Imagine there are two masses, alone in the cosmos. We could call them A and B but I'm tired of Alice and Bob, so let's call them Amy and Sheldon and let's assume, that Ernst Mach was right and that they cannot deduce their acceleration relative to that unmeasurable concept 'absolute space', and can only deduce their acceleration with respect to each other. How romantic! Here they are, and I'm assuming they're wearing futuristic transparent plastic shields (a la Galaxy Quest) to keep them alive in space:
Now let's imagine that Sheldon has a jet pack. It's just the kind of thing Sheldon would have in such a circumstance. Now he fires it and accelerates to the right with respect to Amy. Physics sees this relative acceleration and decides to form a Rindler horizon to Sheldon's left and according to MiHsC this damps the Unruh radiation on the left side of him so he feels more radiation pressure from the right than the left and that pushes him back a little against his acceleration to the right. "Oh, yes", drawls Sheldon, "that's Mike's quaint little explanation for inertia isn't it? I deduce that Mike's writing this story". Very clever Sheldon, but what about Amy? Physics sees Amy accelerating to the left with respect to Sheldon and puts a Rindler horizon to Amy's right which damps the Unruh radiation there and drags her to the right. Oddly enough, Amy is now following Sheldon's motion! "This is very annoying" thinks Amy since she's trying to play hard to get (difficult enough with Sheldon already!), but she is willing to admit, being a member of the fair sex, that this is logical in the MiHsCian world.
What all of this means is that when you consider Mach and MiHsC, and you have two bodies side by side in an empty universe. If you move one, the other will move to follow it. If you have three bodies though, it won't be the same since the mutual accelerations are now more complex, so that if Howard and his turtleneck was there as well, then Amy would be less sensitive to Sheldon's movements and could play hard to get more successfully. This is what is predicted by MiHsC for this contrived situation.
So where's the evidence? Well, in our far more complex world it is difficult to set this experiment up, but in my opinion an inkling of this occurred when Martin Tajmar span his supercooled disc and a nearby accelerometer moved with the disc without frictional contact, rather similar to the way that Amy moved with Sheldon in the thought experiment. Indeed MiHsC predicts these Tajmar results pretty well (McCulloch, 2011). This effect is likely to be more obvious on a cosmic scale, since objects in deep space are closer to being lone masses, and it has been found recently for example that quasar and galaxy spins are aligned.
McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 39002. arXiv
McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 39002. arXiv
I thought about your Gedankenexperiment (I'm allowed to write it this way.. I'm German :p).
Imagine a 2D Euclidean coordinate system with three masses, which each have a considerable distance in between them. Mass A is in the origin of the coordinate system. Mass B is somewhere exactly on the (vertical) Y-axis and mass C is exactly on the (horizontal) X-axis. I want to call this an 'orthogonal placement of masses'.
If A accelerates towards C, then the distance between A and B obviously changes less quickly, than it does between A and C. I think it should then logically follow, that the farther B is away from A, when A is accelerating towards C, the less B should matter in this whole situation. If, in fact, the distance(A,B) is large enough, the effect of B on A while accelerating should become negligible.
So.. not all masses present in the universe should have a uniform influence on inertial effects, derived from Rindler horizons? What do you think about my extension of your Gedankenexperiment?
Thanks: a interesting point. I have considered this: in the referenced paper I modeled the decay of the effect of a mass on the inertia of another one with 1/distance^2, like gravity (see the paragraph before eq. 6). I had no logical reason to chose an inverse square, but this particular result wasn't very sensitive to it.
It is interesting that if there are only 2 masses and you move them apart then initially, using Mach's approach, you might say that the effect should not diminish with distance, since we can still only determine the acceleration of each mass with reference to the other mass. It may be that one can derive a distance dependence by quantifying the greater inaccuracy in measuring the acceleration of the other mass (using light) from a distance.
Regarding inertia and gravity in context with Rindler horizons, I think it might be like this:
- Inertia is based on dynamically created Rindler horizons.
- Gravity is based on static (or 'frozen') Rindler horizons.
The ultimate static Rindler or information horizon is.. a Black Hole. However, as Hawking radiation illustrates, even such an impressive information horizon like a Black Hole finally 'evaporates'.
