Having quickly read the article: it says that the Casimir effect, which has been confirmed experimentally, can be derived theoretically without any reference to zero-point energy. Further, that a more careful computation of the Casimir effect shows that it does, in fact, depend on the fine-structure constant and goes to zero if the fine structure constant does. The Casimir effect thus depends on electromagnetic interactions and is not merely an effect of (free) zero-point energy.

Dear Raman,

I have read the article entitled " What is Heisenberg's Uncertainty Principle" published in the Guardian and found it to be interesting and worth being distributed.

Today I have reread it and found between the article's lines the answer to your question.

Here is the full article:

he uncertainty principle is one of the most famous (and probably misunderstood) ideas in physics. It tells us that there is a fuzziness in nature, a fundamental limit to what we can know about the behaviour of quantum particles and, therefore, the smallest scales of nature. Of these scales, the most we can hope for is to calculate probabilities for where things are and how they will behave. Unlike Isaac Newton's clockwork universe, where everything follows clear-cut laws on how to move and prediction is easy if you know the starting conditions, the uncertainty principle enshrines a level of fuzziness into quantum theory.

Werner Heisenberg's simple idea tells us why atoms don't implode, how the sun manages to shine and, strangely, that the vacuum of space is not actually empty.

An early incarnation of the uncertainty principle appeared in a 1927 paper by Heisenberg, a German physicist who was working at Niels Bohr's institute in Copenhagen at the time, titled "On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics". The more familiar form of the equation came a few years later when he had further refined his thoughts in subsequent lectures and papers.

Heisenberg was working through the implications of quantum theory, a strange new way of explaining how atoms behaved that had been developed by physicists, including Niels Bohr, Paul Dirac and Erwin Schrödinger, over the previous decade. Among its many counter-intuitive ideas, quantum theory proposed that energy was not continuous but instead came in discrete packets (quanta) and that light could be described as both a wave and a stream of these

quanta. In fleshing out this radical worldview, Heisenberg discovered a problem in the way that the basic physical properties of a particle in a quantum system could be measured. In one of his regular letters to a colleague, Wolfgang Pauli, he presented the inklings of an idea that has since became a fundamental part of the quantum description of the world.

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The uncertainty principle says that we cannot measure the position (x) and the momentum (p) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. Multiplying together the errors in the measurements of these values (the errors are represented by the triangle symbol in front of each property, the Greek letter "delta") has to give a number greater than or equal to half of a constant called "h-bar". This is equal to Planck's constant (usually written as h) divided by 2π. Planck's constant is an important number in quantum theory, a way to measure the granularity of the world at its smallest scales and it has the value 6.626 x 10-34 joule seconds.

One way to think about the uncertainty principle is as an extension of how we see and measure things in the everyday world. You can read these words because particles of light, photons, have bounced off the screen or paper and reached your eyes. Each photon on that path carries with it some information about the surface it has bounced from, at the speed of light. Seeing a subatomic particle, such as an electron, is not so simple. You might similarly bounce a photon off it and then hope to detect that photon with an instrument. But chances are that the photon will impart some momentum to the electron as it hits it and change the path of the particle you are trying to measure. Or else, given that quantum particles often move so fast, the electron may no longer be in the place it was when the photon originally bounced off it. Either way, your observation of either position or momentum will be inaccurate and, more important, the act of observation affects the particle being observed.

The uncertainty principle is at the heart of many things that we observe but cannot explain using classical (non-quantum) physics. Take atoms, for example, where negatively-charged electrons orbit a positively-charged nucleus. By classical logic, we might expect the two opposite charges to attract each other, leading everything to collapse into a ball of particles. The uncertainty principle explains why this doesn't happen: if an electron got too close to the nucleus, then its position in space would be precisely known and, therefore, the error in measuring its position would be minuscule. This means that the error in measuring its momentum (and, by inference, its velocity) would be enormous. In that case, the electron could be moving fast enough to fly out of the atom altogether.

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Heisenberg's idea can also explain a type of nuclear radiation called alpha decay. Alpha particles are two protons and two neutrons emitted by some heavy nuclei, such as uranium-238. Usually these are bound inside the heavy nucleus and would need lots of energy to break the bonds keeping them in place. But, because an alpha particle inside a nucleus has a very well-defined velocity, its position is not so well-defined. That means there is a small, but non-zero, chance that the particle could, at some point, find itself outside the nucleus, even though it technically does not have enough energy to escape. When this happens – a process metaphorically known as "quantum tunneling" because the escaping particle has to somehow dig its way through an energy barrier that it cannot leap over – the alpha particle escapes and we see radioactivity.

A similar quantum tunnelling process happens, in reverse, at the centre of our sun, where protons fuse together and release the energy that allows our star to shine. The temperatures at the core of the sun are not high enough for the protons to have enough energy to overcome their mutual electric repulsion. But, thanks to the uncertainty principle, they can tunnel their way through the energy barrier.

