Why uncertainty principle

Heisenberg's Uncertainty Principle states that there is inherent uncertainty in the act of measuring a variable of a particle. Commonly applied to the position and momentum of a particle, the principle states that the more precisely the position is known the more uncertain the momentum is and vice versa. This is contrary to classical Newtonian physics which holds all variables of particles to be measurable to an arbitrary uncertainty given good enough equipment.

The Heisenberg Uncertainty Principle is a fundamental theory in quantum mechanics that defines why a scientist cannot measure multiple quantum variables simultaneously. Until the dawn of quantum mechanics, it was held as a fact that all variables of an object could be known to exact precision simultaneously for a given moment. Newtonian physics placed no limits on how better procedures and techniques could reduce measurement uncertainty so that it was conceivable that with proper care and accuracy all information could be defined.

Heisenberg made the bold proposition that there is a lower limit to this precision making our knowledge of a particle inherently uncertain. More specifically, if one knows the precise momentum of the particle, it is impossible to know the precise position, and vice versa. This relationship also applies to energy and time, in that one cannot measure the precise energy of a system in a finite amount of time. More clearly:.

Aside from the mathematical definitions, one can make sense of this by imagining that the more carefully one tries to measure position, the more disruption there is to the system, resulting in changes in momentum.

For example compare the effect that measuring the position has on the momentum of an electron versus a tennis ball. These photon particles have a measurable mass and velocity, and come into contact with the electron and tennis ball in order to achieve a value in their position.

When the photon contacts the electron, a portion of its momentum is transferred and the electron will now move relative to this value depending on the ratio of their mass. The larger tennis ball when measured will have a transfer of momentum from the photons as well, but the effect will be lessened because its mass is several orders of magnitude larger than the photon.

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.

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 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. However, we have also seen that they reached such conclusions by starting from radical and controversial assumptions.

This entails, of course, that their radical conclusions remain unconvincing for those who reject these assumptions. Indeed, the operationalist-positivist viewpoint adopted by these authors has long since lost its appeal among philosophers of physics. So the question may be asked what alternative views of the uncertainty relations are still viable. Of course, this problem is intimately connected with that of the interpretation of the wave function, and hence of quantum mechanics as a whole.

Since there is no consensus about the latter, one cannot expect consensus about the interpretation of the uncertainty relations either. In quantum mechanics a system is supposed to be described by its wave function, also called its quantum state or state vector. The operational meaning of these probability distributions is that they correspond to the distribution of the values obtained for these quantities in a long series of repetitions of the measurement.

More precisely, one imagines a great number of copies of the system under consideration, all prepared in the same way. On each copy the momentum, say, is measured. Generally, the outcomes of these measurements differ and a distribution of outcomes is obtained.

The theoretical momentum distribution derived from the quantum state is supposed to coincide with the hypothetical distribution of outcomes obtained in an infinite series of repetitions of the momentum measurement.

The same holds, mutatis mutandis , for all the other physical quantities pertaining to the system. Note that no simultaneous measurements of two or more quantities are required in defining the operational meaning of the probability distributions. The uncertainty relations discussed above can be considered as statements about the spreads of the probability distributions of the several physical quantities arising from the same state.

Inequality 9 is an example of such a relation in which the standard deviation is employed as a measure of spread. From this characterization of uncertainty relations follows that a more detailed interpretation of the quantum state than the one given in the previous paragraph is not required to study uncertainty relations as such.

In particular, a further ontological or linguistic interpretation of the notion of uncertainty, as limits on the applicability of our concepts given by Heisenberg or Bohr, need not be supposed. Of course, this minimal interpretation leaves the question open whether it makes sense to attribute precise values of position and momentum to an individual system.

Some interpretations of quantum mechanics, e. The only requirement is that, as an empirical fact, it is not possible to prepare pure ensembles in which all systems have the same values for these quantities, or ensembles in which the spreads are smaller than allowed by quantum theory. Although interpretations of quantum mechanics, in which each system has a definite value for its position and momentum are still viable, this is not to say that they are without strange features of their own; they do not imply a return to classical physics.

We end with a few remarks on this minimal interpretation. First, it may be noted that the minimal interpretation of the uncertainty relations is little more than filling in the empirical meaning of inequality 9.

As such, this view shares many of the limitations we have noted above about this inequality. Indeed, it is not straightforward to relate the spread in a statistical distribution of measurement results with the inaccuracy of this measurement, such as, e. Moreover, the minimal interpretation does not address the question whether one can make simultaneous accurate measurements of position and momentum. As a matter of fact, one can show that the standard formalism of quantum mechanics does not allow such simultaneous measurements.

But this is not a consequence of relation 9. Rather, it follows from the fact that this formalism simply does not contain any observable that would accomplish such a task. If one feels that statements about inaccuracy of measurement, or the possibility of simultaneous measurements, belong to any satisfactory formulation of the uncertainty principle, one will need to look for other formulations of the uncertainty principle.

