Muon's time dilation

[Alan Grayson]

The claim is that the muon's half life is increased from its measured value in the lab frame, to an extended value when observed by a stationary observer seeing the muon in motion. But how is the lab frame different from the rest frame in which the muon is is observed as moving? They seem like the same frame. AG

[Brent Meeker]

On 6/10/2025 8:14 PM, Alan Grayson wrote:

The claim is that the muon's half life is increased from its measured value in the lab frame, to an extended value when observed by a stationary observer seeing the muon in motion. But how is the lab frame different from the rest frame in which the muon is is observed as moving? They seem like the same frame. AG --

You've confused yourself by not mentioning it's motion in the lab frame, which is implicitly zero.  So it's comparing the half-life in the muon's frame with the muon's half-life as it travels at near light speed.



David H. Frisch and Smith (1963) measured approximately 563 muons per hour in six runs on Mount Washington. By measuring their kinetic energy, mean muon velocities between 0.995 c and 0.9954 c were determined. The target was located in Cambridge, Massachusetts with a difference in height of 1907 m, which should be traversed by the muons in about 6.4 µs. Assuming a mean lifetime of 2.2 µs, only 27 muons would reach this location if there were no time dilation. However, approximately 412 muons per hour arrived in Cambridge, resulting in a time dilation factor of 8.8±0.8.

Frisch and Smith showed that this is in agreement with the predictions of special relativity: The time dilation factor for muons on Mount Washington traveling at 0.995 c to 0.9954 c is approximately 10.2. Their kinetic energy and thus their velocity was diminished until they reached Cambridge to 0.9881 c and 0.9897 c due to the interaction with the atmosphere, reducing the dilation factor to 6.8. So between the start (≈ 10.2) and the target (≈ 6.8) an average time dilation factor of 8.4±2 was determined by them, in agreement with the measured result within the margin of errors (see the above formulas and the image for computing the decay curves).

Brent

[Alan Grayson]

On Tuesday, June 10, 2025 at 9:37:53 PM UTC-6 Brent Meeker wrote:

On 6/10/2025 8:14 PM, Alan Grayson wrote:

The claim is that the muon's half life is increased from its measured value in the lab frame, to an extended value when observed by a stationary observer seeing the muon in motion. But how is the lab frame different from the rest frame in which the muon is is observed as moving? They seem like the same frame. AG --

You've confused yourself by not mentioning it's motion in the lab frame, which is implicitly zero.  So it's comparing the half-life in the muon's frame with the muon's half-life as it travels at near light speed.

How is sitting in a lab observing the muons fly by, different from sitting atop a mountain watching them fly by? AG 

[Brent Meeker]

On 6/10/2025 8:46 PM, Alan Grayson wrote:

On Tuesday, June 10, 2025 at 9:37:53 PM UTC-6 Brent Meeker wrote:

On 6/10/2025 8:14 PM, Alan Grayson wrote:

The claim is that the muon's half life is increased from its measured value in the lab frame, to an extended value when observed by a stationary observer seeing the muon in motion. But how is the lab frame different from the rest frame in which the muon is is observed as moving? They seem like the same frame. AG --

You've confused yourself by not mentioning it's motion in the lab frame, which is implicitly zero.  So it's comparing the half-life in the muon's frame with the muon's half-life as it travels at near light speed.

How is sitting in a lab observing the muons fly by, different from sitting atop a mountain watching them fly by? AG

I wonder why I bother to write answers, when you don't even read the first line.

Brent

[Alan Grayson]

You're mistaken, totally. I read your message. ISTM, the frame atop the mountain is at rest and the muons fly by, whereas the earth bound lab is in the same situation.  AG

[Brent Meeker]

It says "...motion in the lab frame...is zero".  And apparently you didn't look at the diagram at all.

Brent

[Alan Grayson]

I glanced at the diagrams. In the lab frame, the muons are moving toward the Earth's surface and beyond, through the Earth, so I see them as moving in the lab frame. Same atop the mountain. AG 

[John Clark]

On Tue, Jun 10, 2025 at 11:46 PM Alan Grayson <agrays...@gmail.com> wrote:

> How is sitting in a lab observing the muons fly by, different from sitting atop a mountain watching them fly by? AG

If you want to measure the half life of a muon in the lab then you make sure that the relative velocity between the lab and the muon is zero, or at least very small. But when you measure the half life of a muon that comes from space when you're sitting on a mountain the muon is moving close to the speed of light relative to your measuring equipment on top of that mountain.  

John K Clark    See what's on my new list at  Extropolis

ebc

[Alan Grayson]

On Wednesday, June 11, 2025 at 5:36:26 AM UTC-6 John Clark wrote:

On Tue, Jun 10, 2025 at 11:46 PM Alan Grayson <agrays...@gmail.com> wrote:

> How is sitting in a lab observing the muons fly by, different from sitting atop a mountain watching them fly by? AG

If you want to measure the half life of a muon in the lab then you make sure that the relative velocity between the lab and the muon is zero, or at least very small.

The condition you claim is necessary, seems impossible, since the lab is at rest and the muon is moving. AG 

[John Clark]

On Wed, Jun 11, 2025 at 7:49 AM Alan Grayson <agrays...@gmail.com> wrote:

>> If you want to measure the half life of a muon in the lab then you make sure that the relative velocity between the lab and the muon is zero, or at least very small.

> The condition you claim is necessary, seems impossible, since the lab is at rest and the muon is moving. AG 

Why is it impossible? Unlike a photon a muon has a nonzero rest mass, therefore a muon can NEVER travel at the speed of light and it is possible to slow them down, and if an experimenter is worth a damn he's going to make sure that relative to his lab equipment it has come to a rest, or at least is moving very slowly, before he measures it's half-life.  

John K Clark    See what's on my new list at  Extropolis

flk