Perhaps the strangest result of the uncertainty principle is what it says about vacuums. Vacuums are often defined as the absence of everything. But not so in quantum theory. There is an inherent uncertainty in the amount of energy involved in quantum processes and in the time it takes for those processes to happen. Instead of position and momentum, Heisenberg's equation can also be expressed in terms of energy and time. Again, the more constrained one variable is, the less constrained the other is. It is therefore possible that, for very, very short periods of time, a quantum system's energy can be highly uncertain, so much that particles can appear out of the vacuum. These "virtual particles" appear in pairs – an electron and its antimatter pair, the positron, say – for a short while and then annihilate each other. This is well within the laws of quantum physics, as long as the particles only exist fleetingly and disappear when their time is up. Uncertainty, then, is nothing to worry about in quantum physics and, in fact, we wouldn't be here if this principle didn't exist.

http://www.theguardian.com/science/2013/nov/10/what-is-heisenbergs-uncertainty-principle

Hoping you enjoy it,

Rafik

I found the article a bit vague in the description of how and what is measured. In its precise mathematical formulation, it is not about the simultaneous measurement of position and momentum (which is impossible), or about the measurement of its position followed as fast as possible by a momentum measurement (or the other way around).

Instead, consider (f.i) a large crop of hydrogen atoms in the ground states, and two experimental setups, one to measure the electron position and one to measure the momentum. Quantum mechanics can be used to compute a mathematical description ("wave function") of an electron in the hydrogen ground state. From this complete description one can compute two probability distributions, one to describe the scatter in the results of position measurements, and one to describe the scatter in momentum measurements. Then the standard deviations of the two probability distributions must obey the Heisenberg uncertainty relation. Mathematically this is just a property relating the behavior of functions and their Fourier transforms, as Christian says.

The same goes for all possible quantum states, including time dependent ones. Although it in some cases may be difficult to imagine how a large set of identical systems can be prepared.

Note that the uncertainty principle can look different in other spaces than infinite euclidean ones. Consider a closed (periodic boundary condition) 1D space of circumference L. Clearly the particle can never be more than a distance L/2 away. At the same time all possible momenta are quantized to discrete values. In particular, a particle in the ground state has exactly zero momentum. What becomes of the uncertainty relation in this case?

Raman, what Christian said pretty much sums it up. Whilst Heisenberg's principle is the most famous,  there is another similar,  interesting limit,  called the Gabor-Heisenberg limit, very useful in signal processing (like,  for instance, a FTIR or FTMW spectrometer,  among others). Stated alternatively, "One cannot simultaneously sharply localize a signal (function f ) in both the time domain and frequency domain ( ƒ̂, its Fourier transform)".

Ales,  I've just read the abstract. It doesn't state nothing of what you said. 

Wrong again. What it states is that the Casimir effect doesn't account for the zero-point energy. So,  the quest is still on. 

'Does not seem to be' is quite different from what you said. We have strong indication that indeed it might not be, but there is still margin for doubt. 

It like UFO's. If you ask me they exist,  I will tell you that most likely they don't. And you might accuse me of being unscientific by not having certain. I'll tell you that it is most likely that UFO's are the product of human irrationality than a manifestation of alien rationality. What I can answer is based on the information I possess at a given time,  so I can't give you assurances, or else I would be lying. The same applies to this subject. 

Having quickly read the article: it says that the Casimir effect, which has been confirmed experimentally, can be derived theoretically without any reference to zero-point energy. Further, that a more careful computation of the Casimir effect shows that it does, in fact, depend on the fine-structure constant and goes to zero if the fine structure constant does. The Casimir effect thus depends on electromagnetic interactions and is not merely an effect of (free) zero-point energy.

There are several reasons to believe in vacuum fluctuations.

The quantization of harmonic oscillations invariably leads to zero-point fluctuations and a zero-point energy. The energy of the latter f.i. contribute to the total energy of crystal lattices. The electromagnetic field is just a special case of a collection of harmonic oscillators; a consistent physical theory dictates that they must be treated in the same way as other systems of the same type. We simply cannot invent a new kind of theory of each phenomena.

The vacuum fluctuations become manifest when we break Lorentz invariance, like by inserting a hydrogen atom into the vacuum. This can f.i. be used to explain (a major part of) Lamb shift in the hydrogen atom.

Calculations also show that vacuum fluctuations will become visible when viewed from a coordinate system under linear accelerations. With a constant linear accelerations it will look hot, i.e. with a black-body thermal spectrum. This kind of effect is actually seen in particle accelerators with polarized beams. Due to the apparent thermal background in becomes impossible to polarize the beam completely. There are some beautiful papers by John Bell and Jon Magne Leinaas from the early 1980's about that. The comparison with accelerator behavior is not perfect, because there are additional contributions to depolarization in an accelerator, and because the acceleration is circular instead of linear. The main point though, is that vacuum fluctuations can become manifest when observed from a non-inertial frame. 

