Relativity and the question of age

[ghwellsjr]

Now I'm going to show the same scenario except that the second red ball will be thrown at a slower speed, 0.479c:

Count the dots again and you will see that the black ball ages by 27 nsecs while the red ball ages by 28 nsecs.

Next, the red ball is thrown at 0.8c:

The black ball ages by 17 nsecs and the red ball by 15 nsec.

Finally, the red ball is thrown at 0.923c:

The black ball ages by 16 nsecs and the red ball by 12 nsecs.

Note also that the order in which the balls hit you is different than the order in which they were thrown.

Also note in these three cases that the time delta in which the balls hit you is not the same as the time delta in which they were thrown.

So now here is your opportunity to explain how "the causal structure", which is clearly apparent in all these diagrams, "results in differential aging".

 

[nitsuj]

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.

I was going to retort to your previous reply, but you're changing the post around to make a point. I'm not gunna "play".

No George, it's one minute between ball throwing. the spacetime interval is crucial...

My post does explain differential aging from a causal perspective.

 

[nitsuj]

It could be interesting to examine the following:

Both a Galilean universe and an SR universe are causal.

Show me causal structure in a gallian universe. We will end with infinite speed...does causal structure make sense when we can go infinitely fast? What does infinite fast mean?Geometry in a Galilean universe excludes time as a component (of the geometry). It even hand waved away the speed of gravity saying it's instant. Yea that makes physical sense

When time is a component of geometry, causal structure leads to differential aging & an invariant speed.

a Galilean universe is full of logic "holes", SR is Fort Knox lol

 

[ghwellsjr]

I was going to retort to your previous reply, but you're changing the post around to make a point. I'm not gunna "play".

I didn't change anything that you specified. And I'm trying to help you make your point.

No George, it's one minute between ball throwing. the spacetime interval is crucial...

Then will you agree that my first diagram in post #35 is similar enough to your scenario that you can make your point with it?

And I thought you said you "cannot read math". How do you determine the spacetime interval in your scenario without math? What is its value and what are the two events that you are calculating it between? And if it's so crucial, why didn't you mention it in your very long post?

My post does explain differential aging from a causal perspective.

Where do you mention any differential aging?

 

[nitsuj]

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.


After that, I invite you to explain how "the causal structure results in differential aging", ok?

The order the balls hit me as I see it, will be the same order every observer sees the balls hit me. No speed can have it such that ball 5 hits before ball 4. For your charting, this is very clear. If there is no separation between me and the ball there is no way to separate it so ball 5 can "get in there" and hit me before ball 4.

This is NOT about the order they seen traveling, it's the order they hit me The order they leave the Single ball throwers hands will also be invariant, what is not invariant is how they are seen traversing spacetime, which is to your point.

I have explained it, you "distort" the meaning, perhaps unintentionally, but none the less spoils any attempt to discuss it

 

[ghwellsjr]

The order the balls hit me as I see it, will be the same order every observer sees the balls hit me.

You are spending a lot of time "making a point" that everyone already agrees with. Yes, whatever order the balls actually hit you is the order you see them hit you and the order that everyone else sees them hit you. I made no comment about this issue. I only showed one frame, your rest frame. I was not and am not concerned with what other frames or observers might see. This issue has absolutely nothing to do with differential aging. If you would show me the two objects/clocks/observers that you are considering to have aged differently, then I can show you how all frames and observers will agree on their differential aging if you want. But you haven't made any comment about this even though I keep asking you to do so.

No speed can have it such that ball 5 hits before ball 4.

I agree, no speed that is applied exactly to every ball will result in them hitting you in a different order. I already stated this fact.

For your charting, this is very clear. If there is no separation between me and the ball there is no way to separate it so ball 5 can "get in there" and hit me before ball 4.

This is NOT about the order they seen traveling, it's the order they hit me The order they leave the Single ball throwers hands will also be invariant, what is not invariant is how they are seen traversing spacetime, which is to your point.

No, that's not my point. I didn't show any scenario transformed between two different frames. All my diagrams were for the same frame, just different scenarios.

I have explained it, you "distort" the meaning, perhaps unintentionally, but none the less spoils any attempt to discuss it

You aren't discussing the issue you claim to be discussing. That's the problem. You think there is some differential aging going on in your scenario but there isn't. If you think there is, please point it out.

 

[Nugatory]

Justin, back in #29 you say

I have to read what world lines are. I imagine it's the same as saying we each have our own proper time. In other words I don't know the strict definition/concept of worldlines well enough to include in a retort/response.

