Is spacetime absolute?

[NowThatWeKnow]

Even though spacetime is expanding, can we consider it at rest with the universe? Maybe time moving forward is the expansion we observe? The rate of time should be constant in the universal frame with spacetime at rest with the CMB and the universe itself.

 

When you move through spacetime you will observe time as you always have. However, depending on your speed, you may be moving accross two minutes of spacetime in one minute. While you observed time as usual, You have moved through time so your clocks will not agree with absolute spacetime.

 

Make a few modifications for GR and this would give us an absolute reference frame for time and speed. Isn't the only thing stopping this our unwillingness to adapt it?

[Martin]

Even though spacetime is expanding, can we consider it at rest with the universe? ...

 

I can only give you my limited take (trying to keep at least one foot in the mainstream, although this is an edgy topic.)

 

I don't think anyone says "spacetime is expanding". The visual metaphor that some scientists like to use is that space is expanding.

 

That is not a mathematical statement so it's fundamentally inaccurate or meaningless, but it is often said as an attempt to give people an intuitive feel for Hubble Law (a pattern of expansion of largescale distances between points at rest w.r.t. the CMB or other criterion of rest.)

 

It also is said to help give intuition for the Friedman model which all cosmo is based on. Everybody uses that model and so far data fits beautifully and they will continue until they find a discrepancy---then they will say Hurrah! something new we get to modify the model. That's how it goes. You refine observation and push the existing equations until something doesn't fit and then it's exciting because you get to change the equations.

 

Well, the Friedman model has an absolute time. And it has an absolute present moment and an absolute space (the slice of spacetime corresponding to Now.)

 

In the Friedman model the rate of expansion is extremely variable.

You should play around with the MORGAN calculator, which gives you the Hubble expansion parameter for any past time you want, or any redshift z.

If you plug in z=1100, to look at the day when the CMB light got loose from the hot fog, the Morgan calculator will tell you what the Hubble rate was on that day. It was very different.

 

Maybe time moving forward is the expansion we observe? The rate of time should be constant in the universal frame with spacetime at rest with the CMB and the universe itself.

 

In some situations it helps to use the scalefactor as a clock, but it doesn't go at a steady rate. There are problems with using some measure of expansion as a time parameter. It's done sometimes but it is not a simple straightforward strategy.

 

I believe in Loop Cosmology they sometimes use the scalefactor as one possible substitute for time but only right around the big bounce, in the fraction of a second before and after, because driven to that by necessity. Classical time is not readily available in those circumstances. So they run their computer models on somewhat unconventional types of time.

 

I can't speak confidently about this---too technical.

 

Make a few modifications for GR and this would give us an absolute reference frame for time and speed. Isn't the only thing stopping this our unwillingness to adapt it?

 

I think not. It's not that simple. If you are doing classical Friedman cosmology you already have absolute time. (Called "universe time" or "Friedman model time")

 

But cosmology is a simplification, (assuming uniformity, homog. and isotropy, is a huge simplification). The full GR theory has no chance of an absolute time.

 

And even with the classical 1922 Friedman model there is a breakdown right at the beginning of expansion. People don't understand what is happening there and there is a lot of research now about that---quantum cosmology. And there is no clear straightforward choice of absolute time right around where the classical theory blows up.

[NowThatWeKnow]

Martin, Thanks for your response. I like the way you step outside the box in your thinking to give clarity to your answers (for beginners), but without actually stepping out of the box.

 

I don't think anyone says "spacetime is expanding". The visual metaphor that some scientists like to use is that space is expanding.

 

Since science uses spacetime as one dimension, and space is expanding, I was trying to tie time to the expansion. It seems that since the expansion is not constant, that may be a bad idea. I guess we could pick any one point in the expanding metric and have that point be at rest w.r.t. the CMB.

 

 

Well, the Friedman model has an absolute time. And it has an absolute present moment and an absolute space (the slice of spacetime corresponding to Now.)

 

This has been a topic of discussion here on SFN often so could you please elaborate on this. I have additional thoughts and questions but additional information here may keep me from saying more foolish things then necessary.

 

The full GR theory has no chance of an absolute time.

 

So the Friedman model and GR are not compatible?

[Martin]

 

So the Friedman model and GR are not compatible?

 

They are very compatible! The Friedman model was derived rigorously from GR. He just added two assumptions that cosmologists normally make---uniformity assumptions: homog and isotropy.

