<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Enrico</i>
<br />It is shown by the formula you presented that:
ds^2/dtau^2 = c^2
If ds/dtau is the velocity in a geodesic path with respect to proper time, the above equation says, that velocity is constant and equal to c in proper time.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
ds is not a "distance" as normally defined in 3-space, but is rather an "interval" in 4-space. So the ratio of a 4-space interval to a proper time interval is a "velocity" in name only. However, no physical, tangible entity has this type of "velocity".
To illustrate, suppose I define a "hyper-temperature" as the ordinary absolute temperature (in degrees Kelvin) multiplied by c. Then you could plainly state that the ratio of hyper-temperatures to absolute temperatures has the constant velocity c. But other than repeating back your initial definition, what have you learned about the physical world?
The metric interval -ds- is like a hyper-temperature. It is the product of the speed of light and a proper time interval. So formally, it has the dimensions of a distance; and we might call it a "proper distance" representing how far a light beam travels in a proper time interval as seen by an observer experiencing that proper time. But noting that the ratio of "proper distance" to proper time is c reveals nothing new, but merely repeats the original definition of proper distance.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Then, one could infer that in proper time, geodesic motion is non-accelerated and no cause is required.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Could you infer that hyper-temperature is non-accelerated? In either case, we are still just talking about a property of a mathematical definition, not about a property of the real world.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Now, you claim that does not correspond to reality, but what is reality after all?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I have a chapter that addresses that interesting question in my book <i>Dark Matter, Missing Planets and New Comets</i>. But without taking your question so generally, in this context, "reality" simply means the physical world, as opposed to the mathematical world. The difference is that reality conforms to the principles of physics, which can be summed up as simply "no magic, no miracles". The relevant examples here are (1) every effect must have an andecedent, proximate cause; and (2) no creation <i>ex nihilo</i> (especially as applied to momentum).
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Many have claimed that coordinate time is an illusion and the "real" time is proper time.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
"Illusion"?? No one who understands the concept could go that far. It is an idealization, but there is nothing illusory about it. For example, in a GR context, coordinate time is the proper time of an ideal clock at rest with respect to the center of mass and located at infinity. All other clocks can be adjusted to give readings equivalent to that on a coordinate time clock.
Of course, in a Lorentzian relativity (LR) context, clocks in the Earth-centered inertial (ECI) frame that are synchronized with the USNO master clock are reading coordinate time for all practical purposes.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">If that is the case, then your stated "principles of physics" do not hold and are phenomenological interpretations or "noumena" in the spirit of Kant.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Logic alone dictates that there can be no instances of realities in which the principles of physics do not hold. In fact, as I argued in my book, finding a genuine violation of a principle of physics would prove that this apparent reality was really a holodeck simulation of reality created by an advanced intelligence.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I hope you don't mind about me bringing up those points. I'm still skeptical to dismiss completely General Relativists claims. I'm skeptical about the principles of physics and skeptical about everything as a matter of fact. Thank you for hosting this discussion.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
The discussion is a good one. But my time availability will remain limited for another week or so. -|Tom|-
