Inflatory Theory question

[Nesti]

I remember reading somewhere that some models of the Inflatory period just after the Big Bang, include the merging of higher dimensions with spacetime to form a single unit; so as temperatures get hotter, dimensions merge into one singular entity.

Now, Einstein said that dimensions are not really there, that dimensions are not a vessel in which the universe resides, but that energy and matter are simply spatially and temporally separated from each other.

So, if we could run the Big Bang in reverse, wouldn’t everything be Lorentz Contracted, both in direction traveling to the origin and perpendicular because of the convergence of matter, so that all frames of reference ultimately contract into dimensionless points?

If that’s true, couldn’t Inflation be akin to a negative effect (a condensation process, a photo negative effect if you like) of a Lorentz Contraction from higher energies to lower energies?

If so, then there is no singular point from which the Big Bang originates, and that all points within the universe simply emerge out of the Planck energy (quantized units) to become Einstein’s “spatially and temporally separated” matter. I could only describe the effect being something like reducing the transparency of a graphic image until it becomes a solid image; the translucency diminishes during the Inflatory [emergence] period and as the matter of the universe reduces down from 'c' while diverging.

If the universe does not come from a single point, then the energy distribution can be uniform and we do not really need the Inflatory Theory model after all.

So in this suggestion, energy/matter emerged from the Planck level at 'c' with almost uniform distribution, and as the spatial and temporal separation increased over time, the speed and energies correspondingly decrease, finally becoming our old and cold universe with the uniform distribution of background radiation as we observe.

In this way, the grittiness of the universe (Planck scalces) is preserved. There still is a question of what came before the Big Bang and/or the emergence idea I've just thrown out there, but that's widely accepted as a mystery anyway.

Awaiting incoming missiles! :lol:

[Jarvamundo]

Ha, nice thought experiment Mark... I'll respectfully bow out now. ;)

"I have always believed that astrophysics should be the extrapolation of laboratory physics, that we must begin from the present universe and work our way backward to progressively more remote and uncertain epochs."
Hannes Alfven

[sjastro]

I've never heard of this definition of inflation before.
Inflation is the metric expansion of space-time, except it happened a lot faster when compared to the metric expansion of the Universe.
Metric expansion is defined as the scale of the Universe changing. Each point in space-time is fixed while the scale increases.



Lorentz contraction is a property of SR for objects travelling in space-time. Here it is space time itself that is changing.
In the Universe's frame of reference (Robertson-Walker space), an object is being carried along by the Hubble flow, it's not moving in space-time, hence Lorentz contraction doesn't occur.

In the observer's frame of reference for any point in the Universe, lorentz contraction will not be observed either as any object approaching the observer will be in the same direction as the observer's line of sight.

Regards

Steven

[bojan]

If it is metric, how all this tally with observed time dilation on distant objects (for example, very far away Supernovae.. their observed light curves are slower)?

[sjastro]

You have two frames of reference. In the Universe frame of reference, objects (not gravitationally bound) are at fixed points while space-time undergoes metric expansion.
Then there is the observers frame of reference. A distant galaxy moving under metric expansion will appear to move way from the observer.
An observer will be able to measure time dilation of a supernova light curve, which like the recession velocity of a distant galaxy is a function of cosmological redshift. This the key point to metric expansion.

For objects moving away in space which are not too distant, time dilation is a function of the velocity of the object and independent of cosmological redshift.

Regards

Steven

[Robh]

How can you differentiate between a doppler red shift and a cosmological red shift or, as distances get further, a combination of the two? Use of standard candles such as type Ia supernovae depends on them performing the same way back into the early Universe. Galaxies can vary enormously in both size and surface brightness and nearby galaxies will have older stars than those further away, so just how reliable is any distance measurement back into the early Universe? Seems like a lot of assumed generalizations.

Regards, Rob.

[Nesti]

If I've got that right, that means there's sort of a dual reality being formed, where all points (all reference frames) within the universe retain laws (doppler effects), and a global reference frame which does not retain the laws (so cannot exist as part of physical spacetime)...this would mean that a Metric Tensor or Metric Inflation, does not have any real [physical] property at all, it can only be a mathematical expression of what's occurring...which would then indicate to me that a gravity wave is also just a dynamic mathematical change within the metric at any given point in spacetime. If that's the case, then a Metric can only effect spacetime, as it is not a physical part of spacetime.