 

GR is the general theory and it can have a variety of solutions. Friedman identified a family of solutions especially relevant to cosmology.

 

Within the context of those solutions, based on the simplifying assumptions which Friedman made, you get these nice features like a universe time.

=================

 

I guess you could say the Friedman model is the application of GR to cosmology---to a homogeneous and isotropic universe.

 

Wikipedia spells Friedman with two N letter. Friedmann (like a German-speaker would) but he was Russian and spelled it with one cyrillic N. For Liberal Arts you might look up Alexander Friedman in Wiki, and also the Friedman equations. Don't let it bug you if you don't understand everything. It's good to get a little exposure.

 

In a simplified uniform universe all that can change is the SIZE, or scalefactor. Raw GR is very complicated and you can get all kind of weirdshaped solutions depending on what you give it. But this is a radical simplification where all you need to worry about is the average density of matter/energy and the scalefactor (and the cosmological constant, or you can lump that in with energy).

 

=====================

 

Have you tried Morgan's calculator? You should. Google "cosmos calculator".

 

set it up by putting in .27, .73, and 71 as the present matter and DE densities, and the Hubble rate. Try it out, like for z = 6 or z = 1000

it will tell you the past Hubble rate and stuff. distance increase rates etc. distances of course.

 

I'm interested if that would work out for you. If you get anything out of trying it out. maybe give me some feedback? thx.

Edited April 17, 2009 by Martin

[Mr Skeptic]

I don't think anyone says "spacetime is expanding". The visual metaphor that some scientists like to use is that space is expanding.

 

Could you just as well say time is contracting?

[NowThatWeKnow]

I am a little confused because first you say

the Friedman model has an absolute time.

Then you say

The full GR theory has no chance of an absolute time.

Then you say

They are very compatible!

 

The Friedman model says we have a homogeneous and isotropic universe. Does that make time absolute in the universe regardless of location? and speed? and gravity? It seems I am still missing something (not unusual).

 

Have you tried Morgan's calculator? You should. Google "cosmos calculator".

Interesting calculator. What I think I am seeing is that the universe expansion was slowing until it was 2.66 billion years old (z=2.5) and then the expansion started accelerating. Is there a known reason for this? The calculator states all speeds are because of the expansion of space and not actual movement.

 

Edit - After looking at the calculator again the numbers started playing tricks on me. I am not certain what I am seeing but will look at it again after some sleep.

Edited April 17, 2009 by NowThatWeKnow

[NowThatWeKnow]

The Morgan calculator is interesting. The information is easy to read but trying to define a trend can be a real brain teaser. Sort of like mixing frames if you aren't careful.

 

I made a little chart with some of the info trying to to make it easier to get the big picture.

 

This still does not answer my questions about absolute time and the Friedman model.

[Martin]

The Morgan calculator is interesting. The information is easy to read but trying to define a trend can be a real brain teaser. Sort of like mixing frames if you aren't careful.

 

I made a little chart with some of the info trying to to make it easier to get the big picture.

 

Great! Glad to see someone getting acquainted with the Morgan calculator. It should agree with the Ned Wright calculator at least to the first 2 or 3 decimal places.

 

 

You may have noticed that the Hubble rate, which today is 71, is on the order of a million back at z=1000-----around when the CMB light started out.

and at z=6 the Hubble rate is about tenfold bigger than it is today.

 

This still does not answer my questions about absolute time and the Friedman model.

 

In GR you are very free to choose whatever coordinates and there is no natural time coordinate that stands out as an obvious choice.

 

The GR equation has many solutions. One particular solution or set of solutions is the Friedman model.

 

Somewhat like you have a general theory of triangles where certain things are shown to hold, like 180 degrees and the Sine Law and the Area formula. (but there is no Pythagoras relation).

 

And then you derive a particular specialized theory of RIGHT triangles from that by narrowing down to where one angle has to be 90 degrees. And you discover some new things are true.

 

You wouldn't want to say Oh no! The theory of right triangles is NOT COMPATIBLE with the general theory of triangles because the specialized theory has Pythagoras and the general theory doesn't! That would be silly. The same way as it is silly to think that Friedman model is incompatible with GR. Friedman model has some extra features, like a natural choice of time coordinate, that come from the extra assumptions that went into it.

