Galaxies in an Expanding Universe

[Richard J. Hanak]

Galaxies in an Expanding Universe
By Richard J. Hanak, June 8, 2002

The Hubble relationship exhibits spherical symmetry. More concisely, Hubble's law is isotropic with respect to Earth. The isotropy of Hubble's law seems to confirm the philosophically attractive notions that when considered on a large enough scale, the universe is centerless, homogeneous, and isotropic about any location.

Let us assume that those notions are correct. If the universe is expanding, its expansion must also be centerless, homogeneous, and isotropic. An isotropically expanding system expands equally in all directions. Suppose that in some time interval the distance between two galaxies were to double. Isotropic expansion would require that the distances between all galaxies double in that same time interval. We can deduce, therefore, that distance ratios and angular relationships must remain constant during the isotropic expansion.

The light arriving from galaxies is our only source for information about them. In the present context we can consider light to include any kind of electromagnetic radiation that originated in a galaxy. Distances are calculated from the intensity of light, sometimes of one resolvable star, sometimes of the whole galaxy. Velocities are calculated from the shifts in wavelength in the spectrum of that light. Is square law the only cause of attenuation of the light intensity? Is the Doppler effect the only cause of red shift?

Hubble recognized that the radiation from the galaxies was emitted long ago. The information the light from galaxies carries to us can only be information about the galaxies as they were and where they were at the time they emitted that light. Expansion takes place during the passage of time. For that reason, time must be taken into account. Let us assume as initial simplifications that mutual gravitation has been negligible, that galaxy velocities have remained constant during the whole time of expansion, and that the velocity of light also remained constant. Adding an early inflationary phase and the decelerating effect of gravitation will not alter the outcome of what follows. For ease of illustration let us assume the Earth and five galaxies equidistant from each other in a ten billion years old universe.



The accompanying diagram (Galaxies in an Isotropically Expanding Universe) presents time vs. distance relationships and velocity vs. distance relationships for an expanding universe. Consider the upper portion of the diagram. The left-hand vertical axis represents time elapsed in billions of years since the beginning of the expansion. The lower horizontal axis represents the distances of galaxies from Earth, measured in light-years. On the top horizontal line of the diagram, the present time, are shown the Earth and five galaxies, equidistant from each other, with their respective velocities. The velocity of galaxy #5, the velocity of light, is shown as a limiting condition.

The lines connecting the present positions of the galaxies to the beginning of the expansion show the positions of the galaxies relative to each other and to the present position of earth at any time in the history of the universe. In order for light from a galaxy to arrive here now, the time it took for its light to travel here has to equal its distance from earth when it emitted that light. For example, five billion years to travel a distance of 5 billion light-years. In the diagram the line for present arrival of light shows this time-distance relationship. Please notice that the oldest light that can possibly reach us now is only half as old as the universe. To observe beyond that limit would require galaxy velocities greater than the velocity of light.

The intersections of the galaxy position lines with the present arrival line show the non-simultaneous distances from which their light was emitted. The vertical dashed lines projected down through the distance axis from those intersections show that distance measurements from arriving light cannot yield equal distances between our galaxies.

Let us now direct our attention to the lower portion of the diagram. The left-hand vertical axis represents velocities (in light-years per year) of our galaxies relative to earth. The horizontal axis above, as before, is distance from Earth’s present position. A curved line (labeled Observable Velocity vs. Distance for Isotropically Expanding Universe) depicts the relationship we should expect between observable distances and velocities of our galaxies. The straight line for Hubble’s Law, shown at the bottom of the diagram, cannot represent observed velocity-distance relationships in an isotropically expanding universe.

Now we can arrive at some conclusions. If the velocity-distance relationship (Hubble’s law) calculated from observed data is linear, the data cannot represent recession velocities in an isotropically expanding universe. If the data do not represent recession velocities, the universe has not been expanding and the observed red shift was caused by something other than the optical Doppler effect. If the universe has not been expanding, any theories requiring such expansion (or contraction) are somehow in error.

[Chuck]

I see an Angelfire logo instead of the image. I'm downloading it and posting it here for others to see:




_________________
Life is like a box of chocolates. All of your choices are bad for you.

<font size=-1>[ This Message was edited by: Chuck on 2002-06-08 22:38 ]</font>

[Espritch]

Maybe I'm misunderstanding your graph but it seems to have a flaw. The line labled "line for present arrival of light" is a straight diagonal which would indicate a linear correlation between distance of an object and arrival time for the light from the object (e.g. light from an object 1 billion light years away would reach us in 1 billion years). But this would not be correct in an expanding universe. The actual distance the light would have to cover would be 1 billion light years plus the additional distance resulting from expansion during the interim (i.e the movement of Earth away from the point of the light's origin). I would think this would need to be represented by a curve.

