True Time & True c: Exploring Light Speed & Relativity

[Idjot]

It seems to me...

If we are moving relative to CBR at 390 km/sec, that should have a minute effect on our atomic clocks that we use to measure c.

In other words, we should be experiencing a small amount of Time Dilation relative to CBR.

Also, at certain times in our rotation, our orbit and even our Sun's orbit around the Milky Way, we could even be accelerating relative to CBR, which would further skew our measurements of c, but I won't get into that here, because I think the 390 km/sec is an average anyway.

Using only our inertial velocity I figured this out:

For every 1 minute that we experience in our 390 km/sec bubble: 1.0000008461714416367280534757218 minutes pass for the CBR.

In 10 billion years, CBR's time will have elapsed more than ours by 84 years, 225 days, 9 hours, 53 minutes, and 8.7 seconds

That doesn't seem like much, because it isn't :) But to me, of all things to consider True Time, this is it. All other times must bow before True Time!

Now let's see what that does to the speed of light:

Earth time measurement of c is 299.792.458 km/sec

According to my calculations...

True c is 299,792.204 km/sec.

That means that in 100 light years, light actually travels 801,563,040 km less than we thought it did, and also making our measurement of 100 light years to be about 44 light minutes and 33.7 light seconds off.

Go ahead. Shoot! :)

 

[russ_watters]

If we are moving relative to CBR at 390 km/sec, that should have a minute effect on our atomic clocks that we use to measure c.

In other words, we should be experiencing a small amount of Time Dilation relative to CBR.

Also, at certain times in our rotation, our orbit and even our Sun's orbit around the Milky Way, we could even be accelerating relative to CBR, which would further skew our measurements of c, but I won't get into that here, because I think the 390 km/sec is an average anyway.

Go ahead. Shoot! :)

Special relativity states the following:
1. The laws of physics are the same for all inertial frames of reference.
2. The speed of light is constant.

So what you are saying does not match how the universe works. Time dilation isn't something that your clock shows, it is something that only shows up when you compare your clock to other clocks. And these clocks may be moving at any speed, so you can't fix your speed at one particular value. Except, of course, that you are always stationary wrt yourself. You could, of course, attach a frame of reference to the CMB and measure a time dilation against it, but that frame and that time dilation don't hold any special meaning. They are not any more or less valid than the time dilation experienced between us and a GPS satellite, for example.

And that also explains why the speed of light is constant for you. The same reasoning applies.

 

[Idjot]

Special relativity states the following:
1. The laws of physics are the same for all inertial frames of reference.
2. The speed of light is constant.

You could, of course, attach a frame of reference to the CMB and measure a time dilation against it, but that frame and that time dilation don't hold any special meaning.

.

1. The CBR is the least inertial frame in the universe. Why should we not try to use it to find the true rate of time elapse? A satellite is in our frame. The dilation of a satellite's clock wouldn't matter because the satellite is moving with us relative to CBR.

2. The speed of light being constant is why it's possible to see that our measurements must be wrong. The speed of light is constant is a law. That our measurement of it must be correct is not. Time may be relative but distance is distance, and we must be experiencing a faster time elapse rate in our frame than CBR is in it's frame due to our velocity relative to it, which is as close to absolute as you can get. The least we can do is try to figure it out.

 

[Idjot]

I'd like to add to this a little:

All of the 'True Time' numbers are taken as if we took an Earth clock and placed it in the CBR, where it would tick faster.

The CBR 'velocity of Earth' measurement was taken from a satellite and although the measurement would be a tiny bit different if taken from CBR, the difference should be minuscule.

By me saying that our measurements are "wrong" I mean that they are wrong compared to what we would measure from the CBR frame of reference, which is considered to be the most stationary reference point in the universe. It does not mean that our measurements are wrong relative to our own time. They are only wrong when using what I called "True Time". In other words, light travels at 299,792.458 km/ Earth sec.
But it travels 299,792.204 km/CBR sec. Realistically, it's still the same distance because our seconds are longer than those of the CBR, when using identical clocks.

I think that this idea is useful when one considers that time in the CBR frame is the fastest in the universe and that by CBR time all other time elapse rates can be measured and then compared to our own. With a few additional calculations to compensate for our time's small difference to CBR's, we can chart the "true" ages of celestial bodies by their own respective velocities relative to us and CBR. It seems to me that this could be useful considering the varyied velocities of objects in the universe. Put simply, objects' ages should be charted for their own frames' times as well as for ours.

