Unruh-Hawking Radiation Observed in Accelerating Electrons

By: William Brown, scientist at the International Space Federation

New research has validated a near 50-year old prediction in a subset of unified physics—combining quantum field theory (QFT) with general relativity (GR)—known as quantum field theory in curved spacetime, with the direct detection of Unruh-Hawking radiation in accelerating electrons. By examining the photon spectrum emitted during the radiative beta decay of free neutrons, the research team was able to identify a perturbation that matches what is expected from an Unruh vacuum thermalization effect. Like the dynamical Casimir effect, in the Unruh effect particles are emitted from the quantum vacuum, and the researchers of the study discuss the equivalency between the two effects. Using an electron-mirror duality, they report agreement between a thermal 1D Planck spectrum and the photon spectrum. These latest observations therefore provide verification of the Unruh effect, additional verification of photon emission from the quantum vacuum via the dynamical Casimir effect (via the mirror-electron duality), and by equivalence Hawking radiation that is predicted to occur around the strong gravitational field of the event horizon of black holes. The research demonstrates that the rapid acceleration of an electron during neutron decay presents a novel system for investigating the intricate interplay between acceleration, spacetime geometry, and thermodynamics; confirming the existence of thermal radiation emitted by an accelerated electron.

Quantum Field Theory in Curved Spacetime (QFT + GR)

Quantum Field Theory in Curved Spacetime (QFT in CST) is a theoretical framework that combines quantum field theory, which describes the behavior of particles and fields in quantum mechanics, with the curved geometry of spacetime as described by general relativity. The aim is to study and understand the behavior of quantum fields in the presence of gravitational fields and curved spacetime geometries. Interestingly, quantum fields do not behave the same way in curved spacetime geometries as they do in quantum mechanics formulated in flat spacetime geometries, in which the evolution of a quantum field or quantum system is not evaluated with the inclusion of interaction of a gravitational field.

In classical physics, gravity is described by general relativity, which models gravity as the curvature of spacetime caused by mass and energy. Quantum field theory, on the other hand, is highly successful in describing the behavior of elementary particles and their interactions. Until the work of Haramein et al., in The Origin of Mass and the Nature of Gravity [1], it was the case that combining quantum mechanics and general relativity directly (without considering quantum fields) often resulted in conceptual and mathematical difficulties, such as infinities and the lack of a consistent framework for a quantum theory of gravity. Recent progress has seen remarkable results, as the study by Haramein et al., is one of the most successful theories to evaluate the function of quantum fields, specifically the quantum vacuum of the electromagnetic field, in the presence of strongly curved spacetime geometries like black holes.

Beyond theoretical development, for empirical investigations Quantum Field Theory in Curved Spacetime has predominantly relied on analog gravity systems for experimental exploration because scientists cannot yet control the gravitational field to produce controlled highly curved spacetime geometries like, for instance, a micro-black hole in the lab. Since we know from relativity theory that gravity and acceleration are equivalent, it is possible to study the effects of highly curved spacetime geometries via extreme acceleration of particles [2]. The results of just such an experiment have recently been released with one of the first ever direct observations of predicted behavior of quantum fields in strongly curved spacetime geometries.

Some key points about Quantum Field Theory in Curved Spacetime are:

1. Quantum Fields in Curved Spacetime:
• Quantum Field Theory in Curved Spacetime provides a way to study quantum fields in the presence of gravitational fields. It extends the principles of quantum field theory to include the effects of curved spacetime.
2. Metric Tensor and Background Geometry:
• The curved spacetime is described by a metric tensor, which encodes information about the geometry of the space at each point. The metric tensor influences the behavior of quantum fields in the same way that the background electromagnetic field would influence charged particles in quantum electrodynamics.
3. Vacuum Fluctuations and Hawking Radiation:
• One of the most famous results in QFT in CST is the prediction of Hawking radiation. In the vicinity of a black hole, quantum field fluctuations near the event horizon can lead to the creation of particle-antiparticle pairs. If one particle falls into the black hole, and the other escapes, an observer at a distance would perceive this as thermal radiation emitted by the black hole.
4. Renormalization and Effective Field Theory:
• Similar to standard quantum field theory, QFT in CST often requires renormalization techniques to handle infinities that arise in certain calculations. Effective field theories are also employed to describe the low-energy behavior of quantum fields in curved spacetime.
5. Applications:
• QFT in CST has applications in understanding the early universe, the behavior of matter in strong gravitational fields, and the study of cosmological phenomena. For example, since the 1970’s it has been known that theory predicts the generation and emission of particles and thermal radiation from the vacuum as the universe expands and such quantum creation processes during the very rapid early expansion of the universe are believed to give rise to temperature anisotropies and polarization patterns in the CMB radiation, which could potentially be detected and analyzed.

