<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;background-color:transparent">On Sat, Oct 10, 2026 at 6:24 PM Jason Resch <<a href="mailto:jasonresch@gmail.com">jasonresch@gmail.com</a>> wrote:</span></div></div><div class="gmail_quote gmail_quote_container"><font face="tahoma, sans-serif" size="4"><b><br></b></font><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div><span class="gmail_default"><font size="4"><font face="arial, helvetica, sans-serif" style="font-weight:bold"></font><font face="tahoma, sans-serif"><b>>> In </b></font></font></span><b><font size="4" face="tahoma, sans-serif">Freeman Dyson<span class="gmail_default">'s</span> paper <a href="https://suli.pppl.gov/2019/course/RevModPhys.51.447.pdf" rel="noreferrer" target="_blank">Time Without End</a><span class="gmail_default"> he admits </span></font><font size="4" face="tahoma, sans-serif"><span style="background-color:transparent">that digital memory is limited by the number of particles<span class="gmail_default"> </span>available to construct it</span><span style="background-color:transparent"><span class="gmail_default">, but he proposes that </span></span><span style="background-color:transparent">an expanding universe might permit analog memory whose capacity grows without bound, even if the number of physical components remains fixed.<span class="gmail_default"> For that to work it would certainly help if space was continuous, but even if it is measuring things with unlimited precision would be, to say the least, challenging. </span></span></font></b></div></div></div></blockquote><div><br></div><div><font size="4" face="georgia, serif"><i><span class="gmail_default" style="font-family:arial,helvetica,sans-serif">> </span>For more memory, you don't need more particles, more volume with finite particles is enough. But more volume can runs into problems when space itself is expanding.</i></font></div></div></div></blockquote><div><br></div><font size="4" face="tahoma, sans-serif"><b>If space is continuous then the number of mathematically possible positional relationships between two particles is infinite, but the number of physically distinguishable positions might not be. That would depend on some laws of physics that we don't know very well, like the rate of black hole evaporation when they become very small. And as you use photons of increasingly small wavelength and increasingly larger energy to distinguish between a tiny change in distance<span class="gmail_default" style=""> </span>between two particles, how do you keep <span class="gmail_default" style="font-family:arial,helvetica,sans-serif">a</span> photon from collapsing into a black hole? </b></font></div><div class="gmail_quote gmail_quote_container"><font size="4" face="tahoma, sans-serif"><b><br></b></font></div><div class="gmail_quote gmail_quote_container"><font size="4" face="tahoma, sans-serif"><b>Maybe you could get around that problem by encoding information in the quantum phase between two particles instead of finding<span class="gmail_default" style=""> </span>the distance between them with ever increasing precision. If things are continuous then the relative quantum phase between two particles can take any value between 0 and 2π, you wouldn't have the black hole problem when you tried to become more precise in your measurements, but there would probably be other difficulties.   </b></font><div><br></div><div><font size="4" face="tahoma, sans-serif"><b>If space is not continuous but<span class="gmail_default" style=""> is still </span>increasing in volume because the number<span class="gmail_default" style=""></span><font style="background-color:transparent"> of <span class="gmail_default" style="">c</span>discrete cells of <span class="gmail_default">a </span>fixed size is increasing<span class="gmail_default" style=""> </span></font><span style="background-color:transparent"><span class="gmail_default" style="">then </span></span><span style="background-color:transparent">more </span><span style="background-color:transparent">possible </span><span style="background-color:transparent">locations<span class="gmail_default" style=""> a particle could be in would also increase allowing you to</span></span><span style="background-color:transparent"> </span><span style="background-color:transparent">encode </span><span style="background-color:transparent">more </span><span style="background-color:transparent">bits<span class="gmail_default" style="">. </span></span><span style="background-color:transparent">This </span><span style="background-color:transparent">does </span><span style="background-color:transparent">not </span><span style="background-color:transparent">require </span><span style="background-color:transparent">continuous </span><span style="background-color:transparent">space </span><span style="background-color:transparent">or </span><span style="background-color:transparent">an </span><span style="background-color:transparent">increasing </span><span style="background-color:transparent">number </span><span style="background-color:transparent">of </span><span style="background-color:transparent">particles<span class="gmail_default" style="">, but t</span></span><span style="background-color:transparent">he </span><span style="background-color:transparent">computer </span><span style="background-color:transparent">must </span><span style="background-color:transparent">be </span><span style="background-color:transparent">able </span><span style="background-color:transparent">to </span><span style="background-color:transparent">read </span><span style="background-color:transparent">the </span><span style="background-color:transparent">stored </span><span style="background-color:transparent">information<span class="gmail_default" style="font-family:arial,helvetica,sans-serif">,</span><span class="gmail_default" style=""> and as  </span></span><span style="background-color:transparent">particles </span><span style="background-color:transparent">become <span class="gmail_default" style="">more</span></span><span style="background-color:transparent"> </span><span style="background-color:transparent">distant information retrieval would become slower and more difficult.<span class="gmail_default" style=""> </span></span><span style="background-color:transparent"> </span></b></font></div><div><font size="4" face="tahoma, sans-serif"><b><span style="background-color:transparent"><br></span></b></font></div><div><font size="4" face="tahoma, sans-serif"><b><span style="background-color:transparent"><span class="gmail_default" style="">John K Clark</span><br></span></b></font></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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