- #31
Kurvature
- 22
- 0
"PeterDonis, post: 5045845, member: 197831"]I should clarify that I have not checked that calculation; I have only skimmed through the thread you linked to.
[Peterr Donis]
Well, if we just look at coordinate time and the ##a(t)## factor, there is one obvious issue. ##a(t)##, from the metric, gives the ratio of proper time to coordinate time at a given instant ##t## of coordinate time, i.e., an interval ##dt## of coordinate time corresponds to an interval ##a(t) dt## of proper time (for an observer at rest in these coordinates).
[Kurvature]
Thank you for clearly explaining the relation of coordinate time to proper time.
I wasn't really clear on that.
So, it becomes clear that the observers in this case who remain at fixed (comoving)
spatial coordinates are NOT SEEING proper time. They are actually seeing
coordinate time. This is in contrast to FRW observers, who actually see proper time!
Believe it or not, this is entirely appropriate for my applied physics problem.
Turns out, that no real human being can actually see proper (wrist watch) time.
Oh sure, he "measures" things by proper wrist watch time, but that isn't the time that
he actually subjectively "sees". This is because all human beings fail to reach
full physical growth (specifically full brain growth in this case) and consequently
everyone's (mental clock) is running slightly slower than his wrist watch.
The world appears to EVERYONE to be both
bigger and faster than it actually is.
But this gets us into off-topic material so I will cease-and-desist here.
Suffice it to say, that the metric that I have proposed is entirely correct!
[Peter Donis]
But we do not know the functional form of ##a(t)##. For all we know, ##a(t)## could be constant (indeed, that case is what you were asking about in the OP in this thread). Without knowing the functional form of ##a(t)##, I don't see how we can know whether it describes "time dilation" or not.
Kurvature]
a(t) is not a constant. In fact a(t) is given by the following curve:
a(t)
oo
|x
|x
| x
| x
| x
| x
| x
| x
| x
|1.20 x x x
|_________________________________________________
0
time ---->
(Note that similar remarks apply to the spatial part of the metric; you are saying the metric describes "expansion", but without knowing the functional form of ##a(t)##, I don't see how we can know whether it does or not.)
[Kurvature]
According to the above curve, a(t) begin very large (at birth) and falls to
a constant value of 1.20 at age 18. This reflects the fact that the
Secular Trend human growth deficit is somewhere around 20%
in the world population.
[Peter Donis]
Also, you appear to be assuming that ##a(t)## increasing with ##t## corresponds to "time dilation". But if ##a(t)## is increasing with ##t##, then the amount of proper time elapsed in a given interval of coordinate time is increasing--i.e., that proper time clocks are "running faster" relative to coordinate time. "Time dilation" is usually used to describe a situation where proper time clocks are "running slower" relative to coordinate time.
[Kurvature]
The human brain is running "slower" then wristwatch proper time... about 20% slower
on average in the world population. More or less in individual cases. My clock is
running slower than yours for instance.
[Kurvature]
Are you saying that there really is a red-shift if the observer uses proper time?
[Peter Donis]
I have not done the calculation, so I can't say. But I think proper time is the appropriate standard to use, not coordinate time
[Kurvature]
Coordinate time turns out to be the appropriate standard to use
In the applied physics problem that I have to deal with.
I'd like to wrap up this discussion with this final post. I am
extremely grateful to you Peter for your explanations and
turning me on to Maxima which is a crucially important
tool for me. And of course, I remain awed and grateful
to Mentz114.
And at the final risk of offending unsuspecting physicists
on this vitally important physics forum, I simply would feel
derelict in my duty if I did not state plainly that these discussions
have confirmed that the (perceptual-psychological) phenomenon
known popularly as "God" has now been proven to exist and is
described by a conformal positively curved (k=1) metric whose
scalar curvature R is equal to 6/a(t)^2 and that a "Field equation
of God" may be written as :
God = scalar R = (% of full brain growth) = 6K/a(t)^2
where K is a proportionality constant.
