## Hubble 'constant'

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nIt seems my view of the measurement of the hubble \'constant\' is faulty.\n\nI was under the impression that:\n\n1) Distances were measured by a standard candle.\n\n2) Redshifts were measured.\n\n3) The two were related using one model of GR since it seemed to me\nthat, for example, using a different (but similar) GR model could still\nreproduce the observations given these do not cover all of spacetime.\n\n\n\n\n--\nOz\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>It seems my view of the measurement of the hubble 'constant' is faulty.

I was under the impression that:

1) Distances were measured by a standard candle.

2) Redshifts were measured.

3) The two were related using one model of GR since it seemed to me
that, for example, using a different (but similar) GR model could still
reproduce the observations given these do not cover all of spacetime.

--
Oz

 PhysOrg.com physics news on PhysOrg.com >> Iron-platinum alloys could be new-generation hard drives>> Lab sets a new record for creating heralded photons>> Breakthrough calls time on bootleg booze


In article , Oz writes: > It seems my view of the measurement of the hubble 'constant' is faulty. > > I was under the impression that: > > 1) Distances were measured by a standard candle. Yes, or standard rod, or some other combination of rungs of the distance ladder. > 2) Redshifts were measured. Yes. > 3) The two were related using one model of GR Yes. Actually, THE model of GR. What do you mean by other models of GR? > since it seemed to me > that, for example, using a different (but similar) GR model could still > reproduce the observations given these do not cover all of spacetime. Can you give an example of what you mean?



were after the American Constitution went into effect, yet there was more personal freedom in pre-industrial America, both before and after the War of Independence, than there was after the Industrial Revolution took hold in this country. We quote from "Violence in America: Historical and Comparative perspectives," edited by Hugh Davis Graham and Ted Robert Gurr, Chapter 12 by Roger Lane, pages $476-478: "$The progressive heightening of standards of property, and with it the increasing reliance on official law enforcement (in 19th century America)$. . .$were common to the whole society$. . .$[T]he change in social behavior is so long term and so widespread as to suggest a connection with the most fundamental of contemporary social processes; that of industrial urbanization itself$. . .$"Massachusetts in 1835 had a population of some 660,940, 81 percent rural, overwhelmingly preindustrial and native born. It's citizens were used to considerable personal freedom. Whether teamsters, farmers or artisans, they were all accustomed to setting their own schedules, and the nature of their work made them physically dependent on each other.

## Hubble 'constant'

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nPhillip Helbig---remove CLOTHES to reply &lt;helbig@astro.multiCLOTHESvax.d\ne&gt; writes\n&gt;In article &lt;B16fFVbV2wtBFwU9@port995.com&gt;, Oz &lt;oz@farmeroz.port995.com&gt;\n&gt;writes:\n&gt;\n&gt;&gt; It seems my view of the measurement of the hubble \'constant\' is faulty.\n&gt;&gt;\n&gt;&gt; I was under the impression that:\n&gt;&gt;\n&gt;&gt; 1) Distances were measured by a standard candle.\n&gt;\n&gt;Yes, or standard rod, or some other combination of rungs of the distance\n&gt;ladder.\n\nOK, so they measured the attenuation and related that to distance.\nOf course distance is a bit tricky when the damned universe won\'t stay\nstill. Obviously some correction for this must be made. What is the\nnormal relationship assumed between attenuation and distance?\n\n&gt;&gt; 2) Redshifts were measured.\n&gt;\n&gt;Yes.\n\nOnce again the redshift varies with distance, and I understand that its\nall reduced back to the clocks of comoving observers. This naturally\nneeds a model of the universe, so which one, and what is the\nrelationship?\n\n&gt;&gt; 3) The two were related using one model of GR\n&gt;\n&gt;Yes. Actually, THE model of GR. What do you mean by other models of\n&gt;GR?\n\nOK, badly expressed. There are presumably a host of models for the\nevolution of a universe all of which are compatible with GR, and\nprobably quite a few of these compatible with observation in our\nuniverse. That\'s what I meant by model.\n\n&gt;&gt; since it seemed to me\n&gt;&gt; that, for example, using a different (but similar) GR model could still\n&gt;&gt; reproduce the observations given these do not cover all of spacetime.\n&gt;\n&gt;Can you give an example of what you mean?\n\nWell, its proposed that the universe will accelerate in its expansion\nhaving been through a period where acceleration was reduced. This is\nslightly different to the earlier theory that didn\'t include this. I\nimagine both models are derived from GR.\n\n--\nOz\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Phillip Helbig---remove CLOTHES to reply <helbig@astro.multiCLOTHESvax.d
e> writes
>In article <B16fFVbV2wtBFwU9@port995.com>, Oz <oz@farmeroz.port995.com>
>writes:
>
>> It seems my view of the measurement of the hubble 'constant' is faulty.
>>
>> I was under the impression that:
>>
>> 1) Distances were measured by a standard candle.

