The ground floor of the new physics building at Colgate University, which features a version of the Heisenberg uncertainty principle.
Image: George Musser
More In This Article
-
Gravity's Engines
We’ve long understood black holes to be the points at which the universe as we know it comes to an end. Often billions of times more massive than the Sun, they...
Read More »
What Einstein's E=mc2 is to relativity theory, Heisenberg's uncertainty principle is to quantum mechanics—not just a profound insight, but also an iconic formula that even non-physicists recognize. The principle holds that we cannot know the present state of the world in full detail, let alone predict the future with absolute precision. It marks a clear break from the classical deterministic view of the universe.
Yet the uncertainty principle comes in two superficially similar formulations that even many practicing physicists tend to confuse. Werner Heisenberg's own version is that in observing the world, we inevitably disturb it. And that is wrong, as a research team at the Vienna University of Technology has now vividly demonstrated.
Led by Yuji Hasegawa, the team prepared a stream of neutrons and measured two spin components simultaneously for each, in direct violation of Heisenberg's version of the principle. Yet, the alternative variation continued to hold. The team reported its results in Nature Physics on January 15. (Scientific American is part of Nature Publishing Group.)
Heisenberg inferred his formulation in 1927 via his famous thought experiment in which he imagined measuring the position of an electron using a gamma-ray microscope. The formula he derived was ε(q)η(p) ≥ h/4π. This inequality says that when you measure the position of an electron with an error ε(q), you cannot help but alter the momentum of the electron by the amount of η(p). An experimenter cannot know both the position and the momentum precisely; he or she must make a tradeoff. "For that reason everything observed is a selection from a plenitude of possibilities and a limitation on what is possible in the future," Heisenberg wrote.
The same year, Earle Kennard, a less-known physicist, derived a different formulation, which was later generalized by Howard Robertson: σ(q)σ(p) ≥ h/4π. This inequality says that you cannot suppress quantum fluctuations of both position σ(q) and momentum σ(p) lower than a certain limit simultaneously. The fluctuation exists regardless whether it is measured or not, and the inequality does not say anything about what happens when a measurement is performed.
Kennard's formulation is therefore totally different from Heisenberg's. But many physicists, probably including Heisenberg himself, have been under the misapprehension that both formulations describe virtually the same phenomenon. The one that physicists use in everyday research and call Heisenberg's uncertainty principle is in fact Kennard's formulation. It is universally applicable and securely grounded in quantum theory. If it were violated experimentally, the whole of quantum mechanics would break down. Heisenberg's formulation, however, was proposed as conjecture, so quantum mechanics is not shaken by its violation.
In 2003 Masanao Ozawa of Nagoya University developed a new formulation of the error–disturbance uncertainty that Heisenberg aimed to express, but this time on much firmer footing. Derived mathematically from quantum measurement theory, the new formulation describes error and disturbance as well as fluctuations: ε(q)η(p) + σ(q)η(p) + σ(p)ε(q) ≥ h/4π. Hasegawa's team is the first to have demonstrated the violation of Heisenberg's inequality and the validity of Ozawa's inequality. It did so by directly measuring errors and disturbances in the observation of spin components. Even when either the source of error or disturbance is held to nearly zero, the other remains finite.
See what we're tweeting about
45 Comments
Add CommentIf an object's properties exist independently of observation, does that mean Schroedinger's cat is finally dead?
Reply | Report Abuse | Link to thisSeeing the new variations on the uncertainty principle makes me very uncertain that scientist are really going to find the facts they need to solve these illusive particles! May be if they keep up the experiments for many years to come,then the chances are they will scratch the surface, but i think it will fool them with many more false conquest!
Reply | Report Abuse | Link to thisI am certain about this - my head hurts after reading this.
Reply | Report Abuse | Link to thisUndercover observers who define my good as evil made me lonely. They altered my behavior.
