Not the science, the personnel.
I was watching "Forbidden Planet" and heard this:
"I'll bet any quantum mechanic in the service would give the rest of his life for a chance to fool around with this gadget."
(one of my my favorite movies nonetheless)
There is also a couple space movies out there where the ship was bombarded by meteorites
And there is Captain Kirk saying that the "circuits are shortening", when Khan was reawakened.
Technical accuracy never stood in the way of entertainment
-
Last edited by megafiddle; 08-03-2014 at 11:37 PM.
Maybe those fragments had bounced off a planet or two before reaching the ship ....Originally Posted by megafiddle
Ironically enough, I was recently reading the wiki and the most elegant explanation for the uncertainty principle was that when you make a position observation, it's reflected as a combination of momentum states of that particle, hence the "uncertainty" because the position measurement is reflected by multiple momentum states. The opposite is true as well, a momentum observation is represented as multiple position states.
It's not only an elegant explanation but the only one that really matters.
The position and momentum wavefunctions are related by the Fourier transform. What's the Fourier transform of a perfectly localized peak? Why, it is a wave that extends throughout all of space. This isn't just a physical truth, it's a mathematical truth.
Code://try //{ if (a) do { f( b); } while(1); else do { f(!b); } while(1); //}
That is pretty funny. Personally, I prefer my sci-fi to be a little more on the credulous side. Star Trek always seemed to me to be more "sci-fantasy" than anything else (I mean, really, like teleporting a person's quantum state - pray tell, what the hell do you do with the *original* "copy" anyway?!).
Except that Heisenberg's Uncertainty Principle is not precisely true, because sometimes (albeit not usually) we *can* measure both the momentum and position of a given particle/wave-state.
Even so, there *will* always be an uncertainty in measurement for one reason or another. For one thing, every particle and every packet of energy in the universe contributes to the overall "field" of forces streaming through a given point in space-time. How can we possibly know all of the initial states of these contributors? We can't! Another interesting force at work in the universe for which we have not only no way of precisely predicting, but no way to even identify exactly...and that is consciousness. If I we're to try to predict the exact interaction of a given particle with your body, for instance, there would be no way I could predict with 100% accuracy the end result simply because YOU, your mind, may have played a part in some aspect of that interaction. How can one possibly quantify that?!
So yes, uncertainty *is* a certainty. Not due to limitations in our implements of measurement, but to the limitations of our own understanding of both the initial conditions and the unpredictable (or random) nature of the influence consciousness exerts on (at least) some systems...
Besides that, there may be other external forces as well for which we may never be made aware of, operating in some other dimension perhaps.
In other words, uncertainty nonetheless reigns in the universe.
Last edited by Sebastiani; 08-04-2014 at 02:20 PM.
I'm not sure what you mean by measuring the position and momentum at the same time. From a purely mathematical perspective, I don't think it's possible to applying the position and momentum operators simultaneously and even then, I don't think that px is equal to xp, considering that x and p are position and momentum operators respectively.
I read up on the Born rule a little bit and the gist is, the only true way to interpret the wave function is probabilistically. Because you have a distribution, you can calculate the standard deviation of the wave or wave packet. Because the momentum space is a reflection of the position space, you have these relationships between the position's standard deviation and the momentum's as well.
This has nothing to do with our own instruments at all. The Born rule is the crux of this and it says that we HAVE to interpret the wave equation as a probability function. Because the Born rule has not yet been disproved (I think he got the Nobel prize for this too), we assume that uncertainty is inherent in the universe itself.
Yes, the non-commutativity of the operators is a proven mathematical certainty, but that still does NOT necessarily mean that simultaneous measurement isn't possible. Anyway, as I already pointed out, there are other sources of uncertainty.
Well right, and in fact every formulation of quantum mechanics, be it matrix mechanics, wave-function-based methods, Feynman's "path integral" technique, or whatever, they all rely on probability density functions.
Last edited by Sebastiani; 08-04-2014 at 06:36 PM.