 

And BTW the choice of Universe Time is optional. It just stands out as a natural choice but if you want to take the trouble you can change to different coordinates. You can always reparametrize. It just makes extra work though.

 

The Wiki article on Friedman equations says briefly how the two Friedman equations are derived from the main equation of GR. It sounds technical but you might want to check it out anyway.

 

I don't quite understand what you are asking, so feel free to rephrase the question. Spell it out in simple language. I'm saying that one is a simplification derived from the other by some simplifying assumptions---which incidentally buys you a few extra goodies, like a natural choice for the time coordinate. So the two are consistent.

 

================

If you look at Wiki article "Friedman equations" you will see that the Hubble rate H(t) is equal to a'(t)/a(t). And you can probably see how the two equations determine the evolution of a(t), the scale factor. Because they tell you its rate of change a' and its second derivative a".

They completely determine the history of expansion, the history of a(t).

And calculators like Morgan essentially embody the Friedman equations in a form that you can play around with them. That is, they embody a simple version of the Einstein equation of GR (with uniformity assumptions).

 

 

 

And so a calculator like Morgan's can tell you Hubble rate H(t) for any past time, as indeed it does for any redshift z you put in. Because H is simply a'/a, and the calculator is computing a(t) and a'(t) so it is very little extra trouble for it to output H(t)

Edited April 17, 2009 by Martin

[NowThatWeKnow]

You may have noticed that the Hubble rate, which today is 71, is on the order of a million back at z=1000-----around when the CMB light started out. and at z=6 the Hubble rate is about tenfold bigger than it is today.

Yes, I was paying attention to the Hubble constant. I figured it would drive you nuts that I did not include it in my chart, as I figured you would consider it one of the most important #'s given.

 

 

I don't quite understand what you are asking, so feel free to rephrase the question. Spell it out in simple language.

 

My question came from what you said in your first post in this thread.

Well, the Friedman model has an absolute time. And it has an absolute present moment and an absolute space (the slice of spacetime corresponding to Now.)

I wanted you to elaborate on what the Friedman model says "absolute time" and "Now" is.

 

I keep seeing a universal Greenwich mean or zulu time that all frames can relate to. Maybe a clock in totally flat space (remove the effects of gravity and static w.r.t. the CMB). I am sure my views are not scientific and would like to hear about what you were referring to in the above quote. Thanks

[WhataBohr]

you might what to take a look at quantum general relativity.. it predicts violent flunctuations in the geometry of spacetime at distances in order of plancks length.. an interesting subject..

[NowThatWeKnow]

you might what to take a look at quantum general relativity.. it predicts violent flunctuations in the geometry of spacetime at distances in order of plancks length.. an interesting subject..

Quantum general relativity? I participate her for fun, not torture. I still get panic attacks when I see "energy stress tensor".

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Could you just as well say time is contracting?

I would be interested in knowing your reasoning with "time is contracting"? Or is that saying that time expanding and time contracting are equally unrealistic?

[Mr Skeptic]

Space and time are in a way related via the speed of light. If time were to contract (or is that expand? eg if 1 new second = 1/2 old seconds) with space left unchanged, then when we use light along with a clock to measure distance, than distances would be greater. I guess this makes more sense when you measure stuff in light-years. If you have two years where you had one before, then you have two light-years where you had one before -- space expanding.

[Martin]

My question came from what you said in your first post in this thread.

 

I wanted you to elaborate on what the Friedman model says "absolute time" and "Now" is.

...

 

OK first we acknowledge that the Ferdman is an approximate. It assumes matter is uniformly distributed which is only approximately true. But it gives a very good approximation at large scale. It is the practical working that people use.

 

Next we have to distinguish between the real observational world, and the mathematical model.

 

It is clear what time is in the model because it is there explicitly in all the formulas. The Freddy model comes with coordinates that split space and time. And it tells you what the present ("now") is. And that now is defined universe-wide. You just have to look at the equations, and the formula for the metric (which is time-varying) and you will see. The metric has a spatial part and a time part. You will see that if e.g. you look at Wiki "friedman equations" if that doesnt work then double the N and say "friedmann equations"

 

The "universe time" that the model comes with is optional, you are free to screw around and reparametrize and mix the coordinates up--as always in GR. But it comes with a simple neat coordinate system.

 

What is more interesting is to discuss the pragmatic observability of Friedman time or sometimes called Universe time.

