On the Hubble expansion and observability

[my_wan]

Although I have philosophical objections to being considered "Against The Mainstream" as I considered some questions seen on this board I have found some problems that will fit this category. At the very least I hope to articulate the range of possibilities. Of particular interest to me are the skeptics.

Questions about expansion and observability have continually came up with varying levels of sophistication. Some deal with how the speed of light is affected by expansion, others simply by the observability. grav has done some fairly sophisticated thinking about the issues. The standard model says that space itself is expanding. I then set out to define it relativistically. The question I'll try to address is can this be incorporated into standard relativity in such a way that we can begin asking empirical questions? To do this I will try to relate the Hubble expansion to an expansion in the spacetime interval that varies with time in the same way GR relates a change in the spacetime interval that varies with position in the feild.

Postulate;
The Hubble expansion is an expansion in the spacetime interval.

Under GR we are familiar with expanding spacetime intervals in terms of a change in curvature or depth of feild. Here we will relate it to a change in time due to expansion. Since this is a preliminary model let's look at known GR effects as seen under Newtonian gravity as a litmus test. Specifically those that lead to the correct advance of the perihelion of mercury. This is mathematically done by applying the Lorentz transform to the instantaneous acceleration of g. As you move a meterstick away from the sun its length is Lorentz Transformed from the suns proper time to smaller units. The observer at the meterstick sees no change in the meterstick units because it represents that observers proper units. That observer will note that the sun will appear to gain mass though because of his smaller proper units. Locally these transformation of units are purely mathematical and don't represent real changes in parameters. However if we consider a mass (A) at the sun and in the proper units of (A) observes an equal mass (B) in outer space then as mass (B) approaches the sun mass (A) will notice that their mass is no longer equal. In fact both masses agree that mass (B) shrank in comparison to (A) even though both masses in their proper frames didn't change. It is this actual change in parameters that leads to the correct advance of the perihelion of mercury.

Now we will consider a uniform expansion in the spacetime interval over time. An observer outside our universe would watch our universe expand. Localy we would see no change because the spacetime interval defines our proper time. This is physically equivalent to the depth of the gravitational field increasing uniformly throughout the universe. If we consider a distant light signal from the past then the information is from a time when the spacetime interval was shorter. The gravitational redshift is z=(ω_o-ω_e)/ω_e, where ω_o is the wavelength defined by the spacetime interval of a distant observer and ω_e is the wavelength in proper units at the source of emission. Modeling expansion this way ω_o is defined by proper units in the present while ω_e is defined by proper units in the past. This indicates that space is in fact expanding but as the distance between points expands so does our meterstick.

Taken at face value this leads to some strange conclusions.
1) The universe is expanding.
2) This Hubble expansion is observed via the redshift.
3) The proper interval between masses are not increasing as a result of this Hubble expansion.

I am not very familiar with the coordinate system used by cosmology. I must remedy this for certain comparisons. However given the addition of velocities as defined by SR this would make it appear as if the farther we look back in time the slower the Hubble expansion will appear or accelerated expansion. This could provide a test if the addition of velocities correctly predict the magnitude of the accelerated expansion. Although the comoving coordinates of cosmology are explicitly designed to wash out the relativistic addition of velocities it doesn't include the above described effects of expansion. I need more data on this.

It is usefull to determine how we might question the legitamacy of tying expansion of space to the spacetime interval in this way. If we assume the absolute magnitude of proper distance is increasing with expansion but maintain a relationship with the spacetime interval it leads to more empirical consequences. It would mean that fundamental physical constants are decreasing with time. In fact the Hubble constant would define the rate at which they decrease. The only remaining approach I can think of is that the spacetime interval has a value independent of particles that exist within it. This would mean that the Big Bang was an event that occurred in a spacetime that had preexisting properties. The Hubble expansion would then be an actual increase in the magnitude of proper distance. The notion that space is what is expanding then becomes untenable, it would merely be a seperation of the masses in it. None of these alternatives are very satisfactory upon inspection but I will entertain them for review. The question here is, "How can we increase the total spacetime without increasing the spacetime interval or proper units of an observer?". Any prior work on this issue would be appreciated.

-"Proper" is always intended here to indicate proper spacetime intervals as defined by a local observer not necessarily the proper distance as defined by Weinberg.