If we view physical 'mass' as a sort of particle type dependent stable topological defect in physical spacetime (that hinders free information exchange in between arbitrary points in spacetime), caused during the events of what we call 'Big Bang', it might become obvious that even 'static' Rindler horizons don't, or rather can't last forever. In the end, any known particle has a statistical half life.. after which it 'evaporates', or after which the topological defect that it represents in spacetime 'normalizes' again to a less disturbed state, that allows better or free information exchange in between arbitrary points in spacetime. We could think of it as a built-in 'self-healing' capability.
Indeed, I think it is all horizons, and I've made many attempts to get gravity from Unruh radiation and sheltering, and from the uncertainty principle, but I think now the route is more radical and more directly involves information. I'm in the process of deriving MiHsC solely from information (only a factor of 2 still stands in my way) and my hope is that gravity will then come out as well.
That extension of your theory sounds fascinating Mike.
I just noticed, in your previous articles and comments under them, that you correctly noticed, that accelerating body feels acceleration (or gravity - you can make difference only by observing the whole system you are in).
So Sheldon with jetpack feels (measures) acceleration, when jetpack is turned on.
Amy is not feeling acceleration, so if the universe modifies rindler radiation symetry without any obvious case (think Amy does not even "make observation" - there is no interaction - of Sheldon with jetpack, turned on or off), it would be quite strange.
So my opinion on this paradox is: no, Amy will not see rindler horizon just because Sheldon accelerates. Rather my explanation is, that the relative acceleration, as observed from other points (including Amy, but not limited to her) will not be the same, as Sheldon would expect from his acceleration measurements. (This is BTW quite similar to situation, when you are accelerating in gravitation field: you also cannot tell, without additional input or observation of system as a whole, how much of the total acceleration you feel is gravity and what is real acceleration. So accelerating Sheldon may not know, what his real acceleration relative to Amy is, just by his accelerometer: but, floating weightles, not orbiting Sheldon or whatever, Amy will not see Rindler horizon)
Anyway the talk about reducing it all to information sounds very interesting to me... it was something I was kind of expecting all the time.
(I post as @TeckaCZ - my e-zine identity - on Twitter, and I admit I am just failed linux software developer, not physicist, although I have some affinity to it)
(eh in previous: "Unruh radiation symetry", sorry, still new to this language)
Ordinarily you would be correct, but remember that I've taken all other matter out of this cosmos, and the way we 'feel' acceleration is via inertia, and I agree with Mach that this is due to the other matter in the cosmos. The only other matter Amy sees is Sheldon who is accelerating with respect to her. So I think she would believe herself to be accelerating and see a Rindler horizon.
Do you consider the universe to be a closed continuum in this picture? I played around a bit with just two masses within an otherwise empty spatial closed continuum with non-zero curvature. If you draw the continuum on paper as a 2D circle and put Amy&Sheldon exactly one half-circle away from each other (to get symmetrical conditions) - what will happen during acceleration?
When Sheldon accelerates towards Amy, he certainly has to use a propulsion system. Let's say he's using a photon rocket. During Sheldon's acceleration, a Rindler horizon forms. The resulting Unruh radiation would push against his acceleration force towards Amy. Amy would see the same thing happening, BUT: Sheldon's photon-rocket photons would inevitable hit Amy and impart the same, but opposite impulse on her that Sheldon experiences.
So, I think that Amy would, in effect, not really move the same way with Sheldon, while Sheldon speeds towards her.
OK. Sheldon's photons would muddy the picture in a closed system, though we can imagine that they are fired away from Amy with no dynamic effect on her and eventually reach the Hubble edge and become unobservable for A and S (admittedly with consequences for information).
For a clean theory, the special cases must be correctly considered and come out of the formulae in a natural way :) .
Good thing you're mentioning the Hubble horizon. Imagine a regular rocket in space. It starts fresh and full and fires until its fuel is depleted. Propellant and rocket speed in opposite directions, the center of mass of (rocket+propellant) doesn't move to suffice conservation of momentum. Let's say that the rocket was so heavy that the propellant moves at double the rocket's speed. After an eternity, the speeding propellant crosses the Hubble horizon and is.. 'gone'. An observer of the rocket could now try to find the mass of a possible propellant, but it's hopeless. There is none to be found.
