LHC and partical decay - time question -

[uperkurk]

If time itself slows down near the speed of light, why don't they prove this by sending a particle which decays over a short period of time around the LHC and see if it decays at the same rate as a particle not moving around the LHC?

Would this not prove that time really does slow down and things "age slower" when moving at near the speed of light?

 

[PAllen]

If time itself slows down near the speed of light, why don't they prove this by sending a particle which decays over a short period of time around the LHC and see if it decays at the same rate as a particle not moving around the LHC?

Would this not prove that time really does slow down and things "age slower" when moving at near the speed of light?

This has been done and verified hundreds of times. But it doesn't show "moving near the speed of light" causes slower aging, because one frame's near speed of light is another frame's rest. What it shows is a form of differential aging between a non-inertial path (around the ring) and a near inertial path (lab instruments). In any case, it is a strong confirmation of special relativity.

 

[Dale]

If time itself slows down near the speed of light, why don't they prove this by sending a particle which decays over a short period of time around the LHC and see if it decays at the same rate as a particle not moving around the LHC?

Would this not prove that time really does slow down and things "age slower" when moving at near the speed of light?

This is an excellent idea. In fact, they do that all the time, not just in the LHC but in all particle accelerators built over the last several decades. The earliest I am aware of were in 1940, but my favorite are Bailey et al.'s muon experiments in the late 1970's.

See:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#particle_lifetimes
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Bailey

 

[Nugatory]

If time itself slows down near the speed of light, why don't they prove this by sending a particle which decays over a short period of time around the LHC and see if it decays at the same rate as a particle not moving around the LHC?

Would this not prove that time really does slow down and things "age slower" when moving at near the speed of light?

Dunno if that particular experiment has been done, but many experiments have observed the lifetime of unstable particles produced by the collisions within accelerators such as the LHC... It's done on a daily basis.

Also, there are the cosmic ray muon experiments and other like it.

take a look at the FAQ at the top of this forum, on experimental support for relativity. This particular result is about as well as established as the fact that if I let heavy objects fall when dropped from the top of a building.

 

[jtbell]

When I was a graduate student 30-35 years ago, one of my friends worked on an experiment involving beams of high-energy sigma and xi hyperons at Fermilab. Their lifetimes at rest are short enough that if they hadn't been time-dilated, they wouldn't have made it into and through the detector!

 

[nitsuj]

If time itself slows down near the speed of light, why don't they prove this by sending a particle which decays over a short period of time around the LHC and see if it decays at the same rate as a particle not moving around the LHC?

Would this not prove that time really does slow down and things "age slower" when moving at near the speed of light?

I thought it proved that length really contracts

 

[ZapperZ]

If time itself slows down near the speed of light, why don't they prove this by sending a particle which decays over a short period of time around the LHC and see if it decays at the same rate as a particle not moving around the LHC?

Would this not prove that time really does slow down and things "age slower" when moving at near the speed of light?

I'm going to criticize you for the way you asked your question, because it made it sound AS IF we either didn't think of doing that, or we haven't done that, when in fact, it is you who are not aware of such a thing. You should, instead, ask if such an experiment has been done, not "why don't they..."

If you had done any kind of a search on something like that, you would have you easily come up with a number of results that would have answered your question, including something like this:

http://www.nature.com/nphys/journal/v3/n12/full/nphys778.html

Zz.

 

[nitsuj]

But it doesn't show "moving near the speed of light" causes slower aging, because one frame's near speed of light is another frame's rest.

I'm confused by this apparent distinction; why doesn't it show "slower aging"?

In the case of "one frame's near speed of light is another frame's rest" there is no difference between comparative motion & in turn "aging".

 

[nitsuj]

If time itself slows down near the speed of light, why don't they prove this by sending a particle which decays over a short period of time around the LHC and see if it decays at the same rate as a particle not moving around the LHC?

Would this not prove that time really does slow down and things "age slower" when moving at near the speed of light?

I am going to praise you for your insight on this experiment.

 

[PAllen]

I'm confused by this apparent distinction; why doesn't it show "slower aging"?

In the case of "one frame's near speed of light is another frame's rest" there is no difference between comparative motion & in turn "aging".

If I say you are aging slow, and you say I am aging slow, who is right? We both are, and this is pure relative motion time dilation, and is observer dependent. However, in the case particles in an accelerator ring, not only do we lab observers see them lasting long, but a hypothetical observer going around with them would conclude we are aging very fast (no Doppler involved - they compare their clock with one 'on the wall of the accelerator' on each circuit). This invariant aspect makes it 'differential aging' rather than pure time dilation. It is different from atmospheric muon to ground tests - there a hypothetical observer moving with the muon would consider that we are aging slow by the same factor we think the muon is aging slow.