Reply | Report Abuse | Link to thisI've read a dozen books and hundreds of papers on quantum mechanics over the years....the only thing I'm certain of is that I get it but that I don't really get it. Actually, I'm not even certain of that.
Reply | Report Abuse | Link to thisthe cat is immortal now
Reply | Report Abuse | Link to thisThat pretty much sums up quantum mechanics. :)
Reply | Report Abuse | Link to thisWell, not exactly. I think it means that his cat is now either alive or dead (as opposed to being both alive AND dead, which is just stupid...).
Reply | Report Abuse | Link to thisHowever, we still don't know which state Pussy's in until we open the box... After all these years, I'm guessing there's gonna be a mess either way :P
"as opposed to being both alive AND dead, which is just stupid"
Reply | Report Abuse | Link to thisWell, clearly schoedinger wasn't all that bright. After all he forgot that the CAT counts as an observer too. if he'd been really smart we'd be talking about Schoedinger's ficus or something like that.
"the cat is immortal now"
Reply | Report Abuse | Link to thisWhy? was King Tut in the box with it?
If I understand correctly, this article states:
Reply | Report Abuse | Link to this- Heisenberg's inequality formulation states that "when you measure the position of an electron with an error, you cannot help but alter the momentum of the electron" - inferring the observer's causal role in producing the measurement result.
- Kennard's formulation actually in use states that "you cannot suppress quantum fluctuations of both position σ(q) and momentum σ(p) lower than a certain limit simultaneously. The fluctuation exists regardless whether it is measured or not, and the inequality does not say anything about what happens when a measurement is performed."
This seems to imply that only Heisenberg's original formulation implies that the act of measurement determines the result while the formulation in use states that measurements do not effect results - that quantum state fluctuations continue independent of measurement.
However, the research report's abstract states:
"The uncertainty principle generally prohibits simultaneous measurements of certain pairs of observables and forms the basis of indeterminacy in quantum mechanics. Heisenberg’s original formulation, illustrated by the famous [gamma]-ray microscope, sets a lower bound for the product of the measurement error and the disturbance. Later, the uncertainty relation was reformulated in terms of standard deviations, where the focus was exclusively on the indeterminacy of predictions, whereas the unavoidable recoil in measuring devices has been ignored. A correct formulation of the error–disturbance uncertainty relation, taking recoil into account, is essential for a deeper understanding of the uncertainty principle, as Heisenberg’s original relation is valid only under specific circumstances. A new error–disturbance relation, derived using the theory of general quantum measurements, has been claimed to be universally valid. Here, we report a neutron-optical experiment that records the error of a spin-component measurement as well as the disturbance caused on another spin-component. The results confirm that both error and disturbance obey the new relation but violate the old one in a wide range of an experimental parameter."
It seems that the new formulation again implies that measurement effects results (disturbances produced by "unavoidable recoil in measuring devices"), even though that error-disturbance relation had been ignored in the Kennard formulation.
Like dbtinc I now have a headache, but what have I misunderstood? An explanation of measuring device "recoil" might be helpful...
Isn't the equation (∆x)(∆p)≥ħ, where ħ= h/2π, not ħ=h/4π? Could someone clear this up for me?
Reply | Report Abuse | Link to thisApparently the delta, pi and h bar symbols didn't format. Oh well. Anyways, my point remains: doesn't the inequality consist of a 2 pi and not a 4 pi in the denominator, as claimed in the article?
Reply | Report Abuse | Link to thisNo, but Berkeley's tree is making a lot of noise.
Reply | Report Abuse | Link to thisI'm uncertain if we can recycle the old jokes.
Reply | Report Abuse | Link to thisKennard was pulled over by a police officer. The officer asks him, "Do you know how fast you were going?" Kennard answers: "No, but I know exactly where I am."
Or, the sign on a dorm room door at Nagoya University, "Ozawa may have slept here."
Kudos to Kennard and Ozawa for reducing the uncertainty in Uncertainty.
suitti: The case went to court but was tossed out because the Police officer was uncertain about what he had observed....AND the case went to court and the driver was found guilty and given 3 days in jail. No way of knowing if the prison cell is empty or if it has the driver in it.