So there is now a rocket body in the local universe that speeds along for now unknownable reasons. Physics is based on empirical data, but in this case we can't find any data about the missing propellant mass. Just going by observables and adding all vectors of the universe, CoM appears to be in a broken state. I think it's glorious :) .
It is interesting that this is similar to the black hole information paradox: a puzzle over what happens to the information represented by matter when it is swallowed by a black hole's event horizon. In our case the rocket propellant is swallowed by the Hubble horizon, and we are inside that horizon.
I think that these kinds of Gedankenexperiment hint towards a possibility to engineer an apparent (local) breaking of CoM by shifting the 50/50 statistics of action&reaction by appropriate usage of the limited speed of light that is the propagation limit of information/energy. I mean.. information loss seems to happen in 'nature' on the Hubble horizon all the time (also caused by limited speed of light!).. so I don't see any reason (for now) why we shouldn't be able to come up with a machine that can do this locally, too.
For many years now, I've been studying possible ways to engineer this kind of effect. After a long elimination process, I eventually came up with a possible solution to make use of the limited speed of information/energy transfer. If you're interested, I could elaborate on my concept (in case, would your plymouth e-mal address be OK?).
DISCLAIMER: Only standard physics involved.
I think we can at least say that the mass-energy of a Black Hole is equivalent to the mass-energy of the stuff that fell into it. The Hubble horizon is much worse, because mass-energy is simply 'disappearing' from our accessible/observable physical reality. Our Hubble horizon limited local universe is losing stuff all the time - momentum vectors, energy, information.. it's like our universe itself is kind of evaporating into nothingness. Maybe there's even a half-life constant for universes in general.. who knows?
What I am trying to show with MiHsC, and the informational version I'm now working on, is that it is not mass-energy that is conserved but mass-energy-information. So information can be converted to inertial mass / energy and vice versa. This thought experiment is an easier way to think about some of the consequences of this.
I'd be interested to hear about your CoM-breaking machine. It doesn't look like an emdrive does it? :) Feel free to contact me at my Plymouth email address.
I assure you - it doesn't look like an EM-drive. :)
I'll prepare a short PDF document. E-mail subject will be a simple "Hi" from a well-known german provider. If nothing arrives, please also look into your spam folder, sometimes this happens (seems random).
I think I am starting to get this example: it is like special relativity: wheile relativity says "there is no absolute frame of reference, all motion is relative", MiHsC says maybe something like "there is no object with absolute mass, all mass is relative".
The trick with your thought experiment is probably, that the only way Sheldon's "backpack" can work in empty "two body universe" and give him some acceleration is by means of photon rocket (ie. emitting some elmg. radiation). The empty two-body universe is in fact cylindrical, so the radiation from Sheldon's photon rocket travels all the way round the universe and then it is seen as kind "background radiation".
I believe the paradox is resolved this way, because any two objects sufficiently isolated from the rest of the universe would than behave this way, which we don't observe very often (unless we are super-cool, super-conducting, or exotic in some other way)
I believe before any of the two objects in empty universe starts to emit any photons, there can't be notion of space, time and acceleration: Sheldon can only start to accelerate when he emits photon, which is the "big bang event" in the two body universe, the information is transmitted and this little universe's Hubble horizont starts to exists with t0 being time of this photon emission.
Amy can start to believe she is moving only after she receives this information or by feeling (measuring) acceleration, which, in this two body universe, will be the same moment (event). But soon (after once more the entire lifetime of our little universe started by first photon emission/acceleration event, which can be pretty soon, for sufficiently small universes) will the photons emmited by Sheldon travel one more time around and interfere with themselves... and this is where things start to be interesting (I have no clue what happens, to be true, but the amount of energy/information being transmitted by accelerating Sheldon now must have definitely increased...)
The problem we have with two body universe may also be topological - ie., the distance between Amy and Sheldon is the same, no matter which direction we look (and it may be also the Planck length of our two body universe). So it is really no surprise Amy is not really moving relative to Sheldon (firing his photon rocket in the single, "any-direction" of two body universe) and she is only heating up (I hope the narrative got more interesting at this point)
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