I came across this a number of years ago while a student, doing a subsidiary on Nuclear physics: it is not an original idea and I have tried to restate it as I remember.
This was presented as a semi-joky _Physics_ thesis paper at a dinner, and not a metaphysical one. It was presented by a real physicist. The main audience was comprised of Classicists, Lawyers and Historians, with us, the resident hard-Scientists, present and passing the Port round.
It has long been thought that ghosts can penetrate closed doors and internal walls of buildings up to say 10cm thick. However, anecdotal evidence suggetss they are confined if present in older buildings with external wall thicknesses of 30-40 cm or more, such as castles, old churches and the like. According to the ideas therefore of Schrödinger 1928, de Broglie and Brillouin also 1928, this would define them as objects whose associated wave functions decrease to 1/e of their full amplitude, and about 10cm from their boundary. A ghost’s de-Broglie-“wavelength” is therefore of about this order, and so their mass at non-relativistic velocities must be less than the elctron by the order of 1E+16, so it must be about 1E-46 Kg or 1E-43 grams. This is astonishingly, almost non-credibly, small, but cannot be mathematically ruled out without testing.
Thus, such an object of this low mass _could_ be accelerated to high velocity with very little energy expenditure. Relativistic effects must thus be taken into account when dealing with its motion (Einstein 1905) and we can see that therefore escape velocities to extract it from the earth’s gravitational field – and indeed to eject it entirely from the solar system, can be theoretically and even practically attained. The energy required for it to escape the earth’s gravitational field is only about 1E-38 Joules: a fine breath of wind would be enough to start such a journey at high speed, and further interactions could lead to relativistic velocities. (See Newton, principia London 1687 for refs to escaping gravitational fields.)
Thus it is unsurprising that despite the astonishingly large number of ghosts possibly formed by Homo sapiens alone over the past few million years, the number of actual “ghosts” “encountered” remains mysteriously small, a few thousands, millions, whatever.
Now, when for example a person is killed with a spear which is not removed, or hanged in metal chains, his/her ghost will remain at the spot, encumbered, and will haunt it even though the event occurred in the open air. The spear or chains are real objects with normal mass. Without these, a ghost could rapidly leave the site and as we can see, could probably leave the earth and possibly the Solar System. However, following death in dungeons or inside old castles with thick walls and small windows, the escape probability is tiny even with the small masses estimated, and the ghost will haunt such a place for many years or centuries. Wearing armour or dragging chains will of course prolong the period enormously, and even such a thing as a layer of dust would create a substantial increase of time.
It is relevant to estimate that a ghost will be accelerated to 1/√2 or about 0.7 x the speed of light, by a tiny amount of work, say about 1E-29 Joule. Its mass is then 2x its rest mass (Einstein 1905) and its wavelength is halved (Schrodinger, de Broglie, Brillouin 1928) and so it is _even less_ able to penetrate a wall or door when its speed has increased a lot. A ghost is rapid motion in a confined space is therefore less likely to escape than when moving slowly, and will be difficult to locate (Heisenberg.) Although its momentum is tiny, it will be enough possibly to displace small objects on collision. Thus, we have a possibly plausible hypothesis about ghosts themselves _and_ also of the “Poltergeist” phenomenon: vases and other light articles are displaced from shelves in a disconcerting manner, since the presence of high-speed ghosts is impossibly to observe directly (Heisenberg again.) Like other elenetary particles such as the neutrino (Pauli 1933), their presence or passage can only be inferred form their secondary effects.
Empirical evidence therefore suggests that one can in no sense at all, eject such a ghost by the use of violence. Any further increase in already high speeds will just make its escape more difficult. The only possibly approach, if the presence of a high-velocity ghost is thought not to be desirable, must thus be to try to calm it and bring it near to rest, so it can glide slowly through the wall. The proceedure of exorcism is probably designed to get this result, though how this is done is not something I or the presenter of this paper even pretended to understand. It follows of course that the attempt is best made in near-darkness.
