Question on the age of universe

[gptejms]

As you go back in time,the gravitating bodies come closer and closer.So the gravitational field gets more and more intense.We know that clocks move slower in the presence of a gravitational field---so as you go back in time the clocks become slower and slower.So how can we say,using today's time, that the age of the universe is 13.5 billion years?We assume that the time would move at the same rate(as it is today) as we go back in time--but this is wrong.

Now if I follow the observation that clocks get slower and slower as we go back in time,I never really get to the origin of universe---at best I'm approaching it asymptotically----so is the age of the universe infinite?

Kindly explain.

Jagmeet Singh

 

[Nereid]

Welcome to Physics Forums Wave's_Hand_Particle!

We know that clocks move slower in the presence of a gravitational field

Slower with respect to what? If it's only with respect to clocks 'not in the presence of a gravitational field' then since there is no such 'external' clock, and the point is moot. You might like to check out Ned Wright's Cosmology Tutorial, I think it covers these, and many other, interesting questions.

 

[LURCH]

Welcome to Physics Forums Wave's_Hand_Particle!Slower with respect to what? If it's only with respect to clocks 'not in the presence of a gravitational field' then since there is no such 'external' clock, and the point is moot. You might like to check out Ned Wright's Cosmology Tutorial, I think it covers these, and many other, interesting questions.

I've had the same question myself, and quite certain that the reference to clocks moving slower is stating the case of a clock further inside a gravitational field (any gravitational field) then the Observer. As we look back in time to our telescopes, we looking at a universe in which every thing was closer to every other thing. Therefore, would if we could observe a clock inside the early universe, it would appear to us that the clock was moving very slowly, would it not?

gp, although I have never been able to find reference to it, i am sure this time dilation must have been taken into account in the calculations of the age of universe. It would simply be too huge of an oversight for the entire Cosmology community to commit in unison.

 

[hellfire]

My understanding: this effect of time dilation due to gravitation takes place e.g. in a Schwarzschild spacetime in which the term dt of the metric is multiplied by a factor which is not constant (it depends on the radial distance to the mass). But the universe can be assumed to be a Robertson-Walker spacetime for nearly the whole cosmological history. In a RW spacetime, dt is multiplied by a constant (ds^2 = -c^2 dt^2 + ...) and thus no time distortion takes place for comoving observers in any age of the universe.

 

[Nereid]

I've had the same question myself, and quite certain that the reference to clocks moving slower is stating the case of a clock further inside a gravitational field (any gravitational field) then the Observer. As we look back in time to our telescopes, we looking at a universe in which every thing was closer to every other thing. Therefore, would if we could observe a clock inside the early universe, it would appear to us that the clock was moving very slowly, would it not?

gp, although I have never been able to find reference to it, i am sure this time dilation must have been taken into account in the calculations of the age of universe. It would simply be too huge of an oversight for the entire Cosmology community to commit in unison.

This is a good question LURCH, and gptejms! And the answer is, of course, that the folk who do cosmology for a living certainly have built all these effects into their models.

But let's see how important this effect might be, in terms of what we humans here on Earth (or in orbit) can see, with photons.

First, I'm sure you'd agree that, whether we need to think in co-moving terms or not (per hellfire), the average gravitational redshift of the present universe is utterly tiny, and we have no hope of ever measuring it! Why? Because the average mass density of the present universe is something like a few H atoms ... per cubic metre. And if we can't observe a gravitational redshift, could we observe a time dilation?

Second, the earliest we can see, using photons, is the surface of last scattering, at a redshift of ~1000. Way back then, ~370,000 years after the Big Bang, the average mass density of the universe was certainly higher than it is today ... how much higher? Well, instead of working that out (see if you can do it), let's ask what's the minimum gravitational redshift we could detect? (Hint: Rebka & Pound) When did the universe have an average mass density that would give rise to such a gravitational redshift?

Third, there are indeed 'gravitational redshift effects' expected in the cosmic background microwave radiation, and they may soon be detected; they're not quite the same as the 'time dilation effect' you two have mentioned. Google on 'Sachs-Wolfe effect' or 'integrated Sachs-Wolfe effect'.

 

[hellfire]

When did the universe have an average mass density that would give rise to such a gravitational redshift?

I think such a situation did never arise. One would experience a *global* gravitational redshift effect in the universe if proper times on different cosmological epochs (but at fixed comoving positions) were different. The rates of proper times at a fixed comoving positions are constant, since g00 = 1 in the RW metric. One may experience local gravitational redshift effects, which arise if one considers photons travellling through a Schwarzschild geometry in the line of sight. Global gravitational redshift would appear in case of a metric different of the RW metric and having a variable g00 term.

