (as a particle) on the top of the Mexican hat, it's easier to make sense of How unstable the top of the Mexican hat is, and How it triggers spontaneous symmetry breaking (SSB), as a system starting at the center MUST spontaneously choose a non-zero, low-energy asymmetric ground state in the valley.
The Higgs field is uniform throughout the Cosmos. And through the view of symmetry breaking, it explains why fundamental particles have consistent masses everywhere.
Higgs Field as a Tachyonic Field
In terms of quantum field theory and elementary particle physics, the Higgs field is considered a Tachyonic field during the unbroken phase of the early Universe.
In this sense, a Tachyon refers to a field with an imaginary mass, that is, a negative mass-squared value ( m2 < 0 ). For the Higgs field, Tachyons do NOT mean particles traveling faster than light. Rather, it signifies the instability of the Higgs field’s initial state.
The Tachyonic Phase and Symmetry Breaking
Before the Universe cooled, the Higgs field permeating the Universe was at a high-energy unbroken state, as visualized at the top of a hill in the Mexican hat potential.
Because the mass-squared was negative ( m2 < 0 ), the Higgs field’s energy was at a local maximum due to the instability. This unstable state is mathematically identical to a Tachyonic field.
Tachyonic Condensation
Just as a marble at the top of a hill of the Mexican hat will inevitably roll down, the Higgs field underwent Tachyonic condensation. This phenomenon fell from the unstable zero-value state toward a stable, non-zero energy state in the circular valley of the hat.
This Tachyonic condensation is just a spontaneous symmetry breaking (SSB). Once the Higgs field settled into its NEW stable vacuum, the Tachyonic negative mass disappeared, and the Higgs field’s dynamic excitations became the real, positive-mass Higgs boson.
The Higgs Boson is a localized, quantized oscillation, essentially represented as a wave or ripple, in the Higgs field, similar to how a photon is a ripple in the electromagnetic field.
Tachyons were initially born from a mathematical theory. So, while they are mathematically consistent within relativistic formulations, Tachyons have NOT been experimentally detected in reality.
Tachyons are elusive. To comprehend the Tachyon completely, we need a broad and deep understanding of elementary particle physics and field theories with unfamiliar, strange mathematical symbols and complicated equations…
Having said that, in a rough sketch, it would be a little easier to make sense if we reverse Tachyons inside out. In this inverse view, Tachyons could be an antiparticle to travel along time without discrepancy.
In my future posts, let's dive deeper into field theories together! Coming soon and stick around!
Further reading (sponsored by Amazon):
● Tom Lancaster, et al. (2014). Quantum Field Theory for the Gifted Amateur (Illustrated edition). 512 pages. Oxford University Press.
(sponsored by Amazon)
“Quantum Field Theory for the Gifted Amateur” is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory! Using numerous worked examples, diagrams, and careful, physically motivated explanations, “Quantum Field Theory for the Gifted Amateur” will smooth the path towards understanding the radically different and revolutionary view of the physical world that quantum field theory provides, and which ALL physicists should have the opportunity to experience!
Table of Contents
0: Overture
I The Universe as a set of harmonic oscillators
1: Lagrangians
2: Simple harmonic oscillators
3: Occupation, number representation
4: Making second quantization work
II Writing down Lagrangians
5: Continuous systems
6: A first stab at relativistic quantum mechanics
7: Examples of Lagrangians, or how to write down a theory
III The need for quantum fields
8: The passage of time
9: Quantum mechanical transformations
10: Symmetry
11: Canonical quantization of fields
12: Examples of canonical quantization
13: Fields with many components and massive electromagnetism
14: Gauge fields and gauge theory
15: Discrete transformations
IV Propagators and perturbations
16: Propagators and Green’s functions
17: Propagators and fields
18: The S-matrix
19: Expanding the S-matrix: Feynman diagrams
20: Scattering theory
V Interlude: wisdom from statistical physics
21: Statistical physics: a crash course
22: The generating functional for fields
VI Path integrals
23: Path integrals: I said to him, “You’re crazy”
24: Field integrals
25: Statistical field theory
26: Broken symmetry
27: Coherent states
28: Grassmann numbers: coherent states
VII Topological ideas
29: Topological objects
30: Topological field theory
VIII Renormalization: taming the infinite
31: Renormalization, quasiparticles and the Fermi surface
32: Renormalization: the problem and its solution
33: Renormalization in action: propagators and Feynman diagrams
34: The renormalization group
35: Ferromagnetism: a renormalization group tutorial
IX Putting a spin on QFT
36: The Dirac equation
37: How to transform a spinor
38: The quantum Dirac field
39: A rough guide to quantum electrodynamics
40: QED scattering: three famous cross-sections
41: The renormalization of QED and two great results
X Some applications from the world
42: Superfluids
43: The many-body problem and the metal
44: Superconduction
45: The fractional quantum Hall fluid
XI Some applications from the world of particle physics
46: Non-abelian gauge theory
47: The Weinberg-Salam model
48: Majorana fermions
49: Magnetic monopoles
50: Instantons, tunneling and the end of the world
A: Further reading
B: Useful complex analysis
Index
