On Sat, Feb 1, 2014 at 12:31 PM, Edgar L. Owen <[email protected]> wrote:
> Jesse, > > Yes, that "being at the same point in spacetime" is CALLED the present > moment that I'm talking about. > But your present moment goes beyond that and says that there is an objective common "present moment" for events that are *not* at the same point in spacetime. My point is that you have no real argument for generalizing "there is an objective truth about whether events coincide at the same point in spacetime" to "there is an objective truth about whether events occur at the same time, event if they are at different points in spacetime"--the first does not in any way imply the second. > > You are probably repeating the claim that 'coordinate time' falsifies > p-time. It doesn't. Coordinate time is an attempt to explain the obvious > problems with clock time not actually explaining a common present moment > that obviously exists. This is done by coordinate time saying OK we have to > account for the twins being at the same point in spacetime when they > compare clocks so let's just invent a coordinate system that acts as if > clock time doesn't have any effect on something we will call coordinate > time. > No, coordinate time is not meant to "explain" how events can coincide in spacetime--rather the basic starting assumption is that spacetime has an objective geometry, different coordinate systems are just ways of labeling that geometry. Think of a globe, with outlines of continents, rivers etc. on it. It's certainly true that you can *describe* the shape of a river or coastline or whatever using some coordinate system defined on the globe (latitude and longitude for example), but the actual geometry of the shapes--including the notion of the "length" along a particular path between two points (like the length along a river between between two branching points)--is assumed to be more fundamental, prior to any choice of coordinate system. Physicists think of spacetime like that--it has an objective geometry, defined in terms of the lengths of any possible path (whether "timelike", "spacelike" or "lightlike"). Coordinate systems are just ways of labeling this preexisting geometry, and all coordinate systems must agree on these more basic "geometric" facts (like the "proper time" along a timelike path between two events). In general relativity the basic idea of the "metric" is to translate between coordinate intervals and "real" geometric quantities like proper time--the equations of the metric will look different when expressed in different coordinate systems, but in each coordinate system you can integrate the metric to calculate proper time along any timelike path, and you'll get the same answer in each case. Suppose instead of a globe we are talking about geometry on a flat plane, which has some roads on it. The geometry of the shape of the roads, the distance along each road between any two points, is again taken as fundamental, but here it would be natural to define a Cartesian coordinate system on the plane to label points, with an x and a y axis. But we have a choice of how to orient these axes--depending on the angle of the axes relative to the geometric features like roads, we may get different answers to questions like "do these two points along the road have the same y-coordinate or different y coordinates"? This is akin to how in flat spacetime, we can choose different inertial coordinate systems which give different answers to questions like "do these two events have the same t-coordinate or different t coordinates?" But clearly for roads on a plane, there is an objective geometric truth about questions like "do these two roads ever meet at the same point on the plane?" or "if these two roads cross at points A and B, what is the length along each road between A and B?" The answers to these questions don't depend on your choice of cartesian coordinate system. Similarly there is an objective answer, in terms of the geometry of paths through spacetime, to questions like "do these two worldlines ever meet at the same point in spacetime?" or "if these two worldlines cross at events A and B, what is the proper time elapsed on each worldline between A and B"? In contrast, your argument seems to be that in order to make sense of questions like "how much has each twin aged between the point where they departed and the point where they reunited", we need an "objective" t-coordinate which gives a single correct answer to whether two events happened at the same t-coordinate or different t-coordinates. But in terms of the analogy, this would be like if someone claimed there was no way to talk about the distance along different roads between places where they cross without having an "objective" cartesian coordinate system which gives a single correct answer to whether two points in space share the same y-coordinate. Presumably you understand why this is silly in the case of 2D geometry, so why isn't it just as silly when it comes to the geometry of paths in 4D spacetime? Can you name any relevant difference between the two cases that would make an objective coordinate system necessary in one case but not the other? > > Coordinate time is half way to p-time but hasn't incorporated the whole > insight... It basically says let's pretend clock time doesn't really happen > so the twins can end up at the SAME point of spacetime because it's obvious > they actually did. > All coordinate systems are defined in terms of local readings on clocks and rulers spread throughout space--in most cases these coordinate clocks and rulers are imaginary, because we can use what's known about physics to deduce what they *would* read in the neighborhood of any event, but it may clarify your understanding of "coordinate time" to imagine that such a network has actually been physically constructed. See http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html#Exploringfor a diagram of what the network would look like to define position and time in an inertial coordinate system, and section 2.1 on p.8 of http://physics.mq.edu.au/~jcresser/Phys378/LectureNotes/VectorsTensorsSR.pdffor a diagram of how this can be extended to arbitrary non-rectilinear coordinate systems. So with that in mind, a statement like "the event of twin A turning 30 and the event of twin B turning 40 both happened at the same spacetime coordinates in my frame, x=5,y=10,z=0,t=10" just means that when twin A turned 30 and Twin B turned 40, they were both next to the same coordinate clock which read a time of 10 when those events happened next to it, and that particular clock the one that's attached to the x=5 marking of an x-axis ruler, the y=10 marking of a y-axis ruler, and the z=0 marking of a z-axis ruler. So it's really just a statement about 3 different clock readings coinciding at the same point in spacetime, rather than just the original 2--which means the notion of "coinciding at the same point in spacetime" has to be more basic than "happening at the same coordinate time", and indeed once you grant this basic geometric notion, you can understand "the event of twin A turning 30 coincided at the same point in spacetime with the event of twin B turning 40" without any need to refer to the fact that both events *also* coincided with the event of that coordinate clock reading 10. Spacetime geometry is the fundamental thing, not coordinate systems. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
