<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif">On Mon, Apr 25, 2016 Anders Sandberg </span><span dir="ltr" style="font-family:arial,sans-serif"><<a href="mailto:anders@aleph.se" target="_blank">anders@aleph.se</a>></span><span style="font-family:arial,sans-serif"> wrote:</span><br></div><div class="gmail_extra"><div class="gmail_quote">
<div bgcolor="#FFFFFF" text="#000000"><span><br></span></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><span><font face="arial, helvetica, sans-serif" style="font-size:large"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">>> </div></font><span style="font-size:large">If
"real" means something that's invariant then curved
spacetime is not real because it looks different for
different observers.</span></span></blockquote><span>
<br></span>
<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Nope. I was using curvature here to denote the metric tensor (or, if
you want to go deep, the Riemann tensor). Tensor equations are
observer-invariant.</div></blockquote><div><br></div><div><div class="gmail_default"><font face="arial, helvetica, sans-serif"></font><font size="4">Yes, tensors measure how far a curve is from a geodesic for a given manifold and all would agree on that, but they won't agree on what manifold they want to use, many different ones and their associated tensors can correctly describe how things move. Everyone will agree on what the minimum length of a spacetime interval between 2 points will be but lots of different manifolds are consistent with that. Equations are just descriptions of physical reality and a gravitational force in flat spacetime is equivalent to curved spacetime and no gravitational force, so just use the manifold that's most convenient. </font></div></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Geodesic curves for one
observer are geodesics for all others.</blockquote><div><br></div><div><font size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">A </div>geodesic<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> is the shortest path between 2 points and all observers will agree about that, and any object that is not accelerating will follow a geodesic through 4D spacetime, and </div><span style="font-family:arial,helvetica,sans-serif">a straight line is not the shortest path between 2 points in curved spacetime.<div class="gmail_default" style="display:inline"> So </div></span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">if you're</div><span style="font-family:arial,helvetica,sans-serif"> in a closed box and feel a 1g acceleration <div class="gmail_default" style="display:inline">pushing your feet to the floor of the box then </div>you know that you can't be on a </span>Geodesic curve<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">; but how can you know if you're in a rocket in intergalactic space in a flat spacetime manifold following a curved timeline or if you're in a curved spacetime manifold sitting on the surface of the earth following a straight timeline? Both will produce the same correct description of the way things move so just use the one you find easiest to calculate. </div></font><br></div></div><div class="gmail_quote"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><br></div></div><div class="gmail_quote"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">Well OK, you really could tell the difference because the guy on the surface of the earth would feel tidal forces and the guy in the rocket accelerating at 1g in deep space would not, but by making the man and the box arbitrarily smaller the tidal force will be arbitrarily smaller.</font></div></div><div class="gmail_quote"><br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>So while you might measure using a different coordinate system from me and get different numbers, there is a simple rescaling between our results.</div></blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">I agree and that rescaling factor is gravity</font></div><font size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">, although</div> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">I've never heard </div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"></div>tensor equations<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> being referred to as simple before. </div></font></div></div><div class="gmail_quote"><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>How observers see things is irrelevant:</div></blockquote><div><br></div><div><font size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">Not to the observers it isn't.</div> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></font></div><div><font size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><br></div></font></div><div><font size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> John K Clark</div></font></div><div><font size="4"><br></font></div><div><br></div><div><br></div></div></div></div>