Jesse, Consider another case:
Consider every observer in the entire universe. Every one of them is always currently in their own local actual time, their present moment. Now consider every last one of them all travel to meet up on earth. Every last one of them continually brings their own actual time with them through the whole trip with no discontinuities and when they meet up they discover that every last one of those local actual times turns out to be the exact SAME actual time, even if every one of their clock times is different. Therefore it is clear that the actual times every one of them was always in was the exact same actual time as all the others were always in, and that demonstrates that the actual times of every observer in the universe is the exact same actual time... Thus there must be a common universal present moment. Edgar On Saturday, February 1, 2014 7:23:19 PM UTC-5, jessem wrote: > > > > On Sat, Feb 1, 2014 at 6:46 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > Jesse, > > You already told us that the twins ARE at the same point in spacetime when > they meet up again. > > Is that not an OBJECTIVE fact? Do we not actually KNOW that? The twins > most certainly DO KNOW it because they can shake hands and look at each > other's clocks at the same time. How can you claim it if it is not a fact > and knowable? Label or not, it is a knowable fact that both twins agree on. > > > Uh, I never said it wasn't an objective knowable fact that they meet and > compare ages at a single point in spacetime, in fact I very clearly said > "there is an objective truth about whether two events coincide at the same > point in spacetime". There is no objective fact about what specific time > coordinate is associated with a given point in spacetime, because that > depends entirely on arbitrary what event we choose to label as t=0 and how > we define simultaneity. > > > > If we agree then that the twins ARE at the SAME point of spacetime when > they meet again, then they must be at the same point in TIME as well as in > space. > > > With respect to any particular coordinate system for labeling "time", > sure, that's true. Similarly if two cars meet at the same point in space, > they must be at the same y-coordinate as well as the same x-coordiante, > regardless of how you choose to define your x and y axes. Are you going to > address the 2D geometric analogy as I asked you to in my next-to-last post > (the one before the one you are responding to here)? You do have a habit of > not addressing questions and arguments that I put to you, even when I > repeatedly ask you politely to address them. Whether you choose to address > it or not, I will continue to compare all your statements to analogous > statements one could make about 2D spatial geometry, in order to > demonstrate to anyone reading along that the resulting conclusions would > make no sense despite the fact that the argument appears to be precisely > analogous. > > > > I call that same point in time what everyone else does, the present moment. > > 1. This clearly demonstrates there is an ACTUAL "same point of TIME" > independent of clock time. > > > I don't know what you mean by "actual". Time is a coordinate, the phrase > "same point in time" has no more coordinate-independent meaning than "same > y-coordinate". Only statements about spacetime geometry can be meaningful > without any notion of a coordinate system--separating them into "space" and > "time" is an artificial coordinate-dependent notion, just like separating > 2D space into the x-axis and the y-axis (though in spacetime it is > objectively meaningful to distinguish particular *paths* through spacetime > depending on whether they are "timelike", "spacelike" or "lightlike"). > > > > 2. This establishes an actual local same time independent of clock time > but not a universal actual same time. > 2. But the proof that that actual same point in time is common and > universal is simple: > > a. The twins are at the same actual point in time both before and after > the trip. > > > The two cars in my example, driving along different roads between two > points A and B where the two roads cross (analogous to the twins who have > different paths through spacetime that "cross" at the event of the > departure and the event of the reunion), are likewise both at the same > y-coordinate at A and at B (regardless of what specific coordinate system > we choose). > > > b. The twins are always in their OWN local present moment continuously > during the trip. > > > The cars are always positioned at their OWN local y-coordinate > continuously during the trip (again regardless of what coordinate system we > choose). > > > > c. Therefore during the trip there must always be a one to one > correspondence between those actual present moments even though the clock > times are not in synch. Because they both begin and end in that