It's really hard to communicate effectively about causality and time without this understanding. Watching you try makes me feel as if I'm watching someone using Roman numerals to explain long division - the representation is getting in the way.

 

[nitsuj]

Justin, back in #29 you sayIt's really hard to communicate effectively about causality and time without this understanding. Watching you try makes me feel as if I'm watching someone using Roman numerals to explain long division - the representation is getting in the way.

I appreciate that with respect to disusing spacetime between objects. Causality is about the objects themselves and observations of them.

I don't need to draw diagrams representing spacetime, for this point. George says we all already agree on causality.

All that I need to do is assume a "global/local/whatever" causality, which isn't at all about spacetime. And either is differential aging, it's about the objects themselves and how physical occurrences "play out" and how we all agree on the order. If it's conceptually necessary, then include the c postulate (speed limit).

 

[WannabeNewton]

Well for starters, causality is all about causal curves so it involves exactly what Nugatory mentioned, and George's point is that differential aging simply deals with the different integrated proper times along two different space-time "trajectories" that have the same initial and terminal points (I put trajectories in quotes because technically nothing moves in space-time so it's not like we're tracing out a curve following the path of a particle in the Newtonian sense of a trajectory) and what you are saying is not related; I'm not sure you understand what causal structure is (and by the way, Galilean space-time is a known construction so what you said in post #38 is incorrect).

 

[nitsuj]

If you think there is, please point it out.

It is there. I'll try to think of a better way to structure what I wrote so the logic is more apparent.

Like I PM'd you, this is really just making a clear distinction between geometry & physical occurrence.

My perspective is you keep discussing spacetime and making diagrams, which isn't at all what this is about. It's about Physical occurrence ordering being invariant as observed happening to a specific object, and you already said you agree with that. We still don't need diagrams to make the "next step" of how a consequence of this is differential aging.

 

[nitsuj]

Well for starters, causality is all about causal curves

(and by the way, Galilean space-time is a known construction so what you said in post #38 is incorrect).

Yea, I can't make anything of that.

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

 

[WannabeNewton]

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

At a basic level:
http://ls.poly.edu/~jbain/spacetime/lectures/11.Spacetime.pdf
http://faculty.arts.ubc.ca/ssavitt/Courses/Phil462B/Galilean%20Spacetime.pdf

At a more advanced level: http://arxiv.org/pdf/gr-qc/0211030v2.pdf

 

[PAllen]

Show me causal structure in a gallian universe. We will end with infinite speed...does causal structure make sense when we can go infinitely fast? What does infinite fast mean?Geometry in a Galilean universe excludes time as a component (of the geometry). It even hand waved away the speed of gravity saying it's instant. Yea that makes physical sense

When time is a component of geometry, causal structure leads to differential aging & an invariant speed.

a Galilean universe is full of logic "holes", SR is Fort Knox lol

Completely wrong on all counts. Galilean relativity is simply the c->∞ limit of SR. It is true that there is no (non-degenerate) spacetime metric, but that is the point - space and time are separable. The causal structure is stronger than SR because all pairs events have invariant (under Galilean transforms) causal order. Thus, both theories have causal structure, but not the same one. Obviously SR matches reality, but that is not relevant.

In case you didn't notice, I was wondering whether there is some validity to what you are arguing: Is the specific causal structure of SR versus Galilean relativity (alone) sufficient to require differential aging? I think the answer is probably yes, with maybe a few technical assumptions required, but I haven't put together a rigorous argument for this.

 

[ghwellsjr]

You aren't discussing the issue you claim to be discussing. That's the problem. You think there is some differential aging going on in your scenario but there isn't. If you think there is, please point it out. [Quote expanded to include context.]

It is there. I'll try to think of a better way to structure what I wrote so the logic is more apparent.

It's not a matter of logic, it's simply a matter of stating which two objects/observers/clocks are the ones engaged in differential aging. I already pointed out what you could have answered:

Consider any two of the ten balls. They start out colocated with the thrower. One of them leaves and goes (is thrown) to you. Some time later, the second ball leaves (is thrown) and goes to you at which point those two balls are again colocated. Now we can calculate (if we know their speeds) the amount of aging each ball achieved from the time they were together, then separated, then rejoined.

But you rejected my suggestion, insisting that somewhere else in your scenario is another example of differential aging. I'm just asking where. You don't have to explain how we determine their respective aging, just who (or what) they are.

Like I PM'd you, this is really just making a clear distinction between geometry & physical occurrence.

