# What time dilation do muon observers experience?

1. Nov 23, 2015

### DAC

Re. time dilation muons, CERN.
Given the accelerated muons were observed to have a lifetime increased by approximately x 29, What happens to the observers life span?
Thank you.

2. Nov 23, 2015

### nrqed

I am guessing you are asking what is observed from the point of view of the muon, or from the point of view of someone in the muon's frame? Then the answer is that the lifetime in that frame is the usual proper lifetime, about $2.2 \mu s$

3. Nov 23, 2015

### Ibix

You never experience time dilation - your clock always ticks at one second per second, you always live your three score years and ten, and that's it. However, you might see someone else's clocks slowed down as a result of high velocity. But it's not just their clocks that slow down - it's all physical processes, including the fast moving person's brain processes, so you shouldn't be surprised that she sees nothing odd about her clocks.

I don't think your question is clear. Do you mean what happens to people travelling along with the muons, or to people working at CERN?

People travelling along with the muons will see the muons decaying with their normal half-life. They will also see the clocks on the wall at CERN ticking once every 29s. The people working at CERN will see the wall clocks ticking once per second, but the muons will decay with a half-life 29 times longer than stationary muons, and the watches of the people travelling along with the muons tick once every 29s.

These two points of view are not contradictory. We have only mentioned one part of the story, time dilation. There are two other effects, length contraction and the relativity of simultaneity, that work with time dilation to make a consistent picture. I advise looking up the Lorentz transforms if you are interested.

4. Nov 23, 2015

### DAC

The muons move relative to the observer and vice versa. So is the observer seen to age more slowly by the same amount.

5. Nov 23, 2015

### Staff: Mentor

If you are talking about Muons in a particle accelerator storage ring, then the Muons frame is highly non inertial. So the time dilation in that frame does not follow the same equations as in inertial frames. In particular, it is not reciprocal. The muon agrees that it decays slower than lab Muons.

6. Nov 23, 2015

### Ibix

As DaleSpam points out, that depends rather a lot on the details of what the observers and the muons are doing.

The case that nrqed and I were implicitly assuming is that the muons are moving in an unaccelerated straight line. In that case the situations are reciprocal - the muons say the wall clocks run slow and the observers say the muons decay slowly. They agree on the factor by which the other is running slow.

If you are actually interested in the case of muons going round in a circle then what you have is a variant of the twin paradox scenario. The observers are the the "stay at home twin" and the muons are the "travelling twin". Both will agree that the observers age faster in this case, although the reasoning from the muons' perspective is quite complex. Again, both will still argue that everything feels normal to them and the other is behaving funny. Look up the twin paradox and understand that first if you want to study this case.

7. Nov 23, 2015