# The Conundrum of the Speed of Light and the Expanding Universe

1. Dec 27, 2009

### Emu

The Two Concepts

The http://en.wikipedia.org/wiki/Speed_of_light"[/URL], through expansion and inflation, as one of the fundamental aspects of the model. The conundrum is that these two concepts seem to be mutually exclusive. The purpose of this article is to bring this conundrum forward and request assistance in resolving it or determining if it is resolvable.

As formulated by Maxwell, the intrinsic properties of space determine the speed of light and these properties have distance as a factor. This article applies the increase in distance to the formula for the speed of light. Some of the effects of the increase in distance are then explored.

[B]The Basics[/B]

There are three properties of Space for this discussion:

The property of space of Distance

The property of space of Permittivity ($$\epsilon$$[SUB]0[/SUB]) for

The property of space of Permeability ($$\mu$$[SUB]0)[/sub] for

The speed of light (c) as formulated by [PLAIN]http://en.wikipedia.org/wiki/Maxwell%27s_equations"[/URL] is a function of the properties of space,
$$$c=\frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}=\frac{1}{\sqrt{\frac{Capacitance}{Distance}\frac{Inductance}{Distance}}}$$$

Maxwell’s formula shows that the speed of light is not independent of the property of distance of space.

The speed of a wave is also calculated from the formula relating [PLAIN]http://en.wikipedia.org/wiki/Electromagnetic_radiation"[/URL]:
$$c=\lambda f$$
Or in terms of wavelength: $$\lambda=\frac{c}{f}$$

[B] Models Where Distance Is Variable[/B]

In the Expanding Universe models such as in the FLRW “Big Bang,” the universe is increasing in size as space expands. This model proposes that for space the property of distance increases over time and is usually formulated as a linear function of time. The increase of distance in space is also a feature of inflationary models wherein there is a short time in which the distance property increases rapidly which is different than the expansion rate of increasing the distance property of space.

The expansion of the universe is often determined by measuring the increasing distances of objects such as stars and galaxies. With the vast space between objects the measurement is usually based on the distance light travels in a year, i.e. close objects are a few [PLAIN]http://en.wikipedia.org/wiki/Lightyear"[/URL] away and distant objects are billions of light years away.

A result of the property of distance changing should be that the electromagnetic properties of space change as well. If distance of space increases then the capacitance per unit distance should decrease proportionately. Inductance per unit distance would also decrease proportionately.

The effect of decreasing the values of \varepsilon0 and \mu0 would be to increase the speed of light. This is shown in the following example: If the metric of distance expanded to 3 times the initial value, this equation shows the calculated increase in the speed of light:
$$(x)c=\frac{1}{\sqrt{\frac{Capacitance}{3Distance}\frac{Inductance}{3Distance}}}=\frac{1}{\sqrt{\frac{1}{9}\frac{Capacitance}{Distance}\frac{Inductance}{Distance}}}=\frac{1}{\frac{1}{3}\sqrt{\frac{Capacitance}{Distance}\frac{Inductance}{Distance}}}=\frac{3}{\sqrt{\frac{Capacitance}{Distance}\frac{Inductance}{Distance}}}=3c$$

This shows that a universe expansion of three increases the speed of light three times.

For the example above, the wavelength would increase three times since “c” increased three times for a constant frequency as space expanded three times.

The expansion of space in the universe should be somehow concurrent so that all space has expanded the same amount at the same time i.e. space should be homogeneous and isotropic according to the [PLAIN]http://en.wikipedia.org/wiki/Cosmological_principle"[/URL].

To visualize how distance changes with expansion, a [PLAIN]http://en.wikipedia.org/wiki/Metric_expansion_of_space"[/URL] is of dots on the surface of a balloon. A line could be drawn connecting two of the dots. We could call this line a unit of distance (“UnitLine”). To mimic the process of expansion, more air is put into the balloon. From our independent vantage point, the dots then seem to move apart. If we used a fixed length measure we could measure the unit distance line at different times and determine how much expansion had occurred.

However, if the UnitLine is used as a basis for measurements, the UnitLine would also increase in length as more air enters the balloon, so there would not been any measurable change in the distance between the dots. This illustrates a general rule that if a metric changes proportionately to what is being measured there will not be any measurable change using that metric.

As shown above, with the speed of light increasing at the same rate of expansion, the distance the light travels in one year would depend on the amount of expansion of space that had occurred, just as in the case of the increasing UnitLine. The distance apart of objects, if measured using the increasing speed of light, would remain the same in light-years. As in the above example, if distance in the universe increased 3 times, the speed of light would increase 3 times as well, so the number of lightyears away for any object would remain the same. The expansion of the universe would not be measurable through a change in distance as measured by the speed of light. Another way of stating this is to say that objects carried by the expansion of space would not appear to be moving.

In contrast to objects carried by the expansion of space, there are objects moving through space.

