Conservation of Energy+Mass+Information?

Here's an attempt to put MiHsC in context. A long time ago Galileo performed carefully timed experiments rolling balls down inclined planes and found that as height was lost, speed was gained in a particular way. This was later modeled using two interchangable kinds of energy: kinetic (speed) and potential (height) and their sum was found to be nearly conserved: PE + KE = constant (some energy leaks to smaller scales as friction, and that is where thermodynamics appears). Then Einstein explosively predicted that one can convert a tiny bit of mass to lots of energy, and reversewise (E=mc^2) so that now mass-energy was conserved: mass + energy = constant. What I think MiHsC is telling us, is that what is actually conserved is:

Energy + Mass + Information = constant

This sum is a 'property' consisting of energy, mass and information that you could call 'EMI', so that EMI is conserved. What might this mean for a real experiment?

Consider a ring in a cryostat, that is suddenly spun. Tajmar et al. found that a nearby gyroscope moved slightly to follow the ring, despite there being no frictional connection. MiHsC predicts this exactly, since the sudden acceleration increases the inertial mass of the gyroscope and to conserve the momentum of the gyro+ring system the gyro has to move with the ring. Can we interpret MiHsC as EMI conservation? Perhaps. When you accelerate the ring, the Rindler horizon seen by the gyroscope, which sees a mutual acceleration, comes closer to it, so it looses information about its environment (I'm not sure how to calculate this yet). To conserve EMI it must gain mass-energy, or inertial mass (this agrees qualitatively with MiHsC).

Conversely as an object's acceleration reduces as it moves away from concentrations of mass into deep space, the Rindler horizon it sees moves away and it gains information (I), so EM must be lost. Therefore inertial mass decreases and the object is more sensitive to external forces and accelerates again. The minimum acceleration of 6.7*10^-10 m/s^2 occurs when the Rindler horizon coincides with the Hubble horizon since then no more information can be gained. The thing now is to see if the maths of this idea predicts the right sort of behaviour..

A New Natural Motion.

As Smolin says (in Time Reborn) "Revolutions in physics can be marked by changes in what is considered natural motion", motion without forces applied. The Greeks thought that natural motion was a dead stop (but this was friction). Galileo showed instead that natural motion was a constant velocity. This enabled him to argue that the Earth was moving around the Sun as Copernicus had said, and explain how this could be so without the Earth leaving a trail of debris behind it in its orbit.

MiHsC might offer a new such revolution since it changes the natural state of motion from Galileo's constant speed to a tiny minimum acceleration of 2c^2/Theta, where c is the speed of light, and Theta is the Hubble distance. This occurs because in MiHsC inertia is caused by Unruh waves and their length increases as accelerations reduce. When accelerations are as low as 2c^2/Theta the Unruh waves exceed the size of the observable universe and this cannot be allowed, since, if it was, the waves would allow us to determine what lies outside the observable universe, which is a paradox. So this information censorship makes the Unruh waves, and inertial mass, dissapear at low accelerations, causing the object to accelerate more with the same outside force - hence the minimum allowed acceleration.

This minimum acceleration is close to the recently-observed cosmic acceleration. It is also likely to change in time, since the size of the observable universe (Theta) increases in time, and the speed of light may vary too. Does this have far reaching consequences, as Galileo's inertia had for the heliocentric theory? At the moment I'm in the process of publishing a paper that shows it produces a cosmology similar to the old Steady State Theory of Fred Hoyle, in which the gravitational mass of the universe increases in time, but MiHsC also predicts a hot early universe, that Steady State didn't. I am just working to publish this, so hopefully I can get it past peer review.

Smolin, L., 2013. Time reborn. Penguin Books Ltd.

McCulloch, M.E., 2010. Minimum accelerations from quantised inertia. EPL, 90, 29001.

McCulloch, M.E., 2014. A toy cosmology from a Hubble-scale Casimir effect, Galaxies, Special Issue.

An Introduction to MiHsC / quantised inertia

The idea of inertia is that in a vacuum, where there is no friction, objects move along in a straight line at constant speed until you push on them. This tendency was first isolated by Galileo, who rolled balls down inclined planes (balls feel less friction). This tendency, inertia, has always been assumed but never explained.

