Relativity and the question of age

[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.