Some candidates for such formulations will be discussed in Section 6. First, however, we will look at formulations of the uncertainty principle that stay firmly within the minimal interpretation, and differ from 9 only by using measures of uncertainty other than the standard deviation. While the standard deviation is the most well-known quantitative measure for uncertainty or the spread in the probability distribution, it is not the only one, and indeed it has distinctive drawbacks that other such measures may lack.

This means, in our view, that relation 9 actually fails to express what most physicists would take to be the very core idea of the uncertainty principle. One way to deal with this objection is to consider alternative measures to quantify the spread or uncertainty associated with a probability density. Here we discuss two such proposals. Landau and Pollak obtained an uncertainty relation in terms of these bulk widths.

Note that bulk widths are not so sensitive to the behavior of the tails of the distributions and, therefore, the Landau-Pollak inequality is immune to the objection above. Thus, this inequality expresses constraints on quantum mechanical states not contained in relation 9.

This, obviously, is not the best lower bound for the product of standard deviations, but the important point is here that the Landau-Pollak inequality 16 in terms of bulk widths implies the existence of a lower bound on the product of standard deviations, while conversely, the Heisenberg-Kennard equality 9 does not imply any bound on the product of bulk widths.

A generalization of this approach to non-commuting observables in a finite-dimensional Hilbert space is discussed in Uffink Another approach to express the uncertainty principle is to use entropic measures of uncertainty.

A nice feature of this entropic uncertainty relation is that it provides a strict improvement of the Heisenberg-Kennard relation. A drawback of this relation is that it does not completely evade the objection mentioned above, i. Then we obtain the uncertainty relation Maassen and Uffink :. Both the standard deviation and the alternative measures of uncertainty considered in the previous subsection and many more that we have not mentioned!

Applied to quantum mechanics, where the probability distributions for position and momentum are obtained from a given quantum state vector, one can use them to formulate uncertainty relations that characterize the spread in those distribution for any given state. The resulting inequalities then express limitations on what state-preparations quantum mechanics allows. They are thus expressions of what may be called a preparation uncertainty principle :.

The relations 9 , 16 , 19 all belong to this category; the mere difference being that they employ different measures of spread: viz. Note that in this formulation, there is no reference to simultaneous or joint measurements, nor to any notion of accuracy like the resolving power of the measurement instrument, nor to the issue of how much the system in the state that is being measured is disturbed by this measurement. This section is devoted to attempts that go beyond the mold of this preparation uncertain principle.

We have seen that in Heisenberg argued that the measurement of say position must necessarily disturb the conjugate variable i. That is, we will look at attempts that would establish a claim which may be called a measurement uncertainty principle.

In quantum mechanics, there is no measurement procedure by which one can accurately measure the position of a system without disturbing it momentum, in the sense that some measure of inaccuracy in position and some measure of the disturbance of momentum of the system by the measurement cannot both be arbitrarily small. This formulation of the uncertainty principle has always remained controversial. Hence this inaccurate observable may be represented as.

Ozawa obtained an inequality involving those two measures, which, however, is more involved than previous uncertainty relations. That is, even without probing the system by a measurement apparatus, one can show that such a lower bound does not exist. An entirely different analysis of the problem of substantiating a measurement uncertainty relation was offered by Busch, Lahti, and Werner Note that these do not refer to a self-adjoint operator!

The distance they chose is the Wasserstein-2 distance, a. Applying this definition to the case at hand, i. First of all, by focusing on the distance 33 this approach is comparing entire probability distributions rather than just the expectations of operator differences.

When this distance is very small, one is justified to conclude that the distribution has changed very little under the measurement procedure. This brings us closer to the conclusion that the error or disturbance introduced is small. But we also think there is an undesirable feature of the BLW approach. This feature, we argue, deprives their result from practical applicability. But the BLW only gives us:.

Summing up, we emphasize that there is no contradiction between the BLW analysis and the Ozawa analysis: where Ozawa claims that the product of two quantities might for some states be less than the usual limit, BLW show that product of different quantities will satisfy this limit.

On the other hand, we also think that the BLW uncertainty relation is not satisfactory. Also, we would like to remark that both protagonists employ measures that are akin to standard deviations in being very sensitive to the tail behavior of probability distributions, and thus face a similar objection as raised in section 5.

The final word in this dispute on whether a measurement uncertainty principle holds has not been reached, in our view. Introduction 2. Heisenberg 2. Bohr 3. The Minimal Interpretation 5.

Alternative measures of uncertainty 5. Uncertainty relations for inaccuracy and disturbance 6. Introduction The uncertainty principle is certainly one of the most famous aspects of quantum mechanics. Bibliography Bacciagaluppi, G. Beller, M. Beckner, W.

Bohr, N. Also in Bohr , Wheeler and Zurek , and Bohr Reissued in Also in Bohr — The library of living philosophers Vol. VII , P. Schilpp ed. Kalckar ed.

Amsterdam: North-Holland. Bub, J. Busch, P. Lahti, and R. Chiribella, G. Condon, E. Eddington, A. Einstein, A. Folse, H. Frank, R. Heisenberg, W. Jacob Aron. People in Science. Articles Videos.