The equivalence principle and
interaction of waves with an
accelerating object
Frank Laboratory of Neutron Physics, JINR
A. FrankA. Frank
ISINN 27, 10-14 June, Dubna
11 June 2019 A.I.Frank. ISINN 27, Dubna
Accelerating Matter Effect
(chronology)
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1977. V. Mikerov numerically investigated the problem of UCN transmission through the
oscillating foil and found that the neutron energy do not conserved at the passing through it.
V.I. Mikerov. PHD thesis, Lebedev Physical Institute, 1977 (was not published)
1982. Kazuo Tanaka solved the problem of transmission of electromagnetic waves through the
linearly accelerating dielectric slab and found that there exists shift in frequency. This shift
depends on the acceleration but not on the velocity K. Tanaka. Phys. Rev. A., 25, 385 (1982)
1993. F.W. Kowalski looking for the new approach to the test of the equivalence principle (EP)
in neutron optics. Solving the problem of neutron transmission through the accelerating sample
came to the contradiction with EP but found that neutron frequency (and energy) change when
neutron passes through an accelerating sample. F. V. Kowalski.Phys. Lett. A.,182, 335 (1993)
1998. V.G. Nosov and A.I. Frank considered the problem of transmission of neutron wave
through the refracting sample moving with acceleration and confirmed the Kovalski formula for
the energy change. V.G. Nosov and A.I.Frank. Phys. of Atomic Nuclei, 61, 613 (1998)
11 June 2019 A.I.Frank. ISINN 27, Dubna
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2006. FLNP-ILL group firstly detected the change of the UCN energy at transmission
through the oscillating silicon slab with quality agreement with Kowalski-Nosov-Frank
(KNF) formula. A.I.Frank et al. JETP letters, 84, 363 (2006)
2008. KNF formula and Tanaka formula were derived in a uniform way from the
equivalence principle. The term “Accelerating matter effect” (AME) was introduced.
A.I.Frank et al. Phys. of Atomic Nuclei, 71, 1656 (2008)
2008, 2011. New observation of AME in the agreement with theory at the level 5-7%.
A.I.Frank et al. Phys. of Atomic Nuclei, 71, 1656 (2008), JETP letters, 93, 361 (2011)
2013г. KNF formula for the neutron wave was derived from the Doppler effect at
refraction. The problem of AME for the birefringent medium was analyzed. AME for
neutrino was predicted. A.I.Frank and V.A.Naumov. Phys. of Atomic Nuclei, 76,1423 (2013)
2014г. Observation of the neutron acceleration at diffraction by a oscillating crystal. V.V.
Voronin et al., JETP letters, 100, 497 (2014)
11 June 2019 A.I.Frank. ISINN 27, Dubna
Doppler effect at refraction
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Refraction of a wave at the border of the moving matter
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Massive particle (neutron)
0
0
11
i
n Vk nk
n v
0 0 vn n(k ) n k k
0
0
mvk
0 01
in k V Doppler shift
0 0i k x te
V
i ii k x te
n
0
1V
v
Light
00kc
ph 2
c 1v v 1
n n
1V
c
Fresnel drag
A.I.Frank and V.A.Naumov. Phys. of Atom. Nuc., 76,1423 (2013)
A.I.Frank. ISINN 27, Dubna
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Transmission of a wave through the moving sample (constant velocity)
When the wave enters into the sample from free space, the frequency of the
wave suffers frequency shift. When the wave comes out of the medium into
free space, the frequency of the wave suffers an inverse frequency shift. For
the constant-velocity motion, these two frequency shifts cancel each other.
V i ii k x te
n
0 0i k x ti (V)e e
00i k x te
V=const
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For the accelerated motion, two frequency shifts do not cancel
because the velocity of the medium is not constant.
Transmission of a wave through the moving sample (accelerated motion)
V=wt
i ii k x te
n
f fi k x ti (t)e e
00i k x te
0f
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Differential Doppler effect and Accelerating Matter Effect
Assumptions:
1)1) Model of effective opticalModel of effective optical is also validis also valid in
the case of accelerating matteraccelerating matter
2) Quasi – classical approach is correct
Kowalski-Nosov-Frank
11 June 2019 A.I.Frank. ISINN 27, Dubna
Observation of the AME in the Observation of the AME in the
experiments with UCNexperiments with UCN
(200(20066--20082008) )
and thermal and thermal neutronsneutrons
(2014(2014--2017)2017)
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UCN spectrometry with Fabry-Perot interferometers
mg=1.02 neV/cmmg=1.02 neV/cm
Energy of the state
2
1,2 1,2
2U b
m
Substrate 1 1
2
Two IFP with variable Two IFP with variable
space between themspace between them
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Principle of the AME experimental observation
10 15 20 25 30
0,0
0,5
1,0
1,5
2,0
2,5
3,0
= 6,5 nev
Co
unt
rate
(a
rb.
un
its)
Distance between the filters (cm)
Variation of the UCN energy
Variation of the count rate
E ≈ (2-5)10-10 eV
Periodically variation of the neutron energy, caused by the sample
acceleration, leads to the periodical oscillation of the count rate
mm
ss
aa
DetectorDetector
NIF
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2a A sin t
13
0,000 0,005 0,010 0,015 0,020 0,025
0,90
0,95
1,00
1,05
1,10
Point 22.0
Measured 21July
Count rate 7.26 0.08
No
rma
lize
d c
ou
nt ra
te
Time (sec)
f (t) 1 Bsin( t )
Frequency f = 40, 60 Hz
Oscillation period 0.025, 0.017 sec
Time of flight 0.11 sec
0.2 neV
2 1E mA L 1 sin t
nK
0 94 0 06K . .
