# Gravity in the expanding universe.

## Main Question or Discussion Point

If the universe is isotropic and the gravitational properties, which we observe in small objects such as planets, stars and even neutron stars and black holes, apply to large objects such as galaxies and even the universe as a whole. Can we then assume that as the universe is expanding it is becoming less dense? As gravity is dependent on both mass and the distance from the centre of gravity, as the universe expands its overall gravity must decrease.

Gravity has a profound effect on time; experiments have demonstrated that the more intense a gravitational field the slower time passes within it. In an expanding universe where gravity is decreasing, it logically follows that time must accelerate. The basic formula for calculating speed/velocity is V=d/t if time is not constant then the very basis for calculating speed indicates that; all velocities (including the speed of light) are relative to our position in time (or distance, in time, from the big bang). I came to this conclusion when reading up on Mach's Principle.

Is this logic sound or have I missed some important factor?

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pervect
Staff Emeritus
Tzemach said:
If the universe is isotropic and the gravitational properties, which we observe in small objects such as planets, stars and even neutron stars and black holes, apply to large objects such as galaxies and even the universe as a whole. Can we then assume that as the universe is expanding it is becoming less dense? As gravity is dependent on both mass and the distance from the centre of gravity, as the universe expands its overall gravity must decrease.

Gravity has a profound effect on time; experiments have demonstrated that the more intense a gravitational field the slower time passes within it. In an expanding universe where gravity is decreasing, it logically follows that time must accelerate. The basic formula for calculating speed/velocity is V=d/t if time is not constant then the very basis for calculating speed indicates that; all velocities (including the speed of light) are relative to our position in time (or distance, in time, from the big bang). I came to this conclusion when reading up on Mach's Principle.

Is this logic sound or have I missed some important factor?

The main thing you are missing is that the speed of light is usually measured with local clocks and local rulers.

Using this standard defintion, the speed of light is always 'c'. The "coordinate speed" of light is not always 'c', however. To define a "coordinate speed", one must set up a coordinate system (A way of "parallel transporting" rulers will also implicitly define a coordinate system, at least over some limited region).

Mach states, “All masses and all velocities, and consequently all forces, are relative. There is no decision about relative and absolute, which we can possibly meet, to which we are forced, or from which we can obtain any intellectual or other advantage.” (Mach, The Science of Mechanics, ch.2, Open Court, 1960)

According to Einstein's formulation (1918), however, Mach's Principle is this: The G-field is without remainder determined by the masses of bodies. Since mass and energy are, according to results of the special theory of relativity, the same, and since we describe energy by the symmetric energy tensor (Tμν), this therefore entails that the G-field is conditioned and determined by the energy tensor. (Translation by C. Hoefer, Barbour & Pfister 1995, 67) General Relativity does not fully concur with Mach’s Principle because although Einstein may have intuitively felt that Mach was correct he was unable to incorporate the concept fully.

Our local clocks and rulers are relative and I think we all understand that, I agree that the speed of light is always C but if our unit of time is relative then surely C must also be relative just as Mach suggests.

pervect
Staff Emeritus
There are several issues here. As far as Mach's principle goes, you might want to talk to Garth about that more. The majority viewpoint is that GR is, as you suggest, not Machian.

This doesn't bother me so much, because it seems that Mach's principle is basically philosophy, and that the difficulties implementing it are mostly related to figuring out what the heck the "principle" actually states. But I suggest you talk to Garth anyway, because he seems to get something useful out of Mach's principle (I don't, particularly).

As far as velocity goes, the coordinate-velocity of light does vary with position. However, that is not the only (nor necessarily the best) way to view velocity.

Basically, there is a hidden issue that you are glossing over. If we have a clock at one location, how do we compare that clock to a clock at another location?

It turns out that there is no general way to do this. We can do it in special situations - when the geometry is static (not changing with time), and the clocks are stationary with respect to each other, we can use the fact that "trip-time" of light signals are constant to compare our clocks. This is the procedure that we use when we say that a clock on a mountain-top is ticking "faster" than one in a valley.

When the clocks move with respect to each other, or the geoemtry is non-static, this simple procedure won't work.

In fact, not only will this simple procedure not work, one can show that if one transports clock A to the same location as clock B to allow one to compare them directly, the results depend on the exact path that one uses. Different paths give different results.

By taking the viewpoint that coordinates are fundamental and first, you are running head-on into these difficulties. The difficultes are all related to how one defines coordinates, and the answers all depend on the details of a particular coordinate system that one picks.