>
>Yes, or standard rod, or some other combination of rungs of the distance

OK, so they measured the attenuation and related that to distance.
Of course distance is a bit tricky when the damned universe won't stay
still. Obviously some correction for this must be made. What is the
normal relationship assumed between attenuation and distance?

>> 2) Redshifts were measured.

>
>Yes.

Once again the redshift varies with distance, and I understand that its
all reduced back to the clocks of comoving observers. This naturally
needs a model of the universe, so which one, and what is the
relationship?

>> 3) The two were related using one model of GR

>
>Yes. Actually, THE model of GR. What do you mean by other models of
>GR?

OK, badly expressed. There are presumably a host of models for the
evolution of a universe all of which are compatible with GR, and
probably quite a few of these compatible with observation in our
universe. That's what I meant by model.

>> since it seemed to me
>> that, for example, using a different (but similar) GR model could still
>> reproduce the observations given these do not cover all of spacetime.

>
>Can you give an example of what you mean?

Well, its proposed that the universe will accelerate in its expansion
having been through a period where acceleration was reduced. This is
slightly different to the earlier theory that didn't include this. I
imagine both models are derived from GR.

--
Oz



In article , Oz writes: > >> It seems my view of the measurement of the hubble 'constant' is faulty. > >> > >> I was under the impression that: > >> > >> 1) Distances were measured by a standard candle. > > > >Yes, or standard rod, or some other combination of rungs of the distance > >ladder. > > OK, so they measured the attenuation and related that to distance. > Of course distance is a bit tricky when the damned universe won't stay > still. Obviously some correction for this must be made. What is the > normal relationship assumed between attenuation and distance? I'm not sure what you mean by "attenuation". Luminosity distance is a factor or $(1+z)**2$ greater than angular-size distance. It is quite tricky but nevertheless straightforward to relate the various distances to one another and to the observed redshift within the context of classical cosmology. Of course, this assumes that GR is correct; other theories might have other relations between redshift and distance. > >> 2) Redshifts were measured. > > > >Yes. > > Once again the redshift varies with distance, and I understand that its > all reduced back to the clocks of comoving observers. This naturally > needs a model of the universe, so which one, and what is the > relationship? I'm not sure what you mean here. If I measure the redshift of an object, then that tells me how much the universe has expanded since the light was omitted---no more and no less. To know more, I have to know what the cosmological parameters are. Again, though, your question is a bit unclear. Yes, a model is needed (and a framework---for example GR---in which that model exists). > OK, badly expressed. There are presumably a host of models for the > evolution of a universe all of which are compatible with GR, and > probably quite a few of these compatible with observation in our > universe. That's what I meant by model. If you mean "different values of the cosmological parameters" then, yes, distance depends on them. However, for the Hubble constant, this is a higher-order correction and not very important. > Well, its proposed that the universe will accelerate in its expansion > having been through a period where acceleration was reduced. This is > slightly different to the earlier theory that didn't include this. I > imagine both models are derived from GR. Yes, and differ in the values of the cosmological parameters. As mentioned above, though, this is not really relevant for the measurement of the Hubble constant. Actually, at higher redshift, one can and does measure the other cosmological parameters via the higher-order effects I mentioned above.