 

[Garth]

Slower with respect to what?

That is the question! As an answer I suggest, “With respect to a clock in the present epoch, compared by the transmission via electromagnetic radiation - light - of a time signal or the frequency of an atomic transition (i.e. red shift)”.

The overall gravitational field in the early universe was stronger than at present, therefore we might worry about having to include a cosmological gravitational red shift on top of the cosmological recession red shift.

However in fact these two red shifts are the same phenomenon, the null-geodesics diverge over curved space-time, but interpreted in two different ways.

As you cannot generally parallel transport a vector, the energy-momentum vector, across space-time curvature you cannot prove that masses remain constant; they have to be defined to be so by a measurement convention.

If atomic masses are assumed constant then the red shift is recessional, but if the measurement convention is that energy is conserved then the energy, i.e. frequency, of the photon conveying the information from the distant object is assumed constant and the red shift is interpreted as gravitational in origin.

These two interpretations are related by a conformal transformation. It depends on how you choose to define the standard by which ancient observations are compared with those of the present epoch.

Garth

 

[yogi]

The notion of a variable time scale, whether due to matter density, or intrinsic to expansion, can lead to significant cosmologically alternatives - such as those mentioned by the originator of this topic. Specifically, a time rate that asympotically approaches zero translates to an infinite age for the universe - there being no beginning in the temporal sense. This also fits with the idea of "matter from nothing" as part of an ongoing process (e.g., perpetual inflation as once suggest by Guth). In this line of inquiry, there is no need to ponder the origin of the big bang or the actuality of a singularity.

 

[Garth]

The notion of a variable time scale, whether due to matter density, or intrinsic to expansion, can lead to significant cosmologically alternatives - such as those mentioned by the originator of this topic. Specifically, a time rate that asympotically approaches zero translates to an infinite age for the universe - there being no beginning in the temporal sense. This also fits with the idea of "matter from nothing" as part of an ongoing process (e.g., perpetual inflation as once suggest by Guth). In this line of inquiry, there is no need to ponder the origin of the big bang or the actuality of a singularity.

Thank you yogi, this post is also concordant with the principles of Self Creation Cosmology. [see my post #1 https://www.physicsforums.com/showthread.php?t=32713&highlight=SCC ]

Garth

 

[gptejms]

Is this what some of you are saying:- 13.5 billion years is the age measured by a comoving observer(i.e. an observer who has been a witness and a part of the expanding universe right from the beginning)?If this is so,is the 't' in RW metric(or whatever) the proper time?Even then, using today's rate of flow of time the age would be infinite .

Is this what some others are saying:-the time dilation caused by gravitational effects would be very small and we can very well ignore it?

Jagmeet Singh

 

[Garth]

Jagmeet thank you for your searching questions.

Is this what some of you are saying:- 13.5 billion years is the age measured by a comoving observer(i.e. an observer who has been a witness and a part of the expanding universe right from the beginning)?

Yes the age of the universe is that as measured by a co-moving observer but such an observer is defined as follows.

The cosmological solution of the GR field equation assumes the universe is homogeneous and isotropic on 'large enough' scales to obtain a model universe. Cosmology is the business of comparing these model universes with the real one by observations. In the model universe the discrete masses of galaxies and stars are smeared out into a representative gas. A co-moving observer is one for whom that gas is stationary for whom the cosmological principle, isotropy and homogeneity, hold - this idealised definition can now be made more exact by defining the co-moving observer as one for whom the CMB is globally isotropic. (Our galaxy is moving at 0.2%c relative to this frame)

If this is so,is the 't' in RW metric(or whatever) the proper time?Even then, using today's rate of flow of time the age would be infinite .

Yes and no! The t in the Robertson-Walker metric is the proper time, that is the time as measured by the co-moving observer's clock, but no the age of the universe, as measured by his clock, will not be infinite it is around 13 - 14 billion years as you said above.

Is this what some others are saying:-the time dilation caused by gravitational effects would be very small and we can very well ignore it?

No - cosmological gravitational effects, caused by the greater density of the representative gas in the ancient past, are the same as recessional time dilation/red shift. They are just another way of interpreting the physical observation. As I said in a previous post if we use a measurement of mass, length and time defined by a constant atomic mass, and hence size and hence atomic frequency, then the universe is expanding, the red shift is predicted by integrating the R-W metric along the light cone null-geodesic and it can be interpreted as recession red shift.