And with that I thank you for your forebearance and
will hightail it out of here and bother you no further.
[Peterr Donis]
Well, if we just look at coordinate time and the ##a(t)## factor, there is one obvious issue. ##a(t)##, from the metric, gives the ratio of proper time to coordinate time at a given instant ##t## of coordinate time, i.e., an interval ##dt## of coordinate time corresponds to an interval ##a(t) dt## of proper time (for an observer at rest in these coordinates).
[Kurvature]
Thank you for clearly explaining the relation of coordinate time to proper time.
I wasn't really clear on that.
So, it becomes clear that the observers in this case who remain at fixed (comoving)
spatial coordinates are NOT SEEING proper time. They are actually seeing
coordinate time. This is in contrast to FRW observers, who actually see proper time!
Believe it or not, this is entirely appropriate for my applied physics problem.
Turns out, that no real human being can actually see proper (wrist watch) time.
Oh sure, he "measures" things by proper wrist watch time, but that isn't the time that
he actually subjectively "sees". This is because all human beings fail to reach
full physical growth (specifically full brain growth in this case) and consequently
everyone's (mental clock) is running slightly slower than his wrist watch.
The world appears to EVERYONE to be both
bigger and faster than it actually is.
But this gets us into off-topic material so I will cease-and-desist here.
Suffice it to say, that the metric that I have proposed is entirely correct!
[Peter Donis]
But we do not know the functional form of ##a(t)##. For all we know, ##a(t)## could be constant (indeed, that case is what you were asking about in the OP in this thread). Without knowing the functional form of ##a(t)##, I don't see how we can know whether it describes "time dilation" or not.
Kurvature]
a(t) is not a constant. In fact a(t) is given by the following curve:
a(t)
oo
|x
|x
| x
| x
| x
| x
| x
| x
| x
|1.20 x x x
|_________________________________________________
0
time ---->
(Note that similar remarks apply to the spatial part of the metric; you are saying the metric describes "expansion", but without knowing the functional form of ##a(t)##, I don't see how we can know whether it does or not.)
[Kurvature]
According to the above curve, a(t) begin very large (at birth) and falls to
a constant value of 1.20 at age 18. This reflects the fact that the
Secular Trend human growth deficit is somewhere around 20%
in the world population.
[Peter Donis]
Also, you appear to be assuming that ##a(t)## increasing with ##t## corresponds to "time dilation". But if ##a(t)## is increasing with ##t##, then the amount of proper time elapsed in a given interval of coordinate time is increasing--i.e., that proper time clocks are "running faster" relative to coordinate time. "Time dilation" is usually used to describe a situation where proper time clocks are "running slower" relative to coordinate time.
[Kurvature]
The human brain is running "slower" then wristwatch proper time... about 20% slower
on average in the world population. More or less in individual cases. My clock is
running slower than yours for instance.
[Kurvature]
Are you saying that there really is a red-shift if the observer uses proper time?
[Peter Donis]
I have not done the calculation, so I can't say. But I think proper time is the appropriate standard to use, not coordinate time
[Kurvature]
Coordinate time turns out to be the appropriate standard to use
In the applied physics problem that I have to deal with.
I'd like to wrap up this discussion with this final post. I am
extremely grateful to you Peter for your explanations and
turning me on to Maxima which is a crucially important
tool for me. And of course, I remain awed and grateful
to Mentz114.
And at the final risk of offending unsuspecting physicists
on this vitally important physics forum, I simply would feel
derelict in my duty if I did not state plainly that these discussions
have confirmed that the (perceptual-psychological) phenomenon
known popularly as "God" has now been proven to exist and is
described by a conformal positively curved (k=1) metric whose
scalar curvature R is equal to 6/a(t)^2 and that a "Field equation
of God" may be written as :
God = scalar R = (% of full brain growth) = 6K/a(t)^2
where K is a proportionality constant.
And with that I thank you for your forebearance and
will hightail it out of here and bother you no further.