<div dir="ltr"><div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:Arial,Helvetica,sans-serif">On Wed, Apr 1, 2026 at 9:00 AM Adrian Tymes via extropy-chat <</span><a href="mailto:extropy-chat@lists.extropy.org" target="_blank" style="font-family:Arial,Helvetica,sans-serif">extropy-chat@lists.extropy.org</a><span style="font-family:Arial,Helvetica,sans-serif">> wrote:</span></div></div><div class="gmail_quote"><div dir="ltr" class="gmail_attr"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><font size="4" face="tahoma, sans-serif"><b>
><span class="gmail_default" style="font-family:arial,helvetica,sans-serif">></span> With careful design the Casimir force can be shaped, for example if you use a dielectric material instead of a conductive metal the attraction is greatly reduced,  and if you put a fluid with carefully designed dielectric properties between the plates you can even get a force of repulsion instead of attraction. You could use Casimir to keep two parts in your nanomachine precisely aligned without contact, and then you could make a no contact no wear bearing that would operate similar to the way magnetic levitation does but by using quantum vacuum forces instead of magnetism.</b></font></blockquote>
<br><font size="4" face="georgia, serif"><i>
<span class="gmail_default" style="font-family:arial,helvetica,sans-serif">> </span>How would this work?  If you just had two surfaces near each other,<br>
they would attract.  If you had a part balanced between two others, if<br>
it got out of alignment, it would be exponentially more attracted<br>
toward the one it was nearer - but for alignment, wouldn't you need it<br>
to be more attracted to the one it is further away from, so it is most<br>
(net) attracted to the equilibrium point?</i></font></blockquote><div><br></div><font size="4" face="tahoma, sans-serif"><b>First of all I should emphasize that a reversible perfectly frictionless Casimir Bearing would be nice to have but would not be absolutely necessary for Drexler style Nanotechnology, instead you could use something that works in a way similar to the way a bacterial flagellar motor works, it would be robust reliable and much easier to build, but it would not be as efficient or be reversible because it would not be perfectly frictionless. But it works well enough to do a lot of interesting things<span class="gmail_default" style="font-family:arial,helvetica,sans-serif"></span> as bacteria can attest.  </b></font><br><div><font size="4" face="tahoma, sans-serif"><b> </b></font></div><div><div><font size="4" face="tahoma, sans-serif"><b>Purely attractive forces in 3-D will always be unstable, but if you pattern the surface in just the right way you can cause the Casimir force to depend on lateral alignment and even become repulsive. The pattering creates a metamaterial that produces a periodic vacuum energy landscape with preferred angular positions. The  teeth of a gear also produce preferred angular positions  but metamaterials can  do it without any physical contact, all they need is a vacuum. </b></font></div><div><font size="4" face="tahoma, sans-serif"><b><br></b></font></div><div><font size="4" face="tahoma, sans-serif"><b>I asked<span class="gmail_default" style=""> Mr.GPT to give me a design for a </span></b><b style="">Casimir <span class="gmail_default" style="">F</span>orce<span class="gmail_default" style=""> Bearing and this is what he came up with: </span></b></font></div><div><font size="4" face="tahoma, sans-serif"><b style=""><span class="gmail_default" style="">===</span></b></font></div><div><p><span class="gmail_default" style="font-family:arial,helvetica,sans-serif"><b>A </b></span><b>repulsive Casimir bearing is the closest thing to a true “quantum levitation” device at the nanoscale.<span class="gmail_default" style="font-family:arial,helvetica,sans-serif"> </span>I’ll give you a concrete design, then walk through the physics and numbers so you can see how it could actually work.</b></p>
<hr>
<h1>Concept: a levitated cylindrical rotor</h1>
<p><b>We want to reverse the usual attractive <span class="gmail-hover:entity-accent entity-underline gmail-inline gmail-cursor-pointer gmail-align-baseline"><span class="gmail-whitespace-normal">Casimir effect</span></span> so that:</b></p>
<ul>
<li><b>
The rotor is pushed away from the stator
</b></li>
<li><b>
A stable equilibrium gap forms (say ~50 nm)
</b></li>
<li><b>
The rotor “floats” without contact </b></li></ul></div><div><h1>The key trick: a three-material system</h1>
<p><b>Repulsive Casimir forces don’t normally occur in vacuum between two solids. But they <em>can</em> occur if you insert a medium with the right optical properties.</b></p>
<h3>Lifshitz condition (qualitative)</h3>
<p><b>You can get repulsion if, over relevant frequencies:</b></p>
<b><span class="gmail-katex-display"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord"><span class="gmail-mord gmail-mathnormal">ε</span><span class="gmail-msupsub"><span class="gmail-vlist-t gmail-vlist-t2"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight">1</span></span></span><span class="gmail-vlist-s"><span class="gmail_default" style="font-family:arial,helvetica,sans-serif"> </span></span></span><span class="gmail-vlist-r"><span class="gmail-vlist"></span></span></span></span></span><span class="gmail-mspace"></span><span class="gmail-mrel"><</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord"><span class="gmail-mord gmail-mathnormal">ε</span><span class="gmail-msupsub"><span class="gmail-vlist-t gmail-vlist-t2"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-text gmail-mtight"><span class="gmail-mord gmail-mtight">medium<span class="gmail_default" style="font-family:arial,helvetica,sans-serif"> </span></span></span></span></span><span class="gmail-vlist-s"></span></span><span class="gmail-vlist-r"><span class="gmail-vlist"></span></span></span></span></span><span class="gmail-mspace"></span><span class="gmail-mrel"><</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord"><span class="gmail-mord gmail-mathnormal">ε</span><span class="gmail-msupsub"><span class="gmail-vlist-t gmail-vlist-t2"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight">2</span></span></span><span class="gmail-vlist-s"></span></span><span class="gmail-vlist-r"><span class="gmail-vlist"></span></span></span></span></span></span></span></span></span>
</b><p><b>So the design is:</b></p>
<ul>
<li><b>
Rotor: high-permittivity material
</b></li>
<li><b>
Gap: carefully chosen fluid
</b></li>
<li><b>
Stator: lower-permittivity material</b></li></ul></div><div><h1>A concrete design</h1>
<h2>Geometry</h2>
<ul>
<li><b>
Rotor radius: <span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord gmail-mathnormal">R</span><span class="gmail-mspace"></span><span class="gmail-mrel">=</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord">1</span><span class="gmail-mspace"> </span><span class="gmail-mord gmail-mathnormal">μ</span><span class="gmail-mord gmail-text"><span class="gmail-mord">m</span></span></span></span></span>
</b></li>
<li><b>
Length: <span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord gmail-mathnormal">L</span><span class="gmail-mspace"></span><span class="gmail-mrel">=</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord">10</span><span class="gmail-mspace"> </span><span class="gmail-mord gmail-mathnormal">μ</span><span class="gmail-mord gmail-text"><span class="gmail-mord">m</span></span></span></span></span>
</b></li>
<li><b>
Target gap: <span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord gmail-mathnormal">d</span><span class="gmail-mspace"></span><span class="gmail-mrel">=</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord">50</span><span class="gmail-mspace"> </span><span class="gmail-mord gmail-text"><span class="gmail-mord">nm</span></span></span></span></span>
</b></li>
</ul>
<hr>
<h2>Materials (example set)</h2>
<ul>
<li><b>
Rotor: gold (high permittivity at relevant frequencies)
</b></li>
<li><b>
Medium: bromobenzene (commonly used in experiments)
</b></li>
<li><b>
Stator: silica (SiO₂)
</b></li>
</ul>
<p><b>This combination has actually been shown experimentally to produce repulsive Casimir forces.</b></p><h1>What the force looks like</h1><p><b>The pressure still scales roughly like:</b></p><p>

