The Light Speed Limit & the Soyuz Express

The further you look away from the Earth, or, it is assumed, away from anywhere, the faster other galaxies appear to recede. This is the well-known Hubble expansion and it is seen in the increasing redshift of distant stars: their light is Doppler-stretched until at the Hubble distance they exceed the speed of light relative to us and dissapear from view, like ambulances travelling away faster than the speed of sound would be silent to us. This is one of the reasons the night sky is dark, and seems initially to be a problem since faster than light travel is supposed to be verboten. This paradox is usually avoided by saying that space itself is expanding. This seems to me to be a fudge, relying on an invisible entity (space). How do you determine experimentally whether space itself is expanding or the stars are moving apart?

MiHsC provides the beginnings of a different view on this. If you modify the inertial mass using both Special Relativity (SR) and MiHsC you get a formula for accelerationa, a, like this: a = F/m*(1-v^2/c^2) + 2c^2/Theta. The first term says that if v=c, no matter what force F you apply you won't get an acceleration from that term. This is why SR precludes crossing the light barrier. However, the new second term from MiHsC says that whatever SR says, there is always a residual minimum acceleration, even when v=c. This is incredibly small: 6.7x10^-10 m/s^2, an acceleration that would produce the speed of light over the age of the universe. A more directly encouraging thing is that it is close to the observed cosmic acceleration.

I submitted a paper on this superlight speculation a couple of years ago to the 100 Year Starship Symposium and another short one a year later to JBIS and haven't heard back from the reviewers yet. Maybe this is because these are a different kind of paper from the ones I normally submit. I tend to only submit papers when I have some experimental data to back the ideas up. With these superlight papers the best I can do so far is say: MiHsC works here and here, and if you extrapolate to the speed of light it predicts a residual acceleration that is close to the cosmic acceleration. This is not an unambiguous test, and the spectre of causality looms large in this area. Anyway, the closest I've got to publishing this so far is a discussion of 'minimum accelerations' in this paper (published in EPL, 90, 29001).

By the way, well done to the Russians. they've just launched a 6 hour fast-track Soyuz to the ISS. I think the Russians have a good attitude to space that could be summarised as: "To the stars, by just doing it."

The Juno flyby

On October the 9th, 2013 the Juno spacecraft en route to Jupiter will fly by the Earth for a gravity assist. Rather like Marty McFly in Back to the Future, who hitched a skateboard ride by holding on to a truck, Juno will hitch a ride for a short time behind the Earth in its orbit. The Earth's gravity will pull it along and speed it up. This is how NASA manage to get spacecraft to Jupiter without the need to launch lots of heavy fuel.

The particularly interesting aspect of this flyby for me is that the spacecraft will approach Earth at a declination of -14 degrees (near the equator) and leave it at +39 degrees (a bit closer to the spin axis). As a result of this, MiHsC predicts a slight jump in speed, beyond the usual one from the gravity assist. This is because as the spacecraft comes in near the equator the acceleration vector of the craft and the acceleration vector of all the masses in the spinning Earth (which point at the spin axis) are pointing at or away from each other, so the mutual accelerations are large, the Unruh waves seen are short and a lower proportion of them are disallowed by the Hubble-scale Casimir effect, so MiHsC doesn't reduce the inertial mass of the craft much. However, when the spacecraft leaves at an angle closer to the Pole (the spin axis) the acceleration vectors of the masses in the spinning Earth are still pointing at the Earth's spin axis and so are now not pointing at the craft, so the mutual Earth-craft accelerations are lower, the Unruh waves lengthen and a greater proportion are disallowed by the Hubble-scale Casimir effect and MiHsC decreases the inertial mass of the spacecraft. To conserve momentum (mv) the craft has to speed up slightly.

Anomalous speed ups like this have been seen in previous flybys (they were first noticed by Antreasian and Guinn, 1998 and Anderson et al., 2008, see also the ISSI Flyby Workshops, 2009, 2010) and MiHsC, as described above, predicts them fairly well: an agreement that is not perfect (follow the link below to see my paper), but is encouraging given there are no adjustable parameters in MiHsC. Of course, you could to some extent use past flybys to predict the next anomaly: the upcoming Juno one will be similar geometrically to the first Galileo flyby which had an anomaly of 4.2 mm/s, but it's not identical and it's surely better to have a theory.. The paper I published on this is freely available from MNRAS here. The specific formula for the predicted anomalous velocity jump (flyby anomaly, or dv) (Eq. 8 in the above paper) is:

dv = 2.8*10^-7*(v2*cos(dec1)-v1*cos(dec2))/(cos(dec1)*cos(dec2))

where the first factor is not adjustable, and depends only on observed and fixed parameters such as the rotation rate of the Earth, the speed of light, the Hubble diameter and the variation of density towards the Earth's core. Dec1 is the incoming declination of the craft (like its latitude in the sky), dec2 is its outgoing declination and v1 and v2 are the initial and final geocentric velocities (in the paper I wrongly used heliocentric ones).

In deriving this formula I made certain geometric assumptions, that seemed reasonable at the time and probably have only a small effect, but with hindsight could be improved on and I'll try to correct those before October (it's not trivial), but into this formula I can put the values for the upcoming Juno flyby that I have obtained from the indispensible JPL HORIZONS website: dec1 = -14 degrees, dec2 = 39 degrees, v1 ~ 10,500 m/s and v2 ~ 10,500 m/s. Therefore the flyby anomaly predicted by MiHsC for Juno on October 9th is: dv ~ +0.75 mm/s ( a speed up) (using heliocentric velocities, of 35000 m/s, as in my previous paper, the prediction is 2.9 mm/s).

Note: the observed Juno flyby appears to be zero, although nothing has been publish to confirm this yet. This certainly puts the cat among the pigeons since it contradicts the pattern seen in the others..

References

Anderson, J.D., J.K. Campbell, J.E. Ekelund, J. Ellis, J.F. Jordan, 2008. Phys. Rev. Lett., 100, 091102.
Antreasian, P.G. and J.R. Guinn, 1998. Paper no. 98-4287 presented at the AIAA/AAS Astrodynamics specialist conference in Boston, USA. http://www.issibern.ch/teams/Pioneer/pa-literature.htm
McCulloch, M.E., 2008. MNRAS, 389, L57-60. PDF
Lammerzahl, C. et al., 2009-2010. Flyby workshop: http://www.issi.unibe.ch/teams/investflyby/index.html

Low-l CMB anomaly & MiHsC

There is one observation I have been thinking about for a while. WMAP, the precursor to Planck, implied that there was a lack of energy in the Cosmic Microwave Background (CMB) at the largest scales. I've often wondered whether this could be due to a Hubble-scale Casimir effect similar to the one that produces MiHsC, but I have not written a paper on the CMB yet because, although these observations are interesting, with data of such distant origin it is difficult to know exactly what one is looking at, and more crucially the WMAP data did not have statistical significance at these large scales (there was not enough data). I hope that the Planck satellite (soon to report) will provide more certainty at these largest scales.