A.I. Frank, P.Geltenbort, G.V.Kulin, et al, Phys. At. Nuclei, 71 (2008) 1656.
2 2
maxw A 60m / s
V A cos t
Oscillation of the count rate and experimental result
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V.V. Voronin et al., JETP letters, 100, 497 (2014)
Yu. P. Braginetz et al.,Phys.At. Nucl. 80, 32 (2017)
Diffraction experiment of the PNPI group
Change of the energy was observed but interpretation of the effect is debatable
11 June 2019 A.I.Frank. ISINN 27, Dubna
The equivalence principle
and
Accelerating Matter Effect
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n n –– refraction indexrefraction index
Accelerating sample and the equivalence principle
S
DetectorDetector
g
n
E mgH
S
w=g
n
L
Detector
E mgH
1. In both cases the energy, measured by the detector, must be the same
due to the equivalence principle
2. Introduction of the refracting slab does not change the energy due to
the energy conservation law (see left fig.)
3. Delay time due to refraction is
During this delay time the detector will continue to
accelerate
v w
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Accelerating sample and the equivalence principle
E mv v S
w=g
n
L
Detector If time delay is the only effect related with
sample then introducing of (accelerating) sample
would result in change of detected energy what
contradicts to the equivalence principle
v w
Consequently for the validity of the equivalence principleConsequently for the validity of the equivalence principle itit is is
necessarynecessary that time delaythat time delay time time due to refraction must be due to refraction must be
accompanied byaccompanied by the change of energy the change of energy
11 June 2019 A.I.Frank. ISINN 27, Dubna
Accelerating Matter Effect in neutron and light optics
d 1 n
nv
19
11E mwd
n
Neutrons Light
Si d 0.6 mm, w 10 g
3E3 10
E
L 1m, w 10 g
155 10
UCNsUCNs
Tanaka formulaTanaka formula KNF formulaKNF formula
21
wdn
c
E m v v
w v nd d d
n 1c c c
w
c c
v
11 June 2019 A.I.Frank. ISINN 27, Dubna
Change of the frequency appears due to Change of the frequency appears due to delay of the wave in a sample, which are delay of the wave in a sample, which are
moving with accelerationmoving with acceleration
20
11E mwd
n
Neutrons Light and relativistic parrticle
21
wdn
c
wE m vw
c
But why the time delay related only with refraction?But why the time delay related only with refraction?
General equation wk
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Any object which transmitting narrowAny object which transmitting narrow--band signal with delay shifts frequency band signal with delay shifts frequency
if it is if it is movingmoving with acceleration.with acceleration.
1.1. Any interaction necessary related with time delayAny interaction necessary related with time delay
2.2. Any device which is transmitting signals always doing that with Any device which is transmitting signals always doing that with
delaydelay
Any object which is scattering a wave or Any object which is scattering a wave or transmitting narrowtransmitting narrow--band signal shifts the band signal shifts the frequency if it is moving with acceleration.frequency if it is moving with acceleration.
A.I.Frank. ISINN 27, Dubna
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Two examples of Two examples of
accelerating objectaccelerating object
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The frequency of the waveThe frequency of the wave, , emitted by a transceiveremitted by a transceiver
moving with acceleration differs from an initial onemoving with acceleration differs from an initial one
f+ t
V wt
Detector & analyzer of frequency
Sound, radio waves, light
f f + f
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Group delay time at neutrons scattering at atomic nucleusGroup delay time at neutrons scattering at atomic nucleus
GDT d
dE
arctg
f ff f
f f
f f if
Scattering amplitude
4t s a f
k
2
4s f
Optical theorem
- total cross-section
- scattering cross-section
- capture cross-section
t
s
a
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Group delay time at neutrons scattering at atomic nucleusGroup delay time at neutrons scattering at atomic nucleus
f f if
b
v
For thermal neutrons 1710 s
time of flight of nucleus
For UCN 1410 s
4
4 4
s at
s s
kkf
f
4
1 sd
dE
v
ak const
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The energy transform at the neutron scattering The energy transform at the neutron scattering
at the sole nucleus moving with accelerationat the sole nucleus moving with acceleration
2E m E
v
v v =v
v w v = w
At SAW propagation the acceleration of the near-surface region is of the order
10 11 210 10 /cm s w
135 10E eV
Solving the problem of neutron scattering by a sole accelerating nucleus it is possible to formulate the dispersion theory of neutron in the accelerating matter in analogy with Fermi’s theory for refraction index.
x
x
For UCN
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ConclusionConclusion
Any object receiving and then radiating a wave Any object receiving and then radiating a wave shifts its frequency if it is moving with shifts its frequency if it is moving with
acceleration acceleration
AcknowledgmentsAcknowledgments
Many thanks to G. Arzumanyan, V. Bushuev, S. Goryunov, G.Kulin and
M. Zakcharov for very fruitful discussions
Thank you for your attention!Thank you for your attention!
11 June 2019 A.I.Frank. ISINN 27, Dubna