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Inertial Mass Separate From Gravitational Mass?
CPerdue writes with this excerpt from the MIT arXiv blog:
"The equivalence principle is one of the more fascinating ideas in modern science. It asserts that gravitational mass and inertial mass are identical. Einstein put it like this: the gravitational force we experience on Earth is identical to the force we would experience were we sitting in a spaceship accelerating at 1g. Newton might have said that the m in F=ma is the same as the ms in F=Gm1m2/r^2. ... All that changes today with the extraordinary work of Endre Kajari at the University of Ulm in Germany and a few buddies. They show how it is possible to create situations in the quantum world in which the effects of inertial and gravitational mass must be different. In fact, they show that these differences can be arbitrarily large."
Because once we have inertial drives, it's only a little while before we can colonize other planets.
The technology lens itself very well to that.
Would this lead to science fictions "Inertial Dampeners"?
I hope this caused some synapses to fire.
I would submit, courteously, that your mother's inertial and gravitic masses are arbitrarily large.
The "show" here is a proof, or rather, a calculation. They describe what kind of experiment can be used to test the calculation (on a Bose-Einstein condensate in free-fall).
The experiment isn't trivial, and these theoreticians won't be the ones doing it. They publish the theory, and everybody else looks at it to see if it's worth the time and money to set up an experiment. That's pretty much canonical science going on there, and doesn't merit being dismissed as "just a pretty theory".
General relativity is known to be incompatible with quantum mechanics. People are still trying to come up with a theory that reconciles the two.
This is similar to the way we knew:
* the constant speed of light (regardless of reference frame) was incompatible with the classical laws of momentum and energy [resolved by Special Relativity]
* the equations for low energy blackbody radiation and high energy blackbody radiation were incompatible with one another [resolved by quantum mechanics]
I haven't RTFA, but if they have something testable, I would think this means we have a basis for making quantitative measurements of what happens where GR and QM collide. (And hence a basis for coming up with a unifying theory.)
In a gravity well, this explains why we need so much fuel to get out. But that assumes that inertial mass acts like gravitional mass. If we change that, then suddenly we use HIGH inertial mass but low gravitational mass as rocket exhaust, tremendously reducing the mass of the rocket's fuel, which has exponential gains in increasing the potential payload.
excitingthingstodo.blogspot.com
Assuming that these guys are right, would the presence of two different effects that we currently group together allow us to generate a model of the universe that doesn't require the vast majority of matter to exist as (currently) undetectable dark matter?
It allows new measurements to find potential deviation in the relation of inertial and gravitational mass. If no deviations are found, then this means nothing for general relativity (the equations would just contain the same quantity under two different names). If deviations are found, then it probably means that GR must be modified.
The Tao of math: The numbers you can count are not the real numbers.
Neutron: Electrically neutral particle. One of the particles out of which atomic nuclei are built.
Interferometry: Measurement of the interference of waves. Remember that according to quantum mechanics, particles also show wave-like properties, especially interference.
The Tao of math: The numbers you can count are not the real numbers.
Imagine if you could lift an aircraft carrier sized ship in to space with nearly no energy, then accelerate to .999 light speed with no more thrust than a model rocket.
Note that one situation means low/zero gravitic mass, the other means low/zero inertial mass. You might be able to arbitrarily control both. You might be able to trade one off for another. Or maybe only modify one. Also, the problems with SR and QM are at a small scale, so your aircraft carrier might only be one atom in diameter or something.
Finally, I haven't read the paper, but it'll be interesting to see how it gets around various perpetual motion type problems. Right off the top of my head, extracting energy from a pendulum where gravitic and inertial mass are different and varying is going to be a serious issue.
Changing inertial mass would do pretty weird things to rotating flywheels. I suppose you could make a spinning flywheel break apart with immense violence at a very low rotational speed. Or rotate a spinning flywheel at insane speeds without it flying apart. All at the same stored energy level. Theres probably a perpetual motion machine that would involve extracting constant energy at a constant torque at high vs low RPMs.
Similar problems at a quantum scale. Otherwise it would be too easy to accelerate two beams of "reduced inertial mass" deuterium to an arbitrarily high velocity and then increase their gravitic mass at the collision point until they fuse.
Finally, the most interesting apps might be arbitrarily increasing inertial and gravitic mass. Increasing gravitic mass would make gravity wave detectors much simpler to make. The odds of increasing the gravitic mass of something small on a spacecraft to something large like a planet seem unlikely aka artifical gravity. Increasing inertial mass might be useful for weapons, armor, pretty much anywhere you use lead, tungsten, or DU.
"Science flies us to the moon. Religion flies us into buildings." - Victor Stenger
Not quite. Acceleration starts at a specific point and "pushes" its way through the object at the speed of sound in the material of the object. If you had a 10 mile long metal bar and were strong enough to shove one end, the other end wouldn't move instantly. Your force would start a compression wave along the metal bar, traveling at the speed of sound though the metal, until it reached the other end. Same with a rocket, the engines apply acceleration at their connection point and the acceleration pushes its way through the materiel. This is why they have to be built out of such strong stuff, it has to be able to withstand the compression forces of the acceleration without fracturing due to stress.
I would think this means we have a basis for making quantitative measurements of what happens where GR and QM collide.
Not quite. They make no assumptions about GR in the article, what they have done is come up with a way to test one of the assumptions of GR - assuming the article passes peer review, arXiv is just a preprint server. There are too possible outcomes to the test they propose: m_i=m_g or m_i!=m_g. In the first case nothing has changed and in the second case one of GR's core assumptions has been dismantled so GR cannot be a fundamental theory since there is a phenomenon which it cannot explain. Hence QM and GR will never 'collide' because GR will have disappeared to be replaced by something else - possibly something which QM has no problem with.