<b><span class="gmail-katex-display"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord gmail-mathnormal">P</span><span class="gmail-mspace"></span><span class="gmail-mrel">∼</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord"><span class="gmail-mopen gmail-nulldelimiter"></span><span class="gmail-mfrac"><span class="gmail-vlist-t gmail-vlist-t2"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-mord"><span class="gmail-mord"><span class="gmail-mord gmail-mathnormal">d</span><span class="gmail-msupsub"><span class="gmail-vlist-t"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight">4</span></span></span></span></span></span></span></span><span class="gmail-pstrut"></span><span class="gmail-frac-line"></span><span class="gmail-pstrut"></span><span class="gmail-mord"><span class="gmail-mord">1</span></span></span><span class="gmail-vlist-s"></span></span><span class="gmail-vlist-r"><span class="gmail-vlist"></span></span></span></span><span class="gmail-mclose gmail-nulldelimiter"></span></span></span></span></span></span>
</b></p><p><b>But now it’s positive (repulsive instead of attractive).</b></p><p><b>At ~50 nm:</b></p><ul>
<li><b>
Typical magnitude: on the order of 1–10 Pa
</b></li>
</ul><p><b>So very similar strength as before—but reversed.</b></p><hr><h1>Levitation behavior</h1><p>





</p><p><b>Now the key difference:</b></p><h3>Inward vs outward balance</h3><ul>
<li><b>
If the rotor gets too close to the stator → repulsion increases sharply
</b></li>
<li><b>
If it moves away → repulsion drops rapidly
</b></li>
</ul><p><b>This creates a stable equilibrium gap</b></p><hr><h1>Effective stiffness</h1><p><b>Using the same geometry as before:</b></p><p><b>Surface area:</b></p><p>