 

[uperkurk]

I'm going to criticize you for the way you asked your question, because it made it sound AS IF we either didn't think of doing that, or we haven't done that, when in fact, it is you who are not aware of such a thing. You should, instead, ask if such an experiment has been done, not "why don't they..."

If you had done any kind of a search on something like that, you would have you easily come up with a number of results that would have answered your question, including something like this:

http://www.nature.com/nphys/journal/v3/n12/full/nphys778.html

Zz.

Yes my wording of questions is awful and yes I should have used "have they conducted such an experient" rather than the words I chose. My bad..

 

[arindamsinha]

...It is different from atmospheric muon to ground tests - there a hypothetical observer moving with the muon would consider that we are aging slow by the same factor we think the muon is aging slow.

I don't get the difference between the LHC particle and cosmic muon in the above. Surely the LHC particle is entitled to think that the tunnel it is traveling has become extremely short, just like the cosmic muon does about its distance to the Earth surface?

 

[PAllen]

I don't get the difference between the LHC particle and cosmic muon in the above. Surely the LHC particle is entitled to think that the tunnel it is traveling has become extremely short, just like the cosmic muon does about its distance to the Earth surface?

No. There are a number of ways to see the difference. It think the simplest, which I already clearly described, is:

The atmospheric muon never gets to compare its 'clock' repeatedly to the same Earth clock. The particle in a ring does. Each time it passes the same hypothetical clock on the ring it sees the ring clock further and further ahead, i.e. faster. There is no interpretation that it make to say the clock it repeatedly encounters and sees running ahead is really slower. There is no doppler, simultaneity, length conrraction, or time dilation interpretation that is involved - you have a direct comparison of co-located clocks. This makes it analagous to the invariant differential aging of the twin paradox, rather than the symmetric time dilation between relatively moving inertial frames.

I think we've gone over this in different threads: you have to let go of any notion that an non-inertial path is equivalent to an inertial path. This is false both in SR and GR.

Another is that the muon never changes inertial frames. The particle in the ring has, at every point around the ring, a different instantly comoving inertial frame, with different simultaneity. This is fundamentally different from the fixed simultaneity for the muon. If you build a coordinate system in which the ring particle is at rest, is has a different metric from the standard Minkowski metric. Using this metric, the ring particle would compute that a lab clock is running fast on average, not slow.

[Edit: Is it possible you didn't know the LHC is a ring? However, even if we talk about a linear accelerator, the situation is different from the atmospheric muon case, in that acceleration is involved. All three of these cases (muon, LINAC, LHC) look similar from Earth lab frame; however, each is quite different from the particle's point of view. ]

 

[arindamsinha]

...The atmospheric muon never gets to compare its 'clock' repeatedly to the same Earth clock. The particle in a ring does. Each time it passes the same hypothetical clock on the ring it sees the ring clock further and further ahead...

Pardon me for persisting. Isn't the above really an experimental set up issue rather than the physics?

For example, instead of a circular ring, we could (theoretically) give the LHC particle a long straight tunnel... (Edit: I see you already referred to this, but why should the initial acceleration matter?)

Alternatively, we could provide the cosmic muon a set of stationary clocks (synchronized with Earth clock) along its path...

I am not talking about the physical feasibility of such set ups, just the 'thought experiment' side of it.

(I did know it was a ring).

 

[PAllen]

Pardon me for persisting. Isn't the above really an experimental set up issue rather than the physics?

For example, instead of a circular ring, we could (theoretically) give the LHC particle a long straight tunnel...

Alternatively, we could provide the cosmic muon a set of stationary clocks (synchronized with Earth clock) along its path...

I am not talking about the physical feasibility of such set ups, just the 'thought experiment' side of it.

But each of these changes the physics. In the straight line cases, where the particle is inertial (or close to it), they could set up their own set of clocks comoving with them, syncrhonized with theirs. Then, they would conclude that the reason the Earth system of clocks thinks their clock is slow is that the Earth clocks are out of synch with each other (as compared to the particle's comoving clocks). Each Earth clock is moving slow compared to the inertial particle's set of clocks - as compared to successive such clocks by direct comparison, but each one is out of synch with its neighboring Earth system clock to a degree that accounts for the discrepancy in interpretation.

Now consider the circular moving particle trying to do this. First issue is how to synchronize their ring of clocks (for example), to compare to lab clocks along the ring. If they use Einstein synchronization from the particle clock as origin, then the result will be that the particle ring of clocks will conclude that each lab ring clock (compared to successive particle ring of clocks) will vary in speed but, on average, run very fast.