In my post above I explained another measurement convention in which the age of the universe is infinite, but generally recession with constant atomic masses is the normal/standard interpretation of Hubble red shift.

There are of course also local gravitational red shifts caused by the concentration of mass in stars etc., which generally can be ignored. However, in the case of a quasar, at whose centre lays a black hole (we think), this might become significant.

Garth

 

[gptejms]

Jagmeet thank you for your searching questions.

Yes and no! The t in the Robertson-Walker metric is the proper time, that is the time as measured by the co-moving observer's clock, but no the age of the universe, as measured by his clock, will not be infinite it is around 13 - 14 billion years as you said above.

Garth

I agree that the age of the universe 'as measured by the co-moving observer' would be 13-14 billion years.But say a hypothetical observer ,whose rate of flow of time is constant and equal to today's rate,were to monitor the evolution of the universe from the very start--would he not measure an infinite time(although infinities can't be measured!)?

 

[Garth]

I agree that the age of the universe 'as measured by the co-moving observer' would be 13-14 billion years.But say a hypothetical observer ,whose rate of flow of time is constant and equal to today's rate,were to monitor the evolution of the universe from the very start--would he not measure an infinite time(although infinities can't be measured!)?

Hmmm. "rate of flow of time" - my watch's rate is one second per second! It only makes sense to talk about time dilation when one clock is compared with another.
Surely you answer your own question, the co-moving observer using a 'physical' clock constructed from atoms will measure the lapsed time since the big bang to be 13 - 14 billion years. However, and this may be 'where you are coming from', do we not have to question the concept of such time at an epoch in the universe's history, close to the big bang, when there were no atoms (it was too hot), let alone clocks constructed from them?
- Garth

 

[gptejms]

Garth,what I meant by rate of flow of time was (/delta t) recorded
by an observer in some epoch of the universe per second of the
observer in today's world.That could well be .001 seconds per second.

 

[Garth]

Hmmm. If you measure time by counting the 'beat' of a photon, sampled from the peak intensity of the CMB Planck spectrum, then as you go back in time the present microwave photon is blue shifted and its frequency or beat increases. As we approach the big bang that increase becomes infinitely large as the blue-shift (going back in time) becomes infinite. [We observe this as the red shift of distant objects becoming infinite as their epoch approaches t = 0.]
Consequently if time is measured by the number of such beats, as there has been an infinite number of them, the universe is infinitely old, as measured by that 'photon clock'.
Is that what you mean?
Garth

 

[gptejms]

Consequently if time is measured by the number of such beats, as there has been an infinite number of them, the universe is infinitely old, as measured by that 'photon clock'.
Is that what you mean?
Garth

Yes.

Jagmeet

 

[pervect]

Interesting. This reminds me of

"TIME WITHOUT END: PHYSICS AND BIOLOGY IN AN OPEN UNIVERSE"
by Freeman Dyson

http://www.aleph.se/Trans/Global/Omega/dyson.txt

but run backwards, towards the begining, instead of forwards, towards the end.

The basic assumption is that energy and time scale inversely, if you scale up the hamiltonian (energy) by some factor lambda, you scale down "time" by the same factor lambda, so that $$\Delta E \Delta t$$ is constant. A higher energy means things happen "faster". This measure of time Dyson calls "biological time".

Dyson raises some other points, I'd have to think about some more, as I re-scan the article (about energy dissipation limits and such).

 

[hellfire]

Hmmm. If you measure time by counting the 'beat' of a photon, sampled from the peak intensity of the CMB Planck spectrum, then as you go back in time the present microwave photon is blue shifted and its frequency or beat increases. As we approach the big bang that increase becomes infinitely large as the blue-shift (going back in time) becomes infinite. [We observe this as the red shift of distant objects becoming infinite as their epoch approaches t = 0.]
Consequently if time is measured by the number of such beats, as there has been an infinite number of them, the universe is infinitely old, as measured by that 'photon clock'.
Is that what you mean?
Garth

You are correct in the sense that if one moves backwards in time through space the frequency of a photon increases, since redshift is a consequence of expansion of space. But you must not consider photons moving through space. In my oppinion, the question to be addressed in order to know the age of the universe, is whether time dilation is observed by a comoving observer which is measuring events at the same comoving position. In that case there is not time dilation, since g00 is a constant in the RW metric. A photon of the cosmic background would have now the same frequency than at z = 1000 if it *could* had been confined at a fixed comoving position. Am I wrong?

