The Famous Quantum Measurement Puzzle has been Solved

on

 The Famous Quantum Measurement Puzzle has Finally been Solved!

YES! The Famous Quantum Measurement Puzzle has been Solved!

What is the puzzle?

The moment a particle is detected at one spot, it's Schrödinger wave instantly collapses everywhere else in the universe.  But that's impossible!  
So we have a puzzle. 
Imagine wave function collapse as something like a balloon that pops.

First of all nothing in our universe happens instantly.   Light from distant galaxies takes millions of years to reach us.  It's certainly not instant.

Is there a puzzle when a particle is detected?

Let's say a light particle (a photon) is detected in my iPhone camera sensor.  The photon is a "quantum" particle described by a wave function.  Before the measurement the probability of finding the particle is spread out, often over a large area, even kilometers.  The particle could be found almost anywhere.  We can't know where it is, we can only calculate the probability of finding it.   The probability distribution is spread out over a large volume of space, like a giant balloon.  But once the particle has been detected I know exactly where it was and when it was found.  Upon detection, the probability suddenly becomes certainty.  It's like the balloon "popped."  The puzzle is how to explain this instantaneous probability wave "collapse" that happens whenever we detect a quantum particle.

It's Like The California Lottery

Let's compare this detection process to the California Lottery.  Before the drawing, any one of the tickets that were purchased and then distributed all over the state could be the winning ticket.  When the winning number is drawn, the probability suddenly changes.  All the losing tickets now have a probability equal to ZERO.  The single winning ticket's chance suddenly changed to ONE (the certain winner).  The tickets themselves didn't change or move, only the probability of winning changed, because of the new information from the drawing.   This is a "collapse" of the probability distribution.  The winning number information quickly (but not instantly) spreads by TV and internet to the ticket holders.

California Lottery Ticket

A photon from Alpha Centauri - The Puzzle!

Now think of one visible light pulse (photon) emitted from an atom on Alpha Centauri.  According to the standard (textbook) view, the probability of detecting it somewhere is spread out in space.  After four years the probability has dramatically spread out like a giant sphere in all directions.  Let's say the photon was detected on earth.  The whole photon suddenly appeared here with all of its energy and momentum in one lump.  We have a lucky (photon) winner!  How does every other possible location in space get notified that the "winning number" has been drawn?  How does this instant collapse of probability actually happen in nature?  Does every photon detection cause messages to go out for trillions of miles to all the losers?  How does nature keep track to make sure there are no multiple winners?  

Whirlpool Galaxy is 23 million light years
away from earth.[NASA Hubble]

What is the solution?

The surprising solution is - There is no collapse!  It was all a huge misunderstanding.  A misinterpretation.  A bad mistake.  Let me explain.

How Photons Really Work (According to me)

Let's go back to that one particular visible light burst (photon) emitted from Alpha Centauri.  It was emitted from an excited atom that transitioned from a higher energy level to a lower one.  During that transition it transmitted a brief burst of electromagnetic waves that spread out in all directions.  Most of the wave is still going outward, but after four years a small part of the wave was absorbed somewhere on earth, maybe in my iPhone camera's sensor.  The rest of the light pulse continues out into space in all directions until it is eventually absorbed thermally and becomes heat energy.  Electromagnetic waves don't collapse, they keep spreading out until they eventually get absorbed.  Like microwaves absorbed by frozen broccoli.  The microwave's energy isn't lost, it turns into heat energy.  Microwaves don't "collapse" they are absorbed and turn into heat.

If the puzzle has been solved, why is it still a puzzle?

I think one reason is because people are tempted to use statistics to describe single events.  Quantum mechanics is a theory of statistical behavior.  It enables us to calculate probabilities accurately and correctly.  For example we can calculate the probability of photon emission or the probability that an electron will tunnel through a potential barrier.  Quantum mechanics is a wonderful and successful framework that describes atomic behavior, semiconductors, lasers and much more.  It answers statistical questions like what is the distribution of electron energy in a copper wire.  Or what frequencies of light will be emitted from a collection of Helium atoms.  

We get into big trouble when we try to use a statistical theory to answer questions that  are not statistical, like which slit did the electron go through?  Is the cat dead or alive?  Statistics can only tell us averages and likelihoods, not definite answers for single events.  

A second reason is because people are tempted to ask about the underlying mechanisms that are not part of that theory.  Quantum mechanics does not tell us how a single electron moves, or explain exactly how a single photon gets from the sun to my camera.  It only predicts the statistical results for many electrons or many photons.  Quantum mechanics accurately calculates the average motion of many electrons, but it can not not give us the trajectory of any particular one of them.  

The Solution to the Measurement Puzzle

If we now go back to the measurement puzzle, the solution is clear, even obvious.  Don't ask about single measurements!  If we limit the discussion to statistics of measurements, there is no more puzzle.  When we calculate the statistics for the behavior of a large number of electrons, there is nothing to "collapse."  The "collapse" only comes up when we try to imagine the motion of a single electron, before and after it is measured (detected).

The puzzle occurs when people claim that the Schrödinger wave instantly collapses everywhere else when a single particle is detected.  The solution is: don't ask what happens during a single event.  The Schrödinger wave function gives information only about statistics.  It does not give a detailed physical description of what happens during a single event.

But what really does happen in a single event?

To describe the underlying detailed process of a single event, like the detection of a single electron or to understand exactly how a single photon behaves going through a double slit, we need a different theory.  Quantum mechanics does not and cannot deal with the underlying detailed mechanisms.  Because it only deals with statistical results and probability.  If you want a detailed description of how a single photon works, you need Quantum Field Theory (QFT).  Below is my understanding of QFT, based on Brooks and Rashkovskiy (See references below).

Quantum Field Theory (QFT)

In the Field Theory model there are only fields.  Everything is fields.  The best example is the electromagnetic field that we all know.  Gravity is another field that everyone is familiar with.  So the detailed picture of how a photon travels through two slits is actually very simple.  The photon is just an electromagnetic wave.  It is a burst emitted by an excited atom so it has a certain frequency and energy.  The wave goes through both slits.  When the wave hits the detector (diode) a small part of it is detected and the rest turns into heat.  The detection process is nothing like the emission process!  Transmitters and receivers operate in vastly different regimes and vastly different power levels. (Compare a TV transmitter with a TV receiver).  In our example the transmitter was a single atom in an excited state,  but the receiver is a semiconductor avalanche diode made of silicon, with a depletion region containing 10^20 electrons.   A tiny fraction of the original transmitted light wave sets off the detector.  It is certainly not the "whole photon" as most people imagine.  The idea of detecting a single "indivisible photon particle" comes from trying to use statistical quantum mechanics to visualize a single event.
Satellite TV receivers in Yangon, 2012.
Transmitters and receivers operate in vastly different
regimes and vastly different power levels

Which theory is right?

Both QM and QFT give the same answer!  So they are both right.  They both agree with experimental results.  Take the above example of light from Alpha Centauri reaching my iPhone.  QM says the probability of detection is very low.  QFT says the power detected is very low.  Either way you get the same number.  The difference is only the explanation.  QM is statistical while QFT is all about fields.
Both QM and QFT are useful models (tools) that can be used to understand and calculate what's happening.  QM does not model the underlying mechanism of single events, although it can correctly predict the probability of a single event.  QFT is much more detailed, so it would be crazy to use it to attempt to calculate the statistics of electrons in a semiconductor diode.

Al Kordesch, January 9, 2022

References

Most of the information in this article comes from the following sources.




Comments

Post a Comment