Remember the Fr. universe is an approximation so we can only hope to observe the approximate time. But there has to be a recipe by which people all over the universe, if they share the same Ned Wright calculator, can observe the same time.

 

Well the answer is easy actually. All over the universe the people can just hold up a thermometer and take the temperature of the CMB sky, and if you and I happened to measure the same temp, then we were part of the same 'now' at that moment. Those two EVENTS were synchro---the events of taking the temp, even if we were billions of lightyears apart.

 

And the Ned Wright calculator can give you the correspondence between CMB temperature and time units (whatever time unit you use, your planet's years, or planck time units, or whatever).

 

It is pragmatically simple all except for the units conversions. We would have to have communicated previously and decided on common units, like kelvin, or if you prefer the Planck temperature unit.

 

So universe time has both a math model aspect and a practical operational aspect. I'll stop so you can ask whatever questions. If any.

[NowThatWeKnow]

Space and time are in a way related via the speed of light. If time were to contract (or is that expand? eg if 1 new second = 1/2 old seconds) with space left unchanged, then when we use light along with a clock to measure distance, than distances would be greater. I guess this makes more sense when you measure stuff in light-years. If you have two years where you had one before, then you have two light-years where you had one before -- space expanding.

 

"If 1 new second = 1/2 old seconds" you would have time segments getting shorter over time, so time is contracting (or is it expanding because it is getting faster?). Therefore it would take longer to cover the same distance making a constant space seem larger. So, the $64,000 question is, 1. Is space expanding? or 2. Is time contracting? The number of miles per light year would seem to remain constant in space so either could be happening. However, Here on Earth where the surface is not expanding, we would have a discrepancy comparing miles per hour. Me thinks space is expanding.

 

I had to think about that for a minute and I may change my mind as time contracts (or expands). Are you trying to make my head hurt?

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Martin, I have a strong interest in cosmology and relativity but my math background is limited so some of the equations are about as useful as an ASCII dump on my PC monitor. I did take a couple years of algebra and geometry but after that I see F-16s over my head. That is one reason I pursue the different calculators so vigorously as they help me grasp the big picture.

 

Well the answer is easy actually. All over the universe the people can just hold up a thermometer and take the temperature of the CMB sky, and if you and I happened to measure the same temp, then we were part of the same 'now' at that moment. Those two EVENTS were synchro---the events of taking the temp, even if we were billions of lightyears apart.

 

What does the temperature being the same mean? That you are at rest with the CMB and/or you are in the same frame? Does gravity have an impact on this 'now'? I understand this is approximate because of matter distribution. Is that because inconsistent matter distribution causes gravity to not be uniform?

 

Can we do this one short step at a time so my questions are not wasted on irrelevant issues? As you have time of course. I do appreciate your continued help.

[Martin]

What does the temperature being the same mean? That you are at rest with the CMB and/or you are in the same frame? Does gravity have an impact on this 'now'? I understand this is approximate because of matter distribution. Is that because inconsistent matter distribution causes gravity to not be uniform?

...

 

Well that is a respectable question, let's see if I can give it an adequate answer. It may take several days and several installments and/or help from others like Swansont etc, but we'll see.

 

Does gravity have an impact on this 'now'? I understand this is approximate because of matter distribution. Is that because inconsistent matter distribution causes gravity to not be uniform?

 

definitely! Fred is an idealization (perfect uniform matter distribn). Let's set non-uniformity effects aside for now.

 

AT REST means the temperature is the same in all directions, except for the 1/1000 of a percent fluctuations that speckle the map. As we actually measure the CMB there is a huge hotspot due to solarsystem motion, which has to be taken out of the data.

 

It is called the dipole. Let's stop and get to know it. Solar speed relative to CMB is 370 km/s and lightspeed is 300,000 km/s so solarspeed as fraction of lightspeed is 370/300000 = 0.0012. That is one tenth of a percent.

 

So the sky temp is one tenth of a percent hotter than average, in the constellation Leo (the direction we are going). And if you adjust for that and take that out, then the rest of the fluctuation is a thousandth of a percent.

 

There's also a coldspot of the same magnitude in the opposite direction for the same Doppler reason, that's why it's called the dipole---there are two poles to the Doppler distortion of the temperature map.