[NB read to the end before replying] Phillip Helbig---remove CLOTHES to reply writes >In article , Oz >writes: > >> >> It seems my view of the measurement of the hubble 'constant' is faulty. >> >> >> >> I was under the impression that: >> >> >> >> 1) Distances were measured by a standard candle. >> > >> >Yes, or standard rod, or some other combination of rungs of the distance >> >ladder. >> >> OK, so they measured the attenuation and related that to distance. >> Of course distance is a bit tricky when the damned universe won't stay >> still. Obviously some correction for this must be made. What is the >> normal relationship assumed between attenuation and distance? > >I'm not sure what you mean by "attenuation". Luminosity distance is a >factor or $(1+z)**2$ greater than angular-size distance. Luminosity is what I meant by attenuation. The observed change in 'brightness'. Is it the energy received per second, or the number of photons/sec? Hmm, could be either but probably energy/s. So let me just confirm what you are saying. There are so many corrections made, often it seems simply assumed, that I need to be clear. I also need to firm up the hazy 'knowledge' of other details. Firstly your expression $(1+z)$. I guess this is related to redshift. Would $a z=1$ correspond to a doubling of wavelength as observed from earth? Hmm. Its not quite so simple as one might imagine on reflection. One is tempted to imagine that an expanding universe might actually look like an inflating balloon taking the surface as a slice of 4D spacetime at the same distance as our target star. This leads one to expect the apparent angular size will remain constant as its (or the light from it) expands with the expanding balloon surface (as a small circle on the balloon would). This doesn't feel right at all, but could be. Better might be to say that space is 'created' at each point in spacetime in which case the angular size will decrease as space expands. [I can't resist an aside here in that this implies that either spacetime thinks stars are contracting or there is an outflow of spacetime from the surface of every body in the universe.] I'm rapidly heading to complete confusion. Let me set out how I see it, and then you can tear me to shreds afterwards. Lets have a standard candle delivering J joules. At a (static universe) distance of r we would receive say $kJ/r^2$ joules in our telescope. [k being some constant of proportionality]. We would thus interpret this as a star r meters away. But if the universe is expanding, but excluding any energy loss due to change of wavelength, then those J joules will be spread.... $oh bu**er$... I'm just about to fall into a GR-trap. How are we to define distance in an expanding universe? After all the star is 'now' further away than it was when the light left it! I understand that the distance is usually defined in the frame, no slice, of comoving observers. To do that we must use a particular GR model of the universe. So let me think. We have an unadjusted figure for distance, based on $kJ/r^2$. We know that the light has been stretched because we know the redshift. That's a historic but observed stretch. We can, then, justifiably *increase* the luminosity (in photon-counts) by the redshift to say how far away the star was from earth $*when$ the light originally left the $star*$. If we use the energy (ie Joules) then we need to put in an extra factor because the stretching of the wavelength implies that, in effect, time has also slowed down. So we need to increase the energy by the redshift factor. So I think the *energy* received by a a telescope viewing a standard candle will have the redshift factor squared, presumably your $(1+z)^2$ (or the inverse because I am relating distance back to the time when the light was emitted). Ah, but assuming an isotopic universe, we also have more recent sections of observed expansion. We can thus plot expansion with time. Hmm, I need to be very careful to keep to what we can actually observe. We can *observe* the distance of standard candles when they emitted their light. We can also say how much expansion has occurred over the period the light has been travelling towards us. We can also tell how long ago (I think this is model-invariant) the light was emitted. So, using many standard candles spaced over a wide range of distances/emission-times we can plot redshift against time since emission. We hope this matches theory. >It is quite >tricky but nevertheless straightforward to relate the various distances >to one another and to the observed redshift within the context of >classical cosmology. Of course, this assumes that GR is correct; other >theories might have other relations between redshift and distance. Oh. Do you mean a particular model based on GR or do you mean GR as 'expansion stretches light'? >> >> 2) Redshifts were measured. >> > >> >Yes. >> >> Once again the redshift varies with distance, and I understand that its >> all reduced back to the clocks of comoving observers. This naturally >> needs a model of the universe, so which one, and what is the >> relationship? > >I'm not sure what you mean here. If I measure the redshift of an >object, then that tells me how much the universe has expanded since the >light was omitted---no more and no less. To know more, I have to know >what the cosmological parameters are. Again, though, your question is a >bit unclear. > >Yes, a model is needed (and a framework---for example GR---in which that >model exists). Do we need both GR AND a model to do the 'historic' graph between redshift and distance? >If you mean "different values of the cosmological parameters" then, yes, >distance depends on them. However, for the Hubble constant, this is a >higher-order correction and not very important. Is this because many models have been discarded as not matching observation or does this mean most reasonable models have much the same form when reasonable parameters are plugged in that match what we observe. Er, or both.... >> Well, its proposed that the universe will accelerate in its expansion >> having been through a period where acceleration was reduced. This is >> slightly different to the earlier theory that didn't include this. I >> imagine both models are derived from GR. > >Yes, and differ in the values of the cosmological parameters. As >mentioned above, though, this is not really relevant for the measurement >of the Hubble constant. Actually, at higher redshift, one can and does >measure the other cosmological parameters via the higher-order effects I >mentioned above. Would it be fruitful to itemise the more important ones, just for interest? -- Oz



