June 16, 2014 17:11 9in x 6in Physics from the Edge b1771-ch07

Chapter 7

MiHsC and Faster Than Light Travel

The conservation of momentum combined with special relativity sug-gests that an object’s inertial mass depends on its velocity v as

mi =m0√1 − v2

c2

(7.1)

where m0 is the rest mass. By playing around with this equation youcan show that when the velocity of an object is small compared to thespeed of light (v � c) the inertial mass is close to the rest mass m0,but when the speed v approaches the speed of light (c) the inertialmass mi approaches infinity and therefore further increases of speedare impossible. This effect has been verified in particle acceleratorsand there are also logical reasons for it (there are restrictions fromcausality too). This limits the range of interstellar travel within thelifetime of those left behind on Earth.

As suggested in this book, MiHsC also affects inertial mass. Com-bining special relativity (Eq. (7.1)) and MiHsC (Eq. (4.7)) producesthis expression for the inertial mass mi

mi = m0(1 − 2c2

aΘ )

(1 − v2

c2 )12

(7.2)

where m0 is the rest mass. Using Newton’s second law gives theacceleration

a =F

mi= F

(1 − v2

c2 )12

m0(1 − 2c2

aΘ )(7.3)

Multiplying both sides by the denominator and rearranging gives

a =F

m0

(1 − v2

c2

) 12

+2c2

Θ(7.4)

127

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June 16, 2014 17:11 9in x 6in Physics from the Edge b1771-ch07

128 Physics from the Edge: A New Cosmological Model for Inertia

The first term on the right hand side is the usual one from specialrelativity that states that if v = c, then no matter how large a force(F ) is applied to an object it will not accelerate. The new result fromMiHsC is the second term, which states that even when v = c therewill always be a minimum acceleration of: 2c2/Θ ∼ 6.7× 10−10 m/s2

even if the force applied (F ) is zero. To explain intuitively: as aspacecraft’s speed approaches c, special relativity predicts that itsinertia increases and the acceleration falls towards zero, but MiHsCsays that inertia depends on the existence of Unruh waves and at lowaccelerations these become too long to fit within the Hubble diam-eter, so whereas special relativity predicts that the inertia increasesto infinity at speed c, MiHsC predicts that as this happens, Unruh-inertia dissipates. The result is that a residual acceleration remains(Eq. (7.4), term 2).

This prediction is supported indirectly by the observations ofPerlmutter et al. (1999) and Reiss et al. (1998) who observed thissame value of acceleration for the distant stars which are travel-ling away at speeds relative to us of close to c. This accelerationhas been attributed to arbitrary ‘dark energy’ but it is predictedby MiHsC.

This suggests a paradox: a star near the observable universe’sedge is moving at speed c, a moment later, because of cosmic acceler-ation, it is moving faster than c. This is contrary to special relativityalone, but not when MiHsC is also considered (Eq. (7.4)).

The minimum acceleration predicted by MiHsC is tiny: from rest,it would take 14 billion years to reach the speed of light (It is inter-esting that the empirical acceleration coefficient needed by MoND(Milgrom, 1983) is of a similar size to that predicted by MiHsC, andas Milgrom noted: would produce the speed of light in the age of theuniverse, 13.7 billion years).

Equation 7.4 implies that the way to boost this force-independentMiHsC acceleration and achieve faster than light (FTL) travel in ashorter time is not to increase F in the first term which will runup against the constraints of special relativity, but instead reduce Θ(the Hubble scale) in the second term.

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MiHsC and Faster Than Light Travel 129

FTL Test 1: Man-Made Event Horizons

Of course, shrinking the observable universe is likely to remain impos-sible for some time, but it may be possible to create a smaller ‘effec-tive’ Hubble scale. I suggested in the papers McCulloch (2008a, 2013)that one way to achieve this would be to use the metamaterialsrecently devised by Pendry et al. (2006) and Leonhardt (2006). Theyhave demonstrated that electromagnetic radiation (which forms partof the Unruh radiation) can be bent around an object, which mustbe smaller than the wavelength, using a metamaterial (a speciallydesigned metal structure), making that object invisible to an observerat that wavelength (cloaking). By instead bending Unruh radiation(or just the EM-component of Unruh radiation) back towards aspacecraft it may be possible to create an event horizon similar tothe one assumed by MiHsC to exist at the edge of the observableuniverse, the size of which is the Θ in Eq. (7.4). The value of Θ isusually 2.7 × 1026 m, but for a spacecraft surrounded by a carefullyarranged metamaterial shell, Θ could be the diameter of the shell,making the MiHsC-acceleration predicted by Eq. (7.4) very muchlarger. The speed of light could then be achieved and passed at amuch greater acceleration. For example, if a craft is accelerated at9.8 m/s2 the wavelength of Unruh radiation would be