Vacuum fluctuations also change the equations for classical electrodynamics; this can be encoded in a Euler-Heisenberg contribution to the Lagrangian for electromagnetism, leading to non-linear classical equations of motion in vacuum. Like everything of these kind, the effects are small.

It is true that the Casimir effect (extra attractive force between two metallic planes) would disappear in a world where the fine structure constant alpha was zero. But so would the metal plates, and the experimenters with their equipment. It is better to say that the vacuum fluctuations of neutrinos do not contribute to the Casimir effect, due to its negligible interaction with metal plates. With alpha being what it is,  it is consistent to attribute the effect to a change of vacuum energy caused by reduced vacuum fluctuations. The alpha-dependent details lie in the how much the high-frequency fluctuations a reduced in real metals; hence idealized calculations cannot be expected to be exact. With real materials one must account for changed interactions in the materials in addition.

If the universe had a cylinder topology in one directions, the Casimir effect would lead to a change in the vacuum energy, of size depending on the circumference of the cylinder. The is not very easy to check experimentally, since there seems to be rather few universes with cylinder topology around (or perhaps not?). But the mathematically predicted effect has nevertheless been verified extremely well, because it is mathematically the same mechanism which gives rise to the thermal Planck spectrum. Which was the first reason to invent quantum mechanics.

Why the total vacuum energy (and associated pressure) does not seem to manifest itself through gravitational effects remains a puzzle. In supersymmetric theories the vacuum energy would be exactly zero. But by looking around we discover that supersymmetry seems to be badly broken. One suspects that there could be some kind of stabilization mechanisms which drives the total vacuum energy to nearly zero, but it is not easy to invent such a mechanism.

It is to some extent a manner of how you interpret the calculations (if at all), and account for the energy budget. Jaffe et al. usually just integrate out the electromagnetic fields, and analyze how the result of that depends on geometry.

That becomes like calculating forces and energies in a system of charges, not looking in detail on where the energy is stored, only the total budget. However, you may take the viewpoint that a large part of the energy is stored in electric fields around the charges, and hence obtain a different budget. For engineering purposes the difference does not matter (the first one is simpler), but GR provide a unique way to locate energy-momentum (i.e, the energy-momentum tensor) --- the one which provides the right source for gravity.

When you calculate the energy momentum tensor of a Casimir effect system, you invariably find the energy change to be located to the otherwise empty region between the plates, caused by a change in vacuum fluctuations. The effects of the metallic media are to modify these fluctuations from their empty-space behavior. But they are still vacuum fluctuations. If you can derive a result without reference to certain interpretations, it does not mean that these interpretations are wrong.

I agree with you completely, but vacuum fluctuations agree with so many other effects and mechanisms already in place in physics, that one cannot just declare them away. It is somewhat different with the energy associated with these fluctuations. For the moment sensible people observe that the enormous energy for certain is not there, put the problem on the back burner, and continue with their life explaining observed phenomena. But sometimes at night, you wake up with a nagging feeling that the problem ought to be described. And make another try until you fall a sleep again. When you find the solution during your dreams, it is all forgotten the next morning...

There was a similar problem in early formulations of the Dirac theory, with the Dirac sea having an infinite charge density. Unobserved. In that case the whole problem can be defined away, by choosing the right (charge-conjugation-symmetric) operator ordering of your charge density operator. No similar method has been found for the vacuum energy.

According to the statistical interpretation of quantum theory, the uncertainty,

expressed by the inequality DP DQ>=1/2, does not refer to simultaneous

measurements of P and Q, but, rather, to separate measurements of P and Q,

performed on separate samples of the physical system in the same state,

where DP and DQ are the standard deviations of these separate separated

measurements.

Giuseppe> ... to separate measurements of P and Q, performed on separate samples of the physical system in the same state

Exactly what I wrote also. No harm repeating it.

Hello,

I suggest that answering this question is straightforward, and is not at all about measurement error, instrument quality, the Casimir effect, vacuum fluctuations, or GR.

The quote says, "[the uncertainty principle] arises from the wave properties inherent in the quantum mechanical description of nature".

How does it arise? Mathematically.

This refers to the intuitive sampling properties of a wave (sine or cosine)  function, which wave is taken as the quantum mechanical description (model) of nature.

If a wave has a finite duration DeltaT, what sort of output response can be expected from a system with bandwidth DeltaF?

Shannon's sampling theorem provides a minimum for the product of DeltaT and DeltaF, for high fidelity. The output response is a good reproduction of the  wave if  DeltaT  is such that 1/DeltaT = 1/c) and  is directly related to the product of two conjugate variables (e.g., frequency and time, position and momentum) in wave mechanics.

Therefore,  as in the quote, there is a minimum (here, expressed as 1/c)  to the product of two conjugate variables -- such as frequency and time, or position and momentum -- due to the wave properties inherent in the quantum mechanical description of nature. This is not a statement about the inaccuracy of measurement instruments, nor a reflection on the quality of experimental methods. This is a mathematical statement.

Cheers,

Ed Gerck