What is Rieman for a conformal metric?

[PeterDonis]

a(t) starts large at birth and falls to 1.20 at age 18 and remains there.

Once again, this isn't really a physical application of the metric in your OP, so it's really off topic for this forum and I can't comment on it.

 

[Kurvature]

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[Peter Donis]
If the function $a(t)$ has the appropriate form for "dilated" to be a reasonable description, yes, you could say this (more precisely, you could say it for observers with constant spatial coordinates in the conformal metric). But it has no physical meaning, because coordinate time has no physical meaning. It's just a convention.

[Kurvature]
Mentz114 analyzed the flat conformal metric ds²=a(t)[dR²-dt²] (wch. is not flat by the way since Riemann=/=0)
and found that it does NOT exhibiit a Hubble Shift. That is a REAL, PHYSICAL result. Are you going to tell me it is not a real, physical result
because "t" in the metric is only coordinate time and has no physical meaning? I seriously doubt the veracity of that assertion.


[Peter Donis]
Not just based on coordinate time, no. See above. Once again, if you want to show that there is "universal time dilation", you have to show that there is some physical invariant that demonstrates it. Just looking at coordinate time and its relationship to proper time is not enough, because, as above, coordinate time has no physical meaning.

[Kurvature]
In my particular physical application the OP conformal metric actually descriibes a real physical situation (not gravitational b.t.w.)
where it is known and directly observable and measureble that there IS a real, universal time dilation. So
again, I don't think I have to worry about your drumbeat assertion that "t" in the metric is merely
a coordinate time and has no physical meaning.

 

[Kurvature]

[Peter Donis]
Once again, this isn't really a physical application of the metric in your OP

[Kurvature]
That's an unsupported assertion, which is demonstrably wrong. But I'm
not about to argue with you.

[Peter donis]
, so it's really off topic for this forum and I can't comment on it.[/QUOTE]

[Kurvature]
I agree that it certainly is off topic in this forum, but that does not support
your false assertion that it is not a physical application. You can't have
your cake and eat it too.

 

[PeterDonis]

That is a REAL, PHYSICAL result.

Yes (assuming the calculation is correct--as I said, I have not checked it). But it still doesn't mean that coordinate time is a physical quantity. The result is not about coordinate time; it's about redshift.

I agree that it certainly is off topic in this forum

Then please don't make claims about it in this forum. For example, this...

In my particular physical application the OP conformal metric actually descriibes a real physical situation (not gravitational b.t.w.) where it is known and directly observable and measureble that there IS a real, universal time dilation.

...is a claim that you should not be making in this forum. In this forum, we use the term "time dilation" to describe a particular set of physical phenomena in particular scenarios that have to do with relativity physics. Other usages of the term (such as the one you appear to be using) are off topic.

 

[Kurvature]

[Kurvature said]
That is a REAL, PHYSICAL result.

[Peter Donis]
Yes (assuming the calculation is correct--as I said, I have not checked it). But it still doesn't mean that coordinate time is a physical quantity. The result is not about coordinate time; it's about redshift.

[Kurvature said]
I agree that it certainly is off topic in this forum

[Peter Donis]
Then please don't make claims about it in this forum. For example, this...

[Kurvature]
In my particular physical application the OP conformal metric actually descriibes a real physical
situation (not gravitational b.t.w.) where it is known and directly observable and measureble
that there IS a real, universal time dilation.

[Peter Donis]
...is a claim that you should not be making in this forum. In this forum, we use the term "time dilation" to describe a particular set of physical phenomena in particular scenarios that have to do with relativity physics. Other usages of the term (such as the one you appear to be using) are off topic

[Kurvature]
I agree, my "relativity physics" application does not coincide
with your "particular relativity physics" focus. I won't mention it any further.
I neither need to or want to.
Meanwhile, I said my thank yous and voiced my appreciation in my last post.
We're done here.

 

[PeterDonis]

We're done here.

Agreed. Thread closed.