present > moment and never leave it during the trip. > > > Do you claim this correspondence would be independent of the choice of > coordinate system? If so the claim is a total non sequitur--WHY should > there be such a "correspondence"? You just assert this without argument, > certainly it doesn't follow from any of the previous premises. Do you think > the premises I listed above concerning the cars lead to the conclusion > "therefore during the trip there must always be a one to one correspondence > between those local y-coordinates even though their odometers are not in > sync", and that this correspondence is the same regardless of the choice of > x-y coordinate system? If not, why should it be any different if we replace > y-coordinate in space with t-coordinate in spacetime, odometer readings at > a given point on a road with clock readings at a given point along a path > through spacetime, etc.? Again, you need to explain what the relevant > difference is or you don't have a leg to stand on. > > > Jesse > > > > > On Saturday, February 1, 2014 5:18:38 PM UTC-5, jessem wrote: > > > > > On Sat, Feb 1, 2014 at 4:28 PM, Edgar L. Owen <edga...@att.net> wrote: > > Jesse, > > PS: If coordinate time is just saying that when the twins meet up again > they are actually at the SAME point in spacetime, but we don't know (can't > agree) what clock time that corresponds to then I agree completely. > > > There is no objective fact to "know" or "not know", it's just a matter of > labeling, just like with x and y coordinates used to label points on a 2D > plane. > > > > > That is exactly what my theory says and what I've always said. > > I just call that same point in spacetime the present moment because it's > standard nomenclature, and it's consistent with everyone's direct > experiential observation. > > > But don't you go beyond that and say that there is an objective truth > about whether events that *don't* happen at the same point in > spacetime--like an event happening to me here in Providence and an event > happening to someone else in Paris--happen at the "same time" or not? Isn't > the "present moment" supposed to say that a bunch of events spread > throughout space are all happening "now"? If so, then as I said there is no > logical justification for going from "there is an objective truth about > whether two events coincide at the same point in spacetime" to "there is an > objective present, such that there is an objective truth about whether two > events happened at the same time even if they didn't coincide in spacetime". > > Jesse > > > > > On Saturday, February 1, 2014 2:45:17 PM UTC-5, jessem wrote: > > > > On Sat, Feb 1, 2014 at 1:58 PM, Edgar L. Owen <edga...@att.net> wrote: > > Jesse, > > Not correct. My present moment does NOT say "that there is an objective > common "present moment" for events that are *not* at the same point in > spaceTIME (my emphasis)." > > My theory says that there is a common universal present moment shared by > all points in SPACE, not spaceTIME. Because clocktimes can obviously have > different t values within that present moment. > > > > That's just semantics, I was using the standard terminology of relativity, > if you want to change the meaning of terms you're free to translate my > statement into your own terminology, but I don't think I got the *meaning* > of your theory wrong. When I said "not at the same point in spacetime" I > meant "events that someone using the labeling system of mainstream physics > would say occur at different points in spacetime", which in terms of your > own theory could cover both events at different p-times as well as events > at the same p-time but different points in space. You believe that for any > pair of events that a physicist says happen at different points in > spacetime, there is an objective truth about whether they happened at the > "same time, different points in space" or "different times". The set of all > events that are happening at the same p-time as what I am experiencing here > and now would be the "objective common present moment", and these are > events a physicist would label as having different points in spacetime, > regardless of how you would label them. So that's what I meant when I said > that you believed there was "an objective common present moment for events > that are not at the same point in spacetime". > > > > > Second, thanks for the long explication following, which I more or less > agree with. > > But my question remains: If coordinate time is just an alternate > coordinate system then for the twins to be at the SAME place in that > coordinate system there must be some actual t-value describing that point > that both twins agree upon. What is that t value, and how does it relate to > the t values of the clock times of the twins' two different clocks? > > > > "Actual t value" in a specific coordinate system, or in some objective > coordinate-independent sense? If the former then sure, within the context > of any given inertial coordinate system there is a specific t-value where > they reunite. You asked in another comment I hadn't responded to yet for an > example, so I'll give you one here. Suppose we have an inertial coordinate > system in which the Earth is at rest (ignoring the fact that it orbits and > doesn't really move inertially for the sake of argument), and in this > system it's located at position x=0 light-years, and there is another > distant planet which I'll call Planet X which is 24 light years away from > Earth, and at rest in Earth's frame so it's always located at x=24 light > years in this frame (assume they both lie along the x-axis so the other > spatial dimensions can be ignored). At t=0 years in this system, two twins, > Alan and Bob, are born on Earth, and each one is given a clock to mark > their age (proper time). Then Bob is immediately placed on a ship which > accelerates in a negligible time to 0.8c in the Earth frame, after which it > moves at constant velocity towards Planet X. Since Planet X is 24 > light-years away it arrives there after 24/0.8 = 30 years, at time t=30 in > the Earth frame. Then the ship accelerates in a negligible time so it is > moving at 0.6c back towards Earth. Then the return leg will take a time of > 24/0.6 = 40 years in the Earth frame. So when Bob returns to Earth, a total > of 30+40 years have elapsed in the Earth frame, so they reunite at > coordinate time t=70 in this frame (and position x=0, since Earth is at > rest at this position). > > Since Alan has been at rest on Earth the whole time, his clock has been > keeping pace with coordinate time in this frame (or with the actual > physical clocks at rest in this frame which can be used to define > coordinate time, as I mentioned in my last comment), so he will be 70 years > old. To find Bob's age we must use the time dilation equation, which says > that if a clock is moving at speed v relative to a given inertial frame, in > a time interval of T in that frame it will only elapse a time of T*sqrt(1 - > v^2/c^2). So if the first leg of the journey from Earth to Planet X lasted > a time of T=30 years in the Earth frame, and Bob was traveling at 0.8c, he > will have aged by 30*sqrt(1 - 0.8^2) = 18 years between leaving Earth and > reaching Planet X. Then since the second leg from Planet X back to Earth > lasted a time of T=40 years in the Earth frame, and Bob was traveling at > 0.6c, during this leg his age increased by 40*sqrt(1 - 0.6^2) = 32 years. > So, when Bob arrives back at Earth his age is 18+32=50 years, twenty years > younger than Alan. > > If we transform this whole scenario into a different frame, the time > coordinates at which Bob arrives at Planet X and arrives back at Earth will > be different, and these frames won't agree that Alan was 30 years old "at > the same time" that Bob was arriving at Planet X. But all other frames will > agree on local matters like the fact that Bob was 18 years old when he > arrived at Planet X, and that when Bob arrived back at Earth he was 50 > years old while Alan was 70 years old. They will also all assign the same > time coordinate to the event of Alan turning 70 and Bob turning 50, > although this time coordinate won't be t=70 as it was in the Earth frame. > If you like I could analyze this scenario using a different inertial frame > and show that these things are true, or you could just take my word for it. > > > > > And of course there simply is NO clock that displays that coordinate time > t value is there? > > > Did you miss the last two paragraphs of my previous post where I addressed > this? (the paragraph that started with "All coordinate systems are defined > in terms of local readings on clocks and rulers spread throughout space"). > As I said there, coordinate times are always ultimately defined in terms of > local readings on a hypothetical lattice of clocks filling space (connected > by rulers which can be used to define coordinate positions), as illustrated > at http://www.upscale.utoronto.ca/GeneralInterest/Harrison/ > SpecRel/SpecRel.html#Exploring -- you could in principle build such a > network, though in practice we can use our knowledge of physics to figure > out what the local readings for each event *would* be without going to the > trouble of constructing all these coordinate clocks. But if you did build > such a network, the coordinate time would just be the reading on the > coordinate clock that's right next to the two twins when they reunite > (coinciding at the same point in spacetime again). > > Jesse > > > > > On Saturday, February 1, 2014 1:21:41 PM UTC-5, jessem wrote: > > > > > On Sat, Feb 1, 2014 at 12:31 PM, Edgar L. Owen <edga...@att.net> 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 &quo > > ... -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