 

The individual motions of other systems relative to CMB have been calculated. The Milky galaxy as a whole. Andromeda as a whole. Some other galaxies and clusters of galaxies, their collective motion relative CMB.

We see it is typically a few hundred clicks---just like us, a few hundred km/s. This is random individual motion that are on top of in addition to the expansion business. Everybody is assumed to have some random individual motion and to be able to adjust for it.

 

So when we go on and talk about observers a billion LY apart reading the same universe time by looking at the sky, we are going to ignore the dipole Doppler effect and assume they all know how to compensate for it. Or simply assume they are all sitting still---at rest relative to Background. That amounts to the same thing.

 

And as I may have said earlier we will also ignore the fact that observers can be at different depths down their local gravity potential pits---being deep down a well makes a clock run slower. But those differences are small in most cases and can be neglected. The real world is not as uniform as the Freddymodel but nearly.

 

Did you see the photograph of Friedman they have in Wikipedia? Does that look like a guy who once held the high altitude ascent world record? Or more like an extreme egg-headed schoolteacher. My hero!

 

========================

 

Now the serious part. We have these observers all over the universe and each one is constantly measuring the average temp of the CMB sky. None of them are moving and they are all at about the same level in gravitational potential. Each measurement is an EVENT. We want to say when two events occur at the same universal time.

 

Being able to say. Having a criterion for two events being synchronous in universal time---that's what assures that universal time (UT) is well-defined.

Assume by some miracle or previously arranged conspiracy they all use kelvin! Units are a pain in the neck so assume they all use kelvin.

 

Now comes the rabbit! The mathematical wand is waved over the mathematical hat. Actually there's nothing to it. It's trivial.

 

You know the event called "recombination" that happened simultaneously all over the universe when it finally got cool enough for the gas to be effectively transparent, so the CMB light got loose. The background dates from that event.

 

Two people that measure the same CMB redshift are at the same time in the Friedman universe.

 

You asked for small steps. One small step is that everybody uses the same Ned Wright calculator. In that calculator there is nothing special about the earth, or sun, or Milkyway galaxy. You just put in the parameters 0.73, 0.27, 71 that anyone anywhere can measure. You have used that calculator and you know that if you put in the CMB redshift it will tell you the time that has elapsed since recombination. Everybody in the universe can do this. (Except for using different time units, they will be able to agree on a single consistent timescale.)

 

There is a consistency check which I have done---it's kind of fun---and you can do if you want. I can talk you through it. It involves using both morgan and wright calculators. The consistency check is like this: What if we had measured the CMB redshift one billion years ago? We would have measured different instead of 0.73, 0.27, 71, 1100. So we would have put different numbers into the calculator. We would have measured a different CMB redshift (not as big as 1100). I can show you how to figure out those things and do the calculation. What you get is the calculator realizes what's happening and it tells you that the time since recombination has been 12.7 billion years instead of 13.7 billion years!

 

Probably there are a lot neater more efficient ways to explain this. I'm taking a operational concrete approach. Instead of writing equations, I am imagining that we give all the observers a calculator and let them empirically determine four numbers (darkenergy fraction, matter fraction, hubblerate, and background redshift).

 

Oh. the CMB redshift is essentially just 3000 kelvin divided by whatever temperature you measure.

For us, since we measure 2.728, the 1+z is about 3000/2.728.

The 3000 is the temperature which is cool enough for the medium to become effectively transparent. that also is the same for everybody everywhere, except for whatever different units they might use.

I have to go. Late for a matinee of Magic Flute! This could be better but hopefully it will be of some use for the time being.

Edited April 19, 2009 by Martin

[Mr Skeptic]

"If 1 new second = 1/2 old seconds" you would have time segments getting shorter over time, so time is contracting (or is it expanding because it is getting faster?). Therefore it would take longer to cover the same distance making a constant space seem larger. So, the $64,000 question is, 1. Is space expanding? or 2. Is time contracting? The number of miles per light year would seem to remain constant in space so either could be happening. However, Here on Earth where the surface is not expanding, we would have a discrepancy comparing miles per hour. Me thinks space is expanding.

 

Wouldn't the same be true of the expansion of space? But gravity and the electromagnetic bonds between atoms keeps everything together. I think

 

I had to think about that for a minute and I may change my mind as time contracts (or expands). Are you trying to make my head hurt?

 

Yup.

[NowThatWeKnow]

Wouldn't the same be true of the expansion of space?