If you are saying that you have not yet gotten to the differential aging part, then I agree. However, you're going to have to start all over again with a different scenario if you want to demonstrate differential aging in your discussion.

My perspective is you keep discussing spacetime and making diagrams, which isn't at all what this is about.

I'm not the only one discussing spacetime (as if there's something wrong with that):

No George, it's one minute between ball throwing. the spacetime interval is crucial...

And you ignored my request for you to tell me what the value of the spacetime interval is and what two events it applies to. This is a simple request and you shouldn't have a problem answering this question.

If you don't like my diagrams, then just ignore them, I thought they would help you in your explanation.

It's about Physical occurrence ordering being invariant as observed happening to a specific object, and you already said you agree with that. We still don't need diagrams to make the "next step" of how a consequence of this is differential aging.

Ok, I will wait for you to present the "next step". I had no idea your long post was not intended to be an explanation of how "causal structure results in differential aging".

 

[nitsuj]

Completely wrong on all counts. Galilean relativity is simply the c->∞ limit of SR. It is true that there is no (non-degenerate) spacetime metric, but that is the point - space and time are separable. The causal structure is stronger than SR because all pairs events have invariant (under Galilean transforms) causal order. Thus, both theories have causal structure, but not the same one. Obviously SR matches reality, but that is not relevant.

In case you didn't notice, I was wondering whether there is some validity to what you are arguing: Is the specific causal structure of SR versus Galilean relativity (alone) sufficient to require differential aging? I think the answer is probably yes, with maybe a few technical assumptions required, but I haven't put together a rigorous argument for this.

The reality point I suppose could be a matter of opinion. The causal structure is NOT stronger...because it doesn't even exist. It's non sense to compare impossible things to reality and pose it as a point.

Again show me causal structure in that "metric" of infinite speed. I'll just go faster.

In case you didn't notice, you said I was wrong on all counts, that contrasts your agreement with how I described the "metric" as not including time. & the lack of a speed limit. Which are the only two points I mentioned in retort.

This is to your point of SR "breaking" causal connection (spacelike), it has too less the non sense of infinite speed.

If you really feel there is a true & meaningful "causal" structure in Galilean geometry you won't ever agree with what I am saying, if you laugh at that proposed structure as physical non sense then you may see where I am "coming from" with my perspective.

And I hope I don't come across as arguing, if it does I don't want to continue...it's not at all how I wish to "present" a perspective.

 

[nitsuj]

And you ignored my request for you to tell me what the value of the spacetime interval is and what two events it applies to. This is a simple request and you shouldn't have a problem answering this question.

If you don't like my diagrams, then just ignore them, I thought they would help you in your explanation.


Ok, I will wait for you to present the "next step". I had no idea your long post was not intended to be an explanation of how "causal structure results in differential aging".

The interval is important because of it's invariance.

I am at work now, and as much as I want too, I got to refrain from "working" at this lol

I'll reply this E.S.T. evening.

A side note your diagrams are awesome! Just for this it's not really relevant to illustrate spacetime. Just to pose an axiom (and maybe a postulate)

 

[nitsuj]

At a basic level:
http://ls.poly.edu/~jbain/spacetime/lectures/11.Spacetime.pdf
http://faculty.arts.ubc.ca/ssavitt/Courses/Phil462B/Galilean%20Spacetime.pdf

At a more advanced level: http://arxiv.org/pdf/gr-qc/0211030v2.pdf

The temporal & spatial dimensions share the same sign in Galilean Newton whatever, reality is they need to be opposite to be representative of the actual structure of spacetime.

 

[PAllen]

The reality point I suppose could be a matter of opinion. The causal structure is NOT stronger...because it doesn't even exist. It's non sense to compare impossible things to reality and pose it as a point.

Causal structure simply means you can specify between some(all) events which one could have influenced the other (causal connection, with direction). In Newtonian physics, for every pair of events, there is the ability to state which one is before the other and could have causally influenced the other. For SR, there is a different causal structure: for some pairs of events you can say one could influence the other; for others you can say neither could influence the other. Newtonian physics time orders all events; SR contains events that cannot be time ordered.

That Newtonian physics: a) has a causal structure b) it is stronger than SR
are mathematical facts. That Newtonian physics does not match experiments is an observational fact. There may someday be an experiment that falsifies SR. That will not change the causal structure of SR or of Newtonian physics. It may require that the causal structure of a successor theory to SR is different from SR.

Do you understand that that one may speak of the characteristics of a theory, irrespective of whether that theory is falsified by experiment?

