But they probably were sure of what they were saying: That there are no direct indications for a big earthquake. Now, if they had claimed that there will not be a big earthquake, things would be different. Just as "I didn't smell something unusual" doesn't mean "the air doesn't contain anything unusual" - there could be something unusual in the air that you cannot smell. If that unusual stuff happened to be poisonous, you cannot blame someone for not having smelled it.
It would violate conservation of momentum, conservation of energy and conservation of angular momentum (if your origin is not on the straight line connecting the two objects). It indeed would not violate conservation of mass, conservation of charge, or conservation of any other non-dynamic quantity.
Any business aware that 99.9% of their competition already cover those 95%, and therefore it's probably much easier to get a large chunk from the 5% if you are any good, than to get a small chunk of the 95%.
As I said, in a language designed for it, you'd easily create and use arbitrary many fine-grained types. However, I don't know a real language where it's easy enough to write new types to make this feasible. For the specific case there are already C++ libraries, therefore it's easy to use them. However, look at boost::units to see the complexity you need to support reasonable flexibility, and ask yourself if you would be willing to write something like that for your project if not some kind soul had already done it for you. And even that solution can go only so far. For example, for processes you have several different times: Wall time, user time and system time. It doesn't make sense to add user or system time to wall time, so you make them different types, right? But it does make sense to subtract them, to find out how much real time was taken away by other processes or interrupts. So you add another type for that difference. I don't think this scenario is supported by boost::units, so you have to write all that stuff yourself.
And then, there's the situation where you have nice matrices and vectors with units, and then you want to pass them to some linear algebra routines. But those routines don't know the unit types. So now you have do to tricks to get your great dimensional units into the pure numerical linear algebra package (you probably don't want to rewrite the linear algebra package).
OK, so a few days before deadline, your boss asks you how far you got with your project, and you tell him "I'm almost finished with the unit types to be used by the code." I don't think your boss will be pleased to hear that.:-)
Hungarian notation to denote the type (like int, pointer, etc) is common, but it's doing it wrong. Correct application of hungarian notation doesn't use type prefixed, but meaning prefixes. For example, imagine a windowing system, where you can have coordinates relative to the window, and relative to the screen. In that case you could e.g. use the prefix w for window-relative coordinates, and s for screen-relative coordinates. Of course both types of coordinates are just pairs of ints, but if you see e.g. sMousePointer, you immediately know that it contains the mouse pointer in screen coordinates, not in window coordinates (which you couldn't see from the type, because both are just coordinates). Also, if you have a statement like
if (sMousePointer.x > wxmin && sMousePointer.y wxmax)
you know immediately that there's something wrong. Without the prefixes, you'd have to look at the logic to spot this problem, because all values are of type int.
Now you could of course make separate types for screen-relative and window-relative coordinates, and also for screen-relative x coordinate, screen-relative y coordinate, window-relative x coordinate and window-relative y coordinate, but at some point 90% of your code would consist of type definitions which all just wrap some simple type.
Now I can imagine some mechanism which would allow you to define such types easy enough to make such a system practical, but I don't think it would work well in any existing language.
What about the starter motor (OK, not electronic, but electric - as would be the main engine in an electric car)? Do you have a crank to start your car?
It will be the ultimate security measure. While it's easy to get someone's fingerprint of an image of his face, most people know how to keep their penis secret.
Don't forget that trolls are also humans, and therefore also have a certain intelligence. If they know that their first chat is a troll test, they will not troll until they get to the real chat.
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.:-)
Well, the throwing people around the bridge might be explained much simpler:
The inertial dampers need a short time to react to acceleration information.
for ship-generated accelerations (impulse engine), the information is already available at the time the acceleration starts, because it's transmitted to the dampers at the same time as to the engine.
The force of a photon torpedo cannot be completely predicted. So the inertial dampers can only incompletely compensate the acceleration.
It suffices if the gravitational field is linear over the size of the experiment. Every smooth function is linear if you look at a sufficiently small region. Since for the Earth's gravitation the linearity is given even for quite macroscopic dimensions (otherwise all your formulas for throwing objects would be wrong), it's even more given for microscopic dimensions like those of quantum experiments.
All they claim is that they have a new way to test the equivalence principle. Indeed, they claim not even that; they just claim their theory might allow an experiment to test the equivalence principle. This is not very extraordinary. Of course the experiment has to be done, but all the paper does is say how to do it.
Consider two giant bouncyballs in space, with the same inertial mass but where ball A has 4 times the gravitational mass of ball B. They start off some distance apart from each other, with velocity 0.
OK.
As they attract each other, B will be accelerating 4 times faster than A since A has 4 times the gravity, and at one point they will meet.
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).
When a body accelerates all its components are accelerated at the same rate. However, when body is subjected to a gravitational attraction, the part of the body nearest the attractor experiences a slightly larger attraction than is experienced by the other end of the attracted body (since the force experienced depends on the distance ** 2 from the attracting body).
Yes. This effect is known as tidal force.
Unless you start talking about single point, infinitely small bodies, the difference in attraction across the gravity gradient will be real.