 

Wait one second. We need to back up. You said

1 new second = 1/2 old seconds...(and)...If you have two years where you had one before

No wonder my head hurt. You have time getting shorter in one place and longer in the other place.

 

If "1 new second = 1/2 old seconds" you have time dilation and dilation is the act of expanding. I believe time dilation allows you to travel further in less time. You also have length contraction so you see space as contracted and I guess it really is relative to your frame.

 

I forgot what I was trying to figure out so I will go read Martin's post.

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Well that is a respectable question, let's see if I can give it an adequate answer. It may take several days and several installments and/or help from others like Swansont etc, but we'll see...

 

...Did you see the photograph of Friedman they have in Wikipedia? Does that look like a guy who once held the high altitude ascent world record? Or more like an extreme egg-headed schoolteacher. My hero!...

 

Friedman looks like an "egg-headed schoolteacher". I wonder if he got married?

 

This post was great for explaining things in a way I can understand. I will put together a summary of what I have learned so far and you can critique it. It is getting late and there are obligations in the morning but I should have some time later in the day tomorrow. I feel good about what I am learning and we can fire up the calculators later. Thanks

 

Edit - I got the same message as you about spreading thanks around.

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Universal time in the Friedman model

 

I understand a universal time (and "now") can be compared and equal at any location in the universe as long as you are at rest with the CMB at that location. The best way for you to determine if you are at rest is a consistent temperature of the CMB in all directions. Because of the motion of the Milky Way we are not at rest with the CMB. Our technology does not allow us to become at rest but our knowledge does allow us to mathmatically adjust for it. It sounds to me like the bottom line is being in the same (at rest) frame so universal time will work.

 

First question:

Since the Milky Way is not at rest and we would have to mathmatically adjust for it, wouldn't that be coming up with a universal time or "now" while frame mixing? Would it be a problem that 1 second in each frame would not have the same duration? Since the differences are small in most cases should we just say close enough knowing there is nothing we can do about it?

 

I know that our universe is only somewhat uniform and can not be considered a true homogeneous and isotropic environment. Your words were "Fred is an idealization (perfect uniform matter distribn)". Would uniformly spaced galaxies of the same size and at rest meet that criteria? It would seem that for true uniformity you would have to break down all matter to it's smallest component and distribute it evenly accross the universe (no galaxies, no stars)

 

Second question

Similar to the first but using gravity. The variable gravity, depending on your location, would make for a variable frame. In most cases the time differences would be small so should we ignore them and again say close enough? Realizing that it would take a true homogeneous and isotropic universe for a true universal time and "now" we just have to accept things for what they are.

Edited April 21, 2009 by NowThatWeKnow
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[Martin]

Friedman looks like an "egg-headed schoolteacher". I wonder if he got married?

 

Any intelligent woman would surely have been thrilled to have him! Unfortunately he caught typhoid fever and died young.

http://www-history.mcs.st-andrews.ac.uk/Biographies/Friedmann.html

 

 

It sounds to me like the bottom line is being in the same (at rest) frame so universal time will work.

What they do is correct the data so that it is as if it were measured by an observer at rest. This is not hard to do because the solarsystem speed is small---only 370 km/s (which includes both the galaxy motion and the motion of the solarsystem within the galaxy, combined)

 

Would it be a problem that 1 second in each frame would not have the same duration? Since the differences are small in most cases should we just say close enough knowing there is nothing we can do about it?

 

I think you can calculate the time dilation effect on the length of one second that results from moving at a speed of 370 km/s. Essentially the speed is 1/1000 of c. And then you square that. So what are we talking about?

0.999999? I think the way you put it, "close enough", describes the situation adequately.

 

It would seem that for true uniformity you would have to break down all matter to it's smallest component and distribute it evenly accross the universe (no galaxies, no stars)

 

Yes! Cosmologists are always talking about the "dust universe". It is an idealization that you can compute with. Imagine matter all spread out uniformly as dust. For a lot of things that's a useful approximation to reality.

 

Seems like you are on the ball and are asking very reasonable questions!

 

 

Similar to the first but using gravity. The variable gravity, depending on your location, would make for a variable frame. In most cases the time differences would be small so should we ignore them and again say close enough? Realizing that it would take a true homogeneous and isotropic universe for a true universal time and "now" we just have to accept things for what they are.

