Probability amplitudes & light / particle wavelengths

In summary, the conversation discusses the concept of coherence length and its relationship to interference in the context of photons. The speaker questions the speed of propagation and time differences for photons taking different paths, but is corrected by the expert who explains that the wave function does not travel at a fixed speed and there is no violation of the speed of light. The expert recommends studying optics and classical fields for a better understanding of the topic.
  • #1
Nick.
15
0
So this is basic question but the more I read the more I am confusing myself!

I was assuming that the wavelength of a photon was the same wavelength as the associated probability amplitude (although a complex number). So to make constructive interference it means one path takes say ten wavelengths more to arrive at the same point in the configuration space...but doesn't that mean path has taken more time than the other? As the photon travels at the speed of light I assume (again probably incorrectly) that if the time was measured it would be seen as taking the shortest path (I am postulating minimum action)...but if that is the case the other longer path hasn't even had enough time to arrive there so it can't interfere with it yet!

Sure - I probably have mix up a few things...some clarity and good further reading suggestions would great...

Thanks.
 
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  • #2
Nick. said:
but doesn't that mean path has taken more time than the other?
Right. As a result, your coherence length has to be long enough to get interference. Your photon is not a point-like object.
 
  • #3
I think your basic assumption of a photon as a particle that traverses a set path to get from point A to point B is incorrect.
 
  • #4
Yes-So wouldn't the interference be in violation of the photon's fixed velocity? If it was interference from the same crest it would make some sense but to get the interference one path is longer than the other (with maximised probabilities at x+nλ).

And still - what time would be measured - the shortest path?
 
  • #5
It may not travel a set path - hence the interference. But we can accurately measure the velocity of a photon - so that is a distance between two points (whatever path it takes in between). As the velocity is fixed, each path has different time...would the velocity equal the time to travel the shortest path?
 
  • #6
Nick. said:
So wouldn't the interference be in violation of the photon's fixed velocity?
No. Your assumption of a fixed position (or emission time) is wrong. Consider the classic equivalent to photons with long coherence length - a continuous wave emitted forever at the same frequency. It does not have a position at all.
Nick. said:
each path has different time
Yes, but emission and absorption do not.
 
  • #7
No I think we are getting sidetracked - I don't think I am going wrong with coherence. The simple fact that we get interference at all demonstrates that there are two (or more) different path lengths for the wave function. My confusion is about time - if the probability wave function path lengths relate to the actual light wavelengths then there is a difference in the speed of propagation. Although tiny in standard experiments (I calculate a difference of 2x10^-15 sec on a interferometer with 1m legs and 500nm laser) it still means something strange is afoot - either the wave function travels faster than light or the light is taking the longest path (unlikely).
 
  • #8
Nick. said:
if the probability wave function path lengths relate to the actual light wavelengths
It does not.
Nick. said:
then there is a difference in the speed of propagation
No, and it would not even if the former was true.
Nick. said:
(I calculate a difference of 2x10^-15 sec on a interferometer with 1m legs and 500nm laser)
What did you calculate, how?
Nick. said:
either the wave function travels faster than light or the light is taking the longest path (unlikely).
Neither. Nothing strange happens.
 
  • #9
Thanks mfb.

Can you expand your answers a little more so I can look them up - or perhaps you have a good reference? I am guessing that your inferring the wave is in a configuration space like a de broglie wave? (So no 'real' relationship with the speeds of particles - it becomes a calculation on probabilities).

Thanks
 
  • #10
Nick. said:
or perhaps you have a good reference?
A book about optics. This is so much easier to understand if you consider the electromagnetic wave as a (classical) field.
 
  • #11
Thanks mfb...any good recommendations?
 
  • #12
My favorite is good old Born and Wolf for classical optics and Scully and Zubairy and afterwards Mandel and Wolf for Quantum Optics.
 

FAQ: Probability amplitudes & light / particle wavelengths

1. What are probability amplitudes?

Probability amplitudes, also known as wave functions, are mathematical expressions that describe the probability of finding a quantum particle in a certain state or location. They are represented by complex numbers and are used in quantum mechanics to predict the behavior of subatomic particles.

2. How are probability amplitudes related to light and particle wavelengths?

In quantum mechanics, particles can exhibit both wave-like and particle-like behavior. The probability amplitude is related to the particle's wavelength through the de Broglie relation, which states that the wavelength is equal to Planck's constant divided by the momentum of the particle. This relationship helps to explain the wave-particle duality of particles like photons, which can behave as both waves and particles.

3. How do probability amplitudes affect the behavior of particles?

Probability amplitudes determine the likelihood of a particle being in a certain state or location. They can interfere with each other, resulting in constructive or destructive interference, which can affect the probability of finding a particle in a particular location. This is known as the wave function collapse and is a fundamental concept in quantum mechanics.

4. Can probability amplitudes be measured?

No, probability amplitudes cannot be directly measured. They are mathematical constructs used to describe the behavior of quantum particles. However, their effects can be observed through experiments, such as the double-slit experiment, which demonstrate the wave-like behavior of particles.

5. How do probability amplitudes relate to the uncertainty principle?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle simultaneously. Probability amplitudes are used to describe the probability of a particle being in a certain position, but the more accurately we know its position, the less accurately we know its momentum, and vice versa. This is because measuring one property affects the other, and probability amplitudes play a crucial role in understanding and quantifying this uncertainty.

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