What is this site about?

This showcase connects a quantum-mechanics idea (VSPD) with how we interpret photon spectra from heavy-ion collisions. Below is a short guide to the concepts and what each part of the page does.

Core idea

• VSPD (Vector-Star Probability Dynamics) is a way of thinking about quantum uncertainty: not as pure randomness, but as a consequence of how long we measure (the measurement duration, written Δt). The longer Δt, the more “paths” or possibilities get summed, and the more spread-out (uncertain) the result looks.
• Hadronic physics here means heavy-ion collisions that create a hot, expanding medium (Quark-Gluon Plasma, QGP). Photons emitted from this plasma have an energy spectrum. Experimentally we often fit an “effective temperature” (T_eff) from the slope of that spectrum.
• The link: maybe part of what we call “effective temperature” comes from the duration of the measurement and the way the plasma expands in time, not only from the plasma’s “true” temperature. This site lets you change Δt and the measurement window and see how the spectrum and T_eff respond.

What you see on each tab

• Theory (Vector-Star): The red lines are “micro-paths.” Think of them as many possible contributions that add up when we measure over a time Δt. When you increase Δt (e.g. in the Synthesis tab), the number of red lines grows—that’s the idea that longer measurement duration means more paths and more apparent spread.
• Application (Photon spectrum): This is a simulated photon energy spectrum in GeV (0.1–1.0 GeV). The vertical axis is logarithmic. The inverse slope of this curve is what we call the effective temperature T_eff. So when the slope changes (because you change Δt or the measurement window), T_eff changes too.
• Synthesis: Here you can (1) move the slider to change Δt / plasma expansion, (2) choose the model (VSPD vs standard), and (3) drag the yellow band on the time graph to change the measurement window. The graph shows the plasma’s evolution in time; the yellow band is the interval over which we “collect” the spectrum. The spectrum and T_eff below update as you change these. The regression line shows how T_eff depends on Δt when we try to “control for” expansion (to avoid spurious correlations).

Key terms

Δt (delta t)

Measurement duration: the length of time over which we imagine gathering the photon signal. In VSPD, larger Δt means more micro-paths are summed and the spectrum can look “warmer” (larger T_eff).

Vector-Star / micro-paths

Individual contributions (the red vectors) that are combined over the measurement window. They represent different possible outcomes that add up to the observed distribution.

Effective temperature (T_eff)

A number we get from the slope of the photon energy spectrum. It looks like a temperature but can mix real thermal effects with effects of flow and measurement duration.

Measurement window (yellow band)

The time interval (on the Synthesis graph) over which the spectrum is integrated. Dragging the edges changes this interval and thus Δt for the calculation.

VSPD vs Standard model

VSPD interprets part of the spectrum shape as coming from duration (Δt) and flow. The standard view treats it as mainly intrinsic thermal randomness. The toggle lets you compare the two interpretations.