 

Yes again! A rough formula for the grav. redshift is z = GM/c²r.

Some numerator GM/c² divided by r, the distance from the center of mass.

 

And we don't differ if we are at the same depth within our respective galaxies. If I climb out of my gravity valley and walk over and descend down into yours then if it's at the same level then the clocks at each of our houses are the same.

 

Since the effect is small it's no big deal in any case.

 

You can estimate it. GM/c² is half the Schwarzschild radius. For solar mass it equals about one mile.

 

Say the mass of our galaxy, inwards from us, is 100 billion solar so the numerator is 100 billion miles.

 

Our distance from galactic center is what? r = 30,000 lightyears?

 

Our grav. redshift, relative to intergalactic space (far far from Milky) is

z = 10¹¹ miles/ 30,000 lightyears.

 

It will be some extremely small number signifying that the grav. redshift effect of our being where we are in the galaxy (compared with out in intergalactic space) is negligible.

 

I'll bet google will compute this

"10^11 miles/30000 lightyears"

 

Yes! Google computes it and says that it is about six tenths of one millionth. So a gravitational effect on time of the order of one millionth.

Edited April 21, 2009 by Martin

[NowThatWeKnow]

Any intelligent woman would surely have been thrilled to have him! Unfortunately he caught typhoid fever and died young.

 

Interesting read. I never knew that much about Friedmann. His busy life and war must have kept him from marriage as 37 years is enough time to be married several times.

 

 

What they do is correct the data so that it is as if it were measured by an observer at rest. This is not hard to do because the solarsystem speed is small... If I climb out of my gravity valley and walk over and descend down into yours then if it's at the same level then the clocks at each of our houses are the same.

 

Since it is unlikely that any two locations would be at rest with the CMB and they would be in their own gravity frames, adjustments would be necessary to build a clock to show exact universal time. In most cases these adjustments would be very small unless you were at relativistic speeds or near a black hole.

 

If two different locations both had their universal clocks set up with adjustments compensating for there local speed and gravity, would you consider these two clocks synchronized? Allowing them to share the same "now" and simultaneous events, even if they were not aware it because of delays in communication?

 

Edit - Would adjustments in universal time because of gravity be made considering the absence of gravity or mean gravity? It sounds like you were using "way out in space" gravity where it is minimal.

Edited April 21, 2009 by NowThatWeKnow

[Martin]

Since it is unlikely that any two locations would be at rest with the CMB and they would be in their own gravity frames, adjustments would be necessary to build a clock to show exact universal time. In most cases these adjustments would be very small unless you were at relativistic speeds or near a black hole.

 

Universe time (or Friedman time, I've also seen it called)....I've never seen anyone spell out in detail how one would go about setting up a network of observers running that time in the real world. One would have to use powerful radios to communicate between galaxies and wait for 100s of million of years to get a reply, and so on.

 

What you are imagining and what we are discussing is, I think, a useful thought experiment.

 

I mean, universal time is obvious to define in a dust universe where the matter really is perfectly uniformly distributed, and that simplified model is pretty close to what we have, so one gets used to thinking in terms of that time---and it is approximately right for a lot of things. But then as a thought experiment we push the envelope and ask how would you establish that as a practical time standard in the real world?

 

What concrete measures to take.

 

Then problems obviously come up like, suppose galaxies are constantly colliding and merging so that over the years they change mass? If an observer lives in some galaxy at some distance from the center, you can't calculate a correction for his gravitational depth that will be constant always correct. Because circumstances change.

 

These slight gravitational corrections are a great nuisance. It seems that one has to constantly re-calculate them.

 

Maybe in the end one has to simply exclude all the observers who live in galaxies because it is too much bother to include them in the network....you see the difficulties of trying to do this rigorously.

 

Also the criterion for being at rest. The CMB is not perfectly uniform, there are temperature fluctuations on the order of 1/1000 of a percent. That means you can't determine your speed relative to it better than 1/1000 of a percent.

 

That is OK if you are nearly at rest because the speed doesn't affect time passage to any substantial degree. But maybe we should exclude observers who are moving at relativistic speeds.

 

It becomes a kind of ad hoc, provisional make-shift affair, this setting up of a practical realworld standard time.

 

Maybe someone smarter and more motivated than I could see how to do it in a way that would include everybody (even those, as you say, close to black holes).

