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

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

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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

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SLIDE 1

Newton force with a delay: 5th digit of G

Lajos Di´

  • si

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´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 1 / 10

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SLIDE 2

1

References

2

Lazy Newton forces

3

Lazy Newton forces - covariant form

4

Background

5

Newton’s law restores for pure gravity

6

Static sources look displaced

7

Proposal of Cavendish test of τG ∼ 1ms

8

Existing and future experimental bounds

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 2 / 10

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SLIDE 3

References

References

[1] L. Di´

  • si, Phys. Lett. A 377, 1782 (2013).

[2] L. Di´

  • si, J. Phys. Conf. Ser. 504, 012020 (2014).

[3] L. Di´

  • si, Found. Phys. 44, 483 (2014).

[4] L. Di´

  • si, 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´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 3 / 10

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Lazy Newton forces

Lazy Newton forces

Assumption: Newton force is emerging with a delay τG > 0. Simplest modification of Newton’s instantaneous law:

Φ( r, t) = ∞ −GM | r − xt−τ|e−τ/τG dτ τG

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 ˙

  • xt vanishes)

free-falling (where gravity g vanishes) Let’s consrtuct the explicite covariant form.

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 4 / 10

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Lazy Newton forces - covariant form

Lazy Newton forces - covariant form

Φ( r, t) = −GM ∞ 1 | r − xt−τ − ˙

  • xtτ +

gτ 2/2| e−τ/τG dτ τG Valid in any inertial frame in the presence of gravity g. Boost and acceleration invariance:

  • xt

= ⇒ xt − vt − at2/2

  • r

= ⇒ r − vt − at2/2

  • g

= ⇒

  • g −

a Let’s see the background!

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 5 / 10

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Background

Background

Quantum foundations - speculative new physics: wave function of massive d.o.f.’s collapses spontaneously at average collapse rate ∼

  • Gρnucl ∼ 1/ms

gravity is emergent, created by wave function collapses at the same rate 1/τG ∼ 1/ms Models: lazy Newton force in a distinguished inertial frame lazy Newton force covariant in any inertial frames Fenomenology of a possible lag τG: 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 τG ∼ 1ms

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 6 / 10

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SLIDE 7

Newton’s law restores for pure gravity

Newton’s law restores for pure gravity

Covariant lazy Newton force: Φ( r, t) = −GM ∞ 1 | r − xt−τ − ˙

  • xtτ +

gτ 2/2| e−τ/τG dτ τG If non-gravitational forces are absent:

  • xt−τ =

xt − ˙

  • xtτ +

gτ 2/2 + h.o.t. ⇒ Φ( r, t) = −GM ∞ 1 | r − xt|e−τ/τG dτ τG = −GM 1 | r − xt| If all forces are purely gravitational (e.g.: solar system) then τG cancels and Newton law is restored. Testing delay τG needs non-gravitational forces.

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 7 / 10

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Static sources look displaced

Static sources look displaced

In Earth gravity g ∼ 103cm/s2: Static source ( xt ≡ x) is being under non-gravitational force −M g. Φ( r, t) = −GM ∞ 1 | r − xt−τ − ˙

  • xtτ +

gτ 2/2| e−τ/τG dτ τG ≈ ≈ −GM 1 | r − ( xt − gτ 2

G)|

⇒ vertical shift δG = gτ 2

G ∼ 10µm

Position of static source looks 10µm upper vs geometric position.

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 8 / 10

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SLIDE 9

Proposal of Cavendish test of τG ∼ 1ms

Proposal of Cavendish test of τG ∼ 1ms

G is uncertain in 400ppm (5th digit) Correction to G from vertical displacement δG ∼ 10µm at L = 10cm horizontal distance between source and probe: Planar setup: G → (1 − 2

3δ2 G/L2)G

⇒ −0.01ppm (9th digit) 45o setup: G → (1 − 6

5δG/L)G

⇒ −120ppm, meaning correction −8 to G ′s 5th digit µm 1 5cm 0cm 1

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 9 / 10

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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¨

  • tWash; Viol-Pink-Grey:

soon testable in optomechanics [Yang et al. arXiv1504.02545]. I put Red Line φ / ω≡τG =1ms. Blue and ∼1kHz ↓ may be irrelevant.

Lajos Di´

  • si (Wigner Center, Budapest)

Newton force with a delay: 5th digit of G 15 Oct 2015, Budapest 10 / 10