Can Light Signals Travel Faster-than-C in Vacuum? Presented at CCFP 2006, Nizhny Novgorod Prof. Heidi Fearn • Department of Physics, California State University Fullerton, Fullerton, CA 92834

Introduction Time Dilation Serious problems with violation of SR… Literature cited

Relativistic causality implies that the front velocity of the pulse Brillouin, “Wave propagation and Group Velocity”, sʹ B • QED as we know it (at low to semi high energies) requires SR and causality! cannot travel faster than the speed of light in a vacuum. The front Academic Press, New York (1960). The commutation relations depend on it. velocity of the pulse is that part of the wave packet that has the Light Clock Experiment highest UV frequency components. This corresponds to a disconti- Wang, et al., Nature 406, 277 (2000). • High energy QED may have problems.. May not depend on SR. Radiation nuity (non-analytic cut) in the pulse. This is the speed at which in- Assume you have a Scharnhorst L L reaction could be re-addressed for example… possibility of removing Stenner et al., Nature 425, 695 (2003). formation flows. 0 0 type experiment in progress Landau poles and all inconsistencies like run-aways and pre-acceleration. s between the mirrors. The velocity Barton & Scharnhorst, J. Phys. Math Gen. 26, v in different frames (one with a • Adler- strong magnetic field effects? Faster-than-c signals? 2037 (1993). Scharnhorst Effect A C Scharnhorst and one without) Milloni & Svozil, Phys. Letts. B248, 437 (1990). v ∆t will measure different velocities 1. Scharnhorst, Phys. Letts. B236, 354 (1990) Feb. perpendicular to the mirrors and 2 Ben-Menahem, Phys. Letts. B250, 133 (1990). ∆ hence register different times. 2. Barton, Phys. Letts. B237, 559 (1990) Mar. t Clarify: Basics of QED sʹ frame of moving light pulse clock Itzykson & Zuber, “Quantum field theory”, 3. Scharnhorst, Annals. of Phys. 7, 700 (1998). s is stationary lab frame. • The method of quantization of the fundamental Lagrangian in QED McGraw Hill, NY (1965). requires commutators of the form which do not allow for signals Path length of moving pulse measured in s = AB + BC Bjorken & Drell, “Relativistic quantum fields”, Casimir Vacuum (interaction between particles/information of any kind) to pass between McGraw Hill, NY (1965). L 2 ½ two space-like separated points. 2 v ∆t c∆t = 2 L0 + Scharnhorst, “The velocities of light in modified ( ( 2 ) ) V⊥ > c • Example of the scalar field quantization follows for simplicity purposes QED vacua” http://arxiv.org/hep-th/9810221 Square 2 2 2 2 2 c = V c ∆t = 4 L0 + v ∆t here- Dittrich & Giess, Phys. Rev. D58, 025004 2 2 2 2 Mirror ∆t (c – v ) = 4 L0 (1998), also their book “Probing the quantum Photon vacuum”, Springer Press. 2 L0 2 L0 / c 2 ∆t = = ϕ α2 π 2 2 ½ 2 ½ Quantization of for the KG field 11 c (c – v ) (1 – v 2) Loudon, R.“Quantum theory of Light” Oxford ∆n≃ – and c⊥ = ≈ (1 – ∆n)c > c /c (mL)4 223452 n r Classical action s[ϕ] is given by, Metric + ---, x → (ct, x) University Press. Proper time ∆to = 2 L0 /c –60 ∆c 1.6 × 10 ∆c –36 as measured Hatfield, B. “Quantum field theory of point ∼ and for L = 1µm we get ≃ 1.6 × 10 4 1 4 µ 2 2 4 on the moving s[ϕ] = ∫d x L(x) = ∫d x [∂ ϕ(x)∂µϕ(x) – m ϕ (x)] particles and strings” c L c γ = 1 2 clock ⇒ ∆t = γ ∆t0 , (1 – v2 )½ According to [1] above, ∆c/c /c2 ∂L • “obviously is far beyond any experimental reach”. We define the conjugate momentum as, π (x) = = ∂tϕ = ϕ Acknowledgments ∂(∂tϕ) I would like to thank the organizers for inviting