Consider something that's moving much faster than us, where the time elapse rate is much slower than our own. To make an extreme example: we may think that a fast moving star lived 6 billion years when in it's own time it really only aged for 4 billion years.

I think it would be presumptuous and inaccurate of us to continue forever thinking that everything in the universe ages in Earth time.

 

[Vanadium 50]

All of the 'True Time' numbers are taken as if we took an Earth clock and placed it in the CBR, where it would tick faster.

But it won't. It will tick slower.

I think it would be presumptuous and inaccurate of us to continue forever thinking that everything in the universe ages in Earth time.

SR does not say this.

 

[russ_watters]

1. The CBR is the least inertial frame in the universe.

What does that mean? That it is special and 'truly' at rest? No.

Why should we not try to use it to find the true rate of time elapse?

We can if we want, but we need to understand that that time dilation carries no special meaning.

A satellite is in our frame. The dilation of a satellite's clock wouldn't matter because the satellite is moving with us relative to CBR.

It isn't in our frame and it matters quite a bit when calculating positions using GPS. That's kinda the whole point here: the correct reference frame to use for "rest" depends on what you are doing with the calculations.

2. The speed of light being constant is why it's possible to see that our measurements must be wrong. The speed of light is constant is a law. That our measurement of it must be correct is not.

No, that is not correct at all. If our measurements about things other than C were wrong, that would be a violation of the first postulate: that all laws of physics are the same regardless of inertial reference frame. If our measurements of C were wrong, that would be a violation of the second.

Time may be relative but distance is distance...

Also wrong, for the same reason. And note that distance being relative is not a new component in Relativity: it dates back to Galileo.

 

[Dale]

Out of curiosity, when you say that the time in the rest frame of the CMBR is "true" time, what do you mean by that? Is it "true" by definition or by experiment. If you are simply defining "true time" = "CMBR time" then it is only a semantic argument. Nobody disagrees with the idea that our clocks run differently than one at rest wrt the CMBR, we just disagree with the characterization of that as "true". If you are not simply defining it to be "true" then what experiment indicates that the CMBR time is more physically significant than any other time?

 

[Naty1]

The CBR is the least inertial frame in the universe

All inertial frames are relative...how do you this one is least?? special relativity says you can't know...there is no absolute...

That means that in 100 light years, light actually travels 801,563,040 km less than we thought it did, and also making our measurement of 100 light years to be about 44 light minutes and 33.7 light seconds off.

In Newtonian physics there is a concept of uniform, universal time. Celestial bodies exert forces between each other at the same time. This permits determination of "true" parameters like distance, and of course, everybody agrees on time because its universal.

Not so in relativity where time and distance data depend on the observer, where ambiguities arise and cannot be resolved. There is no Lorentz frame that can be selected in order to define "true" parameters between astronomical bodies, for example to be used in computing gravitational interactions...frames of reference determine what we observe, not any absolute value of distance nor time... there are no absolutes except the speed of light in appropriate frames of reference.

Also, at certain times in our rotation, our orbit and even our Sun's orbit around the Milky Way, we could even be accelerating relative to CBR

,

It comes at us uniformly from all directions...space is isotropic...it does not vary over time...

 

[Idjot]

SR does not say this.

I never said I was quoting SR.

 

[Idjot]

1. The CBR is the least inertial frame in the universe.

What does that mean? That it is special and 'truly' at rest? No.

What I mean is that it has been determined to be the one thing in the universe that is moving the slowest and is everywhere so it makes a great reference for measuring velocity of objects.

Why should we not try to use it to find the true rate of time elapse?

We can if we want, but we need to understand that that time dilation carries no special meaning.

Are you sayng that time dilation doesn't physically happen? Are you suggesting that you would not come home having aged less than your twin brother after your long flight at high velocity?

A satellite is in our frame. The dilation of a satellite's clock wouldn't matter because the satellite is moving with us relative to CBR.

It isn't in our frame and it matters quite a bit when calculating positions using GPS. That's kinda the whole point here: the correct reference frame to use for "rest" depends on what you are doing with the calculations.

Don't be so difficult. You know what I mean. We don't measure the speed Earth is moving through the universe relative to a satellite. The satellite is moving with us.

2. The speed of light being constant is why it's possible to see that our measurements must be wrong. The speed of light is constant is a law. That our measurement of it must be correct is not.

No, that is not correct at all. If our measurements about things other than C were wrong, that would be a violation of the first postulate: that all laws of physics are the same regardless of inertial reference frame. If our measurements of C were wrong, that would be a violation of the second.

