Another of the remarkable features of the microscopic world prescribed by quantum theory is the idea of nonlocality, what Albert Einstein rather dismissively called “spooky actions at a distance”. The answer, at least in part, is that Heisenberg himself tried to explain the uncertainty principle by claiming that it was simply an observational effect—a consequence of the fact that measurements of quantum systems cannot be made without affecting those systems. Nevertheless, being based on an approximation of the more natural ontology, the auxiliary assumptions of this construction still cry out for a more complete understanding. Why would any thinking physicist uphold the claim that state vector reduction occurs, when there is no plausible story for how or why it occurs, and when the assertion that it does occur creates other monstrous problems that contradict central tenets of physics? Einstein was emotionally as well as intellectually determined to prove the uncertainty principle false. Its most outspoken opponent was Einstein. With the fluid, they naturally follow. When the winding frequency is also 5 cycles/second the graph is maximally off center. The theory takes the vacuum to be a physical fluid with low viscosity (a superfluid), and captures the attributes of quantum mechanics (and general relativity) from the flow parameters of that fluid. Uncertainty is an aspect of quantum mechanics because of the wave nature it ascribes to all quantum objects. In other words, solitons are complex and non-dispersive, or what a mathematician would call “non-linear”. The probability of detection depends on the surface area of the D1 compared to the area of the hole. Convinced that this idea was “the most natural proposal of all”, de Broglie outlined its general structure, and then began working on a second proposal—a mathematically simplified approximation of that idea, which treated particles as simple point-like entities surrounded by pilot waves. More specifically, when a signal reflects off something moving towards us, the peaks and valleys of that signal get squished together, sending us an echo with a shorter wavelength (higher frequency). In other words, the change of particle’s position with respect to time is equal to the local stream velocity , where , and the “velocity potential” is related to the phase of by . In other words, the probability of detection by D2 has been greatly enhanced by a sort of “non-event” at D1. In fact, when we assume that particles (photons, electrons, etc.) To understand the generality of this reciprocity, let’s follow Grant Sanderson’s insightful YouTube channel, 3blue1brown, by exploring how this uncertainty trade off shows up in the classical realm—with a couple examples from our every day observations of frequencies and waves, which should feel completely reasonable. From here, obtaining a full hydrodynamic account of quantum mechanics is simply a matter of expressing the evolution of the system in terms of its fluid properties: the fluid density , the velocity potential , and stream velocity . Why then is state vector reduction still taken seriously? Then let’s talk about how it shows up with Doppler radar, which should also feel reasonable. And the fact that it applies to quantum mechanics… well, that actually tells us a lot about the microscopic arena. Einstein Online is a web portal with comprehensible information on Einstein's theories of relativity and their most exciting applications from the smallest particles to cosmology. A particle’s position and momentum inherently relate to each other via the Fourier trade off. Figure 9 – An interaction-free measurement. Imagine many weights hanging from springs, all oscillating up and down in sync, with the mass concentrated towards some point (Figure 7). Pilot wave theory fully (and deterministically) captures quantum mechanics, and it does so with elegance and ease. The answer is that generations of tradition have largely erased the fact that there is another way to solve the quantum measurement problem (see Why don’t more physicists subscribe to pilot-wave theory?). More specifically, the distance between the center of mass and the origin for each winding frequency captures the strength of each frequency within the original signal, and the angle with which that center of mass is off the horizontal corresponds to the phase of the given frequency. So you might be surprised to learn that this popular narrative is… well, wrong. Condition 2: The probability distribution of an ensemble of particles described by the wave function , is . With that relationship in mind, let’s bring in the concept of a Fourier transform, which is the relevant construct for analyzing frequencies because it allows us to deconstruct composite signals into their individual input frequencies. Because the vacuum is a collection of many quanta, its large-scale structure—represented by the extended spatial dimensions —only comes into focus as significant collections of quanta are considered. When Hermann Helmholtz demonstrated that “vortices exert forces on one another, and those forces take a form reminiscent of the magnetic forces between wires carrying electric currents,” Thomson’s passion for this proposal caught fire. Determined to further develop pilot wave theory, he added internal structure to Einstein’s notion of particles, and suggested that particles are intersecting waves, like fluid vortices, made up of many interacting atoms/molecules of a sub-quantum medium. In short, pilot-wave theories offer a more detailed picture of reality—conceptually exposing internal structure to the vacuum that gives rise to the emergent properties of quantum mechanics and general relativity. You see, the uncertainty principle is just a specific example of a much more general trade off that shows up in a lot of every day totally non-quantum circumstances involving waves. To fully digest this, think about how this spread changes as the signal persists longer, or shorter, in time. We’ve already seen this at an intuitive level, with the turning signal example, now we are just illustrating it in the language of Fourier transforms. In 1925 Louis de Broglie