This is because the velocity of a ghost due even just to thermal effects will be large at STP, in view of their small mass. Thus the mean kinetic energy of ghosts at say 20C or 293K at 3kT/2 Joules (Maxwell 1860, Boltzmann 1872) corresponds to a rather relativistic figure. Few ghosts wil be moving slowly enough to be seen, unless they are very cold or attach themselves to some material object.
When light strikes the surface of an object, it appears to exert pressure (Maxwell 1873) and carries momentum (de Broglie 1920s.)One photon of visible light say at 5E+14 Hz incident on a ghost and reflected, could transfer momentum 2hf/c, say 1E-27 J s m-1, whihc would cause its acceleration to a high velocity. An unloaded ghost, or one not holding ont an objetc or person, would be removed rapidly if the walls were thin, or otherwise display poltergeist phenomema. Presumably the reflection coefficient of a ghost’s surface must be very much less than 100% or it might never be seen at all. no doubt for this reason it seems the general lore that ghosts are only seen under very low-light conditions.
This, to examine a ghost, one ought not to shine a torch at it, but to use a more suitable thing like a shielded candle.
Of course, the low mass leads to a very ;arge wavelength shift, Δλ , of radiation incident on a ghost surface and scattered by it (Compton 1923) and the value of Δλ for mass=1E-46 kg can be as much as 1E+4 metres. Thus, everything such as light, infra-red and the like, will be scattered at long radio frequencies. therefore the scattering of shortwave em radiation by ghosts in flight through the Universe must be a major source of cosmic RF noise. attempts so far by astronomers and cosmologists to explain this noise have taken too little account IMHO of this possible contribution.
It has sometimes been tought that ghosts prodice a sensation of cold in their environment. this may be understood if they have just retuend from deep space where the radiation temperature is believed to be about 2.72K (Penzias and Wilson 1965.) It is less obvious why this is so if they have been resident for some time. But if the observation is right, then it imples that ghosts have a high specific heat capacity, which indicates that despite their low mass they are _not_ structureless objects. More research into the possibility of reliabel evidence about the K temperature and heat capacity of ghosts is indicated.
The idea of a quasiparticle of large area and volume was at the time of this paper new to physics, though it does not appear to be excluded a priori even now. Whether such an object would seem to be hot or cold to us when stationary is not obvious, as temperature and specific heat of ordinary particles does eem to depend on the state of motion. Thus even if the observation was correct, it is not certain that ghosts have structure – they may still be elementary particles. Moreover the observation itself might be wrong. the impression of cold might be an illusion, a result of fright on the part of the observer, or just the result of faulty reporting. It is possible that the observer might feel cold through experienceing fear, although it’s not obvious, metaphysically, why such a reaction ought to occur.
Thus we must consider if the situation of the concept of a quasi-particle is applicable. It’s then desirable to investigate a ghost’s spin properties, which would tell us whether they obey the Fermi-Dirac (1926) or the Bose-Einstein (1924) statistics. For increasing the potential reliability of results in this matter, the behaviour of observable ghosts in strong magnetic fields would be instructive.
If ghosts tend to accumulate in a sink in any part of the Universe, and if they can be seen to behave as particles, then they will constitute a “degenerate” or condensed population even at low density, say 1 ghost per cubic metre. How it will be will depend on which statistics (see above ) they obey.
It is tempting to envisage that in human and other vertebrate or invertabrate ghosts with sexual differences a trace of this is carried over, and might be representable by the antisymmetric wave functions characteristic of the Fermi-Dirac statistics. Particles obeying these would of course have half-integral spin, and the ultimate state would be one in which ghosts of opposite spin had paired up to occupy correctly the energy states available. This highly satisfactory disposition from the point of view of the physicist might well constitute a state of Nirvana or bliss, which all ghosts are seeking to achieve.
Whether there is such a sink of ghosts, whether these terms are really appropriate for such a state, and where in the Universe it might be, remain problems we might only solve in the far future. Meanwhile, the above might offer a hypothesis which meets the requirements of a contribution to theoretical science: it co-ordinates the known facts and empirical observations in the llight of existing knowledge, it is not contrary to know facts, and it suggests further llines of enquiry that could be pursued in the future. Furthermore, it illuminates an area of human experience previously thought to be inaccessible to the Scientific Method.