I already addressed this earlier when I explained my meaning of "wrong"

Time may be relative but distance is distance...

Also wrong, for the same reason. And note that distance being relative is not a new component in Relativity: it dates back to Galileo.

I know what you mean about distance being relative but apparently you don't understand anything I say. What I meant by "distance is distance" is that 390 km is real. If we really are moving at 390km/sec then our time must be different from something that ISN'T crossing that distance in that amount of time.

I may not spout Einstein quotes and complex formulas in every other post, but I am still capable of objective reasoning and your tone suggests that you have no patience for someone less educated than yourself. If you suspend your desire to shoot me down for a moment and try to understand the concept behind my 'unruly' and 'unschooly' method of presentation, you might actually see something you could contribute to with your knowlege, rather than a scratching post.

 

[Idjot]

It comes at us uniformly from all directions...space is isotropic...it does not vary over time...

What I meant is that we may occasionally be experiencing acceleration on our way toward "Leo"

 

[Idjot]

Out of curiosity, when you say that the time in the rest frame of the CMBR is "true" time, what do you mean by that? Is it "true" by definition or by experiment. If you are simply defining "true time" = "CMBR time" then it is only a semantic argument. Nobody disagrees with the idea that our clocks run differently than one at rest wrt the CMBR, we just disagree with the characterization of that as "true". If you are not simply defining it to be "true" then what experiment indicates that the CMBR time is more physically significant than any other time?

Saying 'true time" is just me having fun with the idea of a reference frame that is universal.
It is only my OPINION that CBR should be used for that purpose. I think that measurements taken relative to CBR would be as close to absolute as we could ever get. Anyone that considers CBR to be no better than anything else for such an application will certainly not agree with anything else I've said here and that's OK with me, but don't tell me I'm breaking laws, because you know that I'm not.

What it boils down to is I'm trying to use Relativity to find an 'absolute' and it ruffles feathers.

Somebody help me defend this idea!
You can't all be naysayers!

 

[JesseM]

Saying 'true time" is just me having fun with the idea of a reference frame that is universal.
It is only my OPINION that CBR should be used for that purpose. I think that measurements taken relative to CBR would be as close to absolute as we could ever get. Anyone that considers CBR to be no better than anything else for such an application will certainly not agree with anything else I've said here and that's OK with me, but don't tell me I'm breaking laws, because you know that I'm not.

What it boils down to is I'm trying to use Relativity to find an 'absolute' and it ruffles feathers.

What you don't seem to understand is that when physicists say there is no preferred frame in relativity, they mean that the laws of physics work the same in all inertial frames--if you want to say that you find the CBR frame the most "natural" one to use in some vague aesthetic sense, that's fine, but the laws of physics won't work differently in that frame than in any other. If I put two physicists in windowless spacecraft moving inertially, and one ship is at rest in the CBR frame while the other is moving at 0.99c relative to it, if they both perform the same experiment inside their respective ships, they will both get the same results, there is nothing in the laws of physics governing any experiment they perform that will allow them to tell which ship they're on.

 

[russ_watters]

1. The CBR is the least inertial frame in the universe.

What does that mean? That it is special and 'truly' at rest? No.

What I mean is that it has been determined to be the one thing in the universe that is moving the slowest...

That's what I figured you meant and it is a pretty straightforward contradiction of Special Relativity. It is quite clearly wrong.

Right now, I can say I'm stationary and the CMB is moving relative to me. That's the entire point of the principle of relativity (the first postulate of Special Relativity). And what the CMB is doing relative to me has no implications for (for example) what a GPS satellite is doing relative to me. A GPS receiver can calculate it's position just fine without knowing it's speed relative to the CMB.

Why should we not try to use it to find the true rate of time elapse?

We can if we want, but we need to understand that that time dilation carries no special meaning.

Are you sayng that time dilation doesn't physically happen? Are you suggesting that you would not come home having aged less than your twin brother after your long flight at high velocity?

That isn't what he said. Having "no special meaning" means just that. It doesn't provide us with any information useful in other calculations. In fact, if you try to include it, you just add complexity while providing no additional value.

A satellite is in our frame. The dilation of a satellite's clock wouldn't matter because the satellite is moving with us relative to CBR.

It isn't in our frame and it matters quite a bit when calculating positions using GPS. That's kinda the whole point here: the correct reference frame to use for "rest" depends on what you are doing with the calculations.

Don't be so difficult. You know what I mean. We don't measure the speed Earth is moving through the universe relative to a satellite. The satellite is moving with us.