Again show me causal structure in that "metric" of infinite speed. I'll just go faster.

I have, multiple times. Causal structure has nothing to do with metric (directly). It is a more primitive structure that can be imposed on a manifold. Given a causal structure, you may or may not be able to introduce a certain type of metric consistent with that structure. For Newtonian causal structure, you cannot introduce a non-degenerate 4-metric (you can introduce a Euclidean 3-metric on each 3-space parametrized by the total causal order) . So what? For SR causal structure, you cannot introduce a Riemannian 4-metric. So what? You can, instead, introduce a pseudo-Riemannian metric.

If you really feel there is a true & meaningful "causal" structure in Galilean geometry you won't ever agree with what I am saying, if you laugh at that proposed structure as physical non sense then you may see where I am "coming from" with my perspective.

See above. There is perfectly meaningful, strong, causal structure in Newtonian physics. It is not 'true' in the sense that it is falsified by experiment, but it is well defined and mathematically consistent.

And I hope I don't come across as arguing, if it does I don't want to continue...it's not at all how I wish to "present" a perspective.

You do come across as argumentative, and you are not succeeding well explaining your perspective.

 

[PeterDonis]

The temporal & spatial dimensions share the same sign in Galilean Newton whatever

No, this is not correct. In fact it doesn't even make sense. For temporal and spatial dimensions to even have signs that can be compared, they have to appear in the same metric. In Galilean/Newtonian physics, they don't; there is no such metric. So you can't even compare the signs of the temporal and spatial dimensions in Galilean/Newtonian physics.

 

[nitsuj]

Causal structure simply means you can specify between some(all) events which one could have influenced the other (causal connection, with direction). In Newtonian physics, for every pair of events, there is the ability to state which one is before the other and could have causally influenced the other. For SR, there is a different causal structure: for some pairs of events you can say one could influence the other; for others you can say neither could influence the other. Newtonian physics time orders all events; SR contains events that cannot be time ordered.

Huh, Then I didn't and still don't understand a causal system/structure. I took it to mean that one thing leads to another and we all agree on that order, and that's it.

I didn't know a causal system was about "could have" & "have had", but thought it was about "will have" & "have had". And I still see no physical significance to "could haves", I see that as merely coordinating / "mapping" positions of objects. Makes me wonder what is a "cause" that never becomes an "effect"?

So with that my perspective was from the object itself. In other words the order of "physical occurrences" as they have happened to an object is invariant. Could be restated as the "historical order" of physical occurrences as they have happened to an object doesn't change.

As those physical occurrences happen to an object the result, or effect propagates to which ever observer cares to observe it. all observers who care to observe this object will see the same ordering regardless of their relative motion. The physical occurrence of the observation itself too is invariant i.e. when the distant observer(s) first receives lightlike information (the effect of what ever cause happened to the observed object). So if all the observers are observing each other they all see this same ordering of these physical occurrences. This is a fundamental "connectedness" (domino / butterfly effect, even determinism) amongst all physical interactions. The fact that there are only two mutual exclusive physically relevant possibilities, will happen , can happen, has motion as implicit. We can measure motion.

From that there is spacetime, which itself isn't physical in the sense discussed above or specifically "involved" in the process. It's just what separates physical occurrences.

Hope that clarifies my perspective in the previous posts, but suppose I wasn't talking about a causal structure at all since that includes the non physical "could have happened".

Thanks for clarifying the definition for me PAllen

And I also see this as more fundamental then the mere metric. The metric isn't much of anything really, but perhaps derived from the physical occurrences, in other words of course there must be time dilation, length contraction, differential aging ect.

I appreciate the importance of theory development, but don't see the physical significance of falsified theories so find it weird to mention them in instances where we are discussing very fundamental physics.

Hopefully there isn't still an argumentative tone to my reply's.

I didn't even know about these things called manifolds and that they are different then metrics ect. This is all making me wish I had gone to school for this stuff (physics). a quick wiki it seems manifold is only spacial.

 

[nitsuj]

No, this is not correct. In fact it doesn't even make sense.

It doesn't make mathematical sense, same way Galilean/Newtonian physics doesn't make physical sense. And here we are not discussing math logic.

temporal and spatial dimensions to even have signs that can be compared, they have to appear in the same metric.

Hey that was my original point to WannabeNewton!

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

Let's not play a term game with what is meant by "geometric structure"

 

[WannabeNewton]

No, that is not Peter's point. Read his paragraph again and read the papers I linked you. In galilean space-time we can completely separate the temporal and spatial dimensions and treat them independently but you seem to think that this implies it doesn't have a space-time structure at all, which is false. It just has a structure that is much stronger than that of Minkowski space-time.