If you avoid coordinates, and assume only that clocks and rulers exist, the description of velocity becomes much simpler. By avoiding the ambiguous procedure of transporting the time from one clock to another clock, one finds that a lot of difficulties disappear.

So all the issues with "variable" velocities are related to the issues of coordinate systems and what is known mathematically as "parallel transport". By insisting on using coordinate dependent physics, you are running head-on into these difficulties.

In short, I'm making a plea for coordinate-INDEPENDENT physics,as the approach is called.

And in coordinate-independent physics, we always measure velocities with a ruler and a clock right at the point where the moving object is. When we do this, we find that the speed of light is a constant, and that in general the laws of physics appear to be the same at any particular point. Going back to the mountain and the valley, the laws of physics on the mountain using the mountain clocks and rulers are the same as the laws of physics in the valley using the valley clocks and rulers.

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Garth
Gold Member
I would say Mach is more than philosophy because it is about how things, accelerations in particular, are measured.

We can construct a metric across space and time, however what do our x's and t's relate to? What is there for the inertial coordinate system to 'hang on' to, what is it that selects one set as inertial frames out of all possible frames of reference? Mach's answer was the presence of other masses.

It may be stated: "The inertia of any system is the result of the interaction of that system and the rest of the universe. In other words, every particle in the universe ultimately has an effect on every other particle." (Wikipedia)

Dicke later extended the principle to conclude that "the gravitational constant should not be an arbitrary constant but rather it should be a function of the mass distribution in the universe"

Tzemach: Gravitational fields do not slow down clocks in themselves. Regular clocks always see time passing at the rate of 'one second per second'. What gravitational fields do affect is the observed rate of one clock when compared with another moving relative to it or at a different gravitational potential to it.

Garth

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Although we cannot compare them is there a way in which we could calculate or imagine that yesterday's clock is moving at a different rate compared to today's clock, because the universe was denser yesterday and hence had a greater gravity?

Garth
Gold Member
No.

If you cannot compare them you would never be able to tell whether the clocks record different time rates.

Garth

I agree that it is impossible to compare yesterday’s clock with today’s clock but isn’t there other physical evidence that points to the probability of a variation in the passage of time?
If this concept were correct, would we not see?
Anomalies in the Lyman-alpha that indicate that the speed of light might have changed.
The greater density and gravitation make it appear that the historic universe contained large quantities of invisible matter.
As our units of time measurement become smaller, the expansion of the universe appears to accelerate as if propelled by some undetectable energy.
Long-range spacecraft that would inexplicably change their velocity.

There have been some recent ArXiV posts that consider time varying scenarios, are there any known groups working on this type of theory?

Garth
Gold Member
Yes, I am! - see http://en.wikipedia.org/wiki/Self_creation_cosmology [Broken] and the published papers referred to in that article, or the thread dedicated to SCC in PF.

My point is that clocks can only record time at 'one second per second'. The concept of a "variation in the passage of time" does not make sense unless you can detect it. Differing clock rates can only be detected by comparing one clock with another one. SCC predicts there is a cosmological clock drift between atomic clock time and ephemeris time.

SCC thereby predicts the Pioneer anomaly as cH. Note: I do not engage in extended discussion on SCC except in the dedicated thread as I do not want to 'clog' up other threads with it.

Garth

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Thankyou, I have been studying published information on SCC and was interested to know if this was the only theory that considered time variation.

Tzemach said:
Can we then assume that as the universe is expanding it is becoming less dense? As gravity is dependent on both mass and the distance from the centre of gravity, as the universe expands its overall gravity must decrease.

Gravity has a profound effect on time; experiments have demonstrated that the more intense a gravitational field the slower time passes within it. In an expanding universe where gravity is decreasing, it logically follows that time must accelerate. The basic formula for calculating speed/velocity is V=d/t if time is not constant then the very basis for calculating speed indicates that; all velocities (including the speed of light) are relative to our position in time (or distance, in time, from the big bang). ?
I think the author of this post has raised some good questions about issues normally glossed over ...For example, there are some interesting relationships between cosmic mass and the size of the universe - specifically, if the total mass of the Universe (assuming critical density) where uniformily spread over the Hubble sphere - you would have about 1 kgm/square meter. The cosmic density is approximately numerically equal to the reciprocal of the Hubble radius. If you use Friedmann's equation for a critical density universe you find a relationship between the velocity of light, Hubbles Factor, the cosmic density, and the gravitational constant (which may not be constant). One of the difficulties is that we do not have a way of measuring the constancy of G that does not involve the effect of one mass upon another - which means we are only actually verifying the constancy of the MG product. If the MG product is constant, we have a very different story of cosmic evolution than that derived by assuming all the matter-energy in the universe came into being in a single instant of nearly infinite density. If the total energy of the universe is dependent upon its size, then there may be good reason to speculate on whether the velocity of light was different in earlier epochs.

