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Physical, conformal age of the universe

Jacek
in Speculations

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3 hours ago, Jacek said:

Enough is enough.

You also need your observer to rest in the CMB reference frame so that his proper time can be equal to the proper age of the universe, so you also need the CMB reference frame.

Why ? What about a geometry without a CMB the metric is perfectly capable of accurate conformal time simply using observer ie the commoving observer now and emitter to any past object including those objects prior to the CMB.

You dont require some special period in our universe history for the equations as is to work. Why would you want to restrict the flexibility it has and apply unnecessary limits ? You can literally take any object at a given redshift and use that as well as the expansion history with the equations above and get an approximate age of when the signal was sent. See the calculator in my signature( it has that very feature).

After all the only two requirements is a geometry and a change in volume over a given time period. The rest of the formulas allows you to determine the volume at a given redshift to determine the scale factor.

You dont require a CMB for that

1 hour ago, studiot said:

Welcome back @Mordred

Season's Greetings.

Thanks merry Xmas and happy new year to you as well

Edited by Mordred

  • Author

If your observer hasn't been at rest in the CMB reference frame since its emission, then his proper time is not equal to the proper age of the universe, neglecting the fact that the emission happened some time after the BB.

You talk too much.

Edited by Jacek

    • -1

    Evidently you have no clue how the metric actually works. Observer is us on Earth, the CMB surrounds Earth and exists everywhere in the Universe today. Its current blackbody temperature is 2.73 Kelvin.

    It did not exist at every moment in the past ie previous to 380 million years after BB.

    Resorting to try and insult me doesn't cut it. Particularly since I do have credentials in the field of Cosmology.

    However as you cannot counter my points I made with anything related to actual physics then its pointless for this thread to continue.

    For the third time conformal time is not proper time. I provided you with the proper time corrections as well as the reason why they are required.

    Edited by Mordred

    • Author

    My patience also has its limits @Mordred

    Not 380 million years, but 380 thousand years after the BB. Quite a significant difference and something to neglect in comparison to 13.8 billion years.

    Your tendency to throw in the bits of information that are actually irrelevant to the discussion, like 2.73K, is just repulsive, and comes from your need to show how smart you are.

    We, on Earth, observe the CMB dipole, because we have a peculiar velocity and we're not at rest with respect to the CMB.

    Your credentials closed your mind so tightly, that you probably can't think for yourself anymore.

    The FLRW metric doesn't work without the CMB reference frame.

    And where did I say that the proper time IS the conformal time... Nowhere @Mordred

    Edited by Jacek

    My patience also has its limits @Mordred

    3 minutes ago, Jacek said:

    Your credentials closed your mind so tightly, that you probably can't think for yourself anymore.

    Another Galileo.

    • Author
    2 minutes ago, StringJunky said:

    My patience also has its limits @Mordred

    Another Galileo.

    And another rat terrier on this fourm.

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    -1
    • Author

    I guess that makes me a rat.

    2 minutes ago, Mordred said:

    Evidently you have no clue how the metric actually works. Observer is us on Earth, the CMB surrounds Earth and exists everywhere in the Universe today. Its current blackbody temperature is 2.73 Kelvin.

    It did not exist at every moment n the past ie previous to 380 million years after BB.

    Resorting to try and insult me doesn't cut it. Particularly since I do have credentials in the field of Cosmology.

    However as you cannot counter my points I made with anything related to actual physics then its pointless for this thread to continue

    Fine dont wish to believe me I provided 2 links clearly showing where your wrong both professionally peer reviewed.

    All you have to do is read them the first link clearly shows conformal time and proper time on 2 seperate graphs. Is Lineweaver and Davies wrong ?

    The second article is also peer reviewed and clearly states commoving distance as being used to calculate age of the Universe.

    So what about those objects prior to the CMB are they ageless as the CMB doesn't exist then ?

    But hey I guess every professional physicist is wrong simply because you dont agree with them. Lmao all you had to do was look at how the scale factor is derived which is required for your formula to realize the CMB itself is irrelevant when the scale factor uses the particle aka cosmological event horizon.

    Edited by Mordred

    • Author

    So you're talking to yourself by quoting yourself...

    Where did I say that the proper time IS the conformal time... Nowhere @Mordred

    1 hour ago, Jacek said:

    My patience also has its limits @Mordred

    Not 380 million years, but 380 thousand years after the BB. Quite a significant difference and something to neglect in comparison to 13.8 billion years.

    Your tendency to throw in the bits of information that are actually irrelevant to the discussion, like 2.73K, is just repulsive, and comes from your need to show how smart you are.

    We, on Earth, observe the CMB dipole, because we have a peculiar velocity and we're not at rest with respect to the CMB.

    Your credentials closed your mind so tightly, that you probably can't think for yourself anymore.

    The FLRW metric doesn't work without the CMB reference frame.

    And where did I say that the proper time IS the conformal time... Nowhere @Mordred

    As you see, I also can talk to myself and quote myself. What a delightful discussion, right?

    Deal with what I wrote.

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    -1
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    3 minutes ago, Mordred said:

    No your obviously ignoring what I've shown you.