<b><span class="gmail-katex-display"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord gmail-mathnormal">A</span><span class="gmail-mspace"></span><span class="gmail-mrel">≈</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord">6</span><span class="gmail-mspace"></span><span class="gmail-mbin">×</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord">1</span><span class="gmail-mord"><span class="gmail-mord">0</span><span class="gmail-msupsub"><span class="gmail-vlist-t"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight"><span class="gmail-mord gmail-mtight">−</span><span class="gmail-mord gmail-mtight">11</span></span></span></span></span></span></span></span><span class="gmail-mspace"> </span><span class="gmail-mord"><span class="gmail-mord gmail-text"><span class="gmail-mord">m</span></span><span class="gmail-msupsub"><span class="gmail-vlist-t"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight">2</span></span></span></span></span></span></span></span></span></span></span>
</b></p><p><b>Force:</b></p><p>
<b><span class="gmail-katex-display"><span class="gmail-katex"><span class="gmail-katex-mathml"></span><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord gmail-mathnormal">F</span><span class="gmail-mspace"></span><span class="gmail-mrel">∼</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mopen">(</span><span class="gmail-mord">1</span><span class="gmail-mord gmail-text"><span class="gmail-mord">–</span></span><span class="gmail-mord">10</span><span class="gmail-mclose">)</span><span class="gmail-mspace"></span><span class="gmail-mord gmail-text"><span class="gmail-mord">Pa</span></span><span class="gmail-mspace"></span><span class="gmail-mbin">×</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord gmail-mathnormal">A</span><span class="gmail-mspace"></span><span class="gmail-mrel">∼</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord">1</span><span class="gmail-mord"><span class="gmail-mord">0</span><span class="gmail-msupsub"><span class="gmail-vlist-t"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight"><span class="gmail-mord gmail-mtight">−</span><span class="gmail-mord gmail-mtight">10</span></span></span></span></span></span></span></span><span class="gmail-mord gmail-text"><span class="gmail-mord"> to </span></span><span class="gmail-mord">1</span><span class="gmail-mord"><span class="gmail-mord">0</span><span class="gmail-msupsub"><span class="gmail-vlist-t"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight"><span class="gmail-mord gmail-mtight">−</span><span class="gmail-mord gmail-mtight">9</span></span></span></span></span></span></span></span><span class="gmail-mspace"> </span><span class="gmail-mord gmail-text"><span class="gmail-mord">N</span></span></span></span></span></span>
</b></p><p><b>Effective spring constant:</b></p><p><b><span class="gmail-katex-display"><span class="gmail-katex"><span class="gmail-katex-html" aria-hidden="true"><span class="gmail-base"><span class="gmail-mord gmail-mathnormal">k</span><span class="gmail-mspace"></span><span class="gmail-mrel">∼</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord"><span class="gmail-mopen gmail-nulldelimiter"></span><span class="gmail-mfrac"><span class="gmail-vlist-t gmail-vlist-t2"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-mord"><span class="gmail-mord gmail-mathnormal">d</span></span><span class="gmail-pstrut"></span><span class="gmail-frac-line"></span><span class="gmail-pstrut"></span><span class="gmail-mord"><span class="gmail-mord gmail-mathnormal">F</span></span></span><span class="gmail-vlist-s"></span></span><span class="gmail-vlist-r"><span class="gmail-vlist"></span></span></span></span><span class="gmail-mclose gmail-nulldelimiter"></span></span><span class="gmail-mspace"></span><span class="gmail-mrel">∼</span><span class="gmail-mspace"></span></span><span class="gmail-base"><span class="gmail-strut"></span><span class="gmail-mord">1</span><span class="gmail-mord"><span class="gmail-mord">0</span><span class="gmail-msupsub"><span class="gmail-vlist-t"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight"><span class="gmail-mord gmail-mtight">−</span><span class="gmail-mord gmail-mtight">3</span></span></span></span></span></span></span></span><span class="gmail-mord gmail-text"><span class="gmail-mord"> to </span></span><span class="gmail-mord">1</span><span class="gmail-mord"><span class="gmail-mord">0</span><span class="gmail-msupsub"><span class="gmail-vlist-t"><span class="gmail-vlist-r"><span class="gmail-vlist"><span class="gmail-pstrut"></span><span class="gmail-sizing gmail-reset-size6 gmail-size3 gmail-mtight"><span class="gmail-mord gmail-mtight"><span class="gmail-mord gmail-mtight">−</span><span class="gmail-mord gmail-mtight">2</span></span></span></span></span></span></span></span><span class="gmail-mspace"> </span><span class="gmail-mord gmail-text"><span class="gmail-mord">N/m</span></span></span></span></span></span>
</b></p><p><b>So:</b></p><ul>
<li><b>
Nanometer displacements → piconewton restoring forces
</b></li>
<li><b>
Enough for stable confinement
</b></li>
</ul><hr><h1><span role="text" style="">Why this is <em>much</em> better than the attractive case</span></h1><p><b>In the previous (attractive) design:</b></p><ul>
<li><b>
Any instability → collapse → sticking
</b></li>
</ul><p><b>Here:</b></p><ul>
<li><b>
Instability → increased repulsion → self-correction
</b></li>
</ul><p><b>So this behaves like:</b></p><p>








