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1. The uncertainty principle says that we cannot measure the position (x) and the momentum (p) of a particle with absolute precision.
2. One way to think about the uncertainty principle is as an extension of how we see and measure things in the everyday world.
3. The uncertainty principle is at the heart of many things that we observe but cannot explain using classical (non-quantum) physics.
4. Perhaps the strangest result of the uncertainty principle is what it says about vacuums.
5. Learn about the uncertainty principle as defined by the properties of waves.
6. The uncertainty principle arises from the wave-particle duality.
7. The uncertainty principle is alternatively expressed in terms of a particle’s momentum and position.
8. In February 1927, the young Werner Heisenberg developed a key piece of quantum theory, the uncertainty principle, with profound implications.
9. Though others may have found the wave approach easier to use, Heisenberg’s matrix mechanics led him naturally to the uncertainty principle for which he is well known.
10. In March he submitted his paper on the uncertainty principle for publication.
11. Niels Bohr pointed out some errors in Heisenberg’s thought experiment, but agreed the uncertainty principle itself was correct, and the paper was published.
12. Heisenberg sometimes explained the uncertainty principle as a problem of making measurements.
13. Physics students are still taught this measurement-disturbance version of the uncertainty principle in introductory classes, but it turns out that it's not always true.
14. When the researchers did the experiment multiple times, they found that measurement of one polarization did not always disturb the other state as much as the uncertainty principle predicted.
15. And according to the uncertainty principle, you can't know the position and momentum of that particle accurately, at the same time.
16. So let's look at a mathematical description of the uncertainty principle.
17. And so let's apply this uncertainty principle to the Bohr model of the hydrogen atom.
18. The uncertainty principle says this isn't true.
19. With light-based analytical instruments the designers of the optics have to struggle with the uncertainty principle.
20. Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics.
21. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.
22. The uncertainty principle was hard even for scientists to accept at first.
23. Before getting into the details, one thing to get clear is that Heisenberg’s “uncertainty principle” is not really a principle at all.
24. We provide a natural derivation and interpretation for the uncertainty principle in quantum mechanics from the stochastic optimal control approach.
25. We show that, in particular, the stochastic approach to quantum mechanics allows one to understand the uncertainty principle through the “thermodynamic equilibrium”.
26. Roughly speaking, the uncertainty principle (for position and momentum) states that one cannot assign exact simultaneous values to the position and momentum of a physical system.
27. formulation of the uncertainty principle no longer follows.
28. In the English literature the name uncertainty principle became most common.
29. A second point is the question whether the theoretical structure or the quantitative laws of quantum theory can indeed be derived on the basis of the uncertainty principle, as Heisenberg wished.
30. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program.
31. Two alternative frameworks for quantum physics offer different explanations for the uncertainty principle.
32. This is the uncertainty principle, the exact limit of which is the Kennard bound.
33. By the time–energy uncertainty principle, they do not have a definite energy, and, each time they decay, the energy they release is slightly different.
34. The letter evolved into a published paper in which Heisenberg presented to the world for the first time what became known as the uncertainty principle.
35. This is known as the Heisenberg uncertainty principle.
36. The uncertainty principle for energy and time can be of great significance if the lifetime of a system is very short.
37. Another consequence of the wave character of all particles is the Heisenberg uncertainty principle, which limits the precision with which certain physical quantities can be known simultaneously.
38. uncertainty principle, which was first laid out by German physicist Werner Heisenberg in 1927.
39. Albert Einstein strongly objected to the uncertainty principle, saying it could not possibly reflect reality, and spent many years arguing with Heisenberg and others.
40. Discussing the uncertainty principle in his 1928 book The Nature of the Physical World, Arthur Eddington felt it opened up a gap in Newtonian determinism that left a space for free will to operate.
41. It’s known as Heisenberg’s uncertainty principle, which indeed means that the star of today’s episode is this fellow right here.
42. one way of explaining the uncertainty principle.
43. It’s a way that I use in describing the uncertainty principle to one of the great string theorists of our age, Sheldon Cooper.
44. Now, look, ba dum bump is a perfectly fine response to that kind of loose description of the uncertainty principle.
45. Heisenberg’s uncertainty principle states that it is impossible to measure or calculate exactly, both the position and the momentum of an object.
46. In the field of quantum mechanics, Heisenberg’s uncertainty principle is a fundamental theory that explains why it is impossible to measure more than one quantum variables simultaneously.
47. In order to illustrate Heisenberg’s uncertainty principle, consider an example where the position of an electron is measured.
48. Applying the same example to a macroscopic object (say a basketball), it can be understood that Heisenberg’s uncertainty principle has a negligible impact on measurements in the macroscopic world.
49. This principle known as the Heisenberg uncertainty principle can be expressed as follows: where is the uncertainty in position, is the uncertainty in momentum, and is the reduced Planck's constant.
50. After Heisenberg, two other scientists, H. P. Robertson and E. Schrödinger, developed his uncertainty principle.
51. In the paper, the author considers the uncertainty relations as implicit evolution equations so the intrinsic nature of the correlations expressed by the uncertainty principle is shown more precisely.
52. The uncertainty principle is usually written with an extra factor of 2π: it takes about one radian rather than a whole cycle.
53. The uncertainty principle prohibits exact knowledge of initial conditions, and therefore repeated performances of such processes will diverge.
54. Some philosophers regard the consequences of the uncertainty principle as having a more fundamental importance.
55. In this paper, we explore OAM entanglement by applying the Heisenberg uncertainty principle to the quantum position correlation within the azimuthal region.
56. This phenomenon can be explained by the Heisenberg uncertainty principle.
57. Such phenomena can be explained by applying the Heisenberg uncertainty principle to the between angular position correlation and OAM correlation.
58. E.G. Revisiting the Derivation of Heisenberg's Uncertainty Principle: The Collapse of Uncertainty at the Planck Scale.
59. In this paper, we will revisit the derivation of Heisenberg's uncertainty principle.
60. Further, Bell's Inequality no longer holds, as the breakdown of Heisenberg's uncertainty principle at the Planck scale opens up the possibility for hidden variable theories.
61. The uncertainty principle is alternatively expressed in terms of a particle's momentum and position.
62. Which brings us to the uncertainty principle.
63. Now the uncertainty principle is not something we notice in everyday life.
64. The reason we don't notice the uncertainty principle in everyday life is because of the size of Planck's constant.
65. You get a similar result when you apply the uncertainty principle to any object large enough to see.

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• [{'LOWER': 'uncertainty'}, {'LEMMA': 'principle'}]