What are, if any, macro effects that can be directly attributed to this?

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In your rush to call everyone "entrenched" or closed-minded or "limited" you fail to note that the "limit" here has a very natural boundary: that point at which the evidence stops. - JayUtah

Science fiction was never meant to be an educational tool. - Editor Amazing Tales

The fundamental idea is that observation affects that which is observed. It's a problem in wildlife biology as much as it is in physics. You go electroshocking an entire stream, not once, not twice, but three times in order to be statistically certain that you got at least 95% of the fish--hey, that's bound to have some effects. And those are certainly macro effects.

In a word, none. The uncertainty limit too small to have any effect for macroscopic objects. The limit is Planck's constant divided (4 times pi). That value is about 5.37x10^-35, with units of Joules times seconds. This is the "error" in our measurements due to the Heisenberg Uncertainty Principle.

A 100 watt light bulbs puts out 100 Joules of energy each second. For comparison, the energy of a one-ton car driving at 60 mph is 0.326 Joules. We might be able to measure that to more places if we wanted to, but not to enough places that uncertainty would be significant.

For the record, even though a lot people agree with Warren's comments, I find it absurd to claim that this is an extension of uncertainty in any way. Uncertainty at the quantum level is built into the universe, and it's a basic property. Pandering to the camera (or the anthropologist), consciously or subconsciously, is not the same phenomenon.

Ditto Tobin wrt Warren's comment, plus this:

Kinetic energy of a one ton car at 60 mph (relative to the road surface):

1 short English ton ~ 907 kg.
60 mph ~ 26.7 m/sec

Newton = kg-m/sec^2, a unit of force (mass times acceleration)

Joule = kg-(m/sec)^2 = N-m, a unit of work (force times distance) or energy (mass times velocity squared)

Watt = Joule/s, a unit of power (energy over time)

So I make it 647 Kilojoules, give or take.

According to James Watt (who extrapolated for data from ponies, sez the ever-unreliable Wikipedia), a horse can sustain an energy output of mechanical work (e.g. turning a millstone) at the rate of 746 Watts, i.e. can keep 7 light bulbs lit for several hours. Supposedly a real horse pulling real hard can produce more like 11 Kilowatts over a shorter period of time.

If our car hits something and suddenly comes to rest (wrt the road surface), 647 Kilojoules is the amount of energy it must expend, in a hurry. So if it stops in a tenth of a second, you could say that the car very briefly produces (on average) an impressive 6 Megawatts. (Unfortunately, this energy is mostly wasted in crumpling the car and the barrier, so it cannot be used to keep 1667 lightbulbs lit for one hour.)

For comparison, a modern railroad locomotive sustainably produces about 6 Megawatts while hauling a heavy train. This power is converted (I guess) into waste heat (via friction with the rails) and local atomospheric turbulence (the engine must push air out of its path, and then there is aerodynamic drag).

http://en.wikipedia.org/wiki/Orders_of_magnitude_(speed)
See
http://en.wikipedia.org/w/index.php?...oldid=16259988
for conversions to geometric units, in which

• angular momentum is measured in units of area,
• mass, energy, and time are all measured in units of length,
• velocity is dimensionless,
• acceleration is measured in units of 1/length (units of path curvature) ,
• energy density, momentum density, and pressure are measured in units of 1/area (units of sectional curvature)

Something I learned from Isaac Asimov: most of the 100 Watts required to operate a lightbulb goes into radiant heat, not visible light. A living human also produces about 100 Watts of waste heat. That's why cramming them into black holes makes 'em testy.

Exercise: get some incandescent lightbulbs (not the Mercury vapor kind!) and drop them from 0.5-2m to determine the average height required to break them. Use your knowledge of Newtonian physics to deduce the energy required to break a lightbulb. Compare with the energy required to keep one lit for six hours. Ponder the ease of destruction versus doing useful work. Then spend some time with ATM, the only place I know where destruction counts as useful work ;-/

Exercise (for those who know how to compute the Newtonian gravitional binding energy of the Sun): what would be the Newtonian energy required to spaghettify the Sun? (That is, radially compress orthogonal to some axis of axial symmetry while simultaneously elongating twice as fast along the axis of symmetry, which changes the surface from a sphere to a prolate spheroid while keeping the volume constant.)

