Is my math wrong or is there a giant hole in QM? As far as I can tell, in QM radioactive decay is always treated as individual probabilities for each activation event. The result of such a system would be linear radioactive decay, but we never see that. We always see exponential radioactive decay which requires then that the decay rate be dependant upon population size.

I have never seen or heard even a postulate at a system or mechanism in either classical or quantum physics that attempts to explain or account for this discrepancy in any way. Am I missing something? Shouldn't this be listed as one of the great all time physics mysteries?

 

As far as I can tell, in QM radioactive decay is always treated as individual probabilities for each activation event. The result of such a system would be linear radioactive decay

 

This is a claim but I see no maths to substantiate it.

 

This seems a fairly easy to follow derivation of radioactivity probability.

 

http://www.csupomona.edu/~pbsiegel/bio431/texnotes/chapter2.pdf

 

This is a claim but I see no maths to substantiate it.

 

 

My point is - the math is all about exponential decay, but the explanatory mechanisms are all discrete. there is nothing in the QM model that I see that corroborates the math.

Did you read the referenced article?

 

If so how do you reconcile the solution to the differential equation (where the exponential comes in) with your theory?

I gather together 128 friends and give them each a coin. They each flip their coin once every minute. If they get heads, they can leave.

 

After one minute, half of them get heads and 64 are left. After two minutes, half of the remaining friends are left and there are 32 left. After three minutes there are 16. Four minutes, 8. Five minutes, 4. Six minutes, 2. After seven minutes, there is one left.

 

Each coin has an individual probability of "decaying" after one minute of 50%. That leads to an exponential decay rate.

Is my math wrong or is there a giant hole in QM? As far as I can tell, in QM radioactive decay is always treated as individual probabilities for each activation event. The result of such a system would be linear radioactive decay, but we never see that. We always see exponential radioactive decay which requires then that the decay rate be dependant upon population size.

 

I have never seen or heard even a postulate at a system or mechanism in either classical or quantum physics that attempts to explain or account for this discrepancy in any way. Am I missing something? Shouldn't this be listed as one of the great all time physics mysteries?

 

Once the element has decayed ( by say spitting out an Alfa particle namely 2 protons and 2 neutrons ) it will not be the same element. mass gone down by 4 charge by 2 . So the population of your original element has gone down by 1 . once the population has halved. However long it takes, that is the half life. the next half life takes the same time but half of a half is a quarter as you only started this time with half the population. next half life (same time half life time ) one eighth of population .

 

So first population say 1000 atoms [ after first half life time = 500 atoms [after 2nd half life 250 atoms after 3rd half life 125 atoms left of original population this is exponential decay.

 

Linear would be say 1000 population decay to 900 decay to 800 decay to 700 [ say every half life ) BUT THIS IS NOT WHAT HAPPENS [its always half the remaing population not a fixed linear amount ]

 

Hope this helps

 

Mike

Edited August 28, 201312 yr by Mike Smith Cosmos

People have considered deviations from the exponential decay in the context of quantum mechanics. I forget the details, but carefully quantum mechanics does seem to allow for this. However, the deviations will be quite small for sensible sized samples watched for a sensible amount of time.

 

I'll see if I can find the paper later on.

 

Edit: The paper is

 

Rothe C, Hintschich SI, Monkman AP. Violation of the exponential-decay law at long times. Phys Rev Lett. 2006 Apr 28;96(16).

Edited August 29, 201312 yr by ajb

Is my math wrong

 

I don't know if your math is wrong sinse you have not provided any math for us to see.