    Tell me does the detail that there is no scale factor in SR or GR elude you ? Both metrics uses proper time

    The FLRW metric is the description of the expanding spacetime governed by GR, and there is a scale factor in this metric. What's more, Friedmann equations are a solution to the Einstein field equations for this metric, and they also contain the different powers of the scale factor corresponding to the changing density parameters. Taking it all into account, how can you say that there is no scale factor in GR?

    Edited by Jacek

    • Author

    Sigh @Mordred indeed. There is a scale factor in the metric tensor in the Einstein field equations for the expanding universe. And the Ricci tensor and the Ricci scalar are non-zero because of it.

    Go ahead, look it up.

    Edited by Jacek

    Fine see chapter 4.2

    https://people.smp.uq.edu.au/TamaraDavis/papers/thesis_complete.pdf

    Go ahead show me one GR textbook or article that shows the metric tensor with the inclusion of the scale factor as per Einstein field equation.

    Feel free to post that reference. If You like I can provide you thr FLRW metric Christoffel as well as the Minkowskii Christoffel and from that you can readily see the difference

    What are your 4 dimension that make up the metric tensor does it include a scale factor go ahead post me a reference showing that the scale factor is included in the metric tensor

    Alternately show where the scale factor is included in GR's four momentum

    Edited by Mordred

    • Author

    You can't be THAT silly...

    The FLRW metric on wikipedia:

    https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric

    When combined with Einstein's field equations, the metric gives the Friedmann equation, which has been developed into the Standard Model of modern cosmology and further developed into the Lambda-CDM model.

    If you write this metric in form of the metric tensor, substitute it into the Einstein field equations and solve them, you will get the Friedmann equations. And there is a scale factor in both the FLRW metric tensor and the FLRW metric equation, not to mention the Friedmann equations.

    Applying the metric to cosmology and predicting its time evolution requires Einstein's field equations and a way of calculating the density, ρ(t), such as a cosmological equation of state. This process allows an approximate analytic solution of Einstein's field equations G_μν + Λg_μν = κT_μν giving the Friedmann equations when the energy–momentum tensor is similarly assumed to be isotropic and homogeneous. Models based on the FLRW metric and obeying the Friedmann equations are called FRW models.

    And check out the Ricci tensor with the scale factor and its derivatives:

    https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Curvature

    "Resident Expert" - unbelievable...

    Edited by Jacek

    Yes exactly you have to derive how to fit the scale factor into GR field equations finally your getting it.

    Now every thing I stated is covered by the Lineweaver Davies dissertation. I suggest you read it including where it discusses superluminal recessive velocity.

    Literally every single statement I mentioned this thread is covered under that dissertation papers.

    Did you not understand why I stated the FLRW metric is a special class of solution of GR which is what your link is highlighting

    Edited by Mordred

    • Author

    Do you have a problem with superluminal recession velocity? Are you sure that's the right thread to post about it?

    No @Mordred the FLRW metric is not a solution to the Einstein Field Equations. The Friedmann equations are a solution to EFE for this metric.

    Are you intentionally being obtuse? What is the distinction between conformal time and proper time when it comes to distance measures. Do I need to repeat the distinction between the two a 5th time ?

    No I do not have a problem with superluminal recessive velocity I know the professionally accept corrections for that and I posted the professionally accepted corrections.

    You however dont want to grasp why proper distance and commoving distance are distinct when it comes to geometry and refuse to acknowledge that conformal time is specific to commoving coordinates not proper distance for proper time.

    Even though I've supplied literature specifically showing that distinction.

    You are aware I hope the Christoffels symbols I mentioned are used to derive the Ricci tensor. Including the one in that wiki link....

    Why not write out the ds^2 line element for Cartesian coordinates then compare that to ds^2 line element of the FLRW metric after all we may as well look at those Christoffel symbols in greater detail so you can understand the Ricci tensor solution thst the wiki link posted.

    Are you familiar with the overdot notation of that Ricci tensor for example which overdose dot describes the acceleration of the scale factor and which overdot describes the velocity ? I ask to make sure you understand that notation

    Edited by Mordred

    • Author

    You say that I "refuse to acknowledge that conformal time is specific to commoving coordinates not proper distance for proper time." Where? Quote me.

    Sure @Mordred write the Christ-awful symbols equation, we need it so much at this point of our conversation... I'm also sure that all the readers would love to see it.

    No @Mordred please, explain as extensively as you can the overdot notation, I'd love to know what first and second order time derivatives are.

    Edited by Jacek

    Good glad you recognize time derivatives now take GR line element and distinguish between proper time and coordinate time under GR...where does proper time under GR reside? As opposed to coordinate time.

    One is invariant to all observers the other is not ....

    Edited by Mordred

    • Author

    Finally, something I can deal with. In case of the FLRW metric the proper time squared is

    dτ²=dt²−a(t)²dr²/c²

    and coordinate time is dt.

    Edited by Jacek

    • Author

    Proper time squared is on the left hand side of the equation I gave.

    Edited by Jacek

    https://en.wikipedia.org/wiki/Proper_time


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    Proper time

    In relativity, proper time (from the Latin proprius, meaning own) along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time

    Now given the above definition is commoving coordinate independent of its geometry ? Or is that now a coordinate time ?

    Any location you choose for a reference point for the emitter or observer is a coordinate dependant event location. The proper time follows the ds^2 line element aka the world line or null geodesic

    Here is the FLRW metric Chrisoffel not that it's needed now given the definition above of proper time.

    Edited by Mordred

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