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

I find that one of the interesting things about the uncertainty principle ΔxΔp≥h/2π can be made "visible" for the lay person by discussing the macrocosmos.

Suppose you have a car driving on the street and you are standing on the pavement with your new digital SLR camera. Now you can do two things with that camera:
1. you can take a pic with a very short exposure time, you can see the car clearly, and determine its location very well, however, you have no information about the speed of the car.
2. you can take a pic with a long exposure time, you will see a very blurred car, stretched over the picture, so you can determine the velocity of the car rather well, but any information about the exact location of the car is lost.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

I do not want to attempt to answer this question because I am not sure I understand it;
I do want to offer this however; The uncertainty principal dictates that just what you did not think could happen does. Just as what you expected does not... This macro evidence what can we offer as proof... All of it. And none of it. I understand me. Does anyone else?

As Tobin Dax stated, such macro observations have nothing to do with the Uncertainty Principle.

No, it has nothing to do with the quantum mechanical UP, but it does help lay persons to understand what we scientists mean, taking a picture of a car (a one time event) can either give the location to a high degree of certainty with no info on the momentum (speed) of the car, or you get the speed rather well determined and lose the info on the precise location of the car.

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Any comments in glorious red are to be considered in ModeratorMode.


善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

Great analogy. Seems like light sure is a big deal no matter where you look, even in analogies.

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Lighten up! This is a stellar board!

tusenfem showed graphically a wonderful example of the concept of the uncertainty principle.

in a nut shell, when an observer like yourself is trying to find and measure a particle, say for instance an electron in a region of space, you will find that the electron is moving, and the more precise you try to measure the "momentum" of the electron, you find that the position of the electron is uncertain.

but why does this happen?

from what i understand, and i may be wrong, but when you try to look at a particle (say an atom), you need a way to observe that particle so you would need to use a photon to observe or see it by looking at the reflected photon. However, when the photon entangled the particle, it changed the momentum/position of the particle by an uncertain amount which would be inversely proportional to the [accuracy] of the position measurement.

http://en.wikipedia.org/wiki/Uncertainty_principle

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-work in progress--

Hmm. Virtual particle/antiparticle pairs, and their relative Hawking radiation; poorly defined energy levels of short-lived states - keeping in mind the Heisenberg's principle doesn't just apply to how we measure but to how states interact. There must be another application just eluding me at the moment.

100 J/s = .134 HP

It takes considerably more horsepower (approximately 40 HP) to sustain your average 2,000 lb vehicle at 60 mph.

40 HP = 29,828 joule/second.

Your statement comparing HP with Joules is a misnomer, as the HP equivalent in the SI system is J/s, not merely Joules.

That and the value of your figure itself is off by several orders of magnitude...

By the way, 100 watt = 100 joule/second.

Thus, a 1 ton car at 60 mph requires 298 times the energy to sustain it's velocity than what it takes to light a 100 W light bulb.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

I see. Apparently he meant the kinetic energy of a 2,000 body moving at 60 mph relative to the ground. That still doesn't excuse his direct comparison of work to energy.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Tobin was clearing referring to the kinetic energy of a one ton automobile moving at 60 mph relative to the road surface. This computation need take no account of frictional forces or air resistance; the same result would be obtained if we envisioned a 907 kg projectile approaching an asteroid at 26.7 m/s.

Mugaliens is referring to the power (energy per unit time) which is required to sustain the automobile's motion, which is the energy lost to frictional forces, air resistance, or "waste heat" (once the car has gotten up to speed; I guess the engine has to work a bit harder in the acceleration phase, especially if the driver puts the pedal to the metal).

For the mathematically inclined: someone should probably mention that the Uncertainty Principle can be considered to arise naturally in functional analysis (the study of linear operators on function spaces, which are typically infinite dimensional, and are often examples of a Hilbert space or Banach space), and there are many generalizations both in pure math and in mathematical physics. A keyword for the pure math side which is becoming increasing popular is Ore algebra and its special case, Weyl algebra. If anyone's interested, I can give citations.

