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  #1  
Old 09-08-2011, 08:40 AM
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Bye Spacetime Hello Phase Space

Beyond space-time: Welcome to phase space

Quote:
But did Einstein's revolution go far enough? Physicist Lee Smolin at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada, doesn't think so. He and a trio of colleagues are aiming to take relativity to a whole new level, and they have space-time in their sights. They say we need to forget about the home Einstein invented for us: we live instead in a place called phase space.
...
So what is phase space? It is a curious eight-dimensional world that merges our familiar four dimensions of space and time and a four-dimensional world called momentum space.
..
The quartet took the standard mathematical rules for translating between momentum space and space-time and applied them to a curved momentum space. What they discovered is shocking: observers living in a curved momentum space will no longer agree on measurements made in a unified space-time. That goes entirely against the grain of Einstein's relativity. He had shown that while space and time were relative, space-time was the same for everyone. For observers in a curved momentum space, however, even space-time is relative.
Seems the technique is somewhat akin to what Witten did to unify competing String Theories, which was akin to what Einstein did to move things along from Newtonian models .. ie: move thinking towards higher dimensions.

The Cosmological Principle, at the end of the day, is a working assumption which provides the fundamental basis for Standard Cosmology with all of its strengths and weaknesses. Is this really the way nature works ? Why should we presume it is necessarily this way ?

Cheers
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  #2  
Old 09-08-2011, 12:58 PM
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renormalised (Carl)
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That was in the latest New Scientist. Bought it yesterday but haven't got up to this story....looks interesting.

BTW....what happened to your Calabi Yau manifold and Witten's Hamster??. Have you just become too chaotic
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  #3  
Old 09-08-2011, 01:04 PM
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Quote:
Originally Posted by renormalised View Post
That was in the latest New Scientist. Bought it yesterday but haven't got up to this story....looks interesting.

BTW....what happened to your Calabi Yau manifold and Witten's Hamster??. Have you just become too chaotic
Captain Chaos strikes again ! .. Quite unstable, really

Thought the new Avatar might be appropriate to this thread, given that it is about migrating our thinking to phase-space …

(but .. then again, I might be wrong )

Cheers
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  #4  
Old 09-08-2011, 01:20 PM
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Where's Agent 86 when you need him
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  #5  
Old 09-08-2011, 02:59 PM
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Its interesting to note that it has been confirmed that high energy photons from a GRB (Gamma Ray Burst) have been observed to arrive ahead of lower energy photons.

This is predicted in Smolin's theory, as momentum space is curved (ie: 'non-metric').

Mind you, they go on to explain that this can also be explained simply by the way they're emitted from the source .. ie: the explosions aren't instantaneous .. they last for several seconds, which would account for the observed delays.

More GRBs are needed in order to pin this one down ..

.. interesting

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  #6  
Old 09-08-2011, 03:24 PM
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For anyone interested, 'Phase Space' can be easily described by a simple moving pendulum. You could plot its height above the ground on the y-axis, and its position either side of the centre along the x-axis (you'd end up drawing an arc of a circle).

To get the phase-space, you could also plot its horizontal position (over time) on the x-axis, and its velocity along the y-axis. This ends up as a (sort of) ellipse.

Here's a good animation showing some phase diagrams of a pendulum in motion.

Cheers
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  #7  
Old 09-08-2011, 03:37 PM
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Well I am interested for one Craig.
If I retain 1% of all I have been reading I will be 100% ahead of where I came from.
Thank you I appreciate it greatly.

alex
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  #8  
Old 09-08-2011, 04:35 PM
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Post

Quote:
Originally Posted by CraigS View Post
Its interesting to note that it has been confirmed that high energy photons from a GRB (Gamma Ray Burst) have been observed to arrive ahead of lower energy photons.

This is predicted in Smolin's theory, as momentum space is curved (ie: 'non-metric').

Mind you, they go on to explain that this can also be explained simply by the way they're emitted from the source .. ie: the explosions aren't instantaneous .. they last for several seconds, which would account for the observed delays.

More GRBs are needed in order to pin this one down ..

.. interesting

Cheers
The other explanation also has to do with the graininess of spacetime and how the gamma rays emitted from the GRB interact with spacetime in their journey to the detectors.

In any case, the emission mechanism could easily explain why, as they have mentioned. The more powerful gamma rays are emitted during the peak of the explosion, with the weaker gamma rays being emitted during the tailing off of the explosion.
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  #9  
Old 09-08-2011, 04:45 PM
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From the article;
Quote:
"Let's say you were patient enough to wait around while a black hole evaporated, a process that could take billions of years. Once it had vanished, you could ask what happened to, say, an elephant that once succumbed to its gravitational grip. But as you look back to the time at which you thought the elephant had fallen in, you would find that locations in space-time had grown so fuzzy and uncertain that there would be no way to tell whether the elephant actually fell into the black hole or narrowly missed it. The information-loss paradox dissolves."
So, at the end of the observation, how can we guarantee we were actually even there to commence observing the location of the elephant to begin with? Does the initial location of the observer not become fuzzed as well in retrospect?
Following that line of thought, should we then not accept that, in this case, observing something over time causes a growing uncertainty about not only the location of the observed object, but also the validity/calibration (any attribute inherent to location) of the observer's measurement device/eyes/experimental setup/question? How can we be sure that, in retrospect, we created the right conditions to commence our observations to begin with?

Maybe I'm dribbling here, but it's mind blowing stuff regardless!
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  #10  
Old 09-08-2011, 05:14 PM
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Quote:
Originally Posted by irwjager View Post
From the article;
So, at the end of the observation, how can we guarantee we were actually even there to commence observing the location of the elephant to begin with? Does the initial location of the observer not become fuzzed as well in retrospect?
Following that line of thought, should we then not accept that, in this case, observing something over time causes a growing uncertainty about not only the location of the observed object, but also the validity/calibration (any attribute inherent to location) of the observer's measurement device/eyes/experimental setup/question? How can we be sure that, in retrospect, we created the right conditions to commence our observations to begin with?

Maybe I'm dribbling here, but it's mind blowing stuff regardless!
Hi Ivo;
Hmm .. there is one invariant though 8d phase space.
If your observation is made in consideration of, and optmised in consideration of all 8 dimensions, then are we not back to the old invariant space-time perspective ?
Perhaps I'm dribbling more than yourself .. I'm still trying to wrap my mind around the concept let alone the ramifications.

Cheers
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  #11  
Old 10-08-2011, 07:45 AM
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Quote:
Originally Posted by renormalised View Post
The other explanation also has to do with the graininess of spacetime and how the gamma rays emitted from the GRB interact with spacetime in their journey to the detectors.

In any case, the emission mechanism could easily explain why, as they have mentioned. The more powerful gamma rays are emitted during the peak of the explosion, with the weaker gamma rays being emitted during the tailing off of the explosion.
Its interesting that they also predict another effect which results from torsion induced by momentum phase space called 'dual gravitational lensing' from their paper: Gamma ray burst delay times probe the geometry of momentum space (Mar 2011):

Quote:
This result shows that in the presence of torsion even if the two photons which are emitted in parallel and at the same time are detected at the same time, they appear to be coming from two different directions in the sky. The difference is proportional to the average photon energy. We may call this effect dual gravitational lensing.
There's quite a lot of thinking that's gone into all this.

The other key paper behind it all is: The principle of relative locality (Jan 2011).

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