Meanwhile physics has moved towards a study of information, and it has been realised in the past few decades that when you accelerate something, say, to the right, information from far to the left can never catch up to it, this means there is an information-boundary or 'horizon' to its left which is like a black hole event horizon (it is called a Rindler horizon). A kind of Hawking radiation comes off this horizon, which is called Unruh radiation (it was proposed by Bill Unruh) and is seen as background radiation, but is seen only by the accelerated object (there is some evidence for Unruh radiation eg: Smolyaninov, 2008).

I have suggested that the waves of Unruh radiation cause inertia as follows: the waves have to fit exactly between the rightwards-accelerating object and the Rindler horizon that forms on the left. This is similar in form to the Casimir effect, but I use logic instead: a non-fitting partial wave would allow us to infer what lies beyond the horizon, so it wouldn't be a horizon anymore. This logic disallows Unruh waves that don't fit on the left: they dissappear. As a result more Unruh radiation pressure hits the object coming from the right than from the left and this imbalance pushes it back against its acceleration, just like inertia. I have shown that this effect is the right size to provide a mechanism for inertia, and so can explain it for the first time (paper) (there's a factor of 2 error in the paper, when corrected the result is within 29% of the Planck mass). An analogy is a boat near a seawall. Seaward of it, waves of all wavelengths can exist for there is no boundary, but between it and the seawall fewer waves can fit: only those that have 'nodes' (the unmoving part of the wave) at the wall and boat. As a result more waves hit the boat from the seaward side, pushing it on average towards the seawall.

It does not end there, however, because, to be tested, a model needs to predict something unexpected, and this model for inertia does. There is also a horizon much further away, at the Hubble horizon, so even to the right of the object some of the Unruh waves are disallowed, especially the very long Unruh waves that you get if the object has a very low acceleration. The new prediction then is that objects with very low acceleration lose inertial mass in a new way. This model for inertia can be called: Modified inertia by a Hubble-scale Casimir effect (MiHsC) or quantised inertia.

In this way, MiHsC solves a problem astronomers have had with galaxies. They are spinning so fast that they should centrifugally explode. Oddly, they don’t explode, so astronomers have had to invent invisible ‘dark’ matter and add it to the galaxies to hold them together with extra gravitational pull. This is a ‘patch’ since it is not predictive: you have to add dark matter 'by hand' to get agreement between standard gravity and the observed spin of the galaxy. Interestingly, the stars at the galaxy’s edge (the ones misbehaving) have low accelerations, so see very long Unruh waves, and MiHsC predicts a loss of inertial mass for them, that reduces the centrifugal outward force on them by just the right amount to make everything fit, see here and here. MiHsC then is an alternative explanation of why galaxies do not break up with the centrifugal forces, and is better than the dark matter hypothesis and MoND because there is only one way to apply MiHsC, and that way works (McCulloch, 2012).

MiHsC also explains other observed anomalies, for example: the recently-observed cosmic acceleration, the low-l cosmic microwave background anomaly (a suppression of patterns at the Hubble scale), the controversial lab experiments of Podkletnov (1992) and Tajmar (2009), the flyby anomaly, the emdrive, and others.. Here is a summary of all these tests.

MiHsC is not fully developed yet, and to do this I need to persuade it to show itself in a controllable and repeatable lab experiment (in progress) but, if confirmed, there are applications. MiHsC predicts that when you suddenly accelerate something (eg: spin a disc very fast) the disc, and objects nearby, should gain a bit of inertial mass and to conserve momentum they will move anomalously: a new way to move things. More generally, MiHsC predicts that whenever you put a horizon into the zero point field it creates a gradient in it that can pull on objects. MiHsC also predicts that you can’t have a constant velocity, zero acceleration, since the Unruh waves would then be longer than the Hubble scale, and none would fit, so inertia would collapse. This modifies special relativity’s insistence on a speed of light limit, and the predicted (tiny) acceleration agrees with the observed cosmic acceleration, as noted above.