What you see as "being difficult" is me telling you the way it is. I know perfectly well what you mean and what you mean is straightforwardly wrong. In fact, that last sentence you wrote is an illustration of why! A velocity is the change in displacement between two objects, not three. There is no need to add a third reference to the calculation. It adds no value. The GPS system works just fine treating the Earth as stationary because that's what the first postulate means.

Time may be relative but distance is distance...

Also wrong, for the same reason. And note that distance being relative is not a new component in Relativity: it dates back to Galileo.

I know what you mean about distance being relative but apparently you don't understand anything I say. What I meant by "distance is distance" is that 390 km is real. If we really are moving at 390km/sec then our time must be different from something that ISN'T crossing that distance in that amount of time.

Yeah, see that's just it - you don't understand it. That 390 km is 390 km to one observer but could be anything to another observer. Distance is observer dependent.

I may not spout Einstein quotes and complex formulas in every other post, but I am still capable of objective reasoning and your tone suggests that you have no patience for someone less educated than yourself. If you suspend your desire to shoot me down for a moment and try to understand the concept behind my 'unruly' and 'unschooly' method of presentation, you might actually see something you could contribute to with your knowlege, rather than a scratching post.

No. I am frustrated because you have no desire to learn. You didn't come here to learn about Relativity, you came to try out an idea that sounds good in your head and you are uninterested in hearing why it isn't correct. It is doubly-frustrating because this misunderstanding you have is very simple and you are simply unwilling to take the tiny effort to understand what those two simple postulates mean. You're trying to invent new physics when really all this is is a reading comprehension problem and you aren't willing to go back and reread what the theory says. You may be capable of objective reasoning, but you haven't demonstrated you are willing to use it.

 

[russ_watters]

Let me tackle this one a little more specifically:

Earth time measurement of c is 299.792.458 km/sec

According to my calculations...

True c is 299,792.204 km/sec.

If a device that on Earth measures the speed of light to be 299.792.458 km/sec is placed in the reference frame of the CMB, it will still measure the speed of light to be 299,792.204 km/sec. That's what it means to be "constant in all inertial reference frames".

 

[Dale]

Saying 'true time" is just me having fun with the idea of a reference frame that is universal.

So then it is just semantics. There is nothing inherently wrong with that, but it is not particularly interesting either. The standard termniology works fine for me.

 

[Idjot]

What you don't seem to understand is that when physicists say there is no preferred frame in relativity, they mean that the laws of physics work the same in all inertial frames--if you want to say that you find the CBR frame the most "natural" one to use in some vague aesthetic sense, that's fine, but the laws of physics won't work differently in that frame than in any other. If I put two physicists in windowless spacecraft moving inertially, and one ship is at rest in the CBR frame while the other is moving at 0.99c relative to it, if they both perform the same experiment inside their respective ships, they will both get the same results, there is nothing in the laws of physics governing any experiment they perform that will allow them to tell which ship they're on.

At it's core, this concept has been difficult for me to articulate. If I say that I'm trying to choose an absolute frame, I'll get another lesson in the basic idea behind Relativity. If I say that faster moving objects age more slowly than we do so we should measure their ages in their own times, I hear the same repetitive lessons in time dilation. Noone seems to understand this idea of mine. It's as if Relativity became a religion at some point and any hint at an absolute or 'true' measurement incites a lynch mob.

But I'll keep trying:

You see, I'm not really looking for the absolute. Just the next best thing to it. A surrogate, if you will...

In your "space craft" traveling inertially through space, everything in it is measured relative to it, right? Right.

Now visualize that spacecraft expanding to contain the entire solar system, the galaxy and finally the entire universe(don't bother with the expanding universe lesson here)

If the universe itself is the "space craft" then how do we measure everything in it? Just like before. BY IT. If you were given the task of finding out how to do this, what would you use? CMBR is what you would use, because it's everywhere. It IS the space craft, not just a tiny object in it.

I am also suggesting that we find a "universal" time by which to measure all other rates of time elapse (note that I did not say 'true' or 'absolute'), using the "space craft" as well.

Does anyone get this yet?

 

[Aether]

Saying 'true time" is just me having fun with the idea of a reference frame that is universal.
It is only my OPINION that CBR should be used for that purpose. I think that measurements taken relative to CBR would be as close to absolute as we could ever get. Anyone that considers CBR to be no better than anything else for such an application will certainly not agree with anything else I've said here and that's OK with me, but don't tell me I'm breaking laws, because you know that I'm not.