In article , Oz writes: > >> >> It seems my view of the measurement of the hubble 'constant' is faulty. > >> >> > >> >> I was under the impression that: > >> >> > >> >> 1) Distances were measured by a standard candle. > >> > > >> >Yes, or standard rod, or some other combination of rungs of the distance > >> >ladder. > >> > >> OK, so they measured the attenuation and related that to distance. > >> Of course distance is a bit tricky when the damned universe won't stay > >> still. Obviously some correction for this must be made. What is the > >> normal relationship assumed between attenuation and distance? > > > >I'm not sure what you mean by "attenuation". Luminosity distance is a > >factor or $(1+z)**2$ greater than angular-size distance. > > Luminosity is what I meant by attenuation. The observed change in > 'brightness'. Is it the energy received per second, or the number of > photons/sec? Hmm, could be either but probably energy/s. Right. > So let me just confirm what you are saying. There are so many > corrections made, often it seems simply assumed, that I need to be > clear. I also need to firm up the hazy 'knowledge' of other details. Right. > Firstly your expression $(1+z)$. I guess this is related to redshift. z is redshift, yes. > Would $a z=1$ correspond to a doubling of wavelength as observed from > earth? Yes. > Hmm. Its not quite so simple as one might imagine on reflection. One is > tempted to imagine that an expanding universe might actually look like > an inflating balloon taking the surface as a slice of 4D spacetime at > the same distance as our target star. This leads one to expect the > apparent angular size will remain constant as its (or the light from it) > expands with the expanding balloon surface (as a small circle on the > balloon would). This doesn't feel right at all, but could be. Right; the angular-size distance essentially measures the proper distance at the time the light was emitted. (Proper distance would be what one would measure with a ruler instantaneously. It is an important conceptual distance in general relativity, but is not something one can actually measure.) The defining angle is that at the observer, and this doesn't change as the universe expands. > Lets have a standard candle delivering J joules. > > At a (static universe) distance of r we would receive say $kJ/r^2$ joules > in our telescope. [k being some constant of proportionality]. > > We would thus interpret this as a star r meters away. Right. This is the definition of luminosity distance. > But if the universe is expanding, but excluding any energy loss due to > change of wavelength, then those J joules will be spread.... > $oh bu**er$... No reason to exclude energy loss due to change in wavelength. Basically, the defining angle for luminosity distance is that at the source. However, as the universe expands, this will correspond to a smaller area at the observer. Hence, one factor of $(1+z)$. Since the wavelength is also stretched, we get another factor of $(1+z)$. In other words, apart from the second factor of $(1+z),$ the luminosity distance basically is the same as the proper distance at the time the light was received at the observer. > I'm just about to fall into a GR-trap. > How are we to define distance in an expanding universe? We define distances via a measurement description. Apart from the three discussed above, there is parallax distance and distance by light-travel time. Apart from the distance by light-travel time, the others are related by simple factors (usually just powers of $(1+z))$. > After all the star is 'now' further away than it was when the light left > it! Right. > So let me think. We have an unadjusted figure for distance, based on > $kJ/r^2$. We know that the light has been stretched because we know the > redshift. > > That's a historic but observed stretch. We can, then, justifiably > *increase* the luminosity (in photon-counts) by the redshift to say how > far away the star was from earth $*when$ the light originally left the > $star*$. > > If we use the energy (ie Joules) then we need to put in an extra factor > because the stretching of the wavelength implies that, in effect, time > has also slowed down. So we need to increase the energy by the redshift > factor. > > So I think the *energy* received by a a telescope viewing a standard > candle will have the redshift factor squared, presumably your $(1+z)^2$ > (or the inverse because I am relating distance back to the time when the > light was emitted). Right. > Ah, but assuming an isotopic universe, we also have more recent sections "Isotropic", presumably. > of observed expansion. We can thus plot expansion with time. Hmm, I need > to be very careful to keep to what we can actually observe. We can > *observe* the distance of standard candles when they emitted their > light. We can also say how much expansion has occurred over the period > the light has been travelling towards us. We can also tell how long ago > (I think this is model-invariant) the light was emitted. No; light-travel time is a function of redshift and the cosmological parameters. > standard candles spaced over a wide range of distances/emission-times we > can plot redshift against time since emission. We hope this matches > theory. Right. > >It is quite > >tricky but nevertheless straightforward to relate the various distances > >to one another and to the observed redshift within the context of > >classical cosmology. Of course, this assumes that GR is correct; other > >theories might have other relations between redshift and distance. > > Oh. > Do you mean a particular model based on GR or > do you mean GR as 'expansion stretches light'? Both. > Do we need both GR AND a model to do the 'historic' graph between > redshift and distance? Yes. > >If you mean "different values of the cosmological parameters" then, yes, > >distance depends on them. However, for the Hubble constant, this is a > >higher-order correction and not very important. > > Is this because many models have been discarded as not matching > observation or does this mean most reasonable models have much the same > form when reasonable parameters are plugged in that match what we > observe. Er, or both.... The former. > >> Well, its proposed that the universe will accelerate in its expansion > >> having been through a period where acceleration was reduced. This is > >> slightly different to the earlier theory that didn't include this. I > >> imagine both models are derived from GR. > > > >Yes, and differ in the values of the cosmological parameters. As > >mentioned above, though, this is not really relevant for the measurement > >of the Hubble constant. Actually, at higher redshift, one can and does > >measure the other cosmological parameters via the higher-order effects I > >mentioned above. > > Would it be fruitful to itemise the more important ones, just for > interest? The cosmological constant $(\lambda)$ and the density parameter $(\Omega)$. See http://www.astro.multivax.de:8000/he...fo/angsiz.html for a discussion of various cosmological distances and the relationships between them.