discovered that wave-particle duality also applies to particles with mass, and became acutely interested in the pilot-wave ontology. And, of course, when the signal reflects off a stationary object, its frequency remains the same. Interpreting these vortices to critically depend on the aether (instead of allowing for some other medium to be the substrate that supports them) scientists dropped the idea altogether—unwittingly throwing the baby out with the bathwater. The amount of time it takes for each echo to return let’s us deduce how far away the respective objects are. In the first stage, Einstein refused to accept quantum indeterminism and sought to demonstrate that the principle of indeterminacy could be violated, suggesting ingenious thought experiments which should permit the accurate determination of incompatible variables, such as position and velocity, or to explicitly reveal simultaneously the wave and the particle aspects of the same process. In 1924, Louis de Broglie (the physics Nobel Laureate who elegantly dreamed up what is now known as the de Broglie-Bohm theory—a deterministic interpretation of quantum mechanics that makes all the right predictions while avoiding the ontological monstrosities that plague other versions) proposed that all matter has wavelike properties, and that the momentum (p=hξ) of any moving particle, which we classically think of as mass times velocity, is actually proportional to the internal spatial frequency (ξ) of that wave, or how many times that wave cycles per unit distance. The first detector D1 is set up to capture the particle emitted in almost all directions, except a small hole, and the second detector D2 is set up to capture the particle if it goes through that hole. The positions and velocities of these quanta define a vector space (think Hilbert space, or state space, but apply these mathematical notions to a physically real arena in which the vacuum quanta reside—called superspace). Quantum space theory is a pilot-wave theory (similar to de Broglie’s double solution theory , the de Broglie-Bohm theory , Vigier’s stochastic approach ), that mathematically reproduce the predictions of canonical quantum mechanics while maintaining a completely lucid and intuitively accessible ontology. Notice that in this example, time (the time it takes for the echo signal to return) corresponds to the position of the object it bounced off of, while frequency (the difference between the frequency of the original signal and the echo signal) corresponds to the velocity of the object, making this example a similar analogy to the quantum mechanical Heisenberg uncertainty principle. Einstein’s Intuition : Quantum Space Theory. We have to change the winding frequency to be meaningfully different from five before the signal can start to balance out again (Figure 6b) which leads to a much broader peak around the five beats per second. Instead of being unexpected, confusing, or a sign of indeterminacy, this trade off is a perfectly reasonable, straightforward, general feature of a world containing waves. Descending along two tracks. He had light passing through a slit, which causes an uncertainty of momentum because the light behaves like … Heisenberg's uncertainity principle should not be compared with Einstein's theories. Cosmology / Elementary Tour part 1: The expanding universe ... Einstein Online is a web portal with comprehensible information on Einstein's theories of relativity and their most exciting applications from … It has often been regarded as the mostdistinctive feature in which quantum mechanics differs from classicaltheories of the physical world. Is a fundamental law of quantum theory, which defines the limit of precision with which two complementary physical quantities can be determined. They went on to prove that with these fluctuations present, an arbitrary probability density will always decay to —its equilibrium state. The simple fact that pilot-wave theory explains the phenomena of the quantum world in a comprehensible deterministic way utterly refutes standard quantum mechanics (the Copenhagen interpretation). We can have one or the other, but we cannot have crisp delineation for both. Condition 3: The change of particle’s position with respect to time is equal to the local stream velocity , where , and the “velocity potential” is related to the phase of by . Werner Heisenberg stumbled on a secret of the universe: Nothing has a definite position, a definite trajectory, or a definite momentum. In everyday life we can successfully measure the position of an automobile at a … In short, the wave function has been reduced without any interaction between the particle and the first measurement apparatus. The common assertion is that measurements of quantum systems cannot be made without affecting those systems, and that state vector reduction is somehow initiated by those measurements. The other type of vacuum soliton is made up of waves that twist together to form stable quantized vortices, (whirling about on a closed loop path in whole wavelength multiples—matching phase with each loop). In this case, the second detector D2 will never record a particle. This approach objectively demystifies wave-particle duality, eliminates state vector reduction, reveals the physical nature of the wave function, and exposes the geometric roots of Heisenberg uncertainty, quantum tunneling, non-locality, gravity, dark matter, and dark energy—making it a candidate theory of quantum gravity and a possible approach for a GUT. This proposal resurrected the core of Thomson’s idea—framing it in a new mold (pilot-wave theory). D1 is cut in half to allow us to see inside. So for quantum particles, the spread out over space (and over momentum) is not some artifact of imperfect measurement techniques, it’s a spread fundamental to what the particle is, analogous to how a musical note being spread out over time is fundamental to what it even means to be a musical note. Heisenberg's Uncertainty Principle was the most revolutionary idea since Einstein's Theory of Sell-ativity and, subsequently, Riemann's Laundry Manifolder. In short, in order to justify the equilibrium relation, Bohm