Is Geometry Truly Frozen in High-Energy Particle Collisions?

[jal]

“the geometry is frozen in”

Here are my questions concerning ...
http://arXiv.org/abs/0903.1474
Soft Physics from RHIC to LHC
Peter Steinberg

Comparing the relevant energy and space-timescales implied by the success of the
hydrodynamical models, the matter at RHIC is formed under quite extreme conditions.
The formation time needed for the hydrodynamic calculations is τ0 =0.6fm/c, or
approximately 2 yoctoseconds (10−24) [11]. This number is far smaller than the time
taken a massless particle to traverse the radius of a hadron(τ ∼1fm/c)[12]. The same
calculations determine that the energy density needed to match the data is around ϵ
∼30 GeV/fm3, about 60 times the density of a nucleon in its rest frame, ϵN ∼500MeV/fm3 .
It should be noted that these estimates do not preclude even higher energy densities at
even earlier times.

One empirically observed feature that should shed light on this is “extended longitudinal scaling”[17]. It
has been observed in proton-proton collisions that the pseudo rapidity density (dNch/dη)
of inclusive charged particle production is energy-independent when viewed in a frame where one or other of the incoming particles is at rest [18]. This is done by using the kinematic variable η′ =η
−ybeam, where ybeam is the rapidity of one of the beams. Results for dN/dη′ are shown for Au+Au collisions at four RHIC energies[19] in the left panel of Fig. 4, where longitudinal scaling is clearly observed. The persistence of this scaling over a factor of ten in energy suggests that no major changes in the particle production occurs over this range.

This suggests that the geometrical configuration of the participants is “frozen in” immediately, consistent with the previous estimates of τo r perhaps even shorter times.

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My understanding of this paper is that once a perfect liquid state has been achieved that this perfect liquid will continue to exist over a large range of density, temp. I don’t see how any changes of those variables can be observed from inside the horizon of the universe. (Irrigardless of your belief in a finite or infinite universe.)

A change that is progressing at c, and heading towards you cannot be observed nor can you observe a change progressing at c, that is going away from you.

You cannot see a photon coming towards you nor a photon going away from you.

Therefore, “change” appears to be “immediate”.

If the geometry is “frozen in” then only an external clock can record the passage of time. From the point of view of the internal observer, change occur “immediately” yet the existing prior conditions could have existed for an extremely long period of “external time”. “Changes” in the universe could have been “progressing” for a long time and there would be no way of being aware of it and of measuring the “progression”.

If correct, how would this change our views of the time frame of the evolution of the early universe prior decoupling?

My second question is ...
What is temp. and how can it be measured when in a perfect liquid state where “the geometry is frozen in”?

(Yes, I looked up the wiki discussion on temp.)
http://en.wikipedia.org/wiki/Temperature

For a system in thermal equilibrium at a constant volume, temperature is thermodynamically defined in terms of its energy (E) and entropy (S).
It is also possible to define temperature in terms of the second law of thermodynamics, which deals with entropy. Entropy is a measure of the disorder in a system.
The argument in the previous section is how the relation between entropy and heat was arrived at historically. Modern definition of temperature is given in Statistical mechanics and it is defined in terms of the fundamental degrees of freedom of a system (see the article entropy for details). Eq.(8) of the previous section is then taken to be the defining relation of the temperature. Eq. (7) can be derived from the definition of entropy.

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[AndyW]

Hello,

Thank you for your questions and insights. I am a scientist who specializes in studying the properties of matter at extreme conditions, such as those found in the collisions at RHIC and the LHC. I would be happy to address your questions and provide some context for the paper you have referenced.

Firstly, I would like to clarify that the paper you have mentioned is not my own, but rather a publication by Peter Steinberg. I am familiar with his work and the topic he is discussing, so I will do my best to answer your questions based on my understanding of his research.

To address your first question, the concept of "frozen geometry" is referring to the idea that once a perfect liquid state has been achieved in a collision, the particles within the system are moving in a coherent and collective manner, as opposed to individual particles moving independently. This state is maintained over a range of densities and temperatures, and is not affected by changes in these variables. This is because the particles are constantly interacting with each other and exchanging energy, which keeps the system in equilibrium. Therefore, from an internal observer's perspective, the system appears to be unchanged, even though it may have been evolving for a longer period of external time.

In terms of the early universe, this concept could potentially change our understanding of the time frame of its evolution. It suggests that the universe may have been in a perfect liquid state for a longer period of external time than previously thought, which could have implications for our understanding of the early universe's expansion and evolution.

Moving on to your second question, temperature in a perfect liquid state can be measured using statistical mechanics and the fundamental degrees of freedom of the system. This is done by measuring the average energy and entropy of the particles within the system, which can then be used to calculate the temperature. It is important to note that in a perfect liquid state, the temperature is not a measure of the average kinetic energy of the particles, as it would be in a gas. Instead, it is a measure of the collective behavior of the particles in the system.

I hope this helps to clarify some of the concepts discussed in the paper you referenced. If you have any further questions, please don't hesitate to ask. As scientists, we are always happy to engage in discussions and share our knowledge and understanding with others. Thank you for your interest in this topic.