My personal guess is that any such experiment will show that m_i=m_g but it will be an interesting test to do and potentially result in a far more accurate test of the equivalence principle.
The key part is the null-grav Bose-condensate at the base. When the temperature falls below 91 micro-kelvins, the resulting phase-change decouples inertial mass from equivalent mass and the gravitational force disappears.
There a few bugs to be worked out however. First, the grav-shield must be aligned within ten arc-seconds perpendicular to main gravitational body (Earth) or gravity leaks through. Second, stray cosmic rays have the disturbing habit of energizing the condensate about the phase-change temp and destroying the null-grav effect. I hope to have fixes by next week.
The standard crackpot "a single equation" makes me want to cry, but the "see t-shirt below" part more than makes up for it.
"Professor" Aquino is widely known as a total nut. For Newton's sake, his theory "includes not only force particles and matter particles, not only general relativity and Quantum Gravity, but also a theory of consciousness"!! He can't publish his papers at the "Journal of New Energy"! Heck, one of his abstracts starts with "The existence of imaginary mass associated to the neutrino is already well-known" (and as a particle physicist, I've never seen any theory or experiment that even suggests an imaginary mass). He was worked at INPE (which is a very respected research institution) in a data-taking-monkey position; then got a job at the Maranhão state university (where there is NO research at all). He is listed at UEMA as having only a masters' degree (no PhD, so he can't have a research position). Please, don't mention him on an article about science. It's just like mentioning a 1940 VW Beetle when discussing today's F1 cars.
"The equivalence principle is one of the corner stones of general relativity. Now physicists have used quantum mechanics to show how it fails."
Alternatively, they could choose to look at this equivalent assertion: The wave-particle duality of matter is one of the cornerstones of quantum mechanics. Now physicists have used general relativity to show how quantum mechanics fails.
Of course, in actuality, they haven't shown anything yet...
OK.
Wrong. B will have a four times as strong gravitational field than A, therefore A will also have four times the acceleration it would have if B had just the same gravitiational mass as A.
Or to put it in formulas:
Be miA (miB) the inertial mass of A (B), mgA (mgB) the gravitiational mass of A (B), G the gravitational constant, r the distance between A and B, and aA (aB) the acceleration of A (B). Then we have miA aA = mgA mgB/r^2 and miB aB = mgA mgB/r^2. Note that the right side is the same in both cases, so if the inertial masses are the same, then also the accelerations will be (especially you'll find that, irrespective of the inertial masses, energy and momentum are conserved). If it were not so, Coulomb interaction would violate those conservation laws, too (because in the above equations, you can easily replace gravitational mass and gravitational constant by charge and 1/(4 pi epsilon0)).
Now what can be shown by your argument is that splitting the gravitational mass further into a "field generating mass" (i.e. one that determines the strength of gravitational field of the object) and a "field reacting mass" (the one which says which force the object experiences in a given gravitational field) and allowing those to be independent would violate the conservation laws. In that case (with mgg being the generating mass, and mgr being the reacting mass), we would get
miA aA = G mgrA mggB/r^2, miB aB = G mgrB mggA/r^2
As you can see, now the terms on the right hand side are not equal any more, and therefore the very scenario you described can happen (just replace "inertial mass" with "field reacting mass" and "gravitational mass" with "field generating mass" in your text).
The Tao of math: The numbers you can count are not the real numbers.
Assuming the acceleration is provided by mechanical means. But if the body in question is a conductor and the accelerating field is a uniform magnetic field, the acceleration is applied to all the particles in the body at the same time and in the same amount. Provided the accelerating force is uniform, it can still, theoretically be distinguished from gravity by its lack of a gradient.
politicians are like babies' nappies: they should both be changed regularly and for the same reasons
Oh, I can easily write all equations of Physics into one equation.
To see how it works, let's assume I want to "unify" the Schrödinger equation and Einsteins field equation (don't worry about the fact that the Schrödinger equation is non-relativistic ...).
Schrödinger: i hbar d/dt psi = H psi [d here should be the partial derivative sign]
Einstein: G = 8 pi gamma/c^4 T [gamma here is the gravitational constant, because G is already used for the Einstein curvature tensor]
The first step is to bring all terms to the left side:
Schrödinger: H psi - i hbar d/dt psi = 0
Einstein: G - 8 pi gamma/c^4 T = 0
Note, however that the "0" in the first equation is a null vector in the quantum mechanical Hilbert space, while in the second equation, it's a tensor in spacetime. Those are not compatible. However, in both cases, we can choose a norm (in the first case, the standard Hilbert space norm can be used; in the second case, any matrix norm will do). Note that the norm need not to make physical sense; the only thing we need is that it maps to the non-negative real numbers, and only the zero object of the respective quantity is mapped to the real number zero. Denoting both norms with ||...||, we get:
Schrödinger: ||H psi - i hbar d/dt psi|| = 0
Einstein: ||G - 8 pi gamma/c^4 T|| = 0
Now we have two non-negative real numbers which shall be zero. Their sum is zero exactly if each one of them is zero. Therefore we can combine the equations into one:
||H psi - i hbar d/dt psi|| + ||G - 8 pi gamma/c^4 T|| = 0
From this equation, one can easily derive both Einstein's field equation and Schrödinger's equation. Therefore I just unified quantum mechanics and general relativity. :-)
The Tao of math: The numbers you can count are not the real numbers.
The point is that, according to the euivalence principle, X g of acceleration due to gravity is indistinguishable from X g of acceleration due to anything else. The article used the specific example of the 1 g you feel at the surface of the Earth.