The Naked Scientists

The Naked Scientists Forum

Author Topic: quantum of probability?  (Read 1781 times)

Offline chiralSPO

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 1879
  • Thanked: 145 times
    • View Profile
quantum of probability?
« on: 10/06/2014 14:22:59 »
Here's a thought that has been sneaking in the back of my mind for a while: Is there a smallest possible nonzero probability, below which there is only zero probability?

Consider, for example, the wavefunction of an electron in the 1s orbital of a hydrogen atom. It is fairly straightforward to calculate the probability of finding that electron as a function of distance from the nucleus. This probability is non-zero at every point in the universe, but vanishingly small at any distance further than (for argument's sake) 10 . Is this universal existence real in any sense, or is this just an artifact of a model that is too simple? (it is often mathematically much simpler so integrate from 0 to ∞ and consider this a limit, than to actually plug in numbers and crunch)

This has implications--some of which are perhaps only philosophical, like if the calculated probability of an event is so small that it could only happen once in 10100 years--but some, like the coupling of wavefunctions through space (and time) for particle exchange or quantum entanglement could have actual measurable and practical ramifications.


 

Offline JP

  • Neilep Level Member
  • ******
  • Posts: 3366
  • Thanked: 2 times
    • View Profile
Re: quantum of probability?
« Reply #1 on: 10/06/2014 17:37:32 »
Part of this comes back to the question of whether infinity/infinitesimal is physical or just an approximation in these fundamental theories.  We don't know the answer.  For example, theories in which probability can take on any value continuously down to zero work and are consistent with observation.  But we could also develop a theory in which the smallest probability is some tiny value that is small enough to also be consistent with observation.  Since we can't tell them apart, there's no real way to say whether one is the more correct theory.

The philosophical implication here is that we really can't ask science to tell us about "ultimate reality" as it can only tell us about what is observable/testable.  Currently we can't distinguish between a universe with tiny minimal probability and continuous probability, so that's a debate best left to philosophy until it enters the realm of testability.
 

Offline chiralSPO

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 1879
  • Thanked: 145 times
    • View Profile
Re: quantum of probability?
« Reply #2 on: 10/06/2014 19:48:41 »
I suppose it depends on how small that quantum might be. I could imagine some chemical systems in which one could measure, with pretty high precision, some very improbable events--and at least set an upper limit on the size of that quantum in the case of a negative result (or determine what it might be in the case of a positive result)

Part of what I'm after is: given the maths of quantum mechanics, is there a reason to impose such a limit? Using the same sort of derivation as that used for determining the Planck length or time could one make a sensical argument for quantizing a unitless number like probability?
 

Offline PmbPhy

  • Neilep Level Member
  • ******
  • Posts: 2762
  • Thanked: 38 times
    • View Profile
Re: quantum of probability?
« Reply #3 on: 11/06/2014 02:08:41 »
Here's a thought that has been sneaking in the back of my mind for a while: Is there a smallest possible nonzero probability, below which there is only zero probability?

Consider, for example, the wavefunction of an electron in the 1s orbital of a hydrogen atom. It is fairly straightforward to calculate the probability of finding that electron as a function of distance from the nucleus. This probability is non-zero at every point in the universe, but vanishingly small at any distance further than (for argument's sake) 10 . Is this universal existence real in any sense, or is this just an artifact of a model that is too simple? (it is often mathematically much simpler so integrate from 0 to ∞ and consider this a limit, than to actually plug in numbers and crunch)

This has implications--some of which are perhaps only philosophical, like if the calculated probability of an event is so small that it could only happen once in 10100 years--but some, like the coupling of wavefunctions through space (and time) for particle exchange or quantum entanglement could have actual measurable and practical ramifications.
Speaking of hydrogen, the possible energies for the hydrogen are discrete for bound electrons and continuous for free electrons. If you construct a wave function which is a superposition of all the eigen functions corresponding to those eigenvalues then the probability distribution will be continuos for all energies above zero, discrete between 0 and -13.6 eV and zero below that.
 

Offline jeffreyH

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 3927
  • Thanked: 55 times
  • The graviton sucks
    • View Profile
Re: quantum of probability?
« Reply #4 on: 11/06/2014 23:47:42 »
The Planck probability. Now that is strange. Quantized probability. We could have the probability particle. Then the infinite improbability drive may even be possible. Anyone got a spare towel?
 

The Naked Scientists Forum

Re: quantum of probability?
« Reply #4 on: 11/06/2014 23:47:42 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums
 
Login
Login with username, password and session length