[Edit: The idea above is to remove all aspects of Doppler, and visual appearance; and use only direct comparison of instantly collocated clocks; every system of clocks is synchronized with the Einstein or radar convention. The results for the circular case are radically different. - for the particle point of view]

 

[arindamsinha]

But each of these changes the physics...

I am not really convinced. This is not to say you are wrong, but just a different way of looking at things perhaps.

I think the underlying physics is the same in both cases (LHC particle and cosmic muon) and the same set of explanations apply to both. What you are explaining looks more like the 'method of measurement' ascribed to observers in the particular experimental set ups.

In the end, it is purely about the velocity and the Lorentz factor 1/√(1-v²/c²) in both cases. The apparent differences in the experimental situation does not affect the results at all.

As Bailey et. al. concluded (I believe) that the rather large acceleration (and therefore the non-inertial frame) in the muon storage ring plays no role in the differential aging, only the velocity makes the difference. Ditto the cosmic muon experiments. These are supposed to be straight forward validations of SR, not involving any particular points of view.

I will not argue further, since you are much more knowledgeable in these things, of course.

 

[PAllen]

As Bailey et. al. concluded (I believe) that the rather large acceleration (and therefore the non-inertial frame) in the muon storage ring plays no role in the differential aging, only the velocity makes the difference. Ditto the cosmic muon experiments. These are supposed to be straight forward validations of SR, not involving any particular points of view.

.

They are straightforward validations. The storage ring is verifying differential aging, the cosmic muons is verifying time dilation measured (using a production event and a reception event that are effectively at rest with each other but separated in distance). For differential aging, the amount of difference does depend only on speed measured in some inertial frame, but the phenomenon - that both particle and lab agree on the result - depends the particle and lab 'clocks' being collocated at two events (and therefore that there are changes of direction = acceleration, involved). For the cosmic muon case, the muon disagrees, and relativity gives no preference to the lab perspective versus the muon perspective.

I am quite sure I have no disagreement with Baily. It is you that does not understand SR well enough to see the whole picture.

 

[arindamsinha]

...It is you that does not understand SR well enough to see the whole picture.

That I can agree with completely.

 

[nitsuj]

If I say you are aging slow, and you say I am aging slow, who is right? We both are, and this is pure relative motion time dilation, and is observer dependent. However, in the case particles in an accelerator ring, not only do we lab observers see them lasting long, but a hypothetical observer going around with them would conclude we are aging very fast (no Doppler involved - they compare their clock with one 'on the wall of the accelerator' on each circuit). This invariant aspect makes it 'differential aging' rather than pure time dilation. It is different from atmospheric muon to ground tests - there a hypothetical observer moving with the muon would consider that we are aging slow by the same factor we think the muon is aging slow.

So the term Time Dilation is specific to symmetrical cases? Everything else you said seems plain as day to me, that said I cannot understand how there is no length contraction / RoS ect because of the constant acceleration.

 

[Dale]

In the end, it is purely about the velocity and the Lorentz factor 1/√(1-v²/c²) in both cases.

The Lorentz factor only applies to inertial frames. That is why you can use it for the reference frame of cosmic muons but not for the reference frame of accelerator muons.

 

[PAllen]

So the term Time Dilation is specific to symmetrical cases? Everything else you said seems plain as day to me, that said I cannot understand how there is no length contraction / RoS ect because of the constant acceleration.

You could conceivably talk about time dilation for coordinates built from an accelerator muon frame. For non-inertial motion you can only talk about local frames in a unique way; then there are many approaches for extending a local frame to coordinate patch. However, typically, it cannot cover much spacetime. So you have a non-unique, quasilocal, coordinate patch in which time dilation takes a complex form [edit: really, the metric takes a complex form; the metric then determines time dilation for a specific path in the coordinates]. Further, in such a coordinate patch, you would typically have features like light and clock paths with coordinate speed greater than c; and your time coordinate would not be everywhere timelike (unless you restrict coverage of your patch even more). Note, this is all SR here - I am not referring to GR at all, just the issues involved in setting up coordinates such that an arbitrary non-inertial world line is the time axis, and coordinate time represents clock time along this world line, and distance coordinates represent proper distance from it according to some reasonable simultaneity convention. Given, especially, the non-uniqueness of all of this, it is rarely useful to talk about an accelerator muon's coordinates (and therefore, about time dilation from the accelerator muon's point of view - that requires such coordinates).

For these reasons, in the accelerator case, we choose to focus on the coordinate independent differential aging rather than the coordinate dependent, complex, time dilation.

 

[nitsuj]

Thanks for the explanation PAllen, it's more clear for me now.