Thank your for your very clear reply to my posting. Phillip Helbig---remove CLOTHES to reply writes >> I'm just about to fall into a GR-trap. >> How are we to define distance in an expanding universe? > >We define distances via a measurement description. Apart from the three >discussed above, there is parallax distance and distance by light-travel >time. Apart from the distance by light-travel time, the others are >related by simple factors (usually just powers of $(1+z))$. OK. Parallax distance I could probably figure out given a precise definition, but that's not important right now. I am intrigued by 'light-travel' time. I wonder if you could say a few words on this. >No; light-travel time is a function of redshift and the cosmological >parameters. >> >It is quite >> >tricky but nevertheless straightforward to relate the various distances >> >to one another and to the observed redshift within the context of >> >classical cosmology. Of course, this assumes that GR is correct; other >> >theories might have other relations between redshift and distance. >> >> Oh. >> Do you mean a particular model based on GR or >> do you mean GR as 'expansion stretches light'? > >Both. I'm slightly puzzled by this. As far as I can see redshift measures the amount of expansion that has occurred during the period the light has been travelling. This is in effect a measurement, and is a fact. Its a distance, be it in space $and/or$ time. The only other way we can get it is if it is lengthened by a climbing from a gravitational well. I had intended to discuss this latter point in this post, in particular the effect of assigning all the redshift this way. I guess this is looking at the redshift as a time, as opposed to a spatial, effect. However I'm not so sure I quite have enough information yet. >The cosmological constant $(\lambda)$ and the density parameter $(\Omega)$. > >See > > http://www.astro.multivax.de:8000/he...fo/angsiz.html > >for a discussion of various cosmological distances and the relationships >between them. I'm leaving this in to remind me to take a look. -- Oz