It suffices if the effect is below measuring accuracy, and therefore negligible.
So in practical terms there is a difference, even if the effect is extremely small.
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.
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.
Slashdot Mirror
But they probably were sure of what they were saying: That there are no direct indications for a big earthquake. Now, if they had claimed that there will not be a big earthquake, things would be different. Just as "I didn't smell something unusual" doesn't mean "the air doesn't contain anything unusual" - there could be something unusual in the air that you cannot smell. If that unusual stuff happened to be poisonous, you cannot blame someone for not having smelled it.
It would violate conservation of momentum, conservation of energy and conservation of angular momentum (if your origin is not on the straight line connecting the two objects). It indeed would not violate conservation of mass, conservation of charge, or conservation of any other non-dynamic quantity.
Any business aware that 99.9% of their competition already cover those 95%, and therefore it's probably much easier to get a large chunk from the 5% if you are any good, than to get a small chunk of the 95%.
As I said, in a language designed for it, you'd easily create and use arbitrary many fine-grained types. However, I don't know a real language where it's easy enough to write new types to make this feasible. For the specific case there are already C++ libraries, therefore it's easy to use them. However, look at boost::units to see the complexity you need to support reasonable flexibility, and ask yourself if you would be willing to write something like that for your project if not some kind soul had already done it for you. And even that solution can go only so far. For example, for processes you have several different times: Wall time, user time and system time. It doesn't make sense to add user or system time to wall time, so you make them different types, right? But it does make sense to subtract them, to find out how much real time was taken away by other processes or interrupts. So you add another type for that difference. I don't think this scenario is supported by boost::units, so you have to write all that stuff yourself.
And then, there's the situation where you have nice matrices and vectors with units, and then you want to pass them to some linear algebra routines. But those routines don't know the unit types. So now you have do to tricks to get your great dimensional units into the pure numerical linear algebra package (you probably don't want to rewrite the linear algebra package).
OK, so a few days before deadline, your boss asks you how far you got with your project, and you tell him "I'm almost finished with the unit types to be used by the code." I don't think your boss will be pleased to hear that. :-)
Hungarian notation to denote the type (like int, pointer, etc) is common, but it's doing it wrong. Correct application of hungarian notation doesn't use type prefixed, but meaning prefixes. For example, imagine a windowing system, where you can have coordinates relative to the window, and relative to the screen. In that case you could e.g. use the prefix w for window-relative coordinates, and s for screen-relative coordinates. Of course both types of coordinates are just pairs of ints, but if you see e.g. sMousePointer, you immediately know that it contains the mouse pointer in screen coordinates, not in window coordinates (which you couldn't see from the type, because both are just coordinates). Also, if you have a statement like
if (sMousePointer.x > wxmin && sMousePointer.y wxmax)
you know immediately that there's something wrong. Without the prefixes, you'd have to look at the logic to spot this problem, because all values are of type int.
Now you could of course make separate types for screen-relative and window-relative coordinates, and also for screen-relative x coordinate, screen-relative y coordinate, window-relative x coordinate and window-relative y coordinate, but at some point 90% of your code would consist of type definitions which all just wrap some simple type.
Now I can imagine some mechanism which would allow you to define such types easy enough to make such a system practical, but I don't think it would work well in any existing language.
What about the starter motor (OK, not electronic, but electric - as would be the main engine in an electric car)? Do you have a crank to start your car?
They are currently preparing the wake-up LAN packet.
Why not instead require the protection resistors?
He's so old that he has a hugely negative user ID, in fact so negative that it underflowed and rolled over to a large positive ID.
Anyone who wants to see male genitalia is a pervert? What about all those who want to see female genitalia?
For trolls, it works reasonably well. Not perfect, but there's no perfect solution anyway.
It will be the ultimate security measure. While it's easy to get someone's fingerprint of an image of his face, most people know how to keep their penis secret.
Don't forget that trolls are also humans, and therefore also have a certain intelligence. If they know that their first chat is a troll test, they will not troll until they get to the real chat.
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. :-)
As long as it's fun, it's no more stupid than anything else you do just for fun. Only if you start to take it seriously, it becomes stupid.
Well, the throwing people around the bridge might be explained much simpler:
It suffices if the gravitational field is linear over the size of the experiment. Every smooth function is linear if you look at a sufficiently small region. Since for the Earth's gravitation the linearity is given even for quite macroscopic dimensions (otherwise all your formulas for throwing objects would be wrong), it's even more given for microscopic dimensions like those of quantum experiments.
All they claim is that they have a new way to test the equivalence principle. Indeed, they claim not even that; they just claim their theory might allow an experiment to test the equivalence principle. This is not very extraordinary. Of course the experiment has to be done, but all the paper does is say how to do it.
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).
Yes. This effect is known as tidal force.
It suffices if the effect is below measuring accuracy, and therefore negligible.
A negligible effect can safely be neglected.
The law of gravity says that fat people are more attractive than thin ones.
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.
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.
One more reason to not use iPad and iPhone.
Wold you also take targeted subtracts? :-)