Also, it appears that the second graph is showing galaxy 5 as having an observed velocity of 1.0. However, the velocity in an expanding universe is a function of distance and since the light we observe would be from an earlier time when the galaxy was closer, the observed velocity would be lower.

Also, it would help if you created two separate graphs. The upper graph section has time as the Y axis while the lower graph has observed velocity as the Y axis. This is kind of like mixing apples and oranges and makes the whole thing rather confusing to me.

<font size=-1>[ This Message was edited by: Espritch on 2002-06-09 01:58 ]</font>

[p9107]

Why did you put two topics on the same subject?

[Richard J. Hanak]

Dear Espritch:

Thank you for your comments. Perhaps the following can help to clarify what I have presented.

Some time before the Inquisition burnt him at the stake for his ideas, Giordano Bruno (1548–1600) stated “The center of the universe is everywhere, and the circumference nowhere.” That idea anticipated twentieth century cosmology with its centerless, unbounded universe. It is presently believed that all motion is relative. Therefore, like Bruno, we can choose any location as our center, origin, or reference point; it might as well be the Earth from which we make our observations.

The galaxy distances we measure and the galaxy velocities we calculate are all relative to the Earth. In this context, then, the Earth does not move away from a source of light; only the source moves away. To consider motions of the earth and a galaxy we must take a reference point distant from either of them. Of course if the Earth were viewed from galaxy M83, for example, the earth would seem to move rather than M83. But we observe from here. Thus the distance traveled by the light is the distance of the galaxy from Earth at the time the galaxy’s light was emitted. In the interim, relative to Earth, the Earth would have stayed put and the galaxy that would have moved away. The light travels no additional distance.

In your second paragraph you suggest that earlier, when galaxies were closer, their velocities were lower. That would imply that the further they separated the higher their velocities became. Accelerations of any kind, whether for a skateboard or a galaxy, require the input of energy. If the galaxies have continuously accelerated since the ‘big bang’, where has the energy for their acceleration come from? If you believe in the ‘big bang’, the galaxies (or their precursors) were set into motion at the beginning. Then, after radiation pressure had spent itself all galaxies (except our neighbor the Andromeda galaxy and a few others we see where one cannibalizes the other) began to coast apart at constant velocities. Mutual gravitational attraction, strangely, seems not to have entered the picture to any appreciable extent. Cosmologists do not know whether the universe will expand forever or eventually collapse.

In a universe undergoing unaccelerated expansion the distances between galaxies increase linearly with time, and since there is no acceleration the relative velocities of galaxies remain constant (i.e., independent of time). Thus, at any one time it is true that velocity = Hubble’s constant multiplied by distance (v= Hd). However, since relative velocities remain constant, it follows that since distances increase with time, the Hubble constant must decrease with time. Hubble’s law cannot be independent of time. Hubble’s law is flawed by the error of time confusion: the confusion of past times with each other and with the present time. See my recent post SPECTROGRAPHIC RED-SHIFT
IS NOT CAUSED BY RECESSION OF GALAXIES for more of this.

As for my duplex graph, once you get used to multiplex graphs they present no problems. They show the relationship of data in one graph to that in another and are a great convenience to the draftsman.

[Espritch]

Your assumption appears to be that the expanding universe model is about objects in the universe moving away from one another through empty space at fixed initial velocities, an essentially Newtonian view of the expanding universe.

However, we do not live in a Newtonian universe. We live in a Einstinian relatavistic universe and in that universe space time is not just empty nothing through which matter moves. It is the fabric of the universe. Matter bends space time to create gravity. And space time in turn effects matter. In the expanding universe model, the recession of the galaxies is the result not of inertial (Newtonia) motion of the galaxies themselvs but rather is a consequence of the expansion of space time itself. In this model, recession rate correlates to distance and does change over time (since distance changes over time).

As an example, consider a hypothetical universe of 3 stars, A, B, and C. Let's assume that at a point in time the distance between A and B is 1 ly. The distance between A and C is 100 ly. If our hypothetical universe is expanding at 1% per year, then over the course of a year, B moves .01 ly away from A. C moves 1 ly (it is receeding from A at the speed of light although, in a strictly Newtonian sense, it isn't moving at all). Now consider these same three stars at an earlier time when they were half as far apart. Assuming the same expansion rate, B would be receding from A at .005 ly/y. C would be receding from A at .5 ly/y. Light in such a model requires more than 1 year to cross a light year because it is moving through space time and space time is itself expanding.

Of couse I'm not a cosmologist so the above explanation is purely a layman's understanding of the concept. That being said, your graph doesn't reflect the dynamics of the expanding universe model as I understand it. So either my understanding of the concept is wrong or yours is.