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

Could it be that all light represents a macro effect of the Uncertainity Principle?

I found this on synchotron radiation:

An ultimate limit on the emittance arises from the uncertainty principle and a limit on the Beta

[This goes beyond my uncertainity principle and is a Noidea Principle, since I no not what it means, but it's somethin'.]

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Lighten up! This is a stellar board!

What if we include annihilation?

Is it possible to know the position and velocity of a single particle at the annihilation event? For example, if we supercool a pool of electrons and inject positrons of various temperatures into the test chamber, can we find out the position of annihilation and kinetic energy of the positron. We would setup the experiment to render the kinetic energy of the electrons as negligible.

Probably none, with a sufficient constraint on what "macro" means. But the uncertainty principle in the sense of ΔEΔt≥h/2π (where "E" is energy and "t" is time) sets the minimum possible width for a spectral emission or absorption feature, and is measurable in a spectroscopy lab. That might not be "macro" enough for you, but I felt like mentioning it to point out that the uncertainty principle is not just the usually cited ΔxΔp≥h/2π but in fact applies to any conjugate pair of quantum mechanical variables, which includes energy and time.

Chris beat me to the point. I have long been fascinated by the amazing coincidence between the behavior of the physical universe (which we assume to exist independently of ourselves) and the mathematical universe (which is an invention entirely of our own minds). That the latter should be so good at predicting the behavior of the former is astounding to me. And a good example of this is the totally unintuitive uncertainty principle from quantum mechanics. In fact it can be derived purely from mathematics with no input from physics, or any consideration of the physical world at all, yet the physical world obeys the purely mathematical constraint.

There is a derivation from Fourier Analysis here: Fourier Transforms and Uncertainty Relations (hosted by the ever useful MathPages.com). This is also discussed in the book From Classical to Quantum Mechanics by Giampiero Esposito, Giuseppe Marmo & George Sudarshan; Cambridge University Press 2004. The niche this book fills for me, which the other quantum mechanics books don't, is the extensive treatment of the methodological links between classical & quantum mechanics, so you can see how they blend together. See section 4.2, page 128, "Uncertainty relations for position and momentum". Here we find out where the uncertainty relation comes from (emphasis in the original):

"The uncertainty relations result directly from Fourier analysis and hence are not an exclusive property of quantum mechanics. A possible formulation is as follows: a non-vanishing function and its Fourier transform cannot both be localized with precision. Indeed, in the framework of classical physics, if f(t) represents the amplitude of a signal (e.g. an acoustic wave or an electromagnetic wave) at time t, its Fourier transform f_t shows how f is constructed from sine waves of various frequencies. The uncertainty relation expresses a restriction with respect to the measurement in which the signal can be bounded in time and in frequency band."
From Classical to Quantum Mechanics, page 128.

So there is an implication that you could measure some fundamental uncertainty in any signal bandwidth, and that should count as macroscopic. But in the presence of more mundane & ordinary noise, I think it would be a challenging measurement to make, assuming that my interpretation is correct.

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The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell

I didn't think my number sounded right, but I was in a hurry and using Google's calculator. I've really got to fix my good ol' TI-85.

Edit after reading through the posts above:
BigDon, I apologize for not giving you a technical response. Obviously a simple explanation that is good enough to answer your question isn't what you were looking for. I know you haven't said so, but everyone else in this thread has. Apparently the word "kinetic" can't be implied.

Further, Mugs, I not once mentioned work or horsepower, and I certainly didn't try to compare them. I was using the light bulb to give an everyday reference to what a Joule is. And I said it right.

And Chris, thanks for the correct calculation. I was working too fast last night.

Cool idea.

In my view, the uncertainty principle in quantum mechanics appears because of the importance of wave mechanics in telling particles how to move. So we should view the uncertainty principle as coming from wave mechanics (which is also what Chris Hillman and Tim Thompson are saying, but from the point of view of the pure mathematics underneath wave mechanics-- we must also observe physically that wave mechanics has a place at the physical table, which also means that Fourier transforms become a relevant way to understand dynamics of particles). Note that as soon as we say the uncertainty principle is an expression of wave mechanics, then the door opens to point to any macroscopic wave phenomenon, and identify that as a macroscopic example of the uncertainty principle, applied to the elementary excitations that comprise that macroscopic wave phenomenon.