Quantum Field Theory in Curved Spacetime represents an important intersection of quantum mechanics and general relativity, addressing fundamental questions about the nature of spacetime and the behavior of matter in extreme gravitational environments, which as we see in The Origin of Mass and the Nature of Gravity, is key to quantum gravity (QM + GR, or unified physics) and understanding the source and origin of mass, nuclear confinement force, and gravity. Now, there is direct experimental observation of one of the key predictions of quantum field theory in curved spacetime.

Analog Gravity Systems

Thermodynamic particle production is a well-delineated prediction within the framework of quantum field theory in curved spacetime and in addition to the well-known Hawking radiation from the quantum vacuum near black hole event horizons, there is also Unruh vacuum thermalization for relativistic accelerating objects, and particle creation from the vacuum by the expansion of the universe—referred to as the Parker’s effect [3]. Particle creation, and hence mass-energy generation from the quantum vacuum has been extensively empirically investigated and verified via analog gravity systems with fluids, superfluids, superconducting circuits (like in an experiment verifying the dynamical Casimir effect [4]), ultra-cold atoms / Bose-Einstein condensates [5] and optical systems.

The beginning of analog gravity systems starts with William Unruh’s seminal paper in 1981 [6], in which he demonstrated the mathematical analogy between the dynamics of sound waves in a supercritical fluid flow and a field at the event horizon of gravitational black holes, laying the theoretical foundation for today’s empirically realized sonic black holes, where Hawking radiation is studied in a controlled laboratory setting [ISF article tunable entanglement in white hole / black hole system]. Unruh is perhaps most famous for his discovery that an accelerating observer in a quantum field will perceive a thermal bath of particles, even in the absence of any thermal radiation as measured by an inertial observer. This effect is closely related to the more well-known Hawking radiation predicted for black holes. This is known as the Unruh Effect.

Understanding the Unruh Effect

The Unruh effect was first proposed by Unruh in 1976 (key developments also came from Paul Davies and Stephen Fulling, so the effect is also referred to as the Fulling-Davies-Unruh effect). The key idea is based on the concept of vacuum fluctuations in quantum fields. According to quantum field theory, even in a vacuum (absence of particles), there are still fluctuations in the quantum fields associated with particles. When an observer accelerates through space, these vacuum fluctuations can appear to the observer as particles because of anisotropy introduced in the quantum vacuum energy density (comprised of all fluctuation modes above the Planck limit) similar to the dynamical Casimir effect. Or, if considered via the equivalence principle, similar to Hawking radiation, where instead of a gravitational event horizon there is an acceleration induced event horizon (called a Rindler horizon), which acts the same way as in the black hole / gravitational case scenario (hence it is an equivalency).

Let us outline this in more detail:

1. Acceleration and Equivalence Principle:
• The Unruh effect is rooted in the equivalence principle, which suggests that an observer in a uniform gravitational field is equivalent to an accelerated observer in flat spacetime. The accelerated observer experiences an event horizon, similar to the event horizon around a black hole.
2. Thermal Bath for Accelerating Observers:
• According to the Unruh effect, an observer undergoing constant acceleration will perceive the vacuum fluctuations as particles, and the spectrum of these particles will appear thermal, resembling a bath of particles with a characteristic temperature. The temperature perceived by the accelerating observer is proportional to their acceleration.
3. Connection to Hawking Radiation:
• The Unruh effect is conceptually similar to Hawking radiation around black holes. In both cases, observers detect thermal radiation where an inertial observer would see none. While Hawking radiation involves the gravitational field near a black hole event horizon, the Unruh effect is associated with the accelerated motion of an observer.
4. Quantum Field Theory in Curved Spacetime:
• The Unruh effect is an example of the broader phenomenon studied in Quantum Field Theory in Curved Spacetime (QFT in CST). It highlights the intricate interplay between acceleration, gravity, and the behavior of quantum fields.

The Unruh effect and the closely related Hawking radiation of black holes has been one of the most important results of theoretical phsyics of the second half of the 20^th century, hinting at a hidden connection between three seemingly vastly different areas of physics (1) general relativity, (2) quantum mechanics, and (3) thermodynamics. As such, the Unruh effect has been a benchmark for theories attempting to unify these areas ever since.

However, detecting the Unruh effect directly has been a challenging endeavor because the required accelerations are typically extremely high, for example for Unruh thermalization to reach room temperature would require an acceleration of about 10²³ m/s². Like in analog gravity systems, there have been experiments with classical analogs of the Unruh effect, which have reported detection and characterization of analog Unruh radiation in a system utilizing water waves [7]. Effectively, this becomes another example of hydrodynamic quantum analog systems where what were thought to be purely quantum effects are replicated in classical systems.

As previous proposals had outlined [ibid. 2], experimental verification would involve creating conditions in which particles experience significant accelerations.