 

[Garth]

But you must not consider photons moving through space.

Why not? As I sit here basking in the sunshine (As I am in England I am being sarcastic here!) I have always considered its photons to have traveled here moving through space (and time) from the Sun.

In my oppinion, the question to be addressed in order to know the age of the universe, is whether time dilation is observed by a comoving observer which is measuring events at the same comoving position. In that case there is not time dilation, since g00 is a constant in the RW metric. A photon of the cosmic background would have now the same frequency than at z = 1000 if it *could* had been confined at a fixed comoving position. Am I wrong?

Clocks do not 'go slow' in a gravitational field! Note that an accelerating clock tells the same time and 'ticks' at the same rate as an un-accelerating one that is "moving momentarily along with" the first. (MTW pg 164 Box 6.2)

By the Equivalence Principle the accelerated frame of reference is equivalent with one in a gravitational field - within a small enough region. Therefore in a gravitational field the clock sitting on the bench tells the same time and 'ticks' at the same rate as the one that has just ("moving momentarily along with" the first) fallen off the bench and is in free-fall. So a clock even in a gravitational field does not lose time! That is, it doesn't "on its own"; the time dilation is only observed when the rates of two clocks separated across space-time curvature are compared.

The time dilation is caused by the photon’s null-geodesics diverging as they traverse the space-like expanding space-time between the clocks.

 

[hellfire]

May be I was not clear, or may be I am just wrong. But let me try again...

Gravitational time dilation in a Schwarzschild spacetime takes place because the timelike coordinate (choosing Schwarzschild coordinates) has a spatial dependence. This leads to the fact that an observer making use of the Schwarzschild coordinates (a remote observer) measures the frequence of photons to be different at different positions. This is because the rate of proper time is different at the measured position wrt the own (the remote observers) proper time.

In case of a RW metric in a comoving coordinate system, the timelike coordinate has neither spatial nor temporal dependence (it is a constant), but the spacelike coordinates have a temporal dependence. This leads to the fact that rates of proper times do only differ if the measured reference frame is moving wrt the comoving coordinate system. If the measured reference frame is also comoving, the time dilation does not take place.

 

[Garth]

hellfire - I would agree with that; the only clarification I would add though is in your statement, "This is because the rate of proper time is different at the measured position wrt the own (the remote observers) proper time." I would add "the rate of proper time is observed to be different"

One cannot talk about "the rate of proper (or otherwise) time" unless you are comparing one clock against another.

Your point about time in the R-W metric is perfectly valid and leads to an interesting point. Any metric depends on the confidence that we can use the unit standards of measurement of mass, length and time defined in a laboratory here and now on Earth at a distant location a long time ago.

However, Weyl’s hypothesis (Weyl, H.: 1918, ‘Gravitation und Electriticitat’ Sitzungsberichte der Preussichen Akad. d. Wissenschaften, English translation, 1923, in: The Principle of Relativity, Dover Publications.) was that a true infinitesimal geometry should recognize only a principle for transferring the magnitude of a vector to an infinitesimally close point, and not throughout the space-time manifold as in GR. This led to the concept that the space-time manifold M is equipped with a class [gµν] of conformally equivalent Lorentz metrics gµν and not a unique metric as in GR.

In a conformal transformation one metric transforms into a physically equivalent alternative according to
gµν → g'µν = W gµν.

There are a class of conformal gravity theories that use this insight such as Jordan's and Hoyle's (and mine cough cough). The conformal factor W (often written Omega^2) varies the definition of mass, length and time over the space-time manifold.

The R-W metric is in the Einstein frame - normal GR in which mass is invariant - and as you rightly pointed out the dt coefficient is constant - unity. In this frame rulers are fixed, the universe expands and red shift is recessional, i.e. a doppler shift.

However a conformal transformation of the metric could, for example, define time as in the 'photonic clock' described earlier and vary mass. Red shift then would be a consequence of atomic masses gaining mass over cosmological time, the opposite of the tired light theory, photons do not lose energy, atomic masses gain it and increase as a result. Compare the energy of the photon with an increasing atomic mass and the result is cosmological red shift. This could also be interpreted as gravitational red shift. In such a conformal frame the universe does not expand at all. Hoyle and Narlikar's (Hoyle & Narlikar, Proc. Roy. Soc. A, 1966, vol 294, 138.) conformal gravity theories fall into this category as does (you guessed it) SCC.

Garth