in http://www.nist.gov/pml/div688/2013_1_17_newera_atomicclocks_3.cfm a atomic clock, using Y-Sr ‘lattice’, is said to achieve 3E-18 accuracy & stability. This would allow to detect time dilation caused by a mere 4 cm altitude difference. If guestimating correctly, this would be equivalent to the gravitational effect of a 19 kg mass at a horizontal distance of 10 cm. Question: would a second 19 kg mass on the opposite side anihilate the effect (null net acceleration) or double it ? Is gravity a normal ‘garden&kitchen’ vectorial field ? Wouter.
________________________________ From: Wouter Meeussen <wouter.meeussen@telenet.be> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, February 9, 2014 12:40 PM Subject: [math-fun] time dilation
in http://www.nist.gov/pml/div688/2013_1_17_newera_atomicclocks_3.cfm a atomic clock, using Y-Sr ‘lattice’, is said to achieve 3E-18 accuracy & stability. This would allow to detect time dilation caused by a mere 4 cm altitude difference.
If guestimating correctly, this would be equivalent to the gravitational effect of a 19 kg mass at a horizontal distance of 10 cm.
Question: would a second 19 kg mass on the opposite side anihilate the effect (null net acceleration) or double it ? Is gravity a normal ‘garden&kitchen’ vectorial field ?
Wouter. _______________________________________________
While the electromagnetic field couples to a 4-vector, the charge density and current density, the gravitational field couples to a 16-component symmetric tensor. The tensor components are energy density, energy flux (power flow), momentum density, and momentum flux (stress). For slowly moving bodies (v << c), and in the case of gravity, not too deep a potential (GM/r << c^2), we have the force laws of Coulomb and Newton.
The gravitational redshift depends on the potential -GM/r, not the acceleration GM/r^2. The presence of the second mass doubles the potential, and thus doubles the time dilation, assuming that the test clock, the masses, and the reference clock far from the masses are all located at the same height on Earth's geoid (equipotential surface). The amount of time dilation, relative to a clock at infinity, is sqrt(1 - 2 G M / r c^2), the lower clock appearing to run slower than the upper clock.
-- Gene
It would nullify it. With both masses in place the "straightest" local path through spacetime would be the same as with neither, so the deviation due to the Earth would be the only effect. Brent On 2/9/2014 12:40 PM, Wouter Meeussen wrote:
in http://www.nist.gov/pml/div688/2013_1_17_newera_atomicclocks_3.cfm a atomic clock, using Y-Sr ‘lattice’, is said to achieve 3E-18 accuracy & stability. This would allow to detect time dilation caused by a mere 4 cm altitude difference.
If guestimating correctly, this would be equivalent to the gravitational effect of a 19 kg mass at a horizontal distance of 10 cm.
Question: would a second 19 kg mass on the opposite side anihilate the effect (null net acceleration) or double it ? Is gravity a normal ‘garden&kitchen’ vectorial field ?
Wouter. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
that's what I call fun: playing with a twisted thought experiment that probes just a bit deeper. About 'deeper', what happens if we surround the clock with masses on all sides? A fortiori, does time dilation increase as we approach a neutron star from the outside, but diminish to zero again if we dive under the surface and approach the centre of it? What about the singularity inside a black hole? Continuity during collapse of a neutron star to a black hole pleads against meekerb's reasoning, I think, but it's not clear. I feel stretched... Eugene: ">The gravitational redshift depends on the potential -GM/r, not the acceleration GM/r^2. The presence of the second mass doubles the potential, and thus doubles the time dilation, assuming ..." meekerb: ">It would nullify it. With both masses in place the "straightest" local path through spacetime would be the same as with neither, ..." Wouter. -----Original Message----- From: meekerdb Sent: Tuesday, February 11, 2014 1:50 AM To: Wouter Meeussen ; math-fun Subject: Re: [math-fun] time dilation It would nullify it. With both masses in place the "straightest" local path through spacetime would be the same as with neither, so the deviation due to the Earth would be the only effect. Brent On 2/9/2014 12:40 PM, Wouter Meeussen wrote:
in http://www.nist.gov/pml/div688/2013_1_17_newera_atomicclocks_3.cfm a atomic clock, using Y-Sr ‘lattice’, is said to achieve 3E-18 accuracy & stability. This would allow to detect time dilation caused by a mere 4 cm altitude difference.
If guestimating correctly, this would be equivalent to the gravitational effect of a 19 kg mass at a horizontal distance of 10 cm.
Question: would a second 19 kg mass on the opposite side anihilate the effect (null net acceleration) or double it ? Is gravity a normal ‘garden&kitchen’ vectorial field ?
Wouter. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On second thought I agree with Gene. It would be an interesting experiment. Brent Meeker On 2/11/2014 12:33 AM, Wouter Meeussen wrote:
that's what I call fun:
playing with a twisted thought experiment that probes just a bit deeper. About 'deeper', what happens if we surround the clock with masses on all sides? A fortiori, does time dilation increase as we approach a neutron star from the outside, but diminish to zero again if we dive under the surface and approach the centre of it? What about the singularity inside a black hole? Continuity during collapse of a neutron star to a black hole pleads against meekerb's reasoning, I think, but it's not clear.
I feel stretched...
Eugene: ">The gravitational redshift depends on the potential -GM/r, not the acceleration GM/r^2. The presence of the second mass doubles the potential, and thus doubles the time dilation, assuming ..."
meekerb: ">It would nullify it. With both masses in place the "straightest" local path through spacetime would be the same as with neither, ..."
Wouter.
-----Original Message----- From: meekerdb Sent: Tuesday, February 11, 2014 1:50 AM To: Wouter Meeussen ; math-fun Subject: Re: [math-fun] time dilation
It would nullify it. With both masses in place the "straightest" local path through spacetime would be the same as with neither, so the deviation due to the Earth would be the only effect.
Brent
On 2/9/2014 12:40 PM, Wouter Meeussen wrote:
in http://www.nist.gov/pml/div688/2013_1_17_newera_atomicclocks_3.cfm a atomic clock, using Y-Sr ‘lattice’, is said to achieve 3E-18 accuracy & stability. This would allow to detect time dilation caused by a mere 4 cm altitude difference.
If guestimating correctly, this would be equivalent to the gravitational effect of a 19 kg mass at a horizontal distance of 10 cm.
Question: would a second 19 kg mass on the opposite side anihilate the effect (null net acceleration) or double it ? Is gravity a normal ‘garden&kitchen’ vectorial field ?
Wouter. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
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Eugene Salamin -
meekerdb -
Wouter Meeussen