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<p>Formulated in the early 20th century to explain the behavior of subatomic particles. QM, and its specializations (quantum field theory, quantum chromodynamics, many-body physics etc.), have been spectacularly successful in explaining microscopic physical phenomena.</p>
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<p>Quantum mechanics, Formulated in the early 20th century, and its specializations (quantum field theory, quantum chromodynamics, many-body physics etc.), have been spectacularly successful in explaining microscopic physical phenomena.</p>
<p>After nearly a century of study, the best (classical) methods for predicting the behavior of general quantum systems require exponential resources.</p>
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<ol>
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<li> The state of \( N \) particles requires at least \( 2^{N} \) numbers to describe.</li>
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<li> For \( N \sim 300 \) (the number of particles in a single uranium atom), \[
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<li> For \( N \sim 300 \) (the number of particles in a single uranium atom and looking only at spin degrees freedom), \[
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<p> 2^{300} \gg \approx 10^{82}\quad (\text{\# of atoms in the observable universe}).
<h2id="the-exponentiality-of-qm-i" class="anchor">The exponentiality of QM I </h2>
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@@ -759,7 +755,7 @@ <h2 id="which-is-wrong" class="anchor">Which is wrong? </h2>
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<li> Option 1: QM is wrong</li>
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<ul>
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<li> Perhaps the most successful theory of nature to date.</li>
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<li> In all its domains of applicability, we have never found experimental disagreement.</li>
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<li> In all its domains of applicability, we have never found experimental disagreement (for example <ahref="https://iopscience.iop.org/article/10.1088/1742-6596/306/1/012036/pdf" target="_self">test of the Pauli principle</a>).</li>
<p>Formulated in the early 20th century to explain the behavior of subatomic particles. QM, and its specializations (quantum field theory, quantum chromodynamics, many-body physics etc.), have been spectacularly successful in explaining microscopic physical phenomena.</p>
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<p>Quantum mechanics, Formulated in the early 20th century, and its specializations (quantum field theory, quantum chromodynamics, many-body physics etc.), have been spectacularly successful in explaining microscopic physical phenomena.</p>
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</div>
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</section>
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@@ -379,7 +379,7 @@ <h2 id="the-exponentiality-of-qm">The exponentiality of QM </h2>
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<p>After nearly a century of study, the best (classical) methods for predicting the behavior of general quantum systems require exponential resources.</p>
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<ol>
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<p><li> The state of \( N \) particles requires at least \( 2^{N} \) numbers to describe.</li>
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<p><li> For \( N \sim 300 \) (the number of particles in a single uranium atom), \[
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<p><li> For \( N \sim 300 \) (the number of particles in a single uranium atom and looking only at spin degrees freedom), \[
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<p> 2^{300} \gg \approx 10^{82}\quad (\text{\# of atoms in the observable universe}).
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\]
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</p></li>
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<section>
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<h2id="the-exponentiality-of-qm-i">The exponentiality of QM I </h2>
<b>How do physicists actually do (quantum) physics?</b>
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<p>
@@ -497,7 +498,7 @@ <h2 id="which-is-wrong">Which is wrong? </h2>
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<p><li> Perhaps the most successful theory of nature to date.</li>
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<p><li> In all its domains of applicability, we have never found experimental disagreement.</li>
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<p><li> In all its domains of applicability, we have never found experimental disagreement (for example <ahref="https://iopscience.iop.org/article/10.1088/1742-6596/306/1/012036/pdf" target="_blank">test of the Pauli principle</a>).</li>
<p>Formulated in the early 20th century to explain the behavior of subatomic particles. QM, and its specializations (quantum field theory, quantum chromodynamics, many-body physics etc.), have been spectacularly successful in explaining microscopic physical phenomena.</p>
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<p>Quantum mechanics, Formulated in the early 20th century, and its specializations (quantum field theory, quantum chromodynamics, many-body physics etc.), have been spectacularly successful in explaining microscopic physical phenomena.</p>
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</div>
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@@ -523,7 +519,7 @@ <h2 id="the-exponentiality-of-qm">The exponentiality of QM </h2>
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<p>After nearly a century of study, the best (classical) methods for predicting the behavior of general quantum systems require exponential resources.</p>
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<ol>
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<li> The state of \( N \) particles requires at least \( 2^{N} \) numbers to describe.</li>
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<li> For \( N \sim 300 \) (the number of particles in a single uranium atom), \[
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<li> For \( N \sim 300 \) (the number of particles in a single uranium atom and looking only at spin degrees freedom), \[
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<p> 2^{300} \gg \approx 10^{82}\quad (\text{\# of atoms in the observable universe}).
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\]
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</p></li>
@@ -534,6 +530,7 @@ <h2 id="the-exponentiality-of-qm">The exponentiality of QM </h2>
<b>How do physicists actually do (quantum) physics?</b>
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<p>
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<li> Option 1: QM is wrong</li>
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<ul>
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<li> Perhaps the most successful theory of nature to date.</li>
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<li> In all its domains of applicability, we have never found experimental disagreement.</li>
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<li> In all its domains of applicability, we have never found experimental disagreement (for example <ahref="https://iopscience.iop.org/article/10.1088/1742-6596/306/1/012036/pdf" target="_blank">test of the Pauli principle</a>).</li>
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