What it boils down to is I'm trying to use Relativity to find an 'absolute' and it ruffles feathers.

Somebody help me defend this idea!
You can't all be naysayers!

In cosmology, using General Relativity, there are concepts of universal time which are prettly close to what you seem to be interested in here. If you look here (http://en.wikipedia.org/wiki/FLRW_metric) under the heading of "General Metric", you can see that two symbols are used there for time, $$\tau$$ for local (proper) time and $$t$$ for "universal time". Learning to use General Relativity will take a lot of work, but it is available for anyone who wants to learn it.

 

[JesseM]

At it's core, this concept has been difficult for me to articulate. If I say that I'm trying to choose an absolute frame, I'll get another lesson in the basic idea behind Relativity.

Actually, from a strictly philosophical perspective there is nothing stopping you from believing in an absolute frame whose measurements of time/distance/simultaneity represent the "real truth"--relativity only says that there is nothing in the laws of physics to distinguish that frame from any other, so there can be no empirical reasons for believing there is anything special about that frame.

If I say that faster moving objects age more slowly than we do so we should measure their ages in their own times, I hear the same repetitive lessons in time dilation. Noone seems to understand this idea of mine. It's as if Relativity became a religion at some point and any hint at an absolute or 'true' measurement incites a lynch mob.

Philosophically, you are free to believe that objects moving relative to some metaphysically preferred frame are "really" aging more slowly. But again, if relativity is correct there will be no physical experiment that will allow you to empirically discern which frame is the absolute frame.

But I'll keep trying:

You see, I'm not really looking for the absolute. Just the next best thing to it. A surrogate, if you will...

In your "space craft" traveling inertially through space, everything in it is measured relative to it, right? Right.

Only if you wish to use the ship's rest frame. Nothing would stop an observer on the ship from measuring time and distance using a system of rulers and clocks that are in motion relative to the ship, it's purely a matter of convention that we define the "ship's frame" in terms of rulers and clocks at rest relative to the ship.

Now visualize that spacecraft expanding to contain the entire solar system, the galaxy and finally the entire universe(don't bother with the expanding universe lesson here)

If the universe itself is the "space craft" then how do we measure everything in it? Just like before. BY IT. If you were given the task of finding out how to do this, what would you use? CMBR is what you would use, because it's everywhere. It IS the space craft, not just a tiny object in it.

I am also suggesting that we find a "universal" time by which to measure all other rates of time elapse (note that I did not say 'true' or 'absolute'), using the "space craft" as well.

Does anyone get this yet?

If you want to define "universal time" in terms of the frame of the CMBR just as a matter of convention, the way time zones on Earth are a convention which everyone agrees to, that's fine. But there is nothing in the laws of physics themselves that should cause you to prefer to use this frame as opposed to any other, that's just an aesthetic decision on your part.

 

[atyy]

Here are some readings you may find useful.

Reference frames attached to the Earth and the sun
Soffel et al, http://arxiv.org/abs/astro-ph/0303376

Effect of solar system motion through the CMB
(Skip the part on inflation)
Wright, http://www.astro.ucla.edu/~wright/cosmo_04.htm
Wright, http://www.astro.ucla.edu/~wright/CMB-DT.html

Estimate of local group motion through the CMB
Padmanabhan, http://books.google.com/books?id=-y...X&oi=book_result&resnum=2&ct=result#PPA379,M1

Cosmic time and expansion of space for observers at rest in the CMB
Francis et al, http://arxiv.org/abs/0707.0380

Other useful assignments of time and space in cosmology
Tsagas et al, http://arxiv.org/abs/0705.4397

"There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe. But for doing any physics experiment, any other frame is as good as this one."
Scott, http://www.astro.ubc.ca/people/scott/faq_basic.html

Test of whether the CMB rest frame violates local Lorentz invariance (including assumptions about the locally measured speed of light). It mentions other tests, so you can look those up in here.
"the cosmic microwave background is chosen as the preferred reference frame."
Bell et al, http://arxiv.org/abs/astro-ph/9512100

 

[Idjot]

Thank you all for your knowledge and insight on this. And thank you Aether and atyy for the links. I'll read them all. It's good to know that not everyone thinks this is completely harebrained.

 

[JesseM]

In cosmology, using General Relativity, there are concepts of universal time which are prettly close to what you seem to be interested in here. If you look here (http://en.wikipedia.org/wiki/FLRW_metric) under the heading of "General Metric", you can see that two symbols are used there for time, $$\tau$$ for local (proper) time and $$t$$ for "universal time". Learning to use General Relativity will take a lot of work, but it is available for anyone who wants to learn it.

