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Do near-light speeds affect the length of a half-life?

 
 
Reply Thu 18 Mar, 2010 07:22 am
For example, muon particles (which are like very big electrons) have a half-life of 2 or so micro-seconds. You'll find them in cosmic rays and the like. I was just curious to whether half-life is affected by space-time relativity?
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Type: Question • Score: 2 • Views: 1,184 • Replies: 8
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RealEyes
 
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Reply Thu 18 Mar, 2010 08:38 am
@RealEyes,
I mean, if you super accelerate a particle, would it lengthen the time it takes to decay?
farmerman
 
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Reply Thu 18 Mar, 2010 08:42 am
@RealEyes,
decay constants of isotopes are compared one to another for both daughter and parent isotope. decays have been measured fromlab experiments of decades so that every radioactive isotope with a hlf life greater than a few tenths of a second and every type of decay has been produced in a tabular form (and is constantly revised so each successive "decimal point " is directly measured as the years progress.
SInce the measurement for radioactive decay constants are derived via direct comparisons of daughter to parent, even if (c) varied significantly, it doesnt get included within the (t) equation . SO any variation in (c) wouldnt add more than a 2% variance to a half life determination of long lived isotopes.

This is a well discussed topic by folks who wish that the age of the earth would be much younger than it is.
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parados
 
  1  
Reply Thu 18 Mar, 2010 09:06 am
@RealEyes,
How do you test the time it decays?

If you are moving at the same speed as the particle then time would be the same for you according to relativity.

If you change the speed of the particle to test it then it is a completely different thing, isn't it?

This is one of those questions that can only be answered theoretically with current technology.
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TheCorrectResponse
 
  2  
Reply Thu 18 Mar, 2010 02:22 pm
@RealEyes,
Yes there is certainly a time dilation effect. In fact cosmic rays are a good example. It is only because of the time dilation effect that cosmic rays do not decay before hitting the ground.

Since the science section of A2K has long since joined the rest of the place as a site for arguments rather than discussion I thought that rather than put it into my own words and then have to argue what the meaning of the word “is” is, I would instead provided a link to the National Accelerator Lab. It explains the whole thing and shows some basic calculations. That way anyone wanting to argue can direct comments to this site.

http://www2.slac.stanford.edu/vvc/theory/relativity.html
farmerman
 
  1  
Reply Thu 18 Mar, 2010 03:13 pm
@TheCorrectResponse,
Were not even arguing the same thing. Your talking about energy output, Im talking actual half life and (LAMBDA) which are measured for each isotope in the periodic table and are based upon RATIOS of daughter to parent isotope. (c) is irrelevant to all but energy output. HAlf life is govered by the number of disintegrations per second per second
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ebrown p
 
  1  
Reply Thu 18 Mar, 2010 03:46 pm
@TheCorrectResponse,
The Correct Response is, of course, correct. The time dilation affect must affect half-lives (which are measured in units of time) or else relativity would be invalid.

But, a warning.... to understand what this means... you need to understand the key principle of Relativity; there are more than one points of view, and they are equally correct.

Take a the proposed decaying substance (which from your point of view is moving very very fast). From your point of view, the substance would decay slower than it should... which makes sense given our understanding of time dilation.

Of course to a person who is sitting on the substance... the substance isn't moving at all (although the Earth and the solar system are hurtling toward them very very fast). To this observer the substance would decay at exactly the "correct" rate, although they would measure the distance between the Earth and the substance as shorter than the original observer.

If you are holding the substance in your hand... then time dilation due to speed has nothing to do with any measurement you might make (no matter how fast some other observer thinks you are moving).

This has been observed by very fast particles which are created at the top of our atmosphere and make it much farther down then they should (given that they should decay before they travel that far).

farmerman
 
  1  
Reply Thu 18 Mar, 2010 03:57 pm
@ebrown p,
since all(N/No) would be reletivistically affected, the "time dilation" would not be relevant
ebrown p
 
  1  
Reply Thu 18 Mar, 2010 05:13 pm
@farmerman,
No Farmerman, there are two (interesting) frames of reference here; yours and the muons'.

The fact is that there are many more muons (which are created in the upper atmosphere) that are detected experimentally on the gound then can be explained without relativity (i.e. distance = rate * time).

From your frame of reference, this is explained by time dilation (the moving particle experiences less time to decay and so fewer of them decay).

Of course, from the muons' frame of reference, the time dilation is irrelevant but the Lorentz contraction reduces the distance it has to travel (meaning the rapidly approaching Earth can cross that distance in a shorter time during which fewer of them decay).



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