Tzemach said:
I agree that it is impossible to compare yesterday’s clock with today’s clock but isn’t there other physical evidence that points to the probability of a variation in the passage of time?
If this concept were correct, would we not see?
Anomalies in the Lyman-alpha that indicate that the speed of light might have changed.
I think that you might want to check out the Magueijo-Moffatt theory on the varialble light speed (VLS) on this. Last I heard though, the theory is not fairing that well.

If time was moving more slowly in a denser historic universe, could this explain some of those astronomical objects, which should not exist? If historic time was passing more slowly then the actual age of the universe, when measured at today’s rate of time, would actually be far older than it appears; - allowing time for these objects to form.

For example, fossil cluster RX J1416.4+2315 Current projections state that this fossil group should not have had enough time to form given the age of the universe, or quasar APM 8279+5255. The red shift of this quasar, a vibrant galaxy with a bright central region and massive central black hole, reveal that it contains much more iron than it should for its age.

Time refers to the rate at which things change - to speed up, or slow down, or stop, is meaningless unless there is an objective measuring standard apart from the universe that would reveal change in the continuous flow of time.

yogi said:
Time refers to the rate at which things change - to speed up, or slow down, or stop, is meaningless unless there is an objective measuring standard apart from the universe that would reveal change in the continuous flow of time.
That is the main problem with which I have been wrestling, there are reasons and indicators that suggest that time should not always progress at the same rate (and relativity provides sets of circumstances where this can be proved) but there are instances where relativity does not appear to go far enough.

Garth
Gold Member
Tzemach said:
That is the main problem with which I have been wrestling, there are reasons and indicators that suggest that time should not always progress at the same rate (and relativity provides sets of circumstances where this can be proved) but there are instances where relativity does not appear to go far enough.
What reasons and indicators? yogi is exactly correct; Tzemach ask yourself the question: "At what rate does time flow?", "How many seconds per second?"

It is a tautology, time can only pass or flow at one second per second.

What you are thinking about is the measure of the rate of one physical process, the ticking of a clock for example, as measured by another clock, which may be measuring time by a different physical process, or which may be in a different frame of reference, one in relative motion, or one situated at a different gravitational potential, for example.

"Does a pendulum clock vary when compared with atomic time, as measured by an atomic clock" (Is the gravitational field changing?)
"Does ephemeris time vary when compared with atomic time?" (Is G varying?)
"Does a radioactive half-life vary with atomic time?" and so on....(Is h changing with time?)

Let me give one illustration.

Consider a massive no-rotating planet with a powerful gravitational field on which a tall tower is constructed.

A clock at the bottom of the tower is observed to 'run slow' when compared to a clock at the top, and gravitational red shift is observed at the top in the light emitted by it (say, as time signal flashes).

If you synchronized two identical clocks, A & B, at the top of the tower and lowered one, A, to the bottom for a period and then raised it to be compared a second time with B, would not A read less time than B had elapsed?" Indeed it would.

Does this then not mean that "time is running more slowly at the bottom than at the top?" In fact it does not, for time has flowed at the rate of "one second per second" for both clocks all the time.

How is this paradox to be resolved?

The answer is to be found by comparing the two world-lines through space-time of both clocks taking the Schwarzschild metric of the planet's gravitational field into account. Integrating along both world-lines we will find that A's world-line is shorter than B's.

It is not that time has elapsed more slowly for A than B, it is that there was less time for A to measure than B.

This experiment was carried out by Gravity Probe A in 1976 and we await the result of its sequel, Gravity Probe B, in 2007!

But note that, in that GP-A NASA JPL website, they continued to promulgate the same confusion!
It is one type of highly accurate clock used to measure infinitesimal changes in the passage of time. The purpose of the experiment was to determine whether time progressed at a different rate in conditions where gravity is weaker.
You must always add "when compared with a clock in the laboratory" (or wherever).

Garth

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