[tusenfem]

As you move a meterstick away from the sun its length is Lorentz Transformed from the suns proper time to smaller units. The observer at the meterstick sees no change in the meterstick units because it represents that observers proper units. That observer will note that the sun will appear to gain mass though because of his smaller proper units.

Nope, I think at most the observer may think that the density of the sun has changed it his measuring rod is changed moving from frame to fram.

[my_wan]

As you move a meterstick away from the sun its length is Lorentz Transformed from the suns proper time to smaller units. The observer at the meterstick sees no change in the meterstick units because it represents that observers proper units. That observer will note that the sun will appear to gain mass though because of his smaller proper units.

Nope, I think at most the observer may think that the density of the sun has changed it his measuring rod is changed moving from frame to fram.

Is that not what I said? I'm looking for where you might take exception.

peice by peice;
1)

As you move a meterstick away from the sun its length is Lorentz Transformed from the suns proper time to smaller units.

It is the meterstick or in you words the "the observer" and "his measuring rod" that I said changed proper units.
2)

The observer at the meterstick sees no change in the meterstick units because it represents that observers proper units..

Surely you can't seriously be saying that a measuring stick in your hand changes length by your own measure as you change depth in a gravitation feild?
3)

That observer will note that the sun will appear to gain mass though because of his smaller proper units.

Keyword; "appear to". I don't claim the sun changed mass but in the new units that are proper to the observer stated here it "appears" to him as if it does.

This is not even anything new to physics and can be checked against the standard model. I'm therefore still lost on what you disagreed with.

It almost appears as though you are arguing on the difference between what is real and what is mathematical artifacts, yet my use of "appear to" makes even this difficult for you. I'm arguing solely on what the respective observers measure. I hope you can make your point a little more clear.

[my_wan]

Perhaps I need to state the case more concisly.

Postulate
The Hubble expansion is an expansion of the spactime interval.

It is assumed that if the Hubble expansion is an expansion of space then it must be reflected in the spacetime interval s² = x² - c² t² of the observers in spacetime. This requires that the Hubble expansion is not observable locally for the same reason that an observer cannot observe ∆s locally as the depth in a gravitational field changes. Such changes are only observable by comparing ∆s to another reference observer as the depth in a gravitional field changes. We can do this by measuring the gravitational redshift of light sent from one gravitational potential to another. To observe the Hubble expansion we can measure this same redshift by recieving a light signal from the past.

The gravitational redshift is z=(ω_o-ω_e)/ω_e.
ω_o is the wavelength as measured by a distant observer.
ω_e is wavelength as measured at the source of emission.

The Hubble redshift is then z_h=(ω_o-ω_e)/ω_e.
ω_o is the wavelength as measured by a future observer.
ω_e is wavelength as measured at the time of emission.

Nothing more than the postulate and the standard model of physics is needed to make the case.

[my_wan]

I disappointed that nobody has made a reasonable case against this. You do not have to be nice about it at all just physically reasonable. I do not even expect this to be right but I can't find an escape within the standard model of physics. I am not so familiar with the standard model of cosmology.

Dan Shiva asked a related question in a more general way and got this answer from Tim Thompson.

To this I responded.

Generally speaking, in general relativity, there are two kinds of time: coordinate time and proper time. The former is the one that is gravity dependent, but the latter is not.

That statement does not really make much sense when coordinate time is nothing more that what proper time would be for an observer at that point. The concept of coordinate time is usefull for speaking about proper times across the entire coordinate system rather than for particular observers. It is not a different "kind of time" or coordinate system. It is not possible to speak of GR being independent of proper time when proper time changes as the depth of field changes and coordinate time is the proper time on the whole coordinate system.

If Tim could enlighten me perhaps I could wash my hands of this thread.

Bjoern also created this thread, "To all proponents of a universe with infinite age" To this I responded.

I am well aware of the empirical issues with trying to claim the observable universe is older than ~15 billion years. It is silly to expect it on prejudice alone. My own ATM posting in this category was born out of attempts to answer questions on this board and the standard model of physics. It is in no way a claim about age in general or even a claim about the legitamacy of the Big Bang. It is merely an attempt to articulate what the Hubble flow can say about it.

If you look at my post history I have not always been especially nice. So I'm looking for an arguement here to relieve myself of this idea.

[grav]

I couldn't really read your original post too well, but I can read your more concise post better. I'm still not sure what you are saying causes a gravitational redshift, however.