I wonder if this was the type of issue which indicated to Einstein that he needed to abolish his universal frame of reference (fixed background structure) after using it to put together SR. From then-on he always worked with "no fixed background structure" in his TOE work.

[sjastro]

A Doppler redshift is a function of the velocity of an object in space relative to the observer. If there was only Doppler redshift then we wouldn't be able to explain the isotropic nature of the Universe. For example redshift surveys of distant galaxies produce the same distribution irrespective of the direction of observation.
This is explained through cosmological redshift caused by metric expansion. Since expansion is scale related every object that is not gravitationally bound is moving away from every other object.

Gravitationally bound galaxy clusters produce a higher Doppler component for the individual galaxies due to motion in space. However since the cosmological component of redshift increases with distance, the contribution of the Doppler effect becomes progressively smaller as the cluster is more distant.

A type Ia supernova follows a common recipe, a white dwarf in a binary star system captures matter from a companion star. When the mass of the white dwarf exceeds 1.4 solar masses it explodes due to carbon fusion. There is no reason to doubt the constancy of the mechanism over time.

Regards

Steven

[sjastro]

Metric expansion is a real effect. When a photon is viewed as a wave rather than a particle, metric expansion causes the wave to stretch out.
The result is that the spectal lines of distant objects are displaced to the red end of the spectrum.

Cosmology only describes what is happening through mathematical modelling. (eg the FLRW metric http://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2% 80%93Robertson%E2%80%93Walker_metri c)

The proposed mechanism for the large metric expansion during the inflation stage for example is based on Quantum Field Theory.

http://en.wikipedia.org/wiki/Vacuum_decay

Regards

Steven

[bojan]

That makes sense.
Redshift means we observe lower frequency of incoming light - however also everything else must slow down (supernova light curve decay rate). Does this slowing down correspond in amount to calculated time dilation? Or there is (much) more to the whole story?

[sjastro]

Time dilation relates to a broadening of the light curves (absolute magnitude vs time plot) and is related to redshift. The light curve of a supernova will be broader for a given redshift when compared to the light curve in the supernova's frame of reference at redshift z=0.

When a photon is emitted from the supernova it takes time t to reach us. The Universe metrically expands a certain amount during this interval. Each successive photon takes a longer time to reach us due to the expansion. The higher the redshift, the greater the expansion, the greater the time dilation.

Regards

Steven

[bojan]

Yes, I understand this mechanism.
However, my question was actually, are the time dilation due to apparent velocities (using Lorentz's transformations) and redshift of the same distant object the same?
Sorry, it just I am lazy to calculate those myself and maybe someone checked those numbers already :-)

[sjastro]

The Lorentz transformation won't work as it only applicable if the recession velocity is constant.

The recession velocity for an expanding metric increases as the distance between the observer and object increases.

Regards

Steven

[Insane Climber]

If the universe did not emerge from a single point or singularity, then how would you explain the current expansion that we observe. On the very big scales gravity is the dominating force, if the universe just poped out of thin air as you suggest then woulden't we see a contraction of the universe cause by the gravitational force bringing matter together?

Actually who am i to say that time is not going in the opposite direction, and that we don't live our lives in reverse?
mmm i just confused myself.

[mjc]

Are you sure lorentz transformations do not apply here. I understand your line of thought in being careful to preclude special relativity where there is acceleration and/or gravity involved. However, the recessional velocities due to the expansion of the universe is not due to motion through space (there's no inertia - stop space expanding and one would not expect the bodies to keep moving - also superluminal velocities are not forbidden). The recessional velocities are a result of distant galaxies comoving with space.

I just found this
http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf (http://www.mso.anu.edu.au/%7Echarley/papers/DavisLineweaver04.pdf)

(Do a search on "expanding confusion" and you'll find more material.)

Which looks pertinant - I've read material by both Davis and Lineweaver before on this subject area and its always been rewarding. I Can't recall if I've read this particular paper before but it covers the same ground.

Just my two cents (they're Euro cents so thats even less now...)


Mark

[sjastro]

Hello Mark,

The point I was making is that a SR Lorentz transformation cannot be used for a comoving coordinate system. For a Lorentz transformation to be applicable, one would need to convert the comoving system into the observer's local coordinates.