<font size=-1>[ This Message was edited by: Espritch on 2002-06-10 22:23 ]</font>

[DoctorDon]

Espritch is right. The galaxies are not moving away from us in a static space. If light is emitted from a galaxy 5 billion light years away, we will observe it more than 5 billion years later, because the intervening space will increase in that time.

Don

[Richard J. Hanak]

Espritch, in answer to your last post (for which I thank you):

Re: Expanding space-time

The fundamental postulates of relativity theory are that the velocity of light is constant and that that the velocity of light is independent of relative motion of a source or observer. Denying either of those postulates denies relativity theory and the expanding universe it predicts. The velocity of light is approximately 186,000 miles per second or 3 times 10 to the tenth power centimeters per seconds (3x10E10 cm/sec). Let us consider the implications of an expanding space-time universe and the constant velocity of light.

In a space-time manifold, space and time are not independent of each other if the velocity of light is Espritch, in answer to your last post (for which I thank you):
constant. Suppose that in a given time interval the universe has expanded to double its starting size. Then 186,000 old miles will have doubled to become 186,000 new miles. In order to keep the velocity of light constant the duration of one old second will also have doubled to become the duration of one new second. That is the only way that the velocity of light could remain constant at 186,000 miles per second.

Let us apply these consequences to galaxies moving away from each other because of space-time expansion. Let a galaxy emit light to Earth at the beginning of a time interval and let that light be observed at the end of that time interval. Now assume that you and I travel with the light and that with the aid of a meter-stick and a timer we measure, piecemeal, how long it takes the light to reach Earth. During the first second after the light was emitted we measure the velocity and find it to be 3x10E10 cm/sec. When the light has reached the midpoint of its journey our new measurement is still 3x10E10 cm/sec. The same is true for the last second of the journey. What has happened is that as space-time expanded our meter-stick has gotten longer and our timer has run proportionally slower. Think of our timer as a pendulum clock whose pendulum arm is also a meter-stick. As the meter-stick gets longer, the clock runs slower. No matter when, each 3x10E10 centimeters the light traveled required only one second.

We have made our measurements. If we now total all the meters traveled and all elapsed seconds in that expanding universe we get the same total meters traveled and seconds elapsed as for a universe without space-time expansion. It seems, then, that light does not travel a longer distance or require more time to get from there to here in an expanding space-time universe than it does in a universe without space-time expansion. In either universe light requires one year to travel a distance of one light-year. Thus, my present arrival of light line should indeed be straight. Also, recession rates would remain constant since although distances have increased, time would have slowed proportionally.

Early in the twentieth century Edwin Hubble proved that galaxies were not nebulous things within our local galaxy, that some were extremely distant, and that our galaxy was not alone in the universe. At that time galaxies (the largest then known structures) were considered to be the ultimate largest structures or “building blocks of the universe.” Cosmological models and theories were built on those ideas and solutions to the field equations of Einstein’s relativity theory. Since then we have discovered two larger structures in our hierarchical universe: galaxy clusters and superclusters. One can only wonder why galaxies have somehow been singled out from all other structures – why only they recede from each other and display recession velocities. Why not superclusters, clusters, the stars in a galaxy, or the electrons in an atom? There does not seem to be any theory that explains the singling out of galaxies.

Some have suggested that the galaxies have not really moved away from us. They claim that the red shift is the result of space-time expanding as light travels through it, so stretching the wavelength of the light to produce the red shift. The wavelength of light is the distance traveled during one cycle of its alternating electromagnetic field. Again, if the velocity of light is constant it follows that if the distance traveled during one cycle increases because of space-time expansion, then the time available for one cycle is stretched out proportionally, and the wavelength is the same as for a space-time that is not expanding.

From the above it seems that we can draw the following conclusions if the velocity of light is constant:

1. We can have no way to know if there is such a thing as space-time expansion.
2. Expanding space-time could not cause recession velocities of galaxies nor could it cause a change in those velocities..
3. The universe is not an isotropically expanding system.

If this is not sufficiently AGAINST THE MAINSTREAM for you, see excerpts of THE UNIVERSE ON TRIAL at

http://www.theuniverse.andmuchmore.com


In 1908 American astronomer W.S. Adams found that the rotation of the Sun could be determined spectrographically. He measured the red shifts and blue shifts of light from the receding and approaching limbs of the Sun. Applying the optical Doppler effect formula, he obtained the receding and approaching velocities of the Sun’s surface at the limbs. The surface rotation rate implied by those velocities was in close agreement with observations of the motion of sunspots since the time of Galileo. We do not need a relativistic universe to explain either those wavelength shifts or the optical Doppler effect. For those things, a Newtonian system is sufficient.

The only function of the relativistic corrections for the Doppler effect is to take into account wavelength shifts when the source velocity is a significant fraction of the velocity of light. It seems strange that a phenomenon that is produced by one cause in a Newtonian universe should have been thought to be producible by a completely different cause in a relativistic universe.