Relativity and the question of age

[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.