How Are Muon Velocities Measured in Storage Rings?

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Discussion Overview

The discussion centers on the measurement of muon velocities in storage rings, particularly in the context of experiments conducted at hadron colliders like CERN. Participants explore the methods used for measuring velocity, the accuracy of these measurements, and the implications of relativistic effects on the results.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether muon velocities are measured directly through a "time of flight" mechanism or derived from the measured Lorentz factor (γ) using the relativistic velocity equation.
  • Another participant states that muon velocity is not directly measured; instead, momentum is measured by observing the curvature of the muon's trajectory in a magnetic field.
  • A different participant mentions that in storage rings, frequency is measured, which corresponds to the beam circulation time, suggesting high accuracy with commercially available equipment.
  • There is a request for more details on the methods used in the Bailey et al. experiment, indicating a lack of access to the original paper.
  • A follow-up question is raised regarding the absence of observed gravitational time dilation despite significant acceleration in the experiments.

Areas of Agreement / Disagreement

Participants express differing views on the methods used to measure muon velocities, with no consensus reached on the specifics of the measurement techniques or their implications.

Contextual Notes

Some participants note limitations in accessing original research papers, which may affect the depth of discussion regarding measurement methods. There is also uncertainty about the relationship between velocity and the Lorentz factor, as well as the implications of gravitational time dilation in the context of the experiments discussed.

arindamsinha
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How accurate are the muon velocity measurements in storage rings, for muons generated in hadron colliders like CERN. How is the velocity measured?

For example, Bailey et. al. confirmed SR mathematical predictions in their famous muon ring experiment (1977), which lists the velocity of muons as 0.9994c and corresponding γ as 29.3 with a very high level of accuracy/confidence.

Did they measure the velocity of muons though some "time of flight" mechanism independent of the γ value, or was it derived using the "relativistic velocity equation" from the measured γ (or the known muon energy level for that matter)?

The reason I ask about the accuracy is that the velocity in fact has to be an even more accurate 0.99942c (using SR time dilation equation 1/√(1-v2/c2)) to arrive at the measured γ of 29.3. Even 0.9994c or 0.9995c produces a hugely different γ at that level of velocity (28.87 and 31.62 respectively!).

Appreciate any answers from anyone who is knowledgeable in this area.
 
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arindamsinha, They don't measure the muon's velocity, they measure its momentum, by observing the curvature of its trajectory in a strong magnetic field.
 
Thanks Bill. Can you give some details how this is done, and how accurate it is?
 
Doesn't the paper by Bailey et al. say anything about the methods used?
 
Actually, in storage rings, what they measure is frequency - the frequency that matches the beam circulation time. Using something cheap and commercially available like a crystal oven gives you eight decimal places of accuracy on the velocity.
 
jtbell, I tried that first, but the paper doesn't seem to be available online for free. One has to buy it from Nature or other websites for $30+.

Vanadium 50, that is very helpful. Is there are link where I can find more detail about the method you mentioned, even if not with respect to the Bailey experiment?
 
You might google "BNL g-2 experiment" and see if there is a good description of the storage ring.
 
Thanks. One other follow-up question - is there an explanation why the experiment didn't show any gravitational time dilation in spite of a very large acceleration?
 

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