 

[nitsuj]

No, that is not Peter's point. Read his paragraph again and read the papers I linked you. In galilean space-time we can completely separate the temporal and spatial dimensions and treat them independently but you seem to think that this implies it doesn't have a space-time structure at all, which is false. It just has a structure that is much stronger than that of Minkowski space-time.

I read it again and guess am still missing the point, I am not saying time doesn't exist in Galilean/Newtonian physics. Of course time is a measure in Galilean/Newtonian physics.

Do you know what I mean by Galilean/Newtonian physics excludes time geometrically?

 

[PeterDonis]

It doesn't make mathematical sense, same way Galilean/Newtonian physics doesn't make physical sense.

No, that's not a valid comparison. Galilean/Newtonian physics is a perfectly valid and consistent mathematical theory; it just doesn't agree with experiment (at least, not if you do a wide enough range of experiments). The comparison you were implying between the signs of the temporal and spatial dimensions can't even be consistently formulated in Galilean/Newtonian physics.

 

[PeterDonis]

Hey that was my original point to WannabeNewton!

Then why are you now taking a position that's opposed to that original point?

 

[nitsuj]

Then why are you now taking a position that's opposed to that original point?

Im not sure which you're referring too?

You know how the geometry of Galilean physics is different from SR? I refer to that as Galilean physics doesn't include time in geometry, SR does.

If you know what I mean, how should it be worded?

 

[nitsuj]

No, that's not a valid comparison. Galilean/Newtonian physics is a perfectly valid and consistent mathematical theory; it just doesn't agree with experiment (at least, not if you do a wide enough range of experiments). The comparison you were implying between the signs of the temporal and spatial dimensions can't even be consistently formulated in Galilean/Newtonian physics.

Yea, it doesn't make mathematical sense, and Galilean/Newtonian physics doesn't make physical sense flat out. Sure within variance it does, but strictly physics doesn't "work" the way Galilean/Newtonian physics calculates it to.

 

[PeterDonis]

Im not sure which you're referring too?

You said your original point to WannabeNewton was the same as the one I made--that in Galilean/Newtonian physics, there is no metric that combines the time and space dimensions. But if that's true, then, as I said, you can't compare the signs of those dimensions, yet you were claiming that those signs can be compared.

You know how the geometry of Galilean physics is different from SR? I refer to that as Galilean physics doesn't include time in geometry, SR does.

That depends on how you want to use the word "geometry". There is certainly a manifold called "Galilean spacetime", which includes time as a dimension. But there is no metric on this manifold; there is only a 3-D metric on each spatial slice of simultaneity. So there's no way of comparing the sign of the time dimension with the signs of the space dimensions. Some people would not use the word "geometry" to describe Galilean spacetime for that reason, since "geometry" does kind of imply that there is a metric on the entire manifold. But regardless of which position you take on that issue, you still can't compare the signs of the time and space dimensions.

 

[PeterDonis]

Yea, it doesn't make mathematical sense

If you want to keep making this assertion, you're going to have to back it up with a detailed explanation of how it can make mathematical sense to compare the signs of the time and space dimensions in Galilean spacetime, when there is no metric that includes both.

and Galilean/Newtonian physics doesn't make physical sense flat out.

Only if you equate "makes physical sense" with "matches all experiments". But if that's the criterion, then GR doesn't make physical sense either, because it doesn't include quantum mechanics. Nor does quantum field theory make sense, because there's no quantum field theory of gravity that covers all experiments. So we don't have any theories that make physical sense by this criterion. That doesn't necessarily make it an invalid criterion, but I'm not sure it's the criterion you really mean to be trying to defend.

strictly physics doesn't "work" the way Galilean/Newtonian physics calculates it to.

Nor does it "work" the way GR calculates it to, or quantum field theory. See above. Nobody knows how physics "really works"; we don't have a single theory that covers it all.

I suppose, having said all that, I should clarify the alternative position, which is the one I favor. According to the alternative position, physical theories are models, and all models are approximations. They are maps, and it's a cardinal error to confuse the map with the territory. GR is a more accurate map than Newtonian physics, but that's all. GR and quantum field theory are maps that cover different portions of the territory. We don't have a single map that covers *all* the territory, and we don't have any map that perfectly represents the territory it covers. (We shouldn't expect to, because the whole point of having maps is to *not* have to cover all the details of the territory, but just cover the information we need. As the saying goes, "the map is not the territory, but you can't fold up the territory and put it in your glove compartment".)