To visualize this in the balloon analogy, let us add a couple of Ants walking on the surface of the balloon. The Ants walk at a fixed pace which is independent of the balloon size. The speed of the ants could be measured using the UnitLine. The speed of the ants would seem to decrease as the balloon increased in size for two distinct reasons. The first is the ant would have to cover more distance as the balloon expanded to get from one dot to another. The second is, the way the ant’s speed is measured, changes with the expansion. In the example above, let us say the ant was walking at the rate of one UnitLine per minute when the UnitLine was drawn and the UnitLine at that instant equaled one foot. Later, when the balloon had increase the distance by 3 times, the ants speed would be only 1/3 yards per minute. Of course, to the disappointment of the Ants, the metric would still be called “UnitLines per minute.”

Since the longer distance and slower speed add together, the decrease in Ant speed would be twice that of the balloon expansion.

We see from the example, objects moving through space slow the more space expands and that this slower speed does not depend on the distance away the objects are.

Let us consider two separate objects moving though space. The first object starts its movement at some time and the second object starts its movement at a later time such as billions of years later. With the universe expansion being homogeneous, the universe would have expanded and slowed everything concurrently. The result is, the time separation of two separate events could not be measured from the amount they had slowed.
[B]
Wavelengths and Frequency in the Expanding Universe Model[/B]

As we know, the speed of light equals the wavelength times the frequency. As shown above the speed of light increases with the expansion of the universe. The formula then is correct for a universe expansion of 3, and the speed of light is 3 times faster, the wavelength is also increased by a factor of 3 for a constant frequency. With this in mind, the emission or absorption of radiation by elements or groups of elements should be similar at any given time. If a spectral emission occurred billions of years ago from an element, the wavelength would have increased as the universe expanded. For the spectral emission from that same element emitted now would also be of lengthened wavelengths since the speed of light has increased as space increased. The effect of this is the spectrum and wavelengths of any emitter would remain identical for the same type of emitter regardless of when the emission occurred.

[B]Summary[/B]

The models of the universe which distance in space increases have unexpected results when the increase in distance is applied to the formula for the speed of light. These unexpected results are often at odds with observations. For example: Observations both of local and [URL]http://www.nature.com/nature/journal/v462/n7271/full/nature08574.html"[/URL] one would expect from light traveling at a fixed speed. This is contrary to the increasing wavelength at a constant frequency as required by increasing distance models. Thus, we have a fundamental conundrum, between a constant speed of light, and the increasing distance models of expansion and inflation.

Last edited by a moderator: May 4, 2017
2. Dec 27, 2009

### DaveC426913

You have not made your case yet. Why do you say they are mutually exclusive?

Last edited by a moderator: May 4, 2017
3. Dec 27, 2009

### sylas

This is not really true. The model proposes that scale factor changes over time. Whether distance changes depends on the end points used to define the distance. Co-moving distances increase; this is one of the most useful co-ordinate systems. But to merely say "distance" increases is not meaningful until you say WHAT distance.

This isn't true; in particular the permittivity and permeability of free space are not expected to change in standard models. As noted above "distance of space" is not a meaningful phrase.

Premise and conclusion are incorrect. Speed of light is believed to remain constant as the universe expands, in standard models of the expanding universe.

Objects are not carried by the expansion of space. Moving through space is all that objects do.

Not if the models are applied correctly.

Cheers -- sylas

4. Dec 27, 2009

### Emu

Thanks DaveC426913 and Sylas for your quick responses.

Dave, the aspects that are "mutually exclusive" are in part pointed out by Sylas. I linked to the Wikipedia topics so that the standard model would not need to be repeated in the post.

Sylas,The errors in the post you point out are those of the effort to combine Maxwell's speed of light formula and the expansion model. The results as described, of this combination, are not part of the standard model and actually point out the inconsistency of using increasing distance (expansion and-or inflation) as a basis for a universe model.

To your point that the standard model proposes a "scale factor": The Wikipedia article of the http://en.wikipedia.org/wiki/Expanding_universe" [Broken] includes the phrase "The non-Euclidean nature of space-time manifests itself by the fact that the distance between points with constant coordinates grows with time, rather than remaining constant." I have used the "distance...grows" as an indication of an "increasing distance" although the metric remains constant.

It would be most instructive if you could provide the math and or physics and apply the models correctly, to show how to incorporate "scale factors over time" into Maxwell's equation for the speed of light, without changing the speed of light.

Last edited by a moderator: May 4, 2017
5. Dec 27, 2009

### sylas

In this case, the "endpoints" of the distance are properly defined... and you need the rest of that paragraph to indicate what co-ordinates you mean. This is a reference to "comoving co-ordinates" ... which I also indicated as one of the defined distances that does expand.

In a sense, this is a bit of a cheat. Co-moving co-ordinates are really just a way of identifying a virtual points that expand away from each other as the universe expands, with no additional peculiar motions over the mean rates for expansion of everything. The expansion still reduces to movements of objects through space as you take it down to smaller local scales such as the size of a galaxy or cluster of galaxies.

Expansion means everything moves away from everything else.

There's nothing to change. Scale factor or the size of the universe has no impact on Maxwell's equations. Maxwell's equations deal with properties of electromagnetic interactions locally. They remain the same no matter what the size or scale of the universe.

Cheers -- sylas

Last edited by a moderator: May 4, 2017