Note that although there is one coordinate system most commonly used in cosmology because it is most convenient (this coordinate system is the one that makes the density of matter/energy throughout space as close to homogeneous as possible at any single coordinate time), there is nothing in the laws of physics that causes this coordinate system to be preferred over others which might use different definitions of simultaneity (and might have different definitions of which clocks were ticking fastest). In GR, when the laws of physics are stated in tensor form, they work the same way in all coordinate systems, because of a principle known as "diffeomorphism invariance"--see this article for a discussion (though it's also worth pointing out that any laws of physics can be made diffeomorphism invariant by putting them in tensor form, so this is sometimes seen as more a matter of mathematical formalism than an insight into physics--see my post #8 on this thread). Besides this, there's also the fact that in any small region of curved spacetime in GR, the laws of physics approach those of special relativity, with the coordinate system of a freely-falling observer in this region being equivalent to an inertial frame in SR, and just as in SR you have an infinite number of different locally inertial frames in this region where the laws of physics work the same even when stated in non-tensor form.

 

[Aether]

Note that although there is one coordinate system most commonly used in cosmology because it is most convenient...in any small region of curved spacetime in GR, the laws of physics approach those of special relativity...

Okay.

...with the coordinate system of a freely-falling observer in this region being equivalent to an inertial frame in SR...

As we zoom in on smaller and smaller regions of curved spacetime in GR, at what point exactly does the absolute simultaneity of coordinate systems that are convenient for use in cosmology become equivalent to the relative simultaneity of inertial frames? At the point where one stops using tensors?

 

[Dale]

As we zoom in on smaller and smaller regions of curved spacetime in GR, at what point exactly does the absolute simultaneity of coordinate systems that are convenient for use in cosmology become equivalent to the relative simultaneity of inertial frames?

There are two answers to this question.

The most direct answer is that you can ignore the curvature as long as the region you are interested in is small enough that the curvature is undetectable with whatever experiment you are considering.

The more important answer is that there is no absolute simultaneity in GR. In fact, time coordinates in GR are even less physically significant than in SR since in SR they are at least determined by the Einstein synchronization procedure and in GR they are not necessarily determined by any physical procedure. Also, there are an infinite number of ways to parameterize any spacetime, all of which are physically indistinguishable and could have a different choice for the time coordinate or even no timelike coordinate at all.

 

[RandallB]

…. CMBR is what you would use, because it's everywhere. It IS the space craft, not just a tiny object in it.

Not sure using the CMBR as a spacecraft is the best analogy. I would rather use the SLS that generated the CBR as close enough to the single event of the Big Bang to be considered Simultaneous based on the SR Simultaneity rule that only local events can be truly Simultaneous.
It may lead to a similar result but for large scale measures I think it applies modern interpretations more directly.

 

[Aether]

The more important answer is that there is no absolute simultaneity in GR.

There are perfectly valid coordinate systems in GR (and in SR) within which absolute simultaneity holds (conventionally).

In fact, time coordinates in GR are even less physically significant than in SR since in SR they are at least determined by the Einstein synchronization procedure and in GR they are not necessarily determined by any physical procedure.

I have not claimed that there is more "physical signifiance" for one valid coordinate system over another.

Also, there are an infinite number of ways to parameterize any spacetime, all of which are physically indistinguishable and could have a different choice for the time coordinate or even no timelike coordinate at all.

I know.

 

[Dale]

There are perfectly valid coordinate systems in GR (and in SR) within which absolute simultaneity holds (conventionally).

I have not claimed that there is more "physical signifiance" for one valid coordinate system over another.

Then I don't know what you mean by "absolute" simultaneity. If it is not coordinate independent and has no physical significance then it sounds like another semantic argument.

 

[JesseM]

As we zoom in on smaller and smaller regions of curved spacetime in GR, at what point exactly does the absolute simultaneity of coordinate systems that are convenient for use in cosmology become equivalent to the relative simultaneity of inertial frames? At the point where one stops using tensors?

As DaleSpam said, your use of the phrase "absolute" simultaneity is confusing, usually "absolute" means "the same in every coordinate system", yet you seem to allow different coordinate systems to have their own distinct "absolute simultaneity". Each coordinate system of course has its own well-defined notion of simultaneity, this is just as true of inertial coordinate systems in SR as it is of cosmological coordinate systems. According to the way you use the phrase "absolute simultaneity", can you imagine any coordinate system where it would not be true that "absolute simultaneity holds"? Doesn't every coordinate system by definition have a single yes-or-no answer to the question of whether two events have the same t-coordinate or not? The point is that in both flat SR spacetime and the curved spacetime found in cosmology you are free to pick different coordinate systems with different definitions of simultaneity, and there is nothing in the laws of physics to cause you to prefer one coordinate system over another.