_{Figure 1. Heuristic interpretation of the Unruh effect for a two-level atomic system. When the atom is at rest (top row), high order (virtual) processes involving the simultaneous emission and absorption of photons are permitted. However, when the atom is accelerated (bottom row), emission and absorption can become decorrelated leaving the atom in an excited state and emitting a photon to a distant observer. Image and image description from [2].}

As can be seen in Figure 1, particles are perpetually interacting with the quantum fluctuations of the vacuum, resulting in effects like the Lamb shift and anomalous magnetic moment of the electron. Particles are constitutively absorbing and emitting virtual photons or—as in the QED shielding of the electron bare charge—virtual particle-antiparticle pairs. When a particle is accelerated, there is an anisotropy introduced to this otherwise uniform absorption and emission of the virtual particles of the quantum vacuum fluctuations and virtual particles become observable or “real”, such that an accelerating particle will see real photons emitted from the vacuum. This is nearly exactly analogous to the dynamical Casimir effect, where the accelerating particle is like a moving mirror and the Rindler horizon (which generates whenever there is an acceleration) is like the secondary surface in between which vacuum modes are excited such that real photons are emitted. Remarkably, recent experiments have reported the direct detection and observation of this electron-mirror duality and measurement of Unruh vacuum thermalization by such accelerating particles.

Electrons as Accelerated Thermometers

While some studies in gravitational wave astronomy have detected significant indications of Planck-scale structure at the event horizon of black holes and Hawking radiation effects [8, 9]—arguably being a direct detection of the QFT in CST effect of Hawking radiation—aside from the analog gravity systems (with indirect evidence) the direct observation of the production of particles from quantum vacuum fluctuations via curved spacetime geometries (like acceleration and gravity) or thermalization of the vacuum has proven difficult to observe experimentally. A breakthrough in this endeavor came from a research group led by physicist Morgan Lynch of Max Planck Institute, in which they examined the radiation emitted by high energy positrons channeled into silicon crystal samples and detected thermalization fully consistent with Fulling-Davies-Unruh temperature (Unruh radiation), presenting evidence for the first observation of acceleration-induced thermality in a non-analog system [10].

In a significant advancement of investigation into particle creation by quantum field in curved spacetime, Morgan lynch and collaborators have detected evidence of Unruh radiation in single accelerated particles. In a breakthrough study the researchers have reported the observation of thermal photons from accelerated electrons [11] as they are emitted during radioactive beta decay of free neutrons (when neutrons are unbound from the nucleus they quickly decay into an electron, proton, and neutrino). With this novel method, beta decay has become a new approach to examining characteristics of thermalized fluctuations in the quantum vacuum. The experimental observation follows from the discovery of the link between the electron of radiative beta decay and the moving mirror of the dynamical Casimir effect.

_{Figure 2. A heuristic diagram demonstrating the equivalence between the Unruh effect (red sphere at top of image, representing an accelerating electron), the dynamical Casimir effect with a rapidly oscillating mirror (teal sphere at middle position, representing a moving mirror stimulating photon emission from the quantum vacuum) and Hawking radiation (represented by the black sphere at the bottom of the image with associated photon thermalization / black hole evaporation). Image reproduced from [11].}

The discovery of the link between the electron of radiative beta decay and the moving mirror of the dynamical Casimir effect was initially detailed by none other than Unruh himself, work that was described with his collaborator Robert Wald in a 1982 paper on the acceleration of radiation and the generalized second law of thermodynamics [12]. That same year a subsequent study by Ford and Vilenkin found that the quantum radiation of scalar particles by a moving mirror reproduced the Fulling-Davies temperature [13], thus theoretically verifying the equivalency of the dynamical Casimir effect with Unruh vacuum thermalization, and though not explicitly stated, the link between the dynamical Casimir effect and Hawking radiation by black holes.

Unified Science- In Perspective

This research is significant because Unruh radiation is equivalent to Hawking radiation via the equivalence principle and it is often rightly referred to as a single effect: Unruh-Hawking radiation. As such, this recent detection of Unruh vacuum thermalization is a verification of Hawking radiation as well. Indeed, Dr. Lynch has used the data from high energy channeling radiation—accelerated quantum electrodynamics—to demonstrate the experimental observation of Hawking radiation [14]. This has significant implications, because studies like The Origin of Mass and the Nature of Gravity demonstrate that mass in the universe has its origin in quantum vacuum fluctuations via Hawking-like radiation. By analyzing the dynamics of quantum vacuum fluctuations in the surrounding strong gravitational field of a micro black hole, with a radius equal to the reduced Compton radius of the Proton, they calculated the resulting Hawking radiation and analyzed its intensity. Remarkably, it was discovered that the mass-energy of the Hawking radiation going from the surface horizon of a micro-black hole at the size of the reduced Compton wavelength of a proton to the surface horizon of a volume at the charge radius of a proton exactly equals the rest-mass of the proton (Figure 3).