λ =4π2βc2

a∼ 7.3 × 1016 m (7.5)

If the spacecraft was surrounded by a metamaterial that bent thiswavelength around it, then according to MiHsC, the object’s inertialmass would reduce. Pendry and Wood (2007) have devised metama-terials that are able to control very low electromagnetic frequenciesincluding wavelengths as large as that above (bending other Unruhfields would be harder).

FTL Test 2: Particle Accelerators

The effects of MiHsC have not been observed in particle accel-erators which accelerate particles to close to the speed of light.This is because these particles travel along circular trajectories

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June 16, 2014 17:11 9in x 6in Physics from the Edge b1771-ch07

130 Physics from the Edge: A New Cosmological Model for Inertia

and are therefore highly accelerated, making MiHsC’s effects lessapparent. This can be shown quantitatively using the combinedMiHsC +relativity model for inertia (Eq. (7.2)). Substituting theacceleration of a particle around the CERN particle accelerator:a = v2/r, where r is the radius of the accelerator and v is the velocity,into Eq. (7.2), we get

mi = m0(1 − 2c2r

v2Θ)

(1 − v2

c2)

12

(7.6)

Replacing all the known constants with values, so: c = 3 × 108 m/s,r = 4 km (for the Large Hadron Collider at CERN), and Θ = 2.7 ×1026 m, gives

mi =m0(1 − 2.6 × 10−6/v2)√

1 − 1.1 × 10−17 × v2(7.7)

Using a binomial series for the denominator: (1 − v2

c2)

12 ∼ 1− v2

2c2· · ·

so that approximately

mi ∼ m0(1 − (2.6 × 10−6/v2))1 − (5.5 × 10−18v2)

(7.8)

The change in the inertial mass from special relativity and MiHsCcan now be found. When v = 0.9c the effect of MiHsC is 22 ordersof magnitude smaller than the change due to relativity, and when v

is higher still, the effect of MiHsC decreases even further. Thereforeit would be extremely difficult to detect the effects of MiHsC in aparticle accelerator.

However, MiHsC predicts that measureable effects, and FTL,might be achieved for systems with high linear velocity with verylow accelerations around them, such as in many of the examples dis-cussed in Chapter 5. Two other possible examples not yet mentionedare cosmic rays entering the atmosphere and galactic axial jets (it ispossible that M87 has an axial jet that actually moves faster thanlight, and not just apparently).

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June 16, 2014 17:11 9in x 6in Physics from the Edge b1771-ch07

MiHsC and Faster Than Light Travel 131

FTL Test 3: Galactic Jets

MiHsC predicts that just as the Earth flyby craft are boosted whenthey exit along the Earth’s polar axis, objects may lose inertial massand be more easily accelerated along galactic axes. Galactic jets havebeen known for some years and Biretta et al. (1999) observed the M87axial jet and calculated the apparent speed of recognisable ‘knots’ oflight within the jet, taking account of the estimated distance to M87.They found an apparent speed of 6c. It was shown by Rees (1966) thatthis apparent superluminal speed is enhanced by an optical illusioncaused by special relativity. From Rees (1966) the apparent speed(vapp) of a relativistic object moving at an angle θ to the observerdepends on its real speed (v) as

vapp =v sin θ

1 − cos θ(7.9)

According to Biretta et al. (1999) the most likely angle of the M87jet to our line of sight is 64.5◦, and they also said that because of theobserved shape of the knots: “placing the jet within 20◦ of the lineof sight presents several challenges”.

Table 1 shows the assumed angle (column 1) and the real veloc-ity implied by the observed apparent velocity of vapp = 6c, usingEq. (7.9). In order to produce real velocities less than the speed oflight for the M87 jet, it is necessary to assume unrealistic angles ofless than 20◦. This of course is a controversial area, and estimatesof the jet’s angle or the distance to M87 may change, but it is possiblethat this is evidence for the FTL speeds that MiHsC implies can beachieved.

Table 1. The assumed angle to the line of sight ofthe M87 jet and the implied absolute speed.

Assumed angle to line of sight Absolute velocity

64◦ 3.7c30◦ 1.6c20◦ 1.06c

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