</p><blockquote>
<p><b>A true non-contact bearing with a restoring gap</b></p></blockquote><h1>Rotation and friction</h1>
<p><b>The rotor can spin because:</b></p>
<ul>
<li><b>
The Casimir force is mostly normal (radial)
</b></li>
<li><b>
It does not strongly oppose tangential motion
</b></li>
</ul>
<p><b>Remaining losses come from:</b></p>
<ul>
<li><b>
Fluid viscosity (important!)
</b></li>
<li><b>
Fluctuation-induced electromagnetic drag (tiny)
</b></li>
</ul>
<p><b>So the dominant dissipation is actually:</b></p>
<blockquote>
<p><b>the fluid you needed to create repulsion</b></p>
</blockquote>
<hr>
<h1>The big tradeoff</h1>
<p><b>This design solves one problem but introduces another:</b></p><h3>Pros</h3><ul>
<li><b>
Stable levitation
</b></li>
<li><b>
No stiction
</b></li>
<li><b>
Passive centering
</b></li>
<li><b>
Potentially reversible (low dissipation)
</b></li>
</ul><h3>Cons</h3><ul>
<li><b>
Requires a liquid medium, not vacuum
</b></li>
<li><b>
Fluid introduces:
</b><ul>
<li><b>
Viscous drag
</b></li>
<li><b>
Thermal noise
</b></li>
<li><b>
Possible chemical complications
</b></li>
</ul>
</li>
</ul><hr><p>





</p><p></p><p></p><h1>Where metamaterials could improve this</h1></div></div><div><p><b>Metamaterials could, in principle:</b></p>
<ul>
<li><b>
Reproduce the “effective medium” condition without a liquid
</b></li>
<li><b>
Create:
</b><ul>
<li><b>
Vacuum-compatible repulsion
</b></li>
<li><b>
Tunable equilibrium gaps
</b></li>
<li><b>
Reduced dissipation
</b></li>
</ul>
</li>
</ul>
<p><b>That’s still mostly experimental, but it’s a major research direction.</b></p>
<hr>
<h1>Stability check (important insight)</h1>
<p><b>This system is stable because:</b></p>
<ul>
<li><b>
The Casimir force is strongly distance-dependent
</b></li>
<li><b>
Repulsion increases faster than any destabilizing drift
</b></li>
</ul>
<p><b>So you get:</b></p><blockquote><p><b>A potential well centered at a finite gap, not at contact</b></p>
</blockquote><p><b>That’s exactly what you want for a bearing.</b></p><hr><h1>Intuition</h1><p><b>The rotor isn’t “floating freely” like in air.</b></p><p><b>It’s more like:</b></p><blockquote>
<p><b>Sitting in a very steep, invisible cushion of quantum pressure that keeps it from touching the walls.</b></p></blockquote><b><font size="4">How far are we?</font><br></b><blockquote><p><b>We already have:</b></p></blockquote><blockquote><ul>
<li><b>
Measurements of Casimir forces in structured geometries
</b></li>
<li><b>
Demonstrations of lateral Casimir forces and torques
</b></li>
<li><b>
Early work on Casimir engineering with metamaterials
</b></li>
</ul><p><b>But we do not yet have:</b></p><p>



</p><ul>
<li><b>
A fully repulsive vacuum Casimir system
</b></li>
<li><b>
A working Casimir bearing</b></li></ul></blockquote><hr><h1>Bottom line</h1><p>








</p><p><b>A repulsive Casimir bearing using a fluid medium:</b></p><ul><li><b>Can genuinely levitate a nanoscale rotor
</b></li>
<li><b>
Provides passive, stable confinement
</b></li>
<li><b>
Allows low-friction rotation
</b></li>
</ul><p><b>But:</b></p><p>

</p><ul>
<li><b>
It trades vacuum operation for fluid damping
</b></li>
<li><b>
And requires very careful material selection</b></li></ul><b><br></b><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><b>=========</b></div></div><div><div class="gmail_default" style=""><font size="4" style="" face="tahoma, sans-serif"><b>John K Clark</b></font></div><br></div></div></div>
</div>