 

If two different locations both had their universal clocks set up with adjustments compensating for there local speed and gravity, would you consider these two clocks synchronized? Allowing them to share the same "now" and simultaneous events, even if they were not aware it because of delays in communication?

 

Yes! That's the idea. It is simpler to consider just two observers. And I'd go further, I would like them both to be at rest with respect to CMB, so there is no local speed to worry about and adjust for. Also let's take them both to be far away from concentrations of mass, so there is little or no gravitational effect. (I'm prejudiced in favor of simplicity and constantly slip into this mode.) Now, even tho they are widely separated and even tho the distance between them may be increasing at a rate which is several times c, they can both measure the expansion age of the universe and find that it is exactly 13.77 billion years and three hours!

 

But if I had to deal with generic observers, who had been moving around in galaxies, then I would have to imagine the entire world line of a given observer. His whole history, say since the time of last scattering ("recombination", the CMB release date). At every epoch I would need to consider his gravitational depth and his motion relative to background. I'd have to integrate all those corrections. Or he would. Sometimes he would be falling towards a coagulating center of mass, a galaxy in formation. He would have to measure his speed relative to background. Sometimes he would be orbiting the center of the galaxy--he would have to measure his speed and his depth and adjust the readings of his personal clock (his "proper time"). He'd be keeping a log, with two time columns, his own personal atomic clock time ("proper") and the adjusted time ("universal"). At times another galaxy would collide with his, and tear his stellar neighborhood, with his planetary system in it, loose and fling it out into intergalactic space. You see computer simulations of galaxies colliding and this happens to parts of them---parts of them splash very slowly. The collisions are sloppy. So lots of things happen that affect his proper time (relative to universal) and they all get entered in his log.

 

But finally when it was all accounted for he also would say that the universe expansion age was 13.77 billion years and 3 hours . Hopefully.

 

Edit - Would adjustments in universal time because of gravity be made considering the absence of gravity or mean gravity? It sounds like you were using "way out in space" gravity where it is minimal.

 

I was thinking in terms of observers all of whose history is out in intergalactic space because it is so much easier to imagine adjusting their timekeeping to accord with universal. You are right to notice this habitual tendency, a kind of bias. If you were a Time Commissioner you could make an arbitrary choice of how to define the standard. Do you use zero gravity (gravity at infinity, so to speak) or average over your network of observers? I would prefer using zero gravity. Perhaps philosophical questions about that, but in practice it seems clear: get way out in space.

 

Certain elements of comedy here. Timekeepers are a special breed. Finicky. A bit obsessive. I understand that nowadays standard earth time is a mathematical construct related to a putative clock at the center of the earth because they wanted to exclude the effects of rotation. Please don't ask why. Arbitrary choices are always involved.

 

In fact universe time is a good idea, and used in mathematical models, but you would have a very hard time establishing a standard version of it. Maybe a practical impossibility.

Good questions. Made me cogitate some.

Edited April 25, 2009 by Martin

[NowThatWeKnow]

...What you are imagining and what we are discussing is, I think, a useful thought experiment...

 

Yes, an abstract thought experiment at best, at least at this time. Who knows though, we may someday have a gravity aware CMB speedodometer connected to an atomic clock. Until then, the fluctuations in speed and gravity because of movement would be difficult to deal with. Today we adjust for SR and GR on our GPS satellites. Tomorrow, absolute universal time.

 

Martin, A special thanks for your answers in this thread. I went out of my way to spread a few over due thanks to well deserving folks but it is still a no go on the thanks button.

[north]

Even though spacetime is expanding, can we consider it at rest with the universe?

 

from what perspective

 

 

Maybe time moving forward is the expansion we observe?

 

so are you saying that time and time alone has a physical influence on physical objects and therefore expansion ?

 

how so ?

[NowThatWeKnow]

Even though spacetime is expanding' date=' can we consider it at rest with the universe? [/quote']

 

from what perspective

 

I see the expansion of space and moving through space as different. If you are at rest with the CMB, you are at rest with space. The CMB temperature will be the same in all directions. Space is still expanding though.

 

 

Maybe time moving forward is the expansion we observe?

 

 

 

so are you saying that time and time alone has a physical influence on physical objects and therefore expansion ?

how so ?

 

I start with maybe and end with a question mark. Is it possible that time is the so called fabric of space and causing the expansion? I realize this is NOT mainstream but food for thought.