If it is the galaxy it is emitted from, then that redshift will be limited to a few parts in a million for a star, and perhaps one in a few hundred thousand or so for a galaxy, and it will have no relation to the overall distance travelled, once far enough away, since almost all of that limit will be reached when it is closer to the point of emission. It would also blueshift again slightly when approaching our galaxy, solar system, and planet.

If you are referring to the entire universe as one great sphere of mass, where the gravitational redshift depends on the gravitational potential between one point and another, then this would create a redshift or blueshift depending on our position in the sphere and that of the point of emission, and all blueshifts from points further from the center than we are, which we don't observe. Also, according to the Big Bang scenario, all points can be considered the center, so there is no particular direction for an overall gravity to act.

I'm not sure if either of these is what you meant, though, so you can let me know.

[my_wan]

The gravitional curvature alone is not all that determines gravitational time dialation. Imagine a large hollow massive sphere. As you approach this sphere the gravitational time dialation will increase as you approach this sphere. If you pass inside this sphere then spacetime will be flat inside, yet the time dialation will remain slowed to that of the surface anywhere inside the sphere. Under GR the depth of field determines relative time dialation not the curvature.

Now imagine two observers seperated inside this sphere and the mass of the sphere is steadily increasing. Inside the time dialtion will steadily increase compared to a far removed observer even though the spacetime inside remains flat. Now when one of our observers sends a light signal to another the signal will be redshifted because of the finite value of C. The second observer will recieve this signal at a later time when the spacetime interval has changed. This is where I get the time dependent Hubble shift zh=(ωo-ωe)/ωe.

The question this posses is, "How can we speak of the Hubble expansion being an expansion of space itself if it has no relation to the spacetime interval?" If we assume the relationship is direct then it leads to this problem with proper distances after a period of expansion. Note that for our sphere the radius appears to decrease for our two observers because our sphere is not expanding with the spacetime.

Your questions are very much appreciated.

[john hunter]

Dear my wan,
You mentioned that any other work on this would be welcome.

In www.rescalingsymmetry.com there is something, and its sister website www.gravity.uk.com.

If you can make a relativistic version, please do.

All the best,

John Hunter

[tusenfem]

I am very confused here, because my_wan seems to be arguing with my_wan, but anywhoooo:

Is that not what I said? I'm looking for where you might take exception.

peice by peice;
1)

It is the meterstick or in you words the "the observer" and "his measuring rod" that I said changed proper units.
2)

Surely you can't seriously be saying that a measuring stick in your hand changes length by your own measure as you change depth in a gravitation feild?
3)

Keyword; "appear to". I don't claim the sun changed mass but in the new units that are proper to the observer stated here it "appears" to him as if it does.

This is not even anything new to physics and can be checked against the standard model. I'm therefore still lost on what you disagreed with.

What I was complaining about was that you said the sun seems to gain mass, and that is not true. The mass remains the same, the rod changes, thus the volume of the sun changes, and with the same mass that means that the density of the sun changes.

[my_wan]

Dear my wan,
You mentioned that any other work on this would be welcome.

In www.rescalingsymmetry.com there is something, and its sister website www.gravity.uk.com.

If you can make a relativistic version, please do.

All the best,

John Hunter

Yes I am in the process of reviewing that work. I assume it is you I emailed about what I was doing. The scaling appears to be tacked onto the standard model as an extra appendage. However by the way the conjecture was defined mc²-GMm/r=0 it appears that the scaling has some level of legitamacy at least as an approximation. I see that the rotation curves are not scaled to any actual galaxy either. Rather than use ∆s as defined by relativity the scaling correction has been attached to newtonian physics in a uniform and frame dependant manner. As I am just getting started coming from an entirely different starting point I'm not ready for a direct comparison. I can't endorse any of the conclusions on that site yet either. I can't even fully endorse my own approach yet. Still too many open questions, including how well it will fit numerically. It idea looks intriguing though. If you are interested I will keep you updated.