 

[nitsuj]

You said your original point to WannabeNewton was the same as the one I made--that in Galilean/Newtonian physics, there is no metric that combines the time and space dimensions. But if that's true, then, as I said, you can't compare the signs of those dimensions, yet you were claiming that those signs can be compared.
That depends on how you want to use the word "geometry". There is certainly a manifold called "Galilean spacetime", which includes time as a dimension. But there is no metric on this manifold; there is only a 3-D metric on each spatial slice of simultaneity. So there's no way of comparing the sign of the time dimension with the signs of the space dimensions. Some people would not use the word "geometry" to describe Galilean spacetime for that reason, since "geometry" does kind of imply that there is a metric on the entire manifold. But regardless of which position you take on that issue, you still can't compare the signs of the time and space dimensions.

Ah okay, yea I presumed the ++++ was comparable to +++-. I don't know math so I guess should not have even tried to make the point from that perspective.

I kinda get the drift of what you are saying, but don't really know about manifolds, which is leading me to think I also don't know what a metric is.

 

[nitsuj]

If you want to keep making this assertion, you're going to have to back it up with a detailed explanation of how it can make mathematical sense to compare the signs of the time and space dimensions in Galilean spacetime, when there is no metric that includes both.

I got to stop making that assertion then.

Only if you equate "makes physical sense" with "matches all experiments". But if that's the criterion, then GR doesn't make physical sense either, because it doesn't include quantum mechanics. Nor does quantum field theory make sense, because there's no quantum field theory of gravity that covers all experiments. So we don't have any theories that make physical sense by this criterion. That doesn't necessarily make it an invalid criterion, but I'm not sure it's the criterion you really mean to be trying to defend.

Ha! touche. I mean the more blantant geometric perspective, where you describe it as "Some people would not use the word "geometry" to describe Galilean spacetime for that reason, since "geometry" does kind of imply that there is a metric on the entire manifold."

In that respect one is more accurate then the other, and suppose theories just "evolve" that way with a clear goal of being accurate in every way.

I suppose, having said all that, I should clarify the alternative position, which is the one I favor. According to the alternative position, physical theories are models, and all models are approximations. They are maps, and it's a cardinal error to confuse the map with the territory. GR is a more accurate map than Newtonian physics, but that's all. GR and quantum field theory are maps that cover different portions of the territory. We don't have a single map that covers *all* the territory, and we don't have any map that perfectly represents the territory it covers. (We shouldn't expect to, because the whole point of having maps is to *not* have to cover all the details of the territory, but just cover the information we need. As the saying goes, "the map is not the territory, but you can't fold up the territory and put it in your glove compartment".)

That's well said PeterDonis. A classic and important saying.

GR was mapped before all of the territory was discovered, it predicted some of the "territory". The logic of Einstein + math of him and friends preceded observation of unusual effects it predicted whether it be black holes or gravitational redshift. I think he even had an air of arrogance in this respect as far as his confidence in the logic of the theory* when original experiments (light bending) failed to agree with in a popularly accepted variance.


*"The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible" Albert Einstein

 

[russelljbarry15]

It is the space-time expanding so nothing is really changing. The galaxies can travel faster than the speed of light. There is nothing in Einsteins theory to prevent space-time expansion faster than the speed of light.

 

[ghwellsjr]

And you ignored my request for you to tell me what the value of the spacetime interval is and what two events it applies to. This is a simple request and you shouldn't have a problem answering this question.

It's about Physical occurrence ordering being invariant as observed happening to a specific object, and you already said you agree with that. We still don't need diagrams to make the "next step" of how a consequence of this is differential aging.

Ok, I will wait for you to present the "next step". I had no idea your long post was not intended to be an explanation of how "causal structure results in differential aging".

The interval is important because of it's invariance.

I am at work now, and as much as I want too, I got to refrain from "working" at this lol

I'll reply this E.S.T. evening.

I'm still waiting for your responses.

 

[nitsuj]

And you ignored my request for you to tell me what the value of the spacetime interval is and what two events it applies to. This is a simple request and you shouldn't have a problem answering this question.

Sorry to be so bold as to ignore your request, but I am unable to formulate a reply. Well besides all of my replies prior to this one.

post #55 where I explain my misunderstanding of Causality, not presuming it is from a "privileged" perspective.

The value of the spacetime interval is it's invariance and as it applies to the opposing ends (events/physical occurrence) of the interval itself; as it always does.