Vacuum effects due to Dirac Sea 1 4 2 2 2 2 me to CCFP 2006. The quantized Hamiltonian is; H = ∫d x (π + |∇ϕ| + m ϕ ) Lorentz Contraction 2 • The electron-positron (Dirac) field profoundly alters the properties Conference Sponsers: of the vacuum in QED relative to those of the classical vacuum: It induces non-linearity’s in Maxwell’s eqns. and a consequent S With the equal time commutators defined as; l Air Force Office of Scientific Research scattering of light by light. r r r r ∆t1 to get from left to right • l sʹ [ϕ(x,t), π(y,t)] = iδ (x – y) ϕ = i[H, ϕ] = π (x) o V ∆ Another more conclusive d1 t2 to get from back to left • The non-linearity’s, jointly with mirror induced changes in the Light Clock experiment ZP Maxwell field, (between parallel mirrors) can cause c to Russian Foundation for Basic Research V r r r r • change or the vacuum to amplify. Not sure which ? [ϕ(x,t), ϕ(y,t)] = [π (x, t), π (y,t)] = 0 π = i[H, π] ⇒ ϕ + m 2ϕ = 0 d2 Remember, the change in c v ∆t1 predicted by the Scharnhorst European Office of Aerospace Research Page 108, Quantum field theory by Itzykson and Zuber. effects is dependent on the and Development When do the Dispersion relations apply? distance between the parallel v ∆t2 • Topic of current research-- mirrors. If the distance between the mirrors is different in one l frame to another in relative For further information • Toll, Phys. Rev. 104, 1760 (1956)- dispersion relations connect proper length of clock = o (as measured in sʹ) The same holds for 2nd Quantization and for ∆ l motion-velocity of light becomes the Re. and Im. parts of the diagonal elements of the scattering proper time for one round trip = t0 = 2 0 /c (as measured in sʹ) Please contact [email protected]. matrix. frame dependent. particles of zero mass d1 = l + v ∆t1 = c ∆t1 ⇒ l = ∆t1 (c – v) More information on this and related projects can be obtained at • Dispersion relations used in QFT first by Gell- Mann, Thirring What value of c do we use in 3 d2 = l – v ∆t2 = c ∆t2 ⇒ l = ∆t2 (c + v) d k 1 –i(k.x) + i(k.x) • http://physics.fullerton.edu/~heidi and Goldberger , Phys. Rev. 95, 1612 (1954). the Lorentz transformations? ϕ(x) = ∫ {a(k)e + a (k)e } π (x) = ϕ (2π) 3 2ω An older e-print relevant here can be found at, l l 2lc 2l/c How do we agree on time k ∆t = ∆t1 + ∆t2 = + = = • Is there a minimum length scale involved which the wavelength 2 2 2 2 http://arxiv.org/quant-ph/0310059. The paper (c – v) (c + v) (c – v ) (1 – v /c ) dilation and Lorentz contraction. of light is not allowed to fall below? How many atoms constitutes will be published in the Laser Physics journal(3) 3 ik.x + 3 3 the minimum number before you can apply the idea of a refractive a(k) = ∫ d x e [ωkϕ(x) + iπ (x)] [a(k), a (k')] = (2π) 2ωkδ (k – k') v17, (2007). time dilation ∆t = γ ∆t0 = γ 2L0 /c index? Is something defined for the vacuum? l • E and B-fields and quantized and then vector potentials are quantized 2L0 /c 2 /c 2 2 ½ • Are we misusing the dispersion relations and idea of refractive ⇒ ∆t = ∆t1 + ∆t2 = = → l = l0 (1 – v /c ) into harmonic oscillator raising and lowering operators, a and a+ terms, (1 – v2/c2) (1 – v2/c2) index for vacuum? with similar commutators as above, FT as needed.