Can you please elaborate on what you mean about simultaneous measurement? I know the position and momentum operators but is there a third one specifically for an instance of both? I imagine that instead of a 1-to-n mapping between states, there would be a m-to-n mapping, where m and n are some number of states corresponding to position and momentum.
It can be expressed in its simplest form as follows: One can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles—its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant.
Those are the words of Werner Heisenberg, of course. He eventually refines the idea with the non-commutativity of conjugates argument. Problem is, it's irrelevant. Remember, we're supposedly talking about the physical act of measurement, yet somehow Heisenberg comes up with this idea that the uncertainty is *solely* due to inherent mathematical limitations of Fourier analysis! What on Earth do analytical techniques have to do with the intrinsic nature of physical systems anyway?
Einstein was more on target. He too realized that uncertainty was inevitable, but rather than provide some ad-hoc quasi-metaphysical explanation that "it's just in the math" (which he did recognize as a procedural source of uncertainty, nonetheless) he instead proposed a no-nonsense "hidden variables" argument, which could then be addressed by simply applying some heuristic error bound.
Heisenberg never referred to the act of measurement as being somehow intrinsically limited. Instead he correctly stated that the act of observation disturbs the system. The Heisenberg Uncertainty Principle was never a statement about observation methods, techniques or technology. Instead, it was about a now well known and understood attribute of quantum systems. It's not his fault that his principle has been (purposely or not) misread by some.
Originally Posted by brewbuck:
Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.
Jodie Foster in Contact,
“If there are 400 billion stars in the galaxy, and just one in a million had planets, and just one in a million of those had life, and just one in a million of those had intelligent life, that still leaves millions of planets to explore.”
Oops!
Originally Posted by brewbuck:
Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.
I'm not sure if there are any mathematical uncertainties in Fourier analysis considering you can integrate it over a continuous domain of any range. I would like to hear more about this.
I would also like to say that, Sebastiani, I'm not sure your post explains measuring position and momentum simultaneously. I'm talking about operators, not people in a lab.
What I mean is that that Fourier analysis is simply a tool of human convention. Using trigonometric functions, we try to break up a waveform into it's spectral components. Analyzing duals (such as position and momentum) yields ambiguous results due to the simple fact that they are complementary and thus non-commutative. Heisenberg saw this as the *source* of uncertainty in the universe! Who are we to say that the universe depends on Fourier transforms though? Perhaps some other mathematical construct may arise which effectively eliminates the need for Fourier analysis altogether (just as quaternions eliminate the singularities encountered when working with Euler angles).
Exactly - the latter is what we should *really* be talking about here! Mathematical operators are mere human constructs that have no place in the formulation of a physical law. It's a procedural issue, nothing more...
I know this is probably going to make you very angry because you seem very adamant but just reading the intro on the wiki, it seems to disagree with what you're talking about.
And I do trust the physicists to maintain the page.Historically, the uncertainty principle has been confused[6][7] with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty.[8] It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems,[4] and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.[9] It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.[10]
I'm confused though. What is it exactly that you're arguing because most of your argument seems to stem from people physically measuring things when I keep referring to the theoretical equations which as far as I can tell have not yet been disproven.
Edit : I guess the real thing you seem to be arguing is that momentum states are conjugate variables to position because we made them that way but I think they just happen to be conjugate to each other and it's for that reason the uncertainty is intrinsic.
Edit edit : I think this should help : http://physics.stackexchange.com/que...iable-of-posit
Last edited by MutantJohn; 08-06-2014 at 02:59 PM.
Right, so in essence it states that Heisenberg produced a flawed theory that was only later refined for rigor (remember, the "observer effect" was Heisenberg's first formulation of the Uncertainty Principle).
No! Remember, the underlying question here is about the uncertainty involved in measurement. Right? Position and momentum are conjugates - so what? Does that mean that we can never-ever-ever measure both at once? Who knows, clever techniques may one day make it possible. Why rule it out on the grounds that our *current* math yields an ambiguous duality? My point is simply that HUP is no law of physics; it's merely a law of the limitations of certain analytical methods, pure and simple...