Because of the exact equivalence between the mass-energy of Hawking radiation for a micro-black hole at the same volumetric dimensions as the proton with the proton rest mass, the results strongly indicate that the observed rest-mass of the proton emerges from quantum vacuum fluctuations as a result of Hawking-like radiation from a micro-black hole. Under conventional considerations, it would be assumed that a proton-sized micro black hole would almost immediately radiate all of its mass-energy via the Hawking gravitational quantum thermalization effect. In fact, calculations would predict a near-instantaneous explosive radiation of vacuum energy. However, Haramein et al., find that there is a core energy density within the volume of the reduced Compton radius of the proton (λ_p) that is nearly equivalent to the Planck energy density (ρ_vac), which is approximately 8 X 10¹¹³ joules per cubic meter, and that this extreme mass-energy density is reduced at λ_p via a screening mechanism that involves decoherence of the quantum vacuum fluctuations and the Hawking-like radiation. Unlike in Quantum Electrodynamics (QED) where the mass of particles are reduced from an infinite 'bare' mass using a shielding mechanism of quantum vacuum fluctuations (of virtual particle-antiparticle pairs), Haramein et al. identify the vacuum fluctuations as the source of mass that is shielded to produce the observed mass-energy density. 

Although the Hawking temperature generated by the Compton horizon λ_p is continuously radiating energy, which we observe as the rest-mass of the proton, by considering the source energy density ρ_vac the research team finds that the proton black hole lifetime is on the order of 10³⁵ years, making the proton energy structure perfectly stable over very long periods of time. So, remarkably, Hawking radiation applied at the particle scale for micro black holes reveals the origin of mass from the quantum vacuum, thermodynamics, and strongly curved spacetime geometry! The fact that Unruh-Hawking radiation has now been empirically measured at the particle level is a significant verification of this discovery by Haramein et al. that demonstrates the rest-mass energy of the proton emerging from Hawking radiation. 

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[3] L. Parker, “Thermal radiation produced by the expansion of the Universe,” Nature, vol. 261, no. 5555, Art. no. 5555, May 1976, doi: 10.1038/261020a0.

[4] Wilson C.M., Johansson G., Pourkabirian A., Simoen M., Johansson J.R., Duty T., Nori F. and Delsing P. 2011 Observation of the dynamical Casimir effect in a superconducting circuit. Nature 479, 376-379. doi:10.1038/nature10561

[5] M. Tolosa-Simeón et al., “Curved and expanding spacetime geometries in Bose-Einstein condensates,” Phys. Rev. A, vol. 106, no. 3, p. 033313, Sep. 2022, doi: 10.1103/PhysRevA.106.033313.

[6] Unruh W. G. 1981 Experimental Black-Hole Evaporation? Physical Review Letters 46, 1351–1353. doi:10.1103/PhysRevLett.46.1351

[7] U. Leonhardt, I. Griniasty, S. Wildeman, E. Fort, and M. Fink, “Classical analog of the Unruh effect,” Phys. Rev. A, vol. 98, no. 2, p. 022118, Aug. 2018, doi: 10.1103/PhysRevA.98.022118.

[8] J. Abedi and N. Afshordi, “Echoes from the Abyss: A Status Update.” arXiv, Jan. 03, 2020. Accessed: Feb. 07, 2024. [Online]. Available: http://arxiv.org/abs/2001.00821

[9] J. Abedi, L. F. L. Micchi, and N. Afshordi, “GW190521: Search for Echoes due to Stimulated Hawking Radiation from Black Holes,” Phys. Rev. D, vol. 108, no. 4, p. 044047, Aug. 2023, doi: 10.1103/PhysRevD.108.044047.

[10] M. H. Lynch, E. Cohen, Y. Hadad, and I. Kaminer, “Experimental observation of acceleration-induced thermality,” Phys. Rev. D, vol. 104, no. 2, p. 025015, Jul. 2021, doi: 10.1103/PhysRevD.104.025015.

[11] M. H. Lynch, E. Ievlev, and M. R. R. Good, “Accelerated electron thermometer: observation of 1D Planck radiation,” Progress of Theoretical and Experimental Physics, vol. 2024, no. 2, p. 023D01, Feb. 2024, doi: 10.1093/ptep/ptad157.

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[13] L. H. Ford and A. Vilenkin, “Quantum radiation by moving mirrors,” Phys. Rev. D, vol. 25, no. 10, pp. 2569–2575, May 1982, doi: 10.1103/PhysRevD.25.2569.

[14] M. Lynch, Experimental observation of Hawking radiation. 2023. doi: 10.13140/RG.2.2.21698.04808.