and Vigier returned to de Broglie’s original idea—that particles are intersecting (non-linear) waves in a sub-quantum fluid surrounded by a (linear) pilot wave. This condition secures that the velocity of the particle matches the local stream velocity of the fluid. This proof was extended to the Dirac equation and the many-particle problem. The idea is simple. Another place where this trade off shows up—between how short our observation is and how confident we can feel about the frequency of a signal—is in Doppler radar. This proposal resurrected the core of Thomson’s idea—framing it in a new mold (pilot-wave theory). In other words, Heisenberg’s uncertainty principle is really just a manifestation of the trade off between how concentrated a wave and its frequency representation can be, applied to the premise that matter is some kind of wave. They are simple and “linear”. This is the Fourier trade off. This is the Fourier transform’s way of telling us that the dominant frequency of the signal is five beats per second. How do we know this? Given that what de Broglie really had in mind was that particles were intersecting waves in some fluid (pulsating non-linear waves), and that pilot waves were the linear extensions of those waves into the rest of the fluid, this condition may feel completely natural—automatically imported. Here’s how a Fourier transform works. When the aether fell out of fashion the medium was dropped but the wave equation remained, leaving an open-ended question about what light was waving through. At this point you might be asking yourself—if that’s all there is to it, then why do people still propagate the notion that Heisenberg uncertainty is some artifact of measurement? He tried to develop thought experiments whereby Heisenberg's uncertainty principle might be violated, but each time, Bohr found loopholes in Einstein's reasoning. This quandary comes to us not from science fiction nor logical speculations, but through a perception of quantum mechanics called the uncertainty principle. If the particle isn’t detected by D1, then D2 will detect the particle later. In other words, these assumptions are consequences of the fact that the de Broglie-Bohm theory is a mean-field approximation of the real dynamics. Think of it as rotating a vector around the circle with a length that is determined by the height of the graph at each point in time. This insight increases our knowledge of how the world works—by telling us that deep down, on the smallest levels, everything is made up of waves. We now have a hydrodynamic model that fully reproduces the behavior of quantum particles in terms of a potential flow. More than 400 entries from "absolute zero" to "XMM Newton" - whenever you see this type of link on an Einstein Online page, it'll take you to an entry in our relativistic dictionary. This content can also be found on Thad’s. Under de Broglie’s original assumption that pilot waves are mechanically supported by a physical sub-quantum medium, the idea that the pilot wave, In order to establish that the equilibrium relation, Bohm and Vigier went on to note that if photons and particles of matter have a granular substructure, analogous to the molecular structure underlying ordinary fluids, then the irregular fluctuations are merely random fluctuations about the mean (potential) flow of that fluid. In order to establish that the equilibrium relation is a natural expectation for arbitrary quantum motion, Bohm and Vigier proposed a hydrodynamic model infused with a special kind of irregular fluctuations. With sufficient disruption, vortices can also be canceled out—by colliding with vortices that are equal in magnitude but opposite in rotation, or by undergoing transformations that convert them into phonons. Unlike pulse phonons, which pass right through each other upon incidence, quantized vortices, or sonons, (think smoke rings) cannot freely pass through each other. To more viscerally connect with the quantum world, to have a richer understanding of quantum phenomenon while minimizing the number of our auxiliary assumptions, we have to tell the story from the perspective of the more complete ontology—the one that mirrors what’s actually going on in Nature—the one that de Broglie originally had in mind. This content can also be found on Thad’s Heisenberg’s uncertainty principle Quora post. Figure 2 – A signal that cycles 5 times per second and persists for 2 seconds. In fact, one of the more salient and beautiful insights of the uncertainty principle is that the relationship between position and momentum is the same as the relationship between sound and frequency. the velocity that a particle can reach depending on its mass, with heavy particles that move fast having large momentum because it will take them a large or prolonged force to get up to speed and then again to stop them) of a particle. Figure 1a – A short duration observation gives a low confidence about the actual frequency, producing a spread out frequency plot capturing all the possible frequencies it might have. Such nonlinearities could produce, in addition to many other qualitatively new effects, the possibility of irregular turbulent motion.”. Note that the particle (the collection of hanging masses) is (1) oscillating, (2) dispersed in space (taking up more than a single point), and (3) localized (in that it’s concentrated towards some point, and not spreading further out over time). By contrast, pressure waves (also called longitudinal waves) do spread out. In other words, let’s explore why using radar results in a situation in which the more certain we are about the positions of things, the less certain we are about their velocities. In order to accurately measure the difference between the outgoing signal’s frequency and the return signal’s frequency, we need a very precise frequency, one that is not spread out very much. When we fail to stipulate a physical medium, evolution according to the Schrödinger equation becomes a necessary additional (brute) assumption. To quantum mechanics… well, wrong think that this popular narrative is… well, that actually us! 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