For example, the fact that your radio can pick up signals from an emitting tower through a window, even when your eye cannot see the tower through that window, is a classic example of the uncertainty principle-- the size of the window gives you some knowledge about the lateral constraints about the location the photons would have to move through, so that imprints an uncertainty onto their lateral momentum. The excitations of visible light are particles with much higher momenta then the radio counterparts that your radio detects, so the same imprinted uncertainty in lateral momentum translates into a very small angle of uncertainty in the direction of the light particles' motion, but a much larger angle of uncertainty in the direction of the radio-wave excitations. At some point the angle of uncertainty in the direction of the radio waves exceeds the angular width of the window, and at that point it is no longer necessary for the location of the radio tower to conform to the window's angular acceptance in order for the radio photons to get to your radio, i.e., you can hear from a tower you can't see. The short term for all that is "diffraction".

Let me second what Ken said. We can see the "uncertainty principle" all the time in macroscopic wave phenomena.

A classic example I remember having to do as an exercise back in school was the frequency-time thing using the Fourier transform. You can show something like

delta-w*delta-t = constant (which I can't remember but it involves pi )

Delta-t is roughly the duration of a signal that you receive and delta-w is the frequency bandwidth. The shorter the bandwidth, the more time it takes to transmit a given amount of information.

For example, delta-w = 0 would be a single frequency, which would be a sine wave that went from -infinity < t < +infinity. Delta-t is infinite (and a pure, eternal sine wave can transmit no information at all, at least in finite time). Delta-t = 0 would be a delta function thing which would consist of all frequencies from 0 to infinity (negative would be involved in the complex form, but that translates into sines and cosines -- I forget all those details :sigh.

IOW, delta-t = 0 requires infinite bandwidth.

That's the Uncertainty Principle in action right there as well. The faster we want to transmit information, the more bandwidth we need.

-Richard

But you got us started on some pretty interesting stuff.

I guess only KenG read my thread on Schubert calculus and how enumerative geometry relates to superstring theory (I haven't actually gotten to that last part yet!).

As an example of the interconnectedness of mathematics, you probably wouldn't guess that the stuff I discuss there about Grassmannians has any relationship with quantum calculus, but it does.

Search John Baez's column This Weeks Finds for a long riff on reflection groups, Coxeter/Dynkin diagrams, semi-simple Lie groups, parabolic subgroups, cohomology of flag manifolds, and more, in which among many other things he used quantum calculus to compute the vector space strucuture of the cohomology ring of a flag manifold (generalization of a Grassmannian). John has discussed many wonderful things, but this was my all time favorite :smile:

(I've been trying to get him to explain the generalization of what I said about the ring structure to general flag manifolds...)

To search his website: try the nifty search bar at upper right on his home page. Years ago, I learned from Dornfest et al. Google Hacks, O'Reilly, 3rd Edition, 2006 how to make a search bar, and passed the trick on to John. My one contribution to mathematical physics :wink:

Fourier transforms: this wonderful topic has been greatly generalized to harmonic analysis, a topic which unifies many ideas from representation theory, operator theory, and theory of PDEs. Applications extend to dynamical systems and analytic number theory. "Harmonics" appear as eigenfunctions of certain linear operators on function spaces (often, partial differential operators such as the Laplace operator), and the general idea is to decompose general functions in our function space into a "sum" of harmonics.

Just a tiny hint of how HUP arises naturally in pure math: it turns out that in operator theory, two natural operators are multiplication by x, written f -> M_x f and differentiation wrt x, f -> D_x f. These two operators do not commute: D_x M_x f = f(x) + M_x D_x f for all functions, so we have

D_x M_x - M_x D_x = I

where I is the identity operator. This is the starting point for learning about the Weyl algebra.

(In symbolic dynamics this is reformulated using shift operators, which suggests, correctly, a connection with tiling dynamical systems such as the space of Penrose tilings.)