Reply | Report Abuse | Link to thisThe one certain thing about any individual who attempts to pin down, with any degree of certainty, the inherent certainty of the causal effects of the uncertainty principle in either the Quantum world or the Cosmic world, is that they will be able to state with 100% certainty after long and exhaustive study that they are unable to state, with any certainty, that they are, in point of fact, certain that they fully comprehend all the implications surrounding the aforementioned certainty of the uncertainty principle given the uncertainty of the statistical weight that can be attached, with any degree of certainty, to their conclusions and hence they will be forced, to admit that they cannot at this time, for certain, state with unequivocal certainty that they have not wasted a great deal of their time. Much as I did writing this and you did reading it. Of this fact, I am almost 100% certain, maybe.
Reply | Report Abuse | Link to thisThe one thing to keep in mind as you try to grasp the implications of the uncertainty principle is that as far as having any noticeable direct effect on our everyday lives goes it is irrelevant. It is only when we start digging down into our toy box looking for more detail that it rears its ugly head. The only way it will become a problem for us is when we attempt to tamper with its working in its realm. We exist on a distinct evolutionary path that has produced beings that can exist side by side with the implications of the uncertainty of the Quantum level since if we could not we would not be here. In effect we do not depend on certainty with regard to predictability within our environment. We are adapted to function at the level of existence that we function at, even though that level has a degree of uncertainty at its quantum foundation level. We think that the concept of what we call a “predictable Order” must underlie all that we perceive. Unfortunately this is just a belief on our part and there is no reason to belief such has to be the case. We may in fact be the natural born offspring of Chaos who simply believe in the Fantasy of an ordered Universe. The fact that some of the greatest minds in Science, over the past decades, struggled with the concept of uncertainty is that they simply refuse to accept that Stable Chaos may be the at foundation of the structure of our Universe instead of the predictable Order that they thought had to be there. When you accept the possibility that apparent order may arise, at some level of existence, from a Universe founded on apparent, or factual, Chaos then you have no objection to acceptance of the principle of Uncertainty.
Reply | Report Abuse | Link to thisNo, I guess what it means is the cat is not quite dead, but if you disturb him to much, he will die. If you leave him alone, and just watch without disturbing his sleep/not-sleep he just stays as he was...indeterminate.
Reply | Report Abuse | Link to this"Apparently the delta, pi and h bar symbols didn't format."
Reply | Report Abuse | Link to thisYou must have observed them, so they didn't format, or maybe they did format, or they could be dead and alive.
Darn, that cat walked across my keyboard again!
and than what!
Reply | Report Abuse | Link to thisI love you man!
Didn't Feynman say, anyone who thinks he's understood quantum mechanics obviously hasn't? And few people knew more about it than him.
Reply | Report Abuse | Link to thisHe also used to tell his students: don't try to understand it - just get on and calculate.
The calculations align staggeringly close with experimental values, and that is what makes quantum mechanic's the only show in town.
If Heisenberg's Uncertainty Priciple "marks a clear break from the classical deterministic view of the universe", does it consititute evidence for the existence of free will?
Reply | Report Abuse | Link to thisIf "An experimenter cannot know both the position and the momentum precisely", does that mean s/he can know one measurement precisely & the other imprecisely - i.e., the position is exactly X & the momentum is somewhere around Y? What if one experimenter tries to get a precise measurement of position without worying about momentum and simultaneously another precisely measures momentum & leaves position alone?
@ AndThenWhat? #17 - I think Socrates said much the same thing, but in fewer words: "The only true wisdom is in knowing that you know nothing."
@ Whammer2 #19 - But surely the cat knows if it's alive?
@ Postman1 - "Darn, that cat walked across my keyboard again!" are you certain? Maybe your keyboard walked across the cat?
@ phalaris - "The calculations align staggeringly close with experimental values, and that is what makes quantum mechanic's the only show in town."
