{"id":4469,"date":"2024-09-22T22:08:30","date_gmt":"2024-09-22T22:08:30","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4469"},"modified":"2024-09-22T22:08:31","modified_gmt":"2024-09-22T22:08:31","slug":"introduction-45","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/09\/22\/introduction-45\/","title":{"rendered":"Introduction"},"content":{"rendered":"\n

The thought that an objective reality does not exist independently of an observer troubled Einstein very much. In opposition to Bohr\u2019s group in Copenhagen, Einstein believed that the fact that quantum mechanics could only provide an answer in terms of probability meant the theory was incomplete. This was a lively discussion he maintained with Bohr for many years.\u2020<\/sup><\/a><\/p>\n\n\n\n

In 1935, Einstein refined the philosophical discussion into a physical argument. At Princeton University, Einstein and his assistants Boris Podolsky and Nathan Rosen authored a paper titled \u201cCan Quantum-Mechanical Description of Physical Reality Be Considered Complete?\u201d40<\/sup> This now-famous paper, better known simply as \u201cthe EPR paper\u201d (for Einstein\u2013Podolsky\u2013Rosen), proposed a thought experiment they felt revealed an underlying, objective reality independent of measurement. The EPR argument seemed to completely contradict the Copenhagen Interpretation.<\/p>\n\n\n\n

At the heart of the EPR thought experiment is a particle source that produces pairs of particles that have some property that is forever linked. For example,\u00a0Figure 136a\u00a0shows what happens when a subatomic particle called a\u00a0pi meson<\/em>\u00a0(also known as a\u00a0pion<\/em>) decays into an electron and its antiparticle\u2014a positron.<\/p>\n\n\n\n

Figure 136\u00a0A number of physical processes can produce entangled particles. (a<\/strong>) A pion can decay into an electron\u2013positron pair that travel in opposite directions and have opposite spin. (b<\/strong>) A UV photon can be converted by a nonlinear optical crystal into two IR photons with opposite polarization.\"\"<\/p>\n\n\n\n

Now, along with mass and charge, electrons have a property known as spin<\/em>. Although electrons don\u2019t really spin like tops, the analogy is appropriate, because an electron\u2019s spin is related to the electron\u2019s angular momentum. Like energy (or its mass equivalent), charge, and momentum, spin is also a conserved amount. Since the spin of the pion is zero, the sum of the spins of the electron and positron produced during the pion\u2019s decay must also be zero. Thus, the electron and positron must travel in exactly opposite directions and must have exactly opposite spins.<\/p>\n\n\n\n

In a similar way, and as shown in\u00a0Figure 136b, a UV photon can be converted by a type of crystal known as a nonlinear optical crystal into two IR photons of opposite polarization. The energy is conserved, because each of the IR photons has one-half the energy of the UV photon. Although each pair will come out of the crystal with a random polarization, the polarizations of the photons within the pair will forever be linked due to conservation of angular momentum.<\/p>\n\n\n\n

The particles generated in pairs by these processes are said to be entangled. According to the Copenhagen Interpretation, two entangled particles share a single wavefunction that is not separable into distinct wavefunctions for each particle. That is, the two particles are linked in such a way that the quantum state of one particle cannot be adequately described without full mention of the other particle, even if the individual particles are separated by a great distance.<\/p>\n\n\n\n

Let\u2019s suppose that you have a pair of entangled particles (for example, an electron\u2013positron pair) separated by a significant distance. Now, say you measure the electron\u2019s spin. This automatically tells you the positron\u2019s spin. Since you have managed to ascertain the positron\u2019s spin without disturbing the positron in any way, Einstein, Podolsky, and Rosen argued that it\u2019s impossible that the positron only came to have the known spin when you measured it, because you didn\u2019t measure it! EPR thus argued that the positron must have had that spin all along.<\/p>\n\n\n\n

That is the key argument behind the EPR paper: that measurements conducted on one of the particles of an entangled pair immediately yields information about the state of the other particle, even if they are separated by a significant distance in space. EPR then claimed that the fact that the state of the positron could be determined without interacting with it meant that its spin had an objective reality regardless of measurement.<\/p>\n\n\n\n

In Einstein\u2019s view, the spins of the two particles are determined together, at the moment they are created. Otherwise, the result of the measurement on the electron would have to be communicated instantaneously to the positron\u2014something Einstein called \u201cspooky action at a distance.\u201d<\/em> This was especially disturbing to Einstein, since the instantaneous transfer of information would break the rule of signaling faster than the speed of light, which would violate Special Relativity.<\/p>\n\n\n\n

Even more problematic for the Copenhagen Interpretation, a pair of entangled particles as described by Einstein could be used to overcome Heisenberg\u2019s Uncertainty Principle. Remember that, according to this principle, you can\u2019t simultaneously measure the position and momentum of a particle with absolute certainty. However, let\u2019s suppose that you prepare a pair of particles with entangled momentum. Measuring the position of one particle would allow us to know the exact position of the other particle (since they were created together and travel in exactly opposite directions), while measuring the second particle\u2019s momentum would allow us to know the first particle\u2019s momentum. If the entangled particles are not in communication via some \u201cspooky telepathy,\u201d then we would indeed be able to simultaneously know a particle\u2019s exact position and momentum.<\/p>\n\n\n\n

You may have figured out by now that if the EPR argument is correct, using the entangled-photon source of\u00a0Figure 136b\u00a0in a double Mach\u2013Zehnder interferometer would allow us to observe an interference pattern (wave-like behavior) and at the same time determine the path taken by a photon (particle-like behavior), in violation of wave\u2013particle duality.41<\/sup><\/p>\n","protected":false},"excerpt":{"rendered":"

The thought that an objective reality does not exist independently of an observer troubled Einstein very much. In opposition to Bohr\u2019s group in Copenhagen, Einstein believed that the fact that quantum mechanics could only provide an answer in terms of probability meant the theory was incomplete. This was a lively discussion he maintained with Bohr […]<\/p>\n","protected":false},"author":1,"featured_media":4470,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[518],"tags":[],"class_list":["post-4469","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-entanglement"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/entanglement-1.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4469","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=4469"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4469\/revisions"}],"predecessor-version":[{"id":4471,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4469\/revisions\/4471"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4470"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4469"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4469"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}