 

[Aether]

Then I don't know what you mean by "absolute" simultaneity.

I clearly said that I was talking about the "absolute simultaneity of coordinate systems that are convenient for use in cosmology".

If it is not coordinate independent and has no physical significance then it sounds like another semantic argument.

Why don't you go back to the other thread where you were claiming that the isotropy of space has been firmly established on the basis of conservation of momentum, show an actual experiment where this has been done, and then accuse me there of making a semantic argument?

 

[JesseM]

I clearly said that I was talking about the "absolute simultaneity of coordinate systems that are convenient for use in cosmology".

Again, this makes little sense if we interpret "absolute" to mean "coordinate-independent" as is normally done, so if you are using a different definition of "absolute", you need to spell out what that definition is. Why couldn't I just as easily talk about the "absolute simultaneity of the inertial coordinate system that is convenient for me to use in SR because it is the frame in which I am at rest"?

 

[Aether]

As DaleSpam said, your use of the phrase "absolute" simultaneity is confusing, usually "absolute" means "the same in every coordinate system", yet you seem to allow different coordinate systems to have their own distinct "absolute simultaneity". Each coordinate system of course has its own well-defined notion of simultaneity, this is just as true of inertial coordinate systems in SR as it is of cosmological coordinate systems. According to the way you use the phrase "absolute simultaneity", can you imagine any coordinate system where it would not be true that "absolute simultaneity holds"? Doesn't every coordinate system by definition have a single yes-or-no answer to the question of whether two events have the same t-coordinate or not?

Again, this makes little sense if we interpret "absolute" to mean "coordinate-independent" as is normally done, so if you are using a different definition of "absolute", you need to spell out what that definition is. Why couldn't I just as easily talk about the "absolute simultaneity of the inertial coordinate system that is convenient for me to use in SR because it is the frame in which I am at rest"?

There is one notion of simultaneity in the FLRW metric, and if we zoom in on smaller and smaller regions of curved spacetime in GR until finally we make a transition to using SR spacetime (with or without inertial frames) then we are moving from one GR coordinate system that is convenient to use in cosmology to a set of SR coordinate systems that are convenient to use in a laboratory. Within this set of SR coordinate systems we could choose to have absolute simultaneity that is consistent with the cosmological coordinate system we are using, or we could choose to have relative simultaneity that is disconnected from our cosmological coordinate system.

The point is that in both flat SR spacetime and the curved spacetime found in cosmology you are free to pick different coordinate systems with different definitions of simultaneity, and there is nothing in the laws of physics to cause you to prefer one coordinate system over another.

I agree, but you are the one who singled out inertial frames as being equivalent to the coordinate system of a freely falling observer in a small region of spacetime in GR. These are not the only valid coordinate systems for freely falling observers. They may be more convenient to use in a small region because they allow us to drop tensor notation, but is there any other reason that you singled them out?

 

[Dale]

I clearly said that I was talking about the "absolute simultaneity of coordinate systems that are convenient for use in cosmology".

It is certainly not standard, but you are obviously free to define "absolute" to mean "convenient for use in cosmology". I have no objection to the claim that the time coordinate in the FLRW metric is convenient for use in cosmology.

Why don't you go back to the other thread ... and then accuse me there of making a semantic argument?

What happened in some other thread is irrelevant to the question of whether or not your argument here in this thread is purely semantic.

 

[JesseM]

There is one notion of simultaneity in the FLRW metric

Only if by "metric" you refer to the expression for the line element in a particular coordinate system, rather than to the curvature of spacetime (a geometrical notion which is expressed differently in different coordinate systems). For the same curved spacetime representing the same FLRW universe, you can come up with an infinite number of different coordinate systems with an infinite number of different definitions of simultaneity.

and if we zoom in on smaller and smaller regions of curved spacetime in GR until finally we make a transition to using SR spacetime (with or without inertial frames) then we are moving from one GR coordinate system that is convenient to use in cosmology to a set of SR coordinate systems that are convenient to use in a laboratory.

Why a "set" rather than a single SR coordinate system which is most convenient to use because it represents the laboratory's rest frame? You're really making an artificial distinction if you act like there's only one possible coordinate system that's "convenient" in cosmology but a set that are "convenient" in SR, this depends on an arbitrary aesthetic choice of what you find convenient.