In article , Oz writes: > Thank your for your very clear reply to my posting. > > Phillip Helbig---remove CLOTHES to reply e> writes > >> I'm just about to fall into a GR-trap. > >> How are we to define distance in an expanding universe? > > > >We define distances via a measurement description. Apart from the three > >discussed above, there is parallax distance and distance by light-travel > >time. Apart from the distance by light-travel time, the others are > >related by simple factors (usually just powers of $(1+z))$. > > OK. Parallax distance I could probably figure out given a precise > definition, but that's not important right now. The important thing is that all distances are defined just as they are in a stationary non-curved space. In that case, all the distances are equivalent: we can use a tape measure (proper distance) to lay out a baseline for surveying using trigonometry (parallax distance) to measure the distance to a lighthouse. Perhaps we will use laser-ranging to measure a longer length (light-travel--time distance). When we know the distance to the lighthouse (and the brightness of it), we can calculate how bright it will appear (luminosity distance). Of course, we can also calculate how big it will appear (angular-size distance). If space is non-stationary $and/or$ curved, then these distances are not necessarily all the same. > I am intrigued by 'light-travel' time. > I wonder if you could say a few words on this. Distance = velocity*time. We know the velocity of light, so there is a distance which corresponds to the time the light was travelling. Of course, in practice we can't actually measure the light-travel time, except perhaps via radar. > >> >It is quite > >> >tricky but nevertheless straightforward to relate the various distances > >> >to one another and to the observed redshift within the context of > >> >classical cosmology. Of course, this assumes that GR is correct; other > >> >theories might have other relations between redshift and distance. > >> > >> Oh. > >> Do you mean a particular model based on GR or > >> do you mean GR as 'expansion stretches light'? > > > >Both. > > I'm slightly puzzled by this. As far as I can see redshift measures the > amount of expansion that has occurred during the period the light has > been travelling. This is in effect a measurement, and is a fact. Its a > distance, be it in space $and/or$ time. It tells us the RATIO of the size of the universe now to that at the time the light was emitted. It doesn't tell us anything about how far the light has actually travelled. Imagine a universe which expands very slowly. In this case, a small redshift can correspond to a large distance. > The only other way we can get it is if it is lengthened by a climbing > from a gravitational well. > > I had intended to discuss this latter point in this post, in particular > the effect of assigning all the redshift this way. I guess this is > looking at the redshift as a time, as opposed to a spatial, effect. > However I'm not so sure I quite have enough information yet. Look for a post by Ted Bunn where he discusses an article by Narlikar in the American Journal of Physics.



Phillip Helbig---remove CLOTHES to reply wrote: > Oz writes: >>I am intrigued by 'light-travel' time. >>I wonder if you could say a few words on this. > > Distance = velocity*time. We know the velocity of light, so there is a > distance which corresponds to the time the light was travelling. Of > course, in practice we can't actually measure the light-travel time, > except perhaps via radar. I don't think that is unambiguous, since time is frame dependent. The only invariant time proper time, which for light is zero. I can *guess* what you mean, and if I really cared I could look it up (assuming everyone uses the same definition). By travel time you could mean the difference in age of the universe (as measured by the CMB temperature) between when the light was emitted and when it was seen. Or you could mean half the round trip time (your mention of radar suggests that), but then you need to specify when (and at which end) the round trip starts or ends. It could be how long ago we would have had to send a signal to receive the echo now, or how long we would have to wait for a signal we sent now. There is the travel time in the CMB frame. The coordinates in which "rest" at each point along the path is defined by the cosmic microwave background being isotropic. Some of those may be equivalent. Ralph Hartley



