Inflatory Theory question

[renormalised (Carl)]

Originally Posted by 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.

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 (Mark)]

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]

Originally Posted by 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

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]

Originally Posted by 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)?

Have a look at figure 4 http://www.mso.anu.edu.au/~charley/p...neweaver04.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/~sja...n_redshift.pdf

Regards

Steven

[bojan]

Thanks :-)
Back to reading...