To do this the distance between the observer and object needs to be broken into small intervals, such that each interval is small enough for metric expansion to be negligible in each interval.
Then apply the Lorentz tranformation to each interval, and sum the time dilation for each interval.

Therefore in a metrically expanding Universe the Lorentz tranformation is multlplied by a scale factor.
Experimentally it is impossible to measure the time dilation using this method as one would require "clocks" in each interval.

Regards

Steven

[renormalised]

Maybe not impossible, Steven, just very difficult. The biggest difficulty is not so much having clocks in every interval, it's how you're going to measure the time difference for each one, whilst taking into account the transition of the moving object from one interval to the other. The impossibility would come in its impracticality.

[sjastro]

Given our current level of technology it's impossible.........

Regards

Steven

[renormalised]

To do it literally, yes.

[bojan]

I am sure the specific experiment can be designed, or some side effect can be figured out that would show if this is true or not.

[renormalised]

It can be designed as a thought experiment, however, to measure the precise amount of time dilation across the transition zone between the intervals would require an infinite number of clocks/timing devices. The reason being you're not just finding the time dilation for one discreet interval, which can be measured using just one clock...from start to finish, but you're also having to measure the time dilation whilst both clocks in adjacent intervals are taking measurements. In order to get the precise timing so an accurate effect is measured you have to know exactly when the moving object leaves one interval for another. At the transition zones, that would require an infinite number of intervals across the dividing line. You could never hope to achieve that...your measurements could only ever be an approximate.

In any case, we couldn't do the experiment in a literal sense because it would require, at the minimum, the ability to travel between the galaxies and we're flat out leaving LEO (which in my opinion is criminal, even given the primitive technology we use).

[bojan]

So what's the point if we cant measure this? Because, if we cant measure, that means the whole thing does not have any effect on us.. which means it is irrelevant (or it IS relevant, but just like the string theory.. mathematically consistent, but can not be proven by experiment)? Just another mind game, in other words..

[mjc]

I'm not comfortable with the view that we can't measure this.
I appreciate the thread by the way.

Why do we need - even in a thought experiment - a huge number of clocks between the source of some event and the observer?

Surely we can observe an event of known duration (if one were close to it) observe another example of such an event at a much larger distance - where duration of event is measured and expected to take longer.

If we know the hubble expansion rate and we know the speed of light then I'm supecting that one then needs to do some integration to find how much extra space lies between the observer and the source compared with the actual amount of space that the photons from that event actually traversed (rather than comoved with) and then see if Lorentz contaction fits the bill or not.

Do this with different events at different distances and see if its consistent.

Am I missing something?

I thought that I had some understanding of this - now I'm beginning to doubt it!

Regards all.

Mark

[sjastro]

It won't work as the observer is at a single fixed origin.

The SR Lorentz transformation is only "accurate" for very short distances in the context of metric expansion.

Each interval has its own origin. A stationary clock (or the observer) is located at the origin for each interval, then there is the moving clock in the interval. The Lorentz transformation for time dilation is calculated for the interval.

Think of this analogy. If we wanted to measure the distance between 2 points on an arc, we could simply draw a straight line between the points and measure the distance along the straight line. The measurement is not going to be accurate. If instead we split the arc into segments and measured the length of each segment, then the sum of the length of the segments will give a more accurate measurement.
The smaller the segment used the greater the accuracy.

The same principles applies for the Lorentz transformation in the metric expansion of space. In this case the segment is the interval over which time dilation is measured.

Not a very practical method for measuring time dilation.
Using the FLRW metric is a lot simpler.

Regards

Steven

[bojan]

OK, so what is the (theoretical) difference in numerical results between this ideal method (which is impossible to perform) and in-accurate but practical and possible method (FLRW metric)?

[sjastro]

Have a look at figure 4 http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf

It shows that SR with a scale factor will produce time dilation exactly as predicted by GR using a FLRW metric.

SR using the Lorentz transformation without the scale factor produces divergent results. Only at very small redshifts can the Lorentz transformation be used to calculate time dilation.

How the FLRW metric works for time dilation and why Lorentz transformation fails unless scaled can be found in the Appendix.
http://users.westconnect.com.au/~sjastro/Tutorial/Time_dilation_redshift.pdf

Regards

Steven

[bojan]

Thanks :-)
Back to reading...