Newton force with a delay: 5th digit of G Lajos Di osi Wigner - PowerPoint PPT Presentation

Newton force with a delay: 5th digit of G Lajos Di´ osi Wigner Center, Budapest 15 Oct 2015, Budapest Acknowledgements go to: Hungarian Scientific Research Fund under Grant No. 103917 EU COST Action MP1209 ‘Thermodynamics in the quantum regime’ Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 1 / 10

References 1 Lazy Newton forces 2 Lazy Newton forces - covariant form 3 Background 4 Newton’s law restores for pure gravity 5 Static sources look displaced 6 Proposal of Cavendish test of τ G ∼ 1ms 7 Existing and future experimental bounds 8 Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 2 / 10

References References [1] L. Di´ osi, Phys. Lett. A 377 , 1782 (2013). [2] L. Di´ osi, J. Phys. Conf. Ser. 504 , 012020 (2014). [3] L. Di´ osi, Found. Phys. 44 , 483 (2014). [4] L. Di´ osi, EPJ Web of Conf. 78 , 02001-(4) (2014). [5] H. Yang, L.R. Price, N.D. Smith, R.X. Adhikari, H. Miao, Y. Chen, arXiv:1504.02545. Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 3 / 10

Lazy Newton forces Lazy Newton forces Assumption: Newton force is emerging with a delay τ G > 0. Simplest modification of Newton’s instantaneous law: � ∞ − GM x t − τ | e − τ/τ G d τ Φ( � r , t ) = | � r − � τ G 0 Non-covariant! Needs a universal distinguished frame. Covariant version: At each t , go to the co-moving—free-falling frame, calculate lazy Newton field, go back to your frame. co-moving (where velocity ˙ � x t vanishes) free-falling (where gravity � g vanishes) Let’s consrtuct the explicite covariant form. Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 4 / 10

Lazy Newton forces - covariant form Lazy Newton forces - covariant form � ∞ 1 e − τ/τ G d τ Φ( � r , t ) = − GM x t − τ − ˙ τ G | � r − � x t τ + � � g τ 2 / 2 | 0 Valid in any inertial frame in the presence of gravity � g . Boost and acceleration invariance: at 2 / 2 � = ⇒ � x t − � vt − � x t at 2 / 2 � = ⇒ � r − � vt − � r � g = ⇒ � g − � a Let’s see the background! Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 5 / 10

Background Background Quantum foundations - speculative new physics: wave function of massive d.o.f.’s collapses spontaneously G ρ nucl ∼ 1 / ms � at average collapse rate ∼ gravity is emergent, created by wave function collapses at the same rate 1 /τ G ∼ 1 / ms Models: lazy Newton force in a distinguished inertial frame lazy Newton force covariant in any inertial frames Fenomenology of a possible lag τ G : non-covariant model: astronomical/cosmological data completely exclude 1ms Cavendish tests allow for lags 1ms or even longer covariant model: astronomical/cosmological data are irrelevant Cavendish tests may detect τ G ∼ 1ms Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 6 / 10

Newton’s law restores for pure gravity Newton’s law restores for pure gravity Covariant lazy Newton force: � ∞ 1 e − τ/τ G d τ Φ( � r , t ) = − GM x t − τ − ˙ τ G | � r − � � x t τ + � g τ 2 / 2 | 0 If non-gravitational forces are absent: x t − ˙ g τ 2 / 2 + h . o . t . � x t − τ = � � x t τ + � ⇒ � ∞ 1 x t | e − τ/τ G d τ 1 Φ( � r , t ) = − GM = − GM | � r − � | � r − � τ G x t | 0 If all forces are purely gravitational (e.g.: solar system) then τ G cancels and Newton law is restored. Testing delay τ G needs non-gravitational forces. Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 7 / 10

Static sources look displaced Static sources look displaced In Earth gravity g ∼ 10 3 cm/s 2 : Static source ( � x t ≡ � x ) is being under non-gravitational force − M � g . � ∞ 1 e − τ/τ G d τ Φ( � r , t ) = − GM ≈ x t − τ − ˙ τ G g τ 2 / 2 | | � r − � � x t τ + � 0 1 ⇒ vertical shift δ G = g τ 2 ≈ − GM G ∼ 10 µ m g τ 2 | � r − ( � x t − � G ) | Position of static source looks 10 µ m upper vs geometric position. Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 8 / 10

Proposal of Cavendish test of τ G ∼ 1ms Proposal of Cavendish test of τ G ∼ 1ms G is uncertain in 400ppm (5th digit) Correction to G from vertical displacement δ G ∼ 10 µ m at L = 10cm horizontal distance between source and probe: Planar setup: G → (1 − 2 3 δ 2 G / L 2 ) G ⇒ − 0 . 01ppm (9th digit) 45 o setup: G → (1 − 6 5 δ G / L ) G ⇒ − 120ppm, meaning correction − 8 to G ′ s 5th digit 1 0 µ m 5cm 1 0cm Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 9 / 10

Existing and future experimental bounds Existing and future experimental bounds Gravity’s phase lag φ vs frequency ω for periodic sources. Blue: excl.by pulsars; ↓ ’s: upper bounds by E¨ otWash; Viol-Pink-Grey: soon testable in optomechanics [Yang et al. arXiv1504.02545]. I put Red Line φ / ω ≡ τ G =1ms. Blue and ∼ 1kHz ↓ may be irrelevant. Lajos Di´ osi (Wigner Center, Budapest) Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 10 / 10