[my_wan]

I am very confused here, because my_wan seems to be arguing with my_wan, but anywhoooo:

Of course I'm arguing with myself. I can't presume from the start that I'm right. So far my brother is my only good tenacious skeptic. Anyway my response here got me to thinking that the Hubble expansion wouldn't impart a real acceleration on mass particles as the expansion is locally symmetric. It would then make the anology in the above response even closer meaning distances under some circumstances would appear to decrease with the Hubble shift. A quick check of the pioneer anomaly showed a nice fit so I searched for prior work and found this http://arxiv.org/abs/astro-ph?papernum=0701132. Although the pioneer anomaly was Erhard Scholz's motivation the effect he describes is identical.

Mostly at this point I'm trying to articulate the differences that might be empirically different under different interpretations of what 'expanding space' might mean physically. Specifically apparent vs real changes in physical constants.

[Squashed]

I think publius has a better handle on the whole state of these affairs but in his absence I will state that length contraction is always a single axis/dimensional phenomenon.

In Special Relativity the length contraction is in the direction of travel which if the travel is along the X-axis then all the length contraction will be evident along the X-axis.

For gravity the length contraction is along the radial vector away from the center of gravity.

So in both cases the length contraction is only evident in one dimension whether this phenomenon actually causes a "density" change, since volume would be affected by length contraction, could be debated.

[my_wan]

I think publius has a better handle on the whole state of these affairs but in his absence I will state that length contraction is always a single axis/dimensional phenomenon.

In Special Relativity the length contraction is in the direction of travel which if the travel is along the X-axis then all the length contraction will be evident along the X-axis.

For gravity the length contraction is along the radial vector away from the center of gravity.

So in both cases the length contraction is only evident in one dimension whether this phenomenon actually causes a "density" change, since volume would be affected by length contraction, could be debated.

Not only are you wrong in both cases it is inmaterial to the case I have made. You appear to be viewing gamma as under the limited viewpoint of apparent changes only. I am not interested in what things appears to look like for a given observer. I am only interested in actual changes of parameters such as the Twin (not a) Paradox in SR and those that lead to the corrected perihelion of mercury in GR. Let's look at your statements individually.

1) Under SR length contraction only occurs on the X-axis of motion.

Apparent length contraction occurs from the apparent change in distance r from an observer. Imagine a large sphere traveling toward you. Looking down the axis of motion you get the standard length contraction. If you look at the sphere at some angle to this axis then the rate of decrease of r will be somewhat slower such that length contraction is somewhat less. This change in the length contraction decreases at all angles out until you view it at right angles to the direction of motion at which point you see no contraction on that axis. The velocity you use for apparent length contracton is defined by the rate of change in the radius from the observer. The end result of all the effects of the Relativity of Rigidity is always the same as if you assumed no length contraction. Even if solid objects appear to bend to accomplish this. As there are no actuall changes in parameters only changes of units it is of no value to explain the effects I have described.

2) For gravity the length contraction is along the radial vector away from the center of gravity.

I am assuming here that the observer is on the surface of the mass therefore not freefalling. Unlike SR under GR every observer in the universe agrees that time is slower for this observer than one placed higher up in the gravitational potential such as on top of a mountain. This means for our observer on the surface the entire universe appears smaller in all directions compared to the one on the mountain. This remains true even if you are at the center of the mass where you feel no gravitational forces. Although these effects are in line with my ideas here you appear to assume that gravitational effects are limited to SR effects induced by the acceleration of g.

[Squashed]

1) Under SR length contraction only occurs on the X-axis of motion.

Apparent length contraction occurs from the apparent change in distance r from an observer. Imagine a large sphere traveling toward you. Looking down the axis of motion you get the standard length contraction. If you look at the sphere at some angle to this axis then the rate of decrease of r will be somewhat slower such that length contraction is somewhat less. This change in the length contraction decreases at all angles out until you view it at right angles to the direction of motion at which point you see no contraction on that axis. The velocity you use for apparent length contracton is defined by the rate of change in the radius from the observer. The end result of all the effects of the Relativity of Rigidity is always the same as if you assumed no length contraction. Even if solid objects appear to bend to accomplish this. As there are no actuall changes in parameters only changes of units it is of no value to explain the effects I have described.

...

Your description sounds like foreshortening in drafting's orthographic projection.

Your sphere example reminds me of this.

In drafting when a line is viewed "end-on" it is a zero-length point but as we deviate our viewing angle from the end-on view the line gains length until finally when viewed perpendicular to the line it shows the line's "true length" - the length of the line can never be increased to a longer length than the true length by any other viewing angle.

This is not how length contraction works.