If no one understands quantum mechanics, doesn't that really make the "calculations" little more than lucky guesses?
Perhaps the reason Feynman took up playing the Bongo Drums was that it allowed him to take out all of his frustrations associated with his attempts to teach his students about theories like the Uncertainty principle all the while knowing that even when class was over none of them would understand it and he knew there was nothing he could do to change that result.
Reply | Report Abuse | Link to thisCanadianOg...I was wonder how pi came into play and now I'm more confused;-) pi is good for 2 and 3d, maybe 4pi has time in it somehow....
Reply | Report Abuse | Link to thisTo quote Feynman: "If you think you understand Quantum Mechanics, you don't."
Reply | Report Abuse | Link to thisPeterT
Could it be as simple as there is no zero point for time, therefore there is no "present" to observe something in?
Reply | Report Abuse | Link to thisThen Einstein believed the uncertainty existed due to the inaccuracy in our measuring devices. He dreamed of the day when we could know if the basic uncertainty was a result of measurement or a property of matter. Have our measuring devices advanced that much past 1927?
Reply | Report Abuse | Link to this"Heisenberg's Uncertainty Principle Is Not Dead" Huh?
Reply | Report Abuse | Link to thisAre you sure about that? Really?
Let's build a GRANT PROPOSAL to study it. And report.
So many great comments here. Why do I bother?
Reply | Report Abuse | Link to thisIf I'm the last comment, does anyone ever read it?
An unseen, impossible -to-understand force that directs the universe? Sounds more like religion than sicence to me. So I guess QM is God to Feynman?
Reply | Report Abuse | Link to thisYou sound so uncertain.
Reply | Report Abuse | Link to thisAs Richard Feynman (one of my heroes) said: "If you think you understand Quantum Mechanics, you DON'T."
Reply | Report Abuse | Link to thisPeterT
One problem resides in the way we understand QM.
Reply | Report Abuse | Link to thisThe way I see it is as follows:
QM does not describe material systems as we are used to in Classical Mechanics. QM has to do with quantum states sustained by a materiality yet it does not represent it.
(see e.g. Advances in Quantum Chemistry vol.61(2011)49-106)
It has to do with possibilities a system may have. The wave function is the representation of an abstract quantum state.
I can understand your frustration: there is no one textbook hinting at this way to understand QM. Heisenberg in a way did it as well as the paper from Maurice hints at.
I apologize for these extra "boring" statements
Yes!
Reply | Report Abuse | Link to thisBut try to be constructive.
Dear PeterT
Reply | Report Abuse | Link to thisThe quotation of yours: "To quote Feynman: "If you think you understand Quantum Mechanics, you don't.""
I do not get the point.
Do we have or have had a Pope? A new Vatican?
It you do not agree on what one means with "understand" quotations of this kind are not useful.
If the cat is already (in fat) dead, it can not be its own observer.
Reply | Report Abuse | Link to thisBut the ONLY way there can be no observer is if the cat is dead.
Reply | Report Abuse | Link to thisNow my heisenberg compensator is useless!
Reply | Report Abuse | Link to thisI read your comment!
Reply | Report Abuse | Link to thisVery good point!
Reply | Report Abuse | Link to thisAnd no one can blame you for that!
Reply | Report Abuse | Link to thisHumm, interesting timing this would come up now.
Reply | Report Abuse | Link to thisTry this out:
high to low entropy, E=h+{a}c/wavelength
low to high entropy, E=h+{a-lesser diesis}c/wavelength.
The lesser diesis is named Einstein's [harmonic] comma, but here it's Maxwell's Demon and it cannot be in two places at the same time so it's measured size relative (compared in ratio) to time cannot be the exact same size twice.
