Jesse, No, it's not just semantics. It's my definition of the present moment. You claim the present moment means something else, but then you don't even believe there IS a present moment which seems a little strange! But be that as it may.
The example you give is just standard relativity theory, just a restatement of the twins. As you yourself note it is frame dependent so that doesn't address my question. There are still two frames with two different clock times that DO NOT agree on any shared coordinate time. Your claim that "they are at the SAME point in coordinate time when they meet up again" seems to imply there is some absolute time common to both twins. If this is NOT your claim, and any particular coordinate time (such as the example you give of a clock left behind with the earth bound twin) is used to somehow claim that they are both at the SAME point in spacetime that would equally be true of a clock that traveled with the OTHER twin. If that is your point then you are still faced with the same problem that those 2 coordinate times do not agree. They claim different coordinate times for the same present moment meeting of the twins and you are faced with the exact same problem you were before, of 2 different clock times AND now coordinate times also in the same actual present moment. It seems to be that you are saying that coordinate time is just some arbitrary choice of clock time. If that's not what you are saying then please explain how the coordinate time in your example in your last sentence differs from the simply being the clock time of the stay at home twin, and why O why should the returning twin accept that, rather than his own clock time, as the ACTUAL time of the meeting up at "the same point in spacetime"? See my point? Edgar 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<javascript:> > > 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 "coordinate time" to imagine that such a >>> network has actually been physically constructed. See >>> http://www.upscale.utoronto.ca/GeneralInterest/ >>> Harrison/SpecRel/SpecRel.html#Exploring for 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.pdf for 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 everything-li...@googlegroups.com <javascript:>. >> To post to this group, send email to everyth...@googlegroups.com<javascript:> >> . >> Visit this group at http://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > -- 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.