2 eggs 1 tablespoon yellow mustard 1 cup seasoned flour oil enough for deep frying 1 loaf French bread Lettuce tomatoes mayonnaise, etc. Marinate the fetuses in the egg-mustard mixture. Dredge thoroughly in flour. Fry at 375° until crispy golden brown. Remove and place on paper towels. Holiday Youngster One can easily adapt this recipe to ham, though as presented, it violates no religious taboos against swine. 1 large toddler or small child, cleaned and de-headed Kentucky Bourbon Sauce (see index) 1 large can pineapple slices Whole cloves Place him (or ham) or her in a large glass baking dish, buttocks up. Tie with butcher string around and across so that he looks like he?s crawling. Glaze, then arrange pineapples and secure with cloves. Bake uncovered in 350° oven till thermometer reaches 160°. Cajun Babies Just like crabs or crawfish, babies are boiled alive! You don?t need silverware, the hot spicy meat comes off in your hands. 6 live babies 1 lb. smoked sausage 4 lemons whole garlic 2 lb. new potatoes 4 ears corn 1 box salt crab boil Bring 3 gallons of water to a boil. Add sausage, salt, crab boil, lemons and garlic. Drop potatoes in, boil for 4 minutes. Corn is added next, boil an additional 11 minutes. Put the live babies into the boiling water and cover. Boil till meat comes off easily with a fork. Oven-Baked Baby-Back Ribs Beef ribs or pork ribs can be used in this recipe, and that is exactly what your dinner guests will assume! An excellent way to expose the uninitiated to this highly misunderstood yet succulent source of protein. 2 human baby rib racks 3 cups barbecue sauce or honey glaze (see index) Salt black pepper white pepper paprika Remove the silverskin by loosening from the edges, then stripping off. Season generously, rubbing the mixture into the baby



In article , Ralph Hartley writes: > Phillip Helbig---remove CLOTHES to reply wrote: > > Oz writes: > >>I am intrigued by 'light-travel' time. > >>I wonder if you could say a few words on this. > > > > Distance = velocity*time. We know the velocity of light, so there is a > > distance which corresponds to the time the light was travelling. Of > > course, in practice we can't actually measure the light-travel time, > > except perhaps via radar. > > I don't think that is unambiguous, since time is frame dependent. The only > invariant time proper time, which for light is zero. > > I can *guess* what you mean, and if I really cared I could look it up > (assuming everyone uses the same definition). > > By travel time you could mean the difference in age of the universe (as > measured by the CMB temperature) between when the light was emitted and > when it was seen. I should have said "cosmic time", which as you say can be measured by the CMB temperature. This is the time measured by observers who are not moving within the universe.



well use veal - after all, you have to be careful - Sicilians are touchy about their young family members... 6 newborn or veal cutlets Tomato gravy (see index) 4 cups mozzarella, 1cup parmesan, 1cup romano Seasoned bread crumbs mixed with parmesan romano salt pepper oregano garlic powder chopped parsley Flour eggwash (eggs and milk) Peanut oil for frying. Pound the cutlets. Dredge in flour, eggs, then the bread crumb mixture. Fry till golden brown in 350° peanut oil. In a baking pan, place a layer of gravy, then one of meat, gravy, and cheese. Another layer each of meat, gravy, and cheese. Then bake at 350° for 45 minutes. Serve on hot pasta with romano cheese. Southern Fried Small-fry Tastes like fried chicken, which works just as well. In fact you may want to practice cutting up whole chickens for frying before you go for the real thing. Whole chicken is much more efficient and inexpensive than buying pieces. 1 tiny human, cut into pieces 2 cups flour Onion, garlic Salt pepper garlic powder cayenne pepper hot sauce, etc. Oil for frying Mix milk, eggs, hot sauce in a bowl, add chopped onion and garlic. Season the meat liberally, and marinate for several hours. Place seasoned flour in a paper or plastic shopping bag,