The size of {a}, the weak force asymmetry value, is a constant and the distance (therefore in the forward arrow of time) light travels in 2.48e-5 seconds. This is a reduced ratio of the distance light travels in one hour added to the distance light travels in one thousand years. Far too big of a number ratio to be a coincidence even if were a match at 10,000 miles! But it's not, its a bulls eye and within .02e-5 sec IMO supporting the UFT equation that revealed it.
The comma produced is a product of asymmetry and the distance light travels in .10e-5 seconds x 2 (.20e-5 sec) at the speed of light in an information concept frame of 453.6 miles.
Here's how I obtained the value of the comma:
Stanford's SLAC E158 weak force asymmetry gain in TOTAL time in the distance light travels in 453.6 miles is 5.17e-5 seconds and CERN's neutrinos also gained 5.17e-5 seconds in TOTAL time in 453.6 miles. Because of their oscillation and asymmetry (if you add asymmetry to time you must add it to space too) the total time is not applied to the forwards arrow of time so they gained the forward distance light travels at the speed of light in 2.48e-5 seconds leaving .10e-5 sec needed to apply to rearward oscillation time/space needed for asymmetry @ 2.68e-5.
In other words:
CERN's neutrinos traveling in the forward arrow of time at v-c/c=2.48e-5 sec in 453.6 miles = SLAC's E158 weak force asymmetry data @ 2.48e-5 in the forward arrow of time creating a remaining .20e-5 harmonic comma needed to apply to the graviton's reverse phase in time. This actually supports the asymmetry in space that Cohen and Glashow showed in VSR although it supports Real Relativity not VSR. The best way to inhibit Cohen-Glashow radiation and protect Special Relativity is to simply accept the fact that the neutrinos did not exceed the speed of light (in transferring the photon's energy) creating the asymmetry of the weak force SLAC's E158 team discovered.
But it still changes physics starting by showing an ether is not needed if space is relative to time by establishing a time based true inertial frame of reference. See my other posts on Mass and CERN's discovery.
John^^
It may come as a surprise 3 to past and present adherents of Heisenberg's Uncertainty Principle (HUP) but recent mathematical progress means we can also look at uncertainty from a theoretical point of view. Quantum theory, depending on HUP, is incomplete as Einstein thought. See book Self-field theory, a new mathematical description of physics, by A.H.J. Fleming, published by Pan-Stanford Press 2012; analytic solutions for the motions of the electron and the proton inside the hydrogen atom have been found obviating the need of the numerical and probabilistic quantum theory. The basis of this new formulation includes the magnetic currents of particles and not just the electric fields as in quantum theory. In this formulation, the photon is composite and hydrogenic-like.
Reply | Report Abuse | Link to thisIt is well known the inequality relationship of HUP applies to any quantum system in general. The equations for the orbital and cyclotron motions of each electron in self-field theory (SFT) are given as two equality equations. Apart from the 'greater than' relationship compared with the exact relationship, the 3 equations are identical. Whereas there is one inexact relationship in HUP there are two equality relationships in SFT. SFT thus completes the Bohr Theory that did not include any magnetic effect on the electron.
In the light of this mathematics HUP can be seen as a theoretical error; in practice it appears as a numerical error in any computer calculations.
Let me add that HUP will always be a good engineering approximation able to be used across domains from photon to universe in the same way that Newton's law of gravitation is still used today by those involved in gravitational research.
Let me further add that the magnetic moments involved in this new mathematics (SFT) at the terrestrial domain may be able to give us much more quantitative information about the way techtonic plates, earthquakes and tsunamis develop over time.
But there are other benefits like 'clean' chemistry waiting to be investigated.
The article states in its conclusion:
Reply | Report Abuse | Link to this"The error–disturbance uncertainty relation is much more important than that of fluctuations," says Akio Hosoya, a theoretical physicist at Tokyo Institute of Technology, "because in physics the final say comes from experimental verification."
Nonsense! The error-disturbance uncertainty relation is important only to the extent that it reveals information about the fluctuations! The fluctuations represent the fundamental physical characteristics of the quantum system - our perception of it does nothing to determine those fundamental characteristics in our absence!