Within this set of SR coordinate systems we could choose to have absolute simultaneity that is consistent with the cosmological coordinate system we are using

How could you "choose to have absolute simultaneity", exactly? Simply by throwing away every local inertial frame except for the one whose definition of simultaneity matched that of the cosmological coordinate system?

I agree, but you are the one who singled out inertial frames as being equivalent to the coordinate system of a freely falling observer in a small region of spacetime in GR. These are not the only valid coordinate systems for freely falling observers. They may be more convenient to use in a small region because they allow us to drop tensor notation, but is there any other reason that you singled them out?

You can "drop tensor notation" in non-inertial coordinate systems too. What makes inertial coordinate systems special is that when you do express the laws of physics in non-tensor form, you find that the laws turn out to obey the exact same equations when expressed in any inertial coordinate system, while they'd obey different equations in non-inertial coordinate systems. This is a symmetry that's built into the laws of physics, we can imagine different laws of physics where this wouldn't be true, in which case all inertial frames wouldn't be on the same footing physically in this way (so all the different inertial frames' definitions of simultaneity wouldn't be on the same footing either).

 

[Aether]

Only if by "metric" you refer to the expression for the line element in a particular coordinate system, rather than to the curvature of spacetime (a geometrical notion which is expressed differently in different coordinate systems).

I am referring to the FLRW metric that I linked to in post #18 above which gives one definition of simultaneity (the hypersurface of homogeneity).

For the same curved spacetime representing the same FLRW universe, you can come up with an infinite number of different coordinate systems with an infinite number of different definitions of simultaneity.

Okay, I didn't claim that this definition was unique, only that it was "one GR coordinate system that is convenient to use in cosmology".

Why a "set" rather than a single SR coordinate system which is most convenient to use because it represents the laboratory's rest frame?

We can define an inertial frame $$\Sigma$$ to represent the laboratory's rest frame, but then we would also need to define frames for objects in relative motion to $$\Sigma$$ to do SR.

You're really making an artificial distinction if you act like there's only one possible coordinate system that's "convenient" in cosmology but a set that are "convenient" in SR, this depends on an arbitrary aesthetic choice of what you find convenient.

I am not claiming that there is only one possible coordinate system that is convenient in cosmology, only giving an example of one that is convenient.

How could you "choose to have absolute simultaneity", exactly? Simply by throwing away every local inertial frame except for the one whose definition of simultaneity matched that of the cosmological coordinate system?

No, I would first define a locally co-moving $$\Sigma$$ inertial frame at any small co-moving region of the cosmological coordinate system, and then use Mansouri-Sexl (aka, LET, GGT, etc.) transforms instead of Lorentz transforms between SR frames in relative motion to $$\Sigma$$.

It is certainly not standard, but you are obviously free to define "absolute" to mean "convenient for use in cosmology". I have no objection to the claim that the time coordinate in the FLRW metric is convenient for use in cosmology.

I have not defined "absolute" to mean "convenient for use in cosmology". My apologies if I used the term "absolute" in a confusing way above. All that I refer to is any given definition of simultaneity that is convenient for use in cosmology which is then heritable by a set of SR coordinate systems at any small region of spacetime within which absolute simultaneity holds by convention.

If it is not coordinate independent and has no physical significance then it sounds like another semantic argument...What happened in some other thread is irrelevant to the question of whether or not your argument here in this thread is purely semantic.

Are you dismissing the way that I used the term "absolute" to describe the definition of simultaneity in the FLRW metric, or are you dismissing my entire attempt to show a spatially homogeneous formulation of SR?

 

[Dale]

My apologies if I used the term "absolute" in a confusing way above. All that I refer to is any given definition of simultaneity that is convenient for use in cosmology which is then heritable by a set of SR coordinate systems at any small region of spacetime within which absolute simultaneity holds by convention.

Definition or convention, calling it "absolute" is still just semantics. The point is that you are free to label the FLRW coordinates as "absolute" and Idjot is free to label the CMBR as "true", but neither choice has any physical significance. It is simply a matter of personal preference.

Are you dismissing the way that I used the term "absolute" to describe the definition of simultaneity in the FLRW metric

Yes. Since you are not using the term "absolute" in a standard manner your argument is semantic. I am not going to attempt to convince you to use the standard definition of "absolute" in order to promote clarity, but I am going to clearly point out that your use of the term is non-standard.