Some suggested reading:

For the formulation of the HUP as Just Another Inequality in L^p spaces :wink:
see problem 32, section 6.3, in my favorite real analysis text:
Gerald B. Folland,
Real Analysis,
Wiley, 1984.

See two old and fairly brief posts by myself on two vast, vast topics:

• representation theory
• harmonic analysis

and see references therein.

A Wikipedia article I only skimmed but it seems OK (the anon is from UofC) is Weyl algebra. Did I mention that the cohomology of Grassmannians has something to do with polynomial rings?

An old but superb exposition of harmonic analysis is
Kenneth I. Gross,
On the Evolution of Noncommutative Harmonic Analysis.
American Mathematical Monthly, Vol. 85, No. 7, 525-548. Aug. - Sep., 1978.
Prof. Gross won the Chauvenet Prize for this paper. Those of you with access to a university library should be able to easily find it on your library shelves, or if your uni is wealthy, at JSTOR. An earlier Chauvenet Prize paper, by Guido Weiss, is a fine introduction to complex methods in fourier transforms.

A fascinating expository post by--- no, darnitall, there be cranks here, I don't want them to go spam his blog with woo. I'll try to remember to PM the link.

Victor Kac and Pokman Cheung.
Quantum Calculus.
Springer, 2002.

Richard Kane,
Reflection Groups and Invariant Theory.
CMS, 2001.

See this stillborn thread if you want to discuss the sampling theorem and what information theory says about HUP.

Cover and Thomas,
Elements of Information Theory.
Wiley, 1991.
(The best of dozens of fine textbooks on information theory, IMO, if only because it gives some impression of the vast reach of Shannon's creation.)

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

What about black holes?*

I thought it was because of quantum mechanical reasons that 'light from them is redshifted and dimmed, and if one considers that light is actually made up of discrete photons, the time of escape of the last photon is actually finite, and not very large'.

*Yes, I realise we can't actually "see" them... yet. But, if we could get close enough to see one, wouldn't its fading to black as it forms be a macroscopic effect of the Uncertainty Principle?... Or is the UP unrelated to the discreteness of photons?

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

Holes, shmoles--- can't everyone just shut up about the darn holes? :wink:

[Edit: sorry, Disinfo, for a moment I forgot I alluded to black holes myself in my second exercise up above. We should move that to a new Q&A thread!]

But seriously, if you guys would give me a chance, general relativity is only a tiny portion of the Stuff We Know About, and I'd really rather talk about something else now and again. For example, I may be the only individual other than Penrose who knows something about both Penrose tilings (harmonic analysis and Pontryagin duality on the torus plays a role, whoopee!) and NP formalism in gtr.

I wouldn't say that, but I wouldn't say "the winking out" of infalling matter is due to HUP either. The exponential decrease in amplitude of signals and the increasing redshift are both classical effects, BTW.

I've discussed at great length in posts in forums like this the questions

• what would we literally see if we were hovering near a black hole?
• what would we literally see if we were falling freely and radially into a black hole?

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

I knew there was something at the tip of my brain! This can certainly have macroscopic effects - I shoot a laser across classrooms with and without a slit in front to demonstrate diffraction on quite a macroscopic scale. And every time one looks through a telescope and sees the Airy rings of a diffraction pattern, that's it again.

Does diffraction have anything to do with uncertainty?

quoting myself:
Is it possible to know the position and velocity of a single particle at the annihilation event? For example, if we supercool a pool of (neutrons) and inject (anti-neutrons) of various temperatures into the test chamber, can we find out the position of annihilation and kinetic energy of the (anti-neutron). We would setup the experiment to render the kinetic energy of the (neutrons) as negligible.

Yes, my post explains how.
No, if you think you have a way to sidestep that limitations of the UP, then you have overlooked something. I don't understand your description of your neutron scenario well enough to find it's flaw.

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Logic is the grammar of truth.

Meaning and absolute certainty are incompatible, and profound meaning and absolute certainty are profoundly incompatible.

The only thing intelligence is capable of is recognizing itself.

Granted. I thought you were offering an example of the UP in practice. I withdraw my criticism of your post.

Would the Casimir Effect be an example of a directly visible phenomenon caused by the UP?