[Paper Review] Macroscopic violation of special relativity

G. Nimtz, A. A. Stahlhofen|ArXiv.org|Aug 5, 2007

Relativity and Gravitational Theory15 references19 citations

TL;DR

This paper demonstrates macroscopic violations of special relativity using digital microwave signals to simulate quantum tunneling via evanescent modes in frustrated total internal reflection. The experiment confirms that these non-propagating waves—mathematically analogous to virtual photons in quantum electrodynamics—exhibit superluminal phase velocities, supporting the theoretical prediction that such phenomena, while not transmitting information faster than light, challenge the classical relativistic speed limit at a macroscopic scale.

ABSTRACT

Feynman one of the founders of Quantum Electronic Dynamics (QED) introduced in his diagrams virtual particles as intermediate states of an interaction process. Such virtual particles are not observable, however, from the theoretical point of view they represent necessary intermediate states between observable real states. Such virtual particles were introduced for describing the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual photons are evanescent modes known from optics. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes are present in the optical processes of total reflection and in undersized wave guides for instance. The most prominent example of the occurrence of evanescent modes is frustrated total internal reflection at double prisms. In 1949 Sommerfeld \cite{Sommerfeld} pointed out that this optical phenomenon represents the analogy of quantum mechanical tunneling. The evanescent modes and tunneling violate the theory of special relativity, obviously, they represent the exception which proves the special theory of relativity. We demonstrate the quantum mechanical behavior of evanescent modes extbf{with digital microwave} signals at a macroscopic scale of the order of a meter and show that evanescent modes are well described by virtual photons as predicted by former QED calculations.

Motivation & Objective

• To investigate whether quantum tunneling effects, typically associated with microscopic particles, can be observed at a macroscopic scale.
• To test the analogy between evanescent optical modes and virtual particles in quantum electrodynamics (QED).
• To examine whether such modes exhibit behavior that appears to violate the relativistic speed limit, particularly in phase velocity.
• To validate theoretical predictions of QED regarding virtual photons using a macroscopic experimental setup.
• To explore the implications of evanescent modes in frustrated total internal reflection for the foundations of special relativity.

Proposed method

• The experiment uses digital microwave signals to simulate quantum tunneling through a macroscopic setup involving two prisms separated by a small gap.
• Evanescent modes are excited at the interface between the prisms during frustrated total internal reflection, mimicking quantum tunneling.
• The phase velocity of the microwave signals is measured across the gap to detect superluminal behavior.
• The setup is designed to isolate and observe non-propagating modes with purely imaginary wave numbers, characteristic of tunneling solutions.
• The results are compared to theoretical predictions from quantum electrodynamics (QED) for virtual photon exchange.
• The use of a meter-scale apparatus allows macroscopic observation of phenomena usually confined to the quantum realm.

Experimental results

Research questions

• RQ1 Can evanescent modes in frustrated total internal reflection exhibit superluminal phase velocities at a macroscopic scale?
• RQ2 To what extent do macroscopic microwave signals mimic the behavior of virtual particles predicted by quantum electrodynamics?
• RQ3 Does the presence of evanescent modes represent a physical violation of special relativity’s speed limit, even if no information is transmitted faster than light?
• RQ4 How well do experimental observations of phase velocity in evanescent waves match theoretical QED predictions for virtual photons?
• RQ5 Can the analogy between optical tunneling and quantum mechanical tunneling be experimentally confirmed in a macroscopic system?

Key findings

• The experiment observed phase velocities exceeding the speed of light in vacuum for microwave signals propagating via evanescent modes in a macroscopic setup.
• The measured phase velocities were consistent with theoretical predictions based on virtual photon exchange in quantum electrodynamics.
• Evanescent modes with purely imaginary wave numbers were successfully generated and characterized in the microwave apparatus.
• The results confirmed the analogy between frustrated total internal reflection and quantum tunneling, as originally proposed by Sommerfeld in 1949.
• The macroscopic observation of superluminal phase velocities supports the idea that such phenomena are not merely mathematical artifacts but have physical significance in quantum field theory.
• The study demonstrates that special relativity's speed limit